Instruction:
I'd like this SVG to be enchanted, glowing with an inner fire. How can I make it radiate with a warm, inviting light?
<svg width="32" height="32" viewBox="0 0 32 32" fill="none" xmlns="http://www.w3.org/2000/svg">
<path d="M10.32 10.64C12.7059 10.64 14.64 8.70587 14.64 6.32C14.64 3.93413 12.7059 2 10.32 2C7.93413 2 6 3.93413 6 6.32C6 8.70587 7.93413 10.64 10.32 10.64Z" fill="#B4ACBC"/>
<path d="M13.34 2C15.73 2 17.67 3.94 17.67 6.33C17.67 6.43325 17.6664 6.53565 17.6593 6.63707L19.32 6.20999C24.884 5.00562 29.9526 9.40868 29.9997 15.0902C29.9999 15.0934 30 15.0967 30 15.1V19.89C30 21.62 29.6 23.02 27.87 23.02H22.22C20.7322 23.02 19.8822 22.2115 19.4833 21.01H16.41C15.01 21.01 13.68 20.49 12.48 19.91L12.1971 21L10.5 21.5L8.94931 21L9.75001 17.87C8.99507 17.0464 8.38614 16.0768 7.97172 15H4.14C2.96 15 2 14.04 2 12.86C2 12.16 2.34 11.51 2.91 11.11L9.03 6.82C9.01 6.66 9 6.5 9 6.33C9 3.94 10.95 2 13.34 2Z" fill="#CDC4D6"/>
<path d="M13.33 9.57996C15.1249 9.57996 16.58 8.12488 16.58 6.32996C16.58 4.53503 15.1249 3.07996 13.33 3.07996C11.5351 3.07996 10.08 4.53503 10.08 6.32996C10.08 8.12488 11.5351 9.57996 13.33 9.57996Z" fill="#FF8687"/>
<path d="M27.0289 23.016C26.4177 23.6357 25.5684 24.0201 24.63 24.0201L18.99 24.0101C17.34 24.0101 16 25.3501 16 27.0001C16 28.6501 17.34 29.9901 18.98 29.9901L23 30.0001C23.55 30.0001 24 29.5601 24.01 29.0001C24.01 28.4501 23.56 28.0001 23.01 28.0001L18.99 27.9901C18.44 27.9901 18 27.5501 18 27.0001C18 26.4501 18.44 26.0101 18.99 26.0101L24.63 26.0201C27.59 26.0201 30 23.6101 30 20.6501V19.8986C29.9955 21.5714 28.6821 22.9336 27.0289 23.016Z" fill="#FF8687"/>
<path d="M22.8167 23C21.4955 22.8684 20.3626 22.0969 19.7321 21H17.1111C16.4938 21 16 21.4444 16 22C16 22.5556 16.4938 23 17.1111 23H22.8167Z" fill="#FF8687"/>
<path d="M8.54003 22.61L8.95003 21H12.19L11.87 22.26C11.73 22.8 11.42 23 11 23H8.84003C8.64003 23 8.49003 22.8 8.54003 22.61Z" fill="#FF8687"/>
<path d="M2 12.84C2 12.46 2.1 12.09 2.29 11.77C2.75 11.9 3.08 12.31 3.08 12.81C3.08 13.32 2.73 13.74 2.26 13.86C2.09 13.56 2 13.21 2 12.84Z" fill="#FF8687"/>
<path d="M6.81 12.62C7.25735 12.62 7.62 12.2574 7.62 11.81C7.62 11.3626 7.25735 11 6.81 11C6.36265 11 6 11.3626 6 11.81C6 12.2574 6.36265 12.62 6.81 12.62Z" fill="#1C1C1C"/>
</svg>

Output:
There are a few different strategies you could use to create this effect. You could add gradient or animate the color to simulate the effect of glowing or flickering light, for example.

Here is an example where I have applied an animated gradient to the logo to make it look like it's glowing. For this, you will need to add a SVG `<animate>` tag to the path elements you want to change the fill of.

```svg
<svg width="32" height="32" viewBox="0 0 32 32" fill="none" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
  <defs>
    <linearGradient id="grad1" x1="0%" y1="0%" x2="100%" y2="0%">
      <stop offset="0%" style="stop-color:#CDC4D6; stop-opacity:1">
        <animate attributeName="stop-color" values="#CDC4D6;#A5B368;#CDC4D6" dur="3s" repeatCount="indefinite" />
      </stop>
      <stop offset="100%" style="stop-color:#A5B368; stop-opacity:1">
        <animate attributeName="stop-color" values="#A5B368;#CDC4D6;#A5B368" dur="3s" repeatCount="indefinite" />
      </stop>
    </linearGradient>
  </defs>
  <path d="M10.32 10.64C12.7059 10.64 14.64 8.70587 14.64 6.32C14.64 3.93413 12.7059 2 10.32 2C7.93413 2 6 3.93413 6 6.32C6 8.70587 7.93413 10.64 10.32 10.64Z" fill="url(#grad1)"/>
  <path d="M13.34 2C15.73 2 17.67 3.94 17.67 6.33C17.67 6.43325 17.6664 6.53565 17.6593 6.63707L19.32 6.20999C24.884 5.00562 29.9526 9.40868 29.9997 15.0902C29.9999 15.0934 30 15.0967 30 15.1V19.89C30 21.62 29.6 23.02 27.87 23.02H22.22C20.7322 23.02 19.8822 22.2115 19.4833 21.01H16.41C15.01 21.01 13.68 20.49 12.48 19.91L12.1971 21L10.5 21.5L8.94931 21L9.75001 17.87C8.99507 17.0464 8.38614 16.0768 7.97172 15H4.14C2.96 15 2 14.04 2 12.86C2 12.16 2.34 11.51 2.91 11.11L9.03 6.82C9.01 6.66 9 6.5 9 6.33C9 3.94 10.95 2 13.34 2Z" fill="url(#grad1)"/>
  <path d="M13.33 9.57996C15.1249 9.57996 16.58 8.12488 16.58 6.32996C16.58 4.53503 15.1249 3.07996 13.33 3.07996C11.5351 3.07996 10.08 4.53503 10.08 6.32996C10.08 8.12488 11.5351 9.57996 13.33 9.57996Z" fill="url(#grad1)"/>
  <path d="M27.0289 23.016C26.4177 23.6357 25.5684 24.0201 24.63 24.0201L18.99 24.0101C17.34 24.0101 16 25.3501 16 27.0001C16 28.6501 17.34 29.9901 18.98 29.9901L23 30.0001C23.55 30.0001 24 29.5601 24.01 29.0001C24.01 28.4501 23.56 28.0001 23.01 28.0001L18.99 27.9901C18.44 27.9901 18 27.5501 18 27.0001C18 26.4501 18.44 26.0101 18.99 26.0101L24.63 26.0201C27.59 26.0201 30 23.6101 30 20.6501V19.8986C29.9955 21.5714 28.6821 22.9336 27.0289 23.016Z" fill="url(#grad1)"/>
  <path d="M22.8167 23C21.4955 22.8684 20.3626 22.0969 19.7321 21H17.1111C16.4938 21 16 21.4444 16 22C16 22.5556 16.4938 23 17.1111 23H22.8167Z" fill="url(#grad1)"/>
  <path d="M8.54003 22.61L8.95003 21H12.19L11.87 22.26C11.73 22.8 11.42 23 11 23H8.84003C8.64003 23 8.49003 22.8 8.54003 22.61Z" fill="url(#grad1)"/>
  <path d="M2 12.84C2 12.46 2.1 12.09 2.29 11.77C2.75 11.9 3.08 12.31 3.08 12.81C3.08 13.32 2.73 13.74 2.26 13.86C2.09 13.56 2 13.21 2 12.84Z" fill="url(#grad1)"/>
  <path d="M6.81 12.62C7.25735 12.62 7.62 12.2574 7.62 11.81C7.62 11.3626 7.25735 11 6.81 11C6.36265 11 6 11.3626 6 11.81C6 12.2574 6.36265 12.62 6.81 12.62Z" fill="#1C1C1C"/>
</svg>
```
This SVG will give the impression of an inner fire in the logo.

NOTE: If you are planning to use this SVG on the web, not all browsers may support SVG animations. Make sure to test on the browsers you plan to support.


Instruction: Develop a Java function that takes in an array and a numerical value as parameters, and outputs the highest value present in the array that does not exceed the provided numerical value.

Output:
Here is a Java function named `findHighestValue` that achieves your requested functionality. The function takes an array of integers and a limit as inputs, then returns the highest value in the array that doesn't exceed the limit provided.

This function uses Java streams to filter out values that are greater than the limit, and find the maximum value from the remaining ones. If no such value is present in the array, `Integer.MIN_VALUE` is returned as a default value.

```java
import java.util.Arrays;

public class Main {
    public static void main(String[] args) {
        int[] array = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        int limit = 6;
        System.out.println(findHighestValue(array, limit));  // Output: 6
    }

    public static int findHighestValue(int[] array, int limit) {
        return Arrays.stream(array)
                .filter(i -> i <= limit)
                .max()
                .orElse(Integer.MIN_VALUE);
    }
}
```

In this example, calling the `findHighestValue` function with an array of numbers and a limit of 6 returns 6, which is the highest number that doesn't exceed the limit.


Instruction:
Write a JavaScript program that given an array of integers, prints the maximum and minimum value of the array without using the built-in Math.max() and Math.min() functions. The program should handle the potential exception of an empty array.

numbers = [2, 3, 6, 9, 5]

Output:
```javascript
const numbers = [2, 3, 6, 9, 5];

function printMinMax(arr) {
    if (arr.length === 0) {
        console.log("The array is empty.");
        return;
    }

    let max = arr[0];
    let min = arr[0];

    for (let i = 1; i < arr.length; i++) {
        if (arr[i] > max) {
            max = arr[i];
        }
        if (arr[i] < min) {
            min = arr[i];
        }
    }

    console.log("Max: " + max);
    console.log("Min: " + min);
}

printMinMax(numbers);
```
In this program:

The printMinMax function takes an array as its parameter.
The function first checks if the array is empty. If it is, it prints a message and returns immediately.
The function then initializes two variables, max and min, to the first element of the array.
Then, it iteratively checks each element in the array: if it's greater than the current max, it becomes the new max; if it's less than the current min, it becomes the new min.
Finally, the function prints the max and min values.


Instruction:
I want to create a hover effect on this SVG for my website. Can you help?
<svg width="32" height="32" viewBox="0 0 32 32" fill="none" xmlns="http://www.w3.org/2000/svg">
<path d="M26.5384 11.9606L29.9784 17.9606C30.2284 18.3906 29.9084 18.9306 29.3884 18.9306C28.9484 18.9206 28.6684 19.4106 28.8084 19.8306L29.2539 21.0706H2.81836L3.25836 19.7706C3.39836 19.3506 3.08836 18.9206 2.64836 18.9206C2.14836 18.9206 1.83836 18.3906 2.08836 17.9606L5.53836 11.9406C5.67836 11.6906 5.82836 11.4006 5.97836 11.1006L6.00836 2.67056C5.97836 2.08056 6.69836 1.77056 7.09836 2.20056L14.1684 7.60056C14.4384 7.81056 14.7784 8 15.1184 8H16.8684C17.2084 8 17.5484 7.81056 17.8184 7.60056L24.8884 2.20056C25.2884 1.77056 26.0084 2.08056 25.9784 2.67056L26.0084 10.9606C26.1584 11.2506 26.3384 11.5706 26.5384 11.9406V11.9606Z" fill="#9B9B9B"/>
<path d="M6.99835 9.77054C6.98835 10.0605 7.28835 10.2705 7.56835 10.1705L11.8684 8.61054C12.1784 8.50054 12.2484 8.08054 11.9784 7.87054L7.69835 4.60054C7.44835 4.32054 6.98835 4.52054 7.00835 4.89054L6.99835 9.77054Z" fill="#D3D3D3"/>
<path d="M25.0083 9.7706C25.0083 10.0606 24.7183 10.2706 24.4383 10.1706L20.1283 8.6106C19.8183 8.5006 19.7483 8.0806 20.0183 7.8706L24.2983 4.6006C24.5483 4.3306 25.0083 4.5306 24.9883 4.9006L25.0083 9.7706Z" fill="#D3D3D3"/>
<path d="M14.0983 30H17.9883C19.1383 30 20.1583 29.2006 20.5483 28.1206L21.2283 24.9406C21.3283 24.4806 21.7583 24.1806 22.2183 24.2306C23.7383 24.4206 26.8983 24.8006 27.5383 24.8006C28.5383 24.8006 28.2183 23.9606 28.2183 23.9606L27.8683 22.9106C27.8183 22.7606 27.6883 21.8906 28.6483 21.9006C29.7283 21.9206 29.1983 20.9106 29.1983 20.9106L24.4383 18.9106C24.4383 18.9106 21.8583 17.6506 20.5883 18.9306L17.6683 21.8706C17.6083 21.9406 17.5283 21.9906 17.4483 22.0406C17.0098 22.2798 16.5316 22.3997 16.0433 22.4105C15.555 22.3997 15.0768 22.2798 14.6383 22.0406C14.5583 21.9906 14.4783 21.9406 14.4183 21.8706L11.4983 18.9306C10.2283 17.6506 7.64831 18.9106 7.64831 18.9106L2.875 20.9106C2.875 20.9106 2.35831 21.9206 3.43831 21.9006C4.39831 21.8906 4.26831 22.7606 4.21831 22.9106L3.86831 23.9606C3.86831 23.9606 3.54831 24.8006 4.54831 24.8006C5.18831 24.8006 8.34831 24.4206 9.86831 24.2306C10.3283 24.1806 10.7583 24.4806 10.8583 24.9406L11.5383 28.1206C11.9283 29.2006 12.9483 30 14.0983 30Z" fill="#D3D3D3"/>
<path d="M11 15C11 14.4477 11.4477 14 12 14C12.5523 14 13 14.4477 13 15V16C13 16.5523 12.5523 17 12 17C11.4477 17 11 16.5523 11 16V15Z" fill="#1C1C1C"/>
<path d="M19 15C19 14.4477 19.4477 14 20 14C20.5523 14 21 14.4477 21 15V16C21 16.5523 20.5523 17 20 17C19.4477 17 19 16.5523 19 16V15Z" fill="#1C1C1C"/>
<path d="M14.7313 20H17.2706C18.3603 20 18.9155 21.521 18.1342 22.4053L16.8594 23.5844C16.3762 24.1385 15.6051 24.1385 15.1219 23.5844L13.8471 22.4053C13.0966 21.5092 13.6415 20 14.7313 20Z" fill="#1C1C1C"/>
<path d="M16.5 24.5C16.5 24.2239 16.2761 24 16 24C15.7239 24 15.5 24.2239 15.5 24.5C15.5 25.1118 15.2758 25.7539 14.8995 26.2362C14.5251 26.7161 14.0338 27 13.5 27C13.2239 27 13 27.2239 13 27.5C13 27.7761 13.2239 28 13.5 28C14.4162 28 15.1749 27.5089 15.688 26.8513C15.803 26.7039 15.9073 26.5463 16 26.3809C16.0927 26.5463 16.197 26.7039 16.312 26.8513C16.8251 27.5089 17.5838 28 18.5 28C18.7761 28 19 27.7761 19 27.5C19 27.2239 18.7761 27 18.5 27C17.9662 27 17.4749 26.7161 17.1005 26.2362C16.7242 25.7539 16.5 25.1118 16.5 24.5Z" fill="#1C1C1C"/>
</svg>

Output:
Sure, you can add hover effect to an SVG by using CSS.
Here are some examples:

1. Change color when hovered:

```html
<style>
svg:hover path {
    fill: #f00; /* change color to red when hovered */
}
</style>
```

2. Grow size when hovered:

```html
<style>
svg:hover {
    transform: scale(1.2); /* 1.2 will make it 20% larger when hovered */
}
</style>
```

3. Apply transition to make the effect smoother:

```html
<style>
svg {
    transition: 0.3s;
}

svg:hover {
    transform: scale(1.2);
}
</style>
```

Just wrap your SVG code with `<div>` tag, then you may add the styles from above into the `<style>` tag then place it inside the `<head>` tag of your HTML file.

For example:

```html
<html>
<head>
<style>
svg {
    transition: 0.3s;
}

svg:hover {
    transform: scale(1.2);
}
</style>
</head>
<body>
<div>
<!-- your SVG code here -->
</div>
</body>
</html>
```

Just replace the comment "your SVG code here" with your actual SVG code.
Remember to modify the CSS code above according to your needs.


Instruction:
Write a JavaScript function to check if a given number is even and return the result as a boolean.
num = 7

Output:
Here is a simple JavaScript function to check whether a number is even or not.

```javascript
function isEven(num) {
    return num % 2 === 0;
}

var num = 7;
console.log(isEven(num));
```
In this function, if the remainder of the number divided by 2 is equal to 0, it means the number is even so it will return true, else it will return false. So if you run this code with num = 7, it will print false because 7 is not an even number.


Instruction:
Develop a Python function that performs a rotation operation on an array by a designated number of positions, organizes the residual segment of the array in a descending sequence, and handles a variety of complex scenarios.

The function should be able to handle edge cases such as an array that is empty, an array that contains a single element, or a rotation number that surpasses the array's limits. It should also be able to manage arrays that contain duplicate elements while maintaining the original order of these elements after sorting (stable sort).

The function should be capable of handling arrays that encompass negative integers, floating point numbers, and even complex numbers. It should also be able to manage arrays with elements of diverse data types (integers, floating point numbers, strings, and complex numbers). The function should arrange the string elements in reverse alphabetical order and position them subsequent to the numeric elements in the sorted segment of the array.

The function should also be proficient in managing arrays with nested arrays and even arrays with nested dictionaries. The nested arrays should be organized in descending order based on the sum of their elements and positioned after the string elements in the sorted segment of the array. The dictionaries should be sorted based on the sum of their values and positioned after the nested arrays in the sorted segment of the array.

Additionally, the function should be able to handle arrays that contain custom objects. The custom objects should be sorted based on a specific attribute and positioned after the dictionaries in the sorted segment of the array.

Consider the following defective code snippet as a reference. This code attempts to rotate and sort the array, but it fails in handling edge cases, maintaining the original sequence of duplicate elements after sorting, managing negative and floating point numbers, sorting elements of diverse data types, and managing nested arrays and dictionaries.

```python
def rotate_and_sort(arr, num):
    arr[:num] = arr[num:] + arr[:num]
    arr[num:] = sorted(arr[num:], reverse=True)
    return arr
```

Your assignment is to rectify this code and incorporate the necessary functionality. The function should return the modified array. The function should also be able to handle large arrays efficiently, without exceeding the time and space complexity of O(n log n). The function should also be able to handle arrays that contain custom objects and sort them based on a specific attribute.

The function should also be able to handle arrays that contain elements of different data types (integers, floating point numbers, strings, complex numbers, nested arrays, dictionaries, and custom objects) in a mixed manner. The function should be able to sort these mixed data types based on their respective sorting rules and position them in the sorted segment of the array in the order of numeric elements, string elements, nested arrays, dictionaries, and custom objects.

Output:
You can implement such a function using the built-in sorted function in Python with a custom comparator function - to handle the complex sorting conditions like sorting strings, nested arrays, dictionaries, and custom objects differently.

Below is a Python function that incorporates the necessary functionality based on the given requirements. The function `rotate_and_sort_advanced()` uses `sorted()` with a custom comparator function that checks for different data types and handles each accordingly:

```python
from collections.abc import Iterable
from collections.abc import Mapping

class CustomObject:
    def __init__(self, attribute):
        self.attribute = attribute

def get_sort_value(item):
    if isinstance(item, int) or isinstance(item, float) or isinstance(item, complex):
        return (0, item)
    elif isinstance(item, str):
        return (1, item)
    elif isinstance(item, Iterable):
        return (2, sum(item))
    elif isinstance(item, Mapping):
        return (3, sum(item.values()))
    elif isinstance(item, CustomObject):
        return (4, item.attribute)

def rotate_and_sort_advanced(arr, num):
    # Handling edge case for empty array and a single element array
    if len(arr) < 2:
        return arr
    # Handling case where rotation number surpasses array's limit
    num %= len(arr)
    # Rotate array
    arr = arr[num:] + arr[:num]
    # Sort
    arr = sorted(arr, key=get_sort_value, reverse=True)
    # Return modified array
    return arr
```

The `CustomObject` class is included for demonstration purposes to create objects with a specific attribute. The `get_sort_value()` function returns a tuple where the first item specifies the data type (0 for numerics, 1 for strings, 2 for nested arrays, 3 for dictionaries, 4 for custom objects), and the second item determines the sort value based on that type. This allows stable sorting of elements based on the given conditions.

This Python function can handle any element including nested arrays, dictionaries, and custom objects. It maintains the original sequence of duplicate elements after sorting and can handle multiple data types in a mixed manner. It also handles special edge cases such as when the array is empty, contains a single element, or when the rotation number surpasses the array's limits. The time and space complexity is O(n log n) where n is the size of the array, which is efficient for large arrays. Please ensure to add appropriate error handling in production-level code.


Instruction: Construct a regular expression to match all plausible international ISBN numbers.

Output:
International Standard Book Number (ISBN) comes in two formats: ISBN-10 and ISBN-13.
ISBN-10 is made up of 10 digits with optional hyphens.
ISBN-13 is made up of 13 digits, starting with '978' or '979', and it also has optional hyphens.

In Python we can use `re` module to create a regular expression for ISBN. Here it is:

```python
import re

def is_valid_isbn(isbn):
    isbn10 = r"^(\d{9}X|\d{10})$"
    isbn13 = r"^(978|979)[-\d]{10}\d$"

    return bool(re.match(isbn10, isbn.replace("-", ""))) or bool(re.match(isbn13, isbn.replace("-", "")))
```

It will check whether the provided string matches the format of either an ISBN-10 or an ISBN-13. The optional hyphens are removed before matching.

In isbn10 regular expression, `\d{9}X` matches 9 digits followed by 'X'(X can be 0-9 or X), and `\d{10}` matches any 10 digits.

In isbn13 regular expression, `(978|979)` matches '978' or '979', `[-\d]{10}` matches 10 digits or hyphens, and `\d$` matches 1 digit at the end of the string.

This is very basic checking and just provides format verification. This won't check whether the ISBN is valid or not based on check digit calculation as per the real-world criteria.


Instruction: Create a program that allows a user to search through a list of books by title or author.

Output:
You can accomplish that by creating a database of books and implementing a search function. Here's how you can do this in Python:

```Python
class Book:
    def __init__(self, title, author):
        self.title = title
        self.author = author

# A list of books
books = [Book("Moby Dick", "Herman Melville"), Book("1984", "George Orwell"), Book("The Great Gatsby", "F. Scott Fitzgerald")]

def search_books(query):
    results = []
    for book in books:
        if query.lower() in book.title.lower() or query.lower() in book.author.lower():
            results.append(book)

    if results:
        for result in results:
            print(f"Title: {result.title}, Author: {result.author}")
    else:
        print("No results found.")

while True:
    user_query = input("Search books by title or author: ")
    if user_query.lower() == "quit":
        break
    else:
        search_books(user_query)
```

In the code snippet above, we first define a class `Book` with two attributes: `title` and `author`. Then, we populate a list with some example books. The `search_books(query)` function takes a user query as a parameter and checks if the query is included in any of the book`s title or author. In case there are matches, they are returned to the user.

Finally, we have a while loop that asks the user for a query to look for in the books list. If the user types "quit", the loop breaks and the program finishes.


Instruction: Compose a Java application that calculates and displays the area along with the circumference of a circle, given the radius as input. This program should incorporate the use of π (Pi) and mathematical equations for these measurements. Additionally, assure the program gracefully handles potential incorrect inputs, such as negative radii.

Output:
Here is a simple Java application that fulfills the above requirements:

```java
import java.util.Scanner;

public class CircleMeasurements {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        System.out.println("Enter the radius of the circle:");

        // Attempts to parse radius from user input
        try {
            double radius = sc.nextDouble();
            // Checks if radius is negative and throws exception if true
            if (radius < 0) throw new Exception("Radius cannot be negative");
            // Calculates and displays area and circumference
            double area = Math.PI * Math.pow(radius, 2);
            double circumference = 2 * Math.PI * radius;
            System.out.println("Area: " + area);
            System.out.println("Circumference: " + circumference);
        } catch (Exception e) {
            // Handles incorrect inputs
            System.out.println("Error: " + e.getMessage());
            System.out.println("Please enter a valid radius.");
        }
    }
}
```

This program starts by prompting the user to enter the radius of the circle. It then reads in the user's input and attempts to parse it as a double. If the radius is less than zero, the program throws an exception since a circle cannot have a negative radius. If the radius is valid, it calculates and displays the area and circumference of the circle. If any errors occur during the process (such as the user entering a non-numeric value or a negative radius), the program catches the exception and displays an appropriate error message.


Instruction:
Given the following erroneous CSS animation code, identify the errors, correct them, and describe the visual effects the corrected code would have.

Erroneous CSS Code:
```css
@keyframs example { 0% {background-Color: red; left:0px; top:;0px} 25% {background-color; yellow; left:200px; top:0px; 50% {background-color: blue; left:200px; top:200px} 75% {background-color green; left:0px; top:200px} 100% {background-color: red; left:0px; top:0px;}
```

Your task includes two parts: firstly, identifying the errors in the code snippet and correcting them; and secondly, interpreting the CSS animation code and providing a description of its visual effects. Consider aspects such as color changes, movement, and the timing of these changes in your description.

Output:
Corrected CSS Code:
```css
@keyframes example {
    0% {
        background-color: red;
        left: 0px;
        top: 0px;
    }
    25% {
        background-color: yellow;
        left: 200px;
        top: 0px;
    }
    50% {
        background-color: blue;
        left: 200px;
        top: 200px;
    }
    75% {
        background-color: green;
        left: 0px;
        top: 200px;
    }
    100% {
        background-color: red;
        left: 0px;
        top: 0px;
    }
}
```
Explanation of Errors:

1. `@keyframs`: This is misspelled. The correct spelling is `@keyframes`.
2. In the 0% keyframe, `top:;0px` should be `top: 0px`.
3. The 25% keyframe `background-color; yellow;` should be `background-color: yellow;`
4. The 50% keyframe was not closed with a curly bracket `}`.
5. The 75% keyframe `background-color green;` should be `background-color: green;`
6. The 100% keyframe was not closed with a curly bracket `}`.
7. The whole animation keyframe syntax was missing the final closing bracket `}`.

Explanation of Visual Effects:
This animation changes both the position and color of an HTML element over time. At the start (0%), the element is at coordinates (0px, 0px) and has a red background color. Just 25% of the way into the animation timeline, the background color changes to yellow and the element moves right to the coordinate (200px, 0px).

In the middle of the animation (50%), the background color changes to blue and the element moves down to (200px, 200px). Then, three-quarters (75%) of the way into the animation, the background color becomes green and the element slides left to the location (0px, 200px), and finally, it returns to its original position (0px, 0px) with its original red background at the end (100%) of the animation timeline.


Instruction:
You have shares in four different companies - A, B, C, and D. Each company has a different annual dividend yield, being 3%, 5%, 7%, and 9% respectively. Your total portfolio is worth $10,000. Using the cumulative dividends earned in a certain year, determine the value of your investments in each company. This should account for fluctuations in the market that affect the value of your shares in each company throughout the year. The dividend earnings of the four companies in that year are as follows:

- Company A: $120
- Company B: $150
- Company C: $210
- Company D: $270

Determine the precise value of your investment in each company by the end of the year, assuming you reinvested your dividends back into the respective companies. Don't forget to account for the change in share price due to the reinvested dividends.

Output:
To determine the value of the investments in each company, we need to reverse engineer the dividend yields. This means we take the dividend payment made by that company and divide by the annual yield rate. Here is how we can determine this:

- Company A is worth $120 / 0.03 = $4,000
- Company B is worth $150 / 0.05 = $3000
- Company C is worth $210 / 0.07 = $3000
- Company D is worth $270 / 0.09 = $3000

Now let's find out how much the investments will be worth at the end of the year with reinvested dividends:

- Company A = $4,000 + $4,000 * 0.03 = $4,120
- Company B = $3,000 + $3,000 * 0.05 = $3,150
- Company C = $3,000 + $3,000 * 0.07 = $3,210
- Company D = $3,000 + $3,000 * 0.09 = $3,270

Note that the values are increasing due to the reinvested dividends; a company paying higher dividends increases in value more.

Therefore, at the end of the year the investments are worth:

- Company A: $4,120
- Company B: $3,150
- Company C: $3,210
- Company D: $3,270

The total value of the portfolio at the end of the year is $4,120 + $3,150 + $3,210 + $3,270 = $13,750.


Instruction:
Determine the cumulative total of every individual element present within the provided two-dimensional matrix.
[[1, 2, 3],[4, 5, 6],[7, 8, 9]]

Output:
```
matrix = [[1, 2, 3],[4, 5, 6],[7, 8, 9]]

def cumulative_total(matrix):
    total = 0

    for i in range(len(matrix)):
        for j in range(len(matrix[i])):
            total += matrix[i][j]

    return total

result = cumulative_total(matrix)
print(result)
```

This code will give you the cumulative total of every individual element present within the given two-dimensional matrix. When you run this code, you will get the output: `45`.


Instruction: Engineer a sophisticated data conservation substructure, integrated within the Django web development framework, capitalizing on the advanced capabilities of the django-storages library, specifically designed to protect multimedia data stored in an Amazon S3 bucket. The design should include exhaustive error management systems and stringent security measures, necessitating a multi-tiered logical reasoning approach for its successful execution. Additionally, the system should be capable of handling large volumes of data, ensuring data integrity, and providing efficient retrieval mechanisms.

Output:
Solution:

Designing an advanced and robust data conservation substructure requires effective planning and a comprehensive understanding of Django's capabilities, django-storages library, and Amazon S3 storage services.

1. **Structure Of Conservation Substructure:**

   To begin, Django’s models will be utilized to structure and define the multimedia data. Classes will be developed for each multimedia data type that require storage.

2. **Integration Of Django-Storages:**

   Django-storages is a powerful, flexible library for handling storage backend. It will be initialized in the settings file of the Django project. Here, the django-storages AWS S3 client is instantiated, allowing for interaction with the S3 storage server.

3. **Amazon S3 Configuration:**

    The AWS access key, secret access key, and bucket name are configured in Django's settings file. Furthermore, while setting AWS_S3_FILE_OVERWRITE = False, the library provides an automatic way of ensuring file uniqueness in case of duplicate names.

4. **Security Measures:**

    Referenced from AWS Security Configuration, we will use bucket policies to manage access to the bucket, the bucket level settings will be managed with ACLs (Access Control Lists), and IAM (Identity and Access Management) services will be leveraged to manage user and group level access permissions.

5. **Error Handling Design:**

    Extensive error handling will be implemented using Django's built-in error handling classes and middleware. These will be expanded with custom error handling that will manage errors related to storage backend interactions.

6. **Data Integrity and Efficient Retrieval Mechanisms:**

    Mechanisms such as checksums and HTTP Etags will be used to ensure data integrity in S3. Boto3 can be used for efficient retrieval and its built-in features can assist in managing larger data sets.

7. **Handling Large Volumes Of Data:**

   Django’s Paginator class will be utilized for easier navigation through the large volume of files. Furthermore, S3's ability to automatically archive the less accessed data to cheaper storage options will be capitalized upon.

8. **Testing:**

    Django’s test suite will be used to systematically verify that all parts of the data conservation substructure perform as intended in different conditions.

9. **Logging:**

    Django’s logging module will be configured to log all errors, data integrity checks and other important information which will be crucial for the system audit and debugging.

The above approach ensures a multi-tiered logical reasoning approach for successful execution of the system. In addition to these, using AWS's additional features like AWS CloudFront (for content delivery network), AWS Glacier(for archiving less accessed data) etc can further improve the system's performance.


Instruction:
Refactor and optimize the given code snippet. However, the given code snippet this time is erroneous.

In the original implementation, it attempted to print all even numbers less than ten in a range. Plausible bugs could be in the range or modulus implementation, or even a syntactic error.

```python
for num in range(15):
  if num // 3 == 0
    print(num)
    print("is an even number");
```

Output:
The given code has several errors:

1. `if num // 3 == 0` - This checks if the result of integer division of a number by 3 is equal to 0. This will only evaluate to True for num equal to 0, not for even numbers.
2. Missing colon at the end of the if statement line.
3. The aim is to print all even numbers less than ten, but the range is set to 15.

Here's the correct version of the code:

```python
for num in range(10):
  if num % 2 == 0:
    print(num, "is an even number")
```

In this refactor, the `range(10)` function is used to generate numbers from 0 to 9. The `if` statement checks if the remainder of integer division (`%`) of the current number by 2 is zero, which is the standard check for even-ness in numbers. If this evaluates as true, then the number is printed as an even number.


Instruction: Determine the sum of all the elements in a multidimensional array of integers (with potentially varying lengths). Also, incorporate error handling for non-integer types.

Output:
Here is a Python solution using a recursive function:

```python
def sum_array(a):
    try:
        return sum(sum_array(i) if isinstance(i, list) else i for i in a)
    except TypeError:
        raise TypeError("Non-integer value found in array")

# Test
arr = [[1, 2, [3]], 4]
print(sum_array(arr))  # Should print 10

arr = [[1, 2, [3, "foo"]], 4]
try:
    print(sum_array(arr))
except TypeError as e:
    print(e)  # Should print "Non-integer value found in array"
```

This function works by checking each element of the array. If an element is a list, it calls itself recursively on that list to sum its elements. Otherwise, it simply adds the element to the total. If it encounters a non-integer, it raises a TypeError.


Instruction:
Refine the following Java code:

import java.util.*;
import java.lang.*;

class Solution {
    /**
    Develop a function to arrange a provided list of integer values
    in an upward order based on both the summation of their respective digits
    and the sum of the absolute values of the digits. If multiple items share
    the same sum, their original list sequence will dictate their order.

    Example:
    Function call: activateOrderingBySum(Arrays.asList(1, 11, -1, -11, -12))
    Returns: [-1, -11, 1, -12, 11]
    Function call: activateOrderingBySum(Arrays.asList())
    Returns: []

     */
    public List<Integer> activateOrderingBySum(List<Integer> nums) {

Output:
Sure, you can refine the Java code as follows:

```Java
import java.util.*;
import java.lang.*;

class Solution {
    public List<Integer> activateOrderingBySum(List<Integer> nums) {
        // Creating a new array list to store the original indexes along with element
        ArrayList<Pair> pairList = new ArrayList<>();

        for(int i = 0; i < nums.size(); i++) {
            pairList.add(new Pair(i,nums.get(i), sumOfDigits(nums.get(i))));
        }
        // Sorting based on sum of digits. If same, maintain original order.
        Collections.sort(pairList, new Comparator<Pair>(){
            public int compare(Pair p1, Pair p2) {
                if(p1.sum != p2.sum)
                  return p1.sum - p2.sum;
                else
                  return p1.index - p2.index; // to maintain original order
            }
        });

        ArrayList<Integer> result = new ArrayList<>();
        for(Pair p : pairList) {
            result.add(p.num);
        }

        return result;
    }

    // Method to calculate the sum of digits and sum of absolute digits
    private int sumOfDigits(int num) {
        int sum = 0;
        while (num != 0) {
            sum += Math.abs(num % 10);
            num = num / 10;
        }
        return sum;
    }

    // Inner class to save index, number and sum of digits of a number
    private class Pair {
        int index;
        int num;
        int sum;

        public Pair(int index, int num, int sum) {
            this.index = index;
            this.num = num;
            this.sum = sum;
        }
    }
}
```

In the code above, we first calculate sums of digits for each number in the list, store this data along with the numbers and their original indexes in a `Pair` class, and then sort based on the sums. In case of sums collision, we compare the original indexes, which achieves the desired stability of the sort. Finally, we generate and return the sorted list. The `Collections.sort` method ensures stable sort due to our implementation of the `compare` method inside the `Comparator` definition.


Instruction:
Construct a function that accepts a list containing subarrays of integers along with an additional parameter specifying a mathematical operation (like 'product', 'mean', 'standard deviation', etc.). The function should perform the given operation for each subarray (considering cumulative sum as the default operation), and then return the mean value of the obtained results. Moreover, the function should be capable of handling any erroneous inputs and throw appropriate custom exceptions.

For example,
```
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
operation = 'product'
```
If an invalid operation is given, the function should throw an error named 'InvalidOperationException'.

Output:
This problem can be solved by Python programming. First, we need to define a function for each mathematical operation we want to support. Then, we use these functions in our main function, which handles the input and computes the mean value of the results.

Here is a Python solution using the numpy module:

```python
import numpy as np

def calc_product(arr):
    return np.prod(arr)

def calc_mean(arr):
    return np.mean(arr)

def calc_standard_deviation(arr):
    return np.std(arr)

def calc_sum(arr):
    return np.sum(arr)

def perform_operation(arr, operation = 'sum'):

    operations = {
        'product': calc_product,
        'mean': calc_mean,
        'standard deviation': calc_standard_deviation,
        'sum': calc_sum
    }

    if operation not in operations:
        raise ValueError('InvalidOperation: Operation not supported')

    results = [operations[operation](subarr) for subarr in arr]
    return np.mean(results)
```
You can use this function like this:

```python
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
operation = 'product'
print(perform_operation(arr, operation))  # outputs: 2160.0
```
If an invalid operation is given, the function will raise a "ValueError: InvalidOperation" exception. For example:

```python
arr = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
operation = 'invalid operation'
print(perform_operation(arr, operation))  # raises ValueError: InvalidOperation exception
```
Note: The problem statement specifies to return the mean value of the results, so this function takes the mean of the list of results from applying the operation to each subarray. If the requirement were different, such as returning the list of results, you would simply return "results" instead of "np.mean(results)".


Instruction: Create a list comprehension to generate a list of all the words in the sentence "Python is amazing", ensuring to exclude prepositions and conjunctions. Furthermore, return the result in reverse order.

Output:
Here is the Python solution using list comprehension:

```python
sentence = "Python is amazing"
prepositions_conjunctions = ["is", "and", "or", "but", "so", "for", "yet", "after", "although", "as", "because", "before", "if", "since", "though", "unless", "until", "when", "while", "where"]

words = [word for word in sentence.split() if word not found in prepositions_conjunctions]
words.reverse()

print(words)
```
This code first splits the sentence into words, then checks each word to see if it's a preposition or conjunction. If it is, it's ignored; otherwise, it's added to the 'words' list. Finally, the words list is reversed and printed.


Instruction: Develop an advanced deep learning model using an under-used activation function to predict the statistical likelihood of a consumer's intent to engage in the procurement of a specific piece of high-end luxury merchandise, taking into consideration real-time socio-economic factors. The model should dynamically adapt to fluctuating market trends and customer purchasing power.

Output:
To solve this problem, we will use Python as a programming language and TensorFlow/Keras as a machine learning library. The activation function we are going to use is the Swish activation function, which is quite underused but might lead to better results in some cases.

First, we need to install necessary libraries. You can do this via pip:
```bash
pip install tensorflow pandas sklearn
```

Here is some python code of a basic outline of the deep learning model:

```python
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense
from tensorflow.keras.activations import swish
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
import pandas as pd

# load your data
df = pd.read_csv('your_data.csv')

# pre-processing: we'll assume the last column is your target and that all other columns are features
X = df.iloc[:, :-1].values
y = df.iloc[:, -1].values

# normalize the data
sc = StandardScaler()
X = sc.fit_transform(X)

# split data into training and test sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=0)

# model
model = Sequential()

# Add some deep learning layers
model.add(Dense(units=32, activation=swish, input_dim=X_train.shape[1]))
model.add(Dense(units=64, activation=swish))
model.add(Dense(units=1, activation='sigmoid'))

# Compile the model
model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])

# Train the model
model.fit(X_train, y_train, epochs=10, batch_size=32)
```
Keep in mind, this is a very basic model and will likely need tuning.

There are two main challenges that need to be tackled in your problem: considering the real-time socio-economic factors and the model's dynamic adaptation to fluctuating market trends and customer purchasing power.

- Considering real-time socio-economic factors: These variables should be included in your model as features when training. They can be used to create various feature combinations that the model can learn from.

- For the model's dynamic adaptation, periodically retrain your model using not only newly acquired data but also the old data. This way, the model will be able to adapt to any fluctuations in market trends and customer purchasing power.

Please replace 'your_data.csv' with your actual dataset path. This model assumes a binary outcome (customer will/will not purchase the product), hence the use of 'binary_crossentropy' in the loss function and sigmoid activation function in the output layer.

More layers and/or neurons in each layer can be added, and the number of training epochs can also be adjusted based on the actual data and problem. It is also recommended to perform a hyperparameter tuning to find the best parameters for the model.

This is just a simple example. In practice, you need to handle issues like data cleaning, handling imbalanced data, evaluating and improving model performance, among other things.


Instruction: Amend and improve a provided error-ridden Python code meant for extracting data from AWS DynamoDB. The improved code should handle potential exceptions and include appropriate comments.

Output:
It's difficult to assist without knowing the specifics of the error-ridden Python code. However, I'll provide a boilerplate Python script that interfaces with Amazon's DynamoDB. This script will utilize exception handling and comments where needed.

```python
# Required Libraries
import boto3
from botocore.exceptions import NoCredentialsError, PartialCredentialsError, SSLError, BotoCoreError, EndpointConnectionError

def get_from_dynamodb(table_name):
    # Initialize an empty response dictionary
    response = {}

    try:
        # Attempt to create a dynamodb resource object using Amazon's boto3 SDK
        dynamodb = boto3.resource('dynamodb')

        # Reference the specified DynamoDB table
        table = dynamodb.Table(table_name)

        # Attempt to retrieve all items from the specified table
        response = table.scan()
    except NoCredentialsError:
        print('No AWS Credentials provided')
    except PartialCredentialsError:
        print('Incomplete AWS Credentials provided')
    except SSLError:
        print('SSL Connection could not be established')
    except BotoCoreError as e:
        print('AWS Service Error: ', e)
    except EndpointConnectionError:
        print('Endpoint Connection Error: Check your AWS config.')
    except Exception as e: # General Exception
        print('Unexpected error: ', e)

    # return the response dictionary (contains items from dynamodb table if successful)
    return response

# Usage
tablename = 'myTable'
data = get_from_dynamodb(tablename)
```

Please, replace 'myTable' with the name of your DynamoDB Table.

This code attempts to connect to your AWS DynamoDB database, access a table specified by the `table_name` parameter, and scan (retrieve all items) from the table. If any fails in these steps, it will print out an appropriate error message.

Please be noted that, to access DynamoDB table with `boto3`, you should have your AWS credentials set up correctly either inside your script or using the AWS CLI. The boto3 looks for credentials in this order:

1. Passing credentials as parameters in the boto.client() method
2. Passing credentials as environment variables
3. Passing credentials in the AWS credentials profile file
4. From an instance profile when running on an EC2 instance

Make sure you have set up the credentials properly to access the DynamoDB table.


Instruction:
In the given Python script, the 'while' loop helps to calculate the factorial of a given number. Now, let's add more complexity.

Refactor the script to not only calculate the factorial of a given number but also to generate a Fibonacci series up to that number. Create the script in a way that we can retrieve the desired factorial or Fibonacci sequence for a specific number through function calls.

Here is the updated beginning of your script, modify it to complete the task:

count = 5
fact = 1

while count > 1:
  fact *= count
  count -= 1

print(fact)

Output:
Here is how you can refactor the script:

```python
def factorial(num):
  fact = 1
  while num > 1:
    fact *= num
    num -= 1
  return fact

def fibonacci(num):
  sequence = []
  a, b = 0, 1
  while a < num:
    sequence.append(a)
    a, b = b, a+b
  return sequence

# Usage
print(factorial(5))          # Output: 120
print(fibonacci(5))          # Output: [0, 1, 1, 2, 3]
```

In this script, two functions are defined: `factorial(num)` and `fibonacci(num)`.

The `factorial(num)` function calculates the factorial of a given number by multiplying it with all numbers less than it until it reaches 1.

The `fibonacci(num)` function generates the Fibonacci series up to the given number by starting with two initial numbers, 0 and 1, and updates these two numbers with the latter and their sum, respectively, in each iteration. This results in a sequence where each subsequent number is the sum of the previous two. It keeps generating numbers in this manner until it hits or surpasses the given number.

You can get the desired output by calling the respective function with the desired number as an argument. The function would return either the factorial or the Fibonacci sequence for that number.


Instruction: Develop a multithreaded Ruby script that calculates and displays the first 100 numbers in the Fibonacci sequence using Matrix exponentiation method with the task separated into multiple threads performing different parts of the calculation. The program should also handle potential synchronization issues that could arise due to multithreading.

Output:
The below code creates a simple Fibonacci sequence using Matrix exponentiation in Ruby. However, the nature of the Fibonacci sequence - where each number depends on the calculation of the previous two numbers, makes it not well suited for parallelisation. In essence, to calculate the Nth number you first need to calculate the N-1 and N-2 numbers. Parallelising this process into separate threads would mean that one thread would constantly be waiting for other threads to finish their computation, effectively making it function the same as a single-threaded solution.

In addition, the added complexity and resource overhead of multithreading would potentially make a multithreaded solution slower than a single threaded one for this specific task.

If parallelisation was absolutely necessary for other reasons (not for performance), Semaphore can be used to handle the synchronization issues.

```ruby
require 'matrix'
class FibMatrix
    attr_accessor :fib_matrix

  def initialize
    @fib_matrix = Matrix[[1,1],[1,0]]
  end

  def calculate(n)
    (fib_matrix ** n)[1, 0]
  end

end

fib = FibMatrix.new
(1..100).each do |n|
  puts fib.calculate(n)
end
```
The primary idea behind this approach is to use the property of Fibonacci numbers that:

```
Fib(2n) = Fib(n)*[2*Fib(n+1) - Fib(n)]

Fib(2n + 1) = Fib(n+1)^2 + Fib(n)^2
```
These two properties allow for execution in `'O(log(n))'` as opposed to `'O(n)'` for the typical iterative solution.

However, keep in mind that Ruby's Matrix class overloads the operation of exponentiation (`**` operator) for matrices. In the case of our 2x2 Fibonacci matrix, squaring the matrix as per the relation above gives the `(n+2)th` Fibonacci number. So, to get the `nth` Fibonacci number, raise the matrix to the `n` power, and then retrieve the appropriate element from the final matrix.


Instruction:
Write the Python code to generate a dictionary named "vehicles" which will hold various types of vehicles as keys (strings), and their attributes as the corresponding values. Each attribute will be another dictionary which has keys denoting attribute name and values as specific details. The attribute dictionary should encompass the following attributes: "color", "year of manufacture", "mileage" and "manufacturer".

For each vehicle type, populate its attribute dictionary with appropriate values. Use at least five different types of vehicles as keys.

Output:
Here is a Python script that fulfills your requirements:

```python
vehicles = {
    "Car": {
        "color": "Red",
        "year of manufacture": 2015,
        "mileage": 50000,
        "manufacturer": "Toyota"
    },
    "Truck": {
        "color": "Blue",
        "year of manufacture": 2010,
        "mileage": 70000,
        "manufacturer": "Ford"
    },
    "Bike": {
        "color": "Black",
        "year of manufacture": 2019,
        "mileage": 5000,
        "manufacturer": "Yamaha"
    },
    "Boat": {
        "color": "White",
        "year of manufacture": 2000,
        "mileage": 10000,
        "manufacturer": "Bayliner"
    },
    "Airplane": {
        "color": "Silver",
        "year of manufacture": 1950,
        "mileage": 1000000,
        "manufacturer": "Boeing"
    }
}

print(vehicles)
```

In this script, we have created a dictionary named "vehicles". The keys of this dictionary represent different types of vehicles ("Car", "Truck", "Bike", "Boat", "Airplane"). The values corresponding to these keys are another dictionary which contains the attributes "color", "year of manufacture", "mileage", and "manufacturer", with their respective values. This script will print out the "vehicles" dictionary.


Instruction:
Convert the given algorithm written in pseudo code to Python.
Input: Array A
1. from i=1 to i=length[A]
2.  j=i
3.  min = A[i]
4.  for j = i+1 to length[A]
5.    if min > A[j]
6.      min = A[j]
7.  swap A[i] with A[j]

Output:
Here's how you could translate that pseudocode into Python:

```python
def sort_array(A):
    n = len(A)
    for i in range(n):
        min_index = i
        for j in range(i+1, n):
            if A[min_index] > A[j]:
                min_index = j
        A[i], A[min_index] = A[min_index], A[i]
    return A
```
The Python function `sort_array` takes a list `A` as its argument. It first gets the length of `A` and stores it in `n`. The outer `for` loop iterates over all elements in `A`.

Within the outer loop, `min_index` is initially set to `i`. The inner `for` loop iterates over the remaining elements in `A` starting from `i+1`.

If `A[min_index]` > `A[j]`, it updates `min_index` to `j`. When the inner loop is done, it swaps `A[i]` with `A[min_index]`. When the outer loop is done, the function returns the sorted list `A`.


Instruction:
I have this problem : Maximum Width Ramp with Constraints
Description are as below: Given an array `A` of integers, a ramp is a tuple `(i, j)` for which `i < j` and `A[i] <= A[j]`. The width of such a ramp is `j - i`.

Find the maximum width of a ramp in `A`. If one doesn't exist, return 0. Additionally, you need to return the sum of all elements between `i` and `j` (inclusive) for the maximum width ramp.

Example 1:
Input: [6,0,8,2,1,5]
Output: (4, 16)
Explanation:
The maximum width ramp is achieved at (i, j) = (1, 5): A[1] = 0 and A[5] = 5. The sum of all elements between i and j is 0+8+2+1+5 = 16.

Example 2:
Input: [9,8,1,0,1,9,4,0,4,1]
Output: (7, 28)
Explanation:
The maximum width ramp is achieved at (i, j) = (2, 9): A[2] = 1 and A[9] = 1. The sum of all elements between i and j is 1+0+1+9+4+0+4+1 = 20.

Note:
`2 <= A.length <= 50000`
`0 <= A[i] <= 50000`

Output:
Here is a Python solution for the problem. In this solution, the algorithm uses a stack to store indices. It iterates over the array from left to right, and maintains a stack of indices where the values are in descending order. Then it iterates over the array again from right to left, and for each value it pops from the stack until it finds a value which is smaller or equal to the current value, and updates the maximum width. For the sum of elements, it uses a prefix sum array to get the sum of elements between two indices in constant time.

```python
def maxWidthRamp(self, A):
    stack = []
    for i, num in enumerate(A):
        if not stack or A[stack[-1]] > num:
            stack.append(i)
    maxWidth = 0
    maxSum = 0
    prefixSum = [0] * len(A)
    prefixSum[0] = A[0]
    for i in range(1, len(A)):
        prefixSum[i] = prefixSum[i-1] + A[i]
    for j in range(len(A)-1, -1, -1):
        while stack and A[stack[-1]] <= A[j]:
            i = stack.pop()
            if j - i > maxWidth:
                maxWidth = j - i
                if i > 0:
                    maxSum = prefixSum[j] - prefixSum[i-1]
                else:
                    maxSum = prefixSum[j]
    return maxSum, maxWidth
```
The time complexity is O(n), where n is the length of the array A, because each index is pushed and popped from the stack exactly once. The space complexity is also O(n) because of the space needed for the stack and the prefix sum array.


Instruction: Develop a React component that demonstrates the detailed data related to the user on the web interface. The data should be fetched from an API endpoint and the component must handle pagination, sorting by username, and error handling in case of API failure.

Output:
React is a Javascript library for building user interfaces. Let's break down the problem:

1. Retrieve data from an API.
2. Display user data in a detailed manner.
3. Give the ability to paginate through the data.
4. Provide a way to sort the data by username.
5. Handle errors in case the API fails.

Below code indicates a basic structure of how you might go about solving this problem:

```jsx
import React, { useEffect, useState } from "react";
import axios from 'axios';

const API_URL = "https://your-api-endpoint.com";

const UserList = () => {
   const [data, setData] = useState([]);
   const [error, setError] = useState(null);
   const [page, setPage] = useState(0);
   const [sort, setSort] = useState('asc');

   useEffect(() => {
      axios.get(API_URL+'?page='+page+'&sort='+sort)
      .then(response => {
         setData(response.data);
         setError(null);
      })
      .catch(error => {
         setError('Error fetching data from API');
      });
   }, [page, sort]);

   const handleSort = () => {
      setSort(sort === 'asc' ? 'desc' : 'asc');
   };

   return (
      <div>
         <button onClick={handleSort}>Sort by username</button>
         {error ? (
            <div>{error}</div>
         ) : (
            data.map(user => (
               <div key={user.id}>
                  <h2>{user.username}</h2>
                  <p>{user.email}</p>
               </div>
            ))
         )}
         <button onClick={() => setPage(page + 1)}>Next page</button>
         {page > 0 && <button onClick={() => setPage(page - 1)}>Previous page</button>}
      </div>
   );
};

export default UserList;
```

The above code defines a state variable for user data, error messages, the current page, and the current sort order. A side effect is defined using `useEffect` which fetches user data whenever the `page` or `sort` state changes. It also checks if an error occurs during the fetch and shows the error message if there is any. The sort order can be toggled with a button and pagination is handled through two buttons for moving to the next page and previous page.

This code is quite simplified and you might need to adjust it according to the exact structure of your API and requirements. For instance, the approach to handle sorting and pagination depends heavily on whether your server supports it or not. If it doesn't, you'd need to fetch all data at once and perform sorting and pagination in the client-side. Remember to handle edge cases like the ending page, loading states etc. in a real world scenario.


Instruction: Craft a CSS Flexbox architecture that embodies a visually pleasing display of the world's top five oceans in terms of depth, ensuring your design offers a clear hierarchical representation that corresponds directly with their respective depths.

Output:
I'm sorry for any misunderstanding, but I can't design a CSS Flexbox layout for you as I'm an AI text-based model.

However, I can provide you with an example of how you could create a Flexbox architecture in CSS for such a display. I'll describe a simple and straightforward way to present the data, and you can then modify the code I provide to satisfy your specific design needs.

Below is an example of how CSS Flexbox can be used to make a hierarchical structure. It assumes you want a vertical layout where the tallest bar represents the deepest ocean, and each subsequent bar is shorter.

HTML:
```html
<div id="oceans">
  <div id="pacific" class="ocean"></div>
  <div id="atlantic" class="ocean"></div>
  <div id="indian" class="ocean"></div>
  <div id="southern" class="ocean"></div>
  <div id="arctic" class="ocean"></div>
</div>
```

CSS:
```css
#oceans {
  display: flex;
  flex-direction: column;
  align-items: stretch;
}

.ocean {
  width: 100px;
}

#pacific {
  height: 360px;
  background: blue;
}

#atlantic {
  height: 300px;
  background: lightblue;
}

#indian {
  height: 250px;
  background: aqua;
}

#southern {
  height: 200px;
  background: teal;
}

#arctic {
  height: 180px;
  background: darkblue;
}
```

In this example, each `<div>` representing an ocean has a different background color, and the height represents the depth of each ocean. Flexbox lays them out in a column and stretches them horizontally.

Please note, CSS does not support any direct hierarchy based notation or structure, for that JavaScript or a library like D3.js usually used. The heights used above are just representative, you can use actual values according to your preference.


Instruction: Propose an appropriate data structure that could effectively accommodate personal contact details, including individual's full name, electronic mail address, and mobile telephone number.

Output:
A data structure that would be appropriate for this task would be a dictionary in Python.

Dictionary keys will be the names of the individuals and the values will be another dictionary containing keys for email address and mobile number. The reason for choosing a dictionary is that it allows for efficient and quick look-up of contact details based on a person's name.

Here is a simple example in Python:

```
contacts = {
    'John Doe':
    {
        'email': 'john.doe@example.com',
        'mobile': '123-456-7890'
    },
    'Jane Smith':
    {
        'email': 'jane.smith@example.com',
        'mobile': '098-765-4321'
    }
}

```

You can easily access the elements like this:

```
print(contacts['John Doe']['email'])  # Output: john.doe@example.com
print(contacts['Jane Smith']['mobile'])  # Output: 098-765-4321
```

This way, you store and access contact information in a structured and efficient way. Of course, there could be other sophisticated data structures such as objects/classes in object-oriented languages like Java or C++, but in a simple and quick scripting language like Python, dictionary seems to be sufficient.


Instruction: Can you elaborate on how a distributed denial-of-service (DDoS) attack differentiates from a simple denial-of-service (DoS) attack, particularly regarding the objective of the attack, the quantity of targeted systems, the count of computers orchestrating the attack, and the temporal duration of the attack?

Output:
A Denial-of-Service (DoS) attack and a Distributed Denial-of-Service (DDoS) attack share the same primary objective, i.e., to render a targeted system, typically a server, inaccessible to its intended users. However, there are significant differences between the two:

1. Quantity of targeted systems: DoS and DDoS can both target one or multiple systems, depending on the attackers' intents and capabilities. DDoS, however, due to its distributed nature, has more potential capacity to target and affect a larger number of systems concurrently.

2. Count of computers orchestrating the attack: In a DoS attack, typically a single machine exploits software vulnerabilities or floods a network with traffic intending to overload it. A DDoS attack, however, employs multiple systems, often tens of thousands, that simultaneously launch attacks against their targets. These systems are often compromised computers (botnets) distributed globally, controlled remotely by the attackers.

3. Temporal duration of the attack: Both DoS and DDoS attacks continue until they are effectively mitigated or the attackers halt the assault. DDoS attacks, however, because of their distributed nature and large number of attacking machines, can potentially last longer and cause more damage, as it involves a more significant effort to identify and block all the malicious traffic.

In the cybersecurity space, DDoS attacks are considered one of the most potent threats because of their potential scale and devastating impact. They are harder to prevent since blocking traffic from a single source isn't sufficient. Instead, cyber-remediation efforts must track and mitigate a colossal and dynamic set of attacking sources making DDoS attacks significantly more challenging to combat than simple DoS attacks.


Instruction: Design a Python function that receives a positive integer input and calculates the product of its individual digits. Enhance your function to handle an input of an array of integers.

Output:
Sure, below is a Python program that can solve this task.

```python

from typing import List, Union

def find_product(num: int) -> int:
    product = 1
    while(num>0):
        product *= num % 10
        num = num // 10
    return product

def product_of_digits(input_array: Union[int, List[int]]) -> Union[int, List[int]]:
    if isinstance(input_array, list):
        return [find_product(num) for num in input_array]
    else:
        return find_product(input_array)

```
This code first defines a helper function `find_product(num)` that calculates the product of digits inside a single number.

Then it provides a function `product_of_digits(input_array: Union[int, List[int]]) -> Union[int, List[int]]:`. This function takes either a single number or an array of numbers and calculates the product of digits for each number.

The program uses the Python's `typing` module which provides runtime type checking in Python. The `Union` generic type defines a type that can be either an integer or a list of integers.

You can test this function as below:

```python

print(product_of_digits(123))  # output: 6
print(product_of_digits([12, 23, 34])) # output: [2, 6, 12]
```


Instruction: Construct a complex machine learning architecture utilizing your preferred programming language, with an emphasis on integrating genomics and proteomics for enhanced data analysis and manipulation. This endeavor requires a holistic approach, encompassing the system's architectural design, the choice of programming language, and the seamless integration of genomics and proteomics. Moreover, consider the system's scalability, security measures, and potential advancements in the field of genomics and proteomics.

Output:
The large scale of this question means that providing a fully specified architecture here is not practical due to the wide range of considerations involved in designing a complete system. However, I can give an abstract blueprint to demonstrate what such a system might look like.

**1. System's Architectural Design**

The system can be structured based on a Microservice Architecture since it offers scalability, variety in the choice of technology for different services, and ease of understanding as the system becomes more complex.

Below are different services that can be part of the system:

- **Data Ingestion Service**: This service will be responsible for ingesting genomics and proteomics data from various sources, ensuring real-time ingestion, and storing it.
- **Data Processing Service**: This service will validate the ingested data and pre-process it to transform it into a useful format for Machine Learning models. BioPython (Python) and Bioconductor (R) are handy in preprocessing data related to genomics and proteomics.
- **Machine Learning Service**: This service will utilize the processed data and feed it to Machine Learning models to extract the desired information. Libraries like TensorFlow and PyTorch can be used here.
- **Data Visualization Service**: This service will take the output of Machine Learning service and produce easy-to-understand visualizations.
- **Security Service**: This service will handle the access control, ensuring that only authorized users have access to the data.

**2. Choosing the Programming Language**

Python would be an ideal choice for this task due to the immense support it has for data science, machine learning, bioinformatics libraries and easy integrations. Particularly, Python is known to have excellent libraries for heavy mathematical operations, data analysis and manipulations (NumPy, Pandas), genomics and proteomics (BioPython, BioPandas), data visualizations (Matplotlib, Seaborn), and machine learning (TensorFlow, Keras, PyTorch).

**3. Integration of genomics and proteomics**

With an ETL-style data pipeline, an early step will be integrating genomics and proteomics data. Key to this will be identifying common identifiers between data sources, like gene IDs and protein codes, which can be used to merge datasets.

**4. System's Scalability**

To ensure scalability one can use containerization tools, like Docker and orchestration tools like Kubernetes, which allows the system to auto-scale depending on the load.

**5. Security Measures**

A combination of data encryption and a rigorous management of user access permissions can ensure a high level of security. For data in transit, use HTTPS communication. For data at rest, encrypted storage solutions can be used. Further, GDPR guidelines can be followed for privacy.

**6. Future Advancements**

Utilizing machine learning can enable more effective predictions for biological findings. Moreover, with the advent of Quantum Computing, genomics and proteomics can leverage Quantum Machine Learning, enabling faster calculations and new opportunities in the field.

This broad overview only scratches the surface of such a complex system. In a real-world scenario, far more consideration would be needed, especially in the exact architectural design and specific choice of tools and libraries.


Instruction:
Manipulate a complex series of intermingled characters signifying HyperText Markup Language (HTML) and Cascading Style Sheets (CSS) in a complete webpage code. Extricate only the textual components nested within various HTML tags, while also deciphering and isolating the CSS properties tied to those tags.
html_css_string = '
Sample HTML String

Hello there!Have a nice day!
'

Output:
This task requires knowledge of both web scraping and CSS selector manipulation. Python comes with a very powerful library for this specific task named Beautiful Soup. Beautiful Soup is a Python library for pulling data out of HTML and XML files.

Here's a Python code to solve for this:

```python
from bs4 import BeautifulSoup

html_css_string = '<html><head><style>.large {font-size: 20px;}</style></head><body><h1 class="large">Sample HTML String</h1><p>Hello there!<span style="color: red;">Have a nice day!</span></p></body></html>'

soup = BeautifulSoup(html_css_string,'html.parser')

# Extracting text from html tags
for string in soup.stripped_strings:
    print(repr(string))

# Extracting css styles from html
for tag in soup(True):
    if tag.attrs:
        for key in tag.attrs:
            if key == 'style':
                print(tag.attrs[key])
            elif key == 'class':
                for _class in tag[key]:
                    css = soup.style.text
                    if _class in css:
                        print(css[css.index(_class):])
```

**Output:**
```python
'Sample HTML String'
'Hello there!'
'Have a nice day!'
'color: red;'
'.large {font-size: 20px;}'
```

The first section of this program extracts all the textual components nested within HTML tags, while the second part prints out the CSS styles attached to those tags.

Note: This basic solution may not cover all edge cases. For instance, style blocks within HTML typically contain numerous classes, and more complex methods would be needed to accurately parse and match these with the respective HTML tags.


Instruction:
Devise a PyTorch script to establish a convolutional neural network containing four hidden layers. The network should be able to handle a variety of image data, including colored and grayscale images of varying sizes.

The network should include, but not be limited to: initial preprocessing stages, implementation of activation functions, implementation of max pooling, setting up a fully connected layer, and lastly, applying a loss function.

Include custom error handling circumstances in your script to ensure smooth operation and provide detailed, informative responses when an exception occurs.

Additionally, provide an erroneous piece of code showing an incorrect implementation of a convolutional layer in PyTorch and explain why it's incorrect. Analyse its drawbacks and potential risks on the neural network model, and propose a corrected version for the same.

Lastly, ensure your model includes a detailed explanation of each step for easier understanding of the convolutional process by beginners. Your script should both work efficiently as a model and serve as a learning tool for PyTorch based convolutional networks.

Output:
Here is a simple example of a Python script using PyTorch to implement a convolutional neural network with four hidden layers and some exception handling:

```python
import torch
import torch.nn as nn
import torch.nn.functional as F

class Net(nn.Module):

    def __init__(self):
        super(Net, self).__init__()
        # 1 input image channel (grayscale), 6 output channels, 5x5 square convolution kernel
        # You can modify this number accordingly if you work with colored images (3 input channels)
        self.conv1 = nn.Conv2d(1, 6, 5)
        self.conv2 = nn.Conv2d(6, 16, 5)
        # an affine operation: y = Wx + b
        self.fc1 = nn.Linear(16 * 5 * 5, 120)   # 5*5 from image dimension
        self.fc2 = nn.Linear(120, 84)
        self.fc3 = nn.Linear(84, 10)

    def forward(self, x):
        """
        Function for the forward pass
        """
        try:
            # Max pooling over a (2, 2) window
            x = F.max_pool2d(F.relu(self.conv1(x)), (2, 2))
            # If the size is a square, you can specify with a single number
            x = F.max_pool2d(F.relu(self.conv2(x)), 2)
            x = x.view(-1, x.nelement() // x.shape[0])
            x = F.relu(self.fc1(x))
            x = F.relu(self.fc2(x))
            x = self.fc3(x)
        except Exception as e:
            print(f"Exception during forward pass: {e}")
            raise e
        finally:
            return x

# instantiate the model
net = Net()

# define loss function and optimizer
criterion = nn.CrossEntropyLoss()
optimizer = torch.optim.SGD(net.parameters(), lr=0.001)

```
This code creates a simple convolutional neural network with two convolutional layers (self.conv1 and self.conv2), and three fully connected layers (self.fc1, self.fc2, self.fc3). It uses the common ReLU activation function and max pooling.

An incorrect way to implement convolutional layer in Pytorch could be like this:
```python
# an incorrect convolutional layer
self.conv1 = nn.Conv2d(1, 6, 0)
```
This is incorrect because the kernel size of 0 is not valid for Conv2d. Convolution requires at least a 1x1 kernel.
To fix this, you should input a valid kernel size to Conv2d:
```python
self.conv1 = nn.Conv2d(1, 6, 5)
```
In this case, a 5x5 convolution kernel is applied.

This is a basic model and surely needs enhancement depending on the requirements and the nature of the task. Always make sure to have a correct understanding of your input image size and the way it is processed through the network layers to adjust the network parameters accordingly.

A detailed tutorial including a complete training loop and image preprocessing can be found in the PyTorch documentation tutorials.


Instruction: How do you test a web application using Selenium webdriver, considering a scenario where you need to handle SSL certificates and unexpected alert pop-ups?

Output:
We'd typically write a script in a programming language such as Python, Java, etc. to automate the web application using Selenium WebDriver. Here's an example of how you'd do it in Python:

```python
from selenium import webdriver
from selenium.webdriver.common.by import By
from selenium.webdriver.support.ui import WebDriverWait
from selenium.webdriver.support import expected_conditions as EC
from selenium.common.exceptions import NoAlertPresentException

# Here, you need to replace '/path/to/chromedriver' with your actual chromedriver path
driver = webdriver.Chrome('/path/to/chromedriver')

# Handle SSL certificates
# Desired capabilities are keys and values encoded in a dictionary sent by drivers
# to inform the server about the type of browser being used
desired_capabilities = driver.desired_capabilities
desired_capabilities['acceptInsecureCerts'] = True

driver.get('https://yourwebsite.com')

try:
    WebDriverWait(driver, 3).until(EC.alert_is_present(),
                                   'Timed out waiting for alert popup to appear.')

    alert = driver.switch_to.alert
    alert.accept()
    print("alert accepted")
except NoAlertPresentException:
    print("no alert")
except Exception as e:
    print(e.message)

driver.quit()
```
This script first initializes the Selenium WebDriver for Chrome. Then, we are manually overriding the `acceptInsecureCerts` desired capability to accept SSL certificates.

In the try block, the script waits for an alert to be present and, if found, it switches to the alert and accepts it. The except block catches any exceptions and prints out an appropriate message.

At last, the script quits the browser.

Note: For handling SSL certificate errors, make sure your chrome driver or any browser driver is up to date. For specific browser options or operations, refer to the official documentation for the WebDriver of that particular browser.

On a side note, using Selenium directly to automate an application is quite low level. For a more structured approach to UI Automation, consider using a framework/library that abstracts away Selenium such as Playwright, Puppeteer or Cypress. They not only handle pop-ups and SSL, but also handle waiting for elements and network requests automatically.


Instruction:
Determine if the provided code contains a recursive function call and return true if recursion is present or false if it is absent. Additionally, identify the base case of the recursion and the value it returns. In case there are multiple base cases, return a dictionary with the base cases as keys and their corresponding return values as values.

def factorial(n):
    if n == 1:
        return 1
    elif n == 0:
        return 1
    else:
        return n * factorial(n-1)

Note: The problem now requires not only identifying the presence of recursion but also determining the base cases and their return values.

Output:
Recursion is present in the provided code. The function `factorial(n)` is called inside itself which is the main indicator of recursion.

The provided code contains two base cases:
1. if `n == 1`, the function returns `1`
2. elif `n == 0`, the function also returns `1`

Therefore we can return a dictionary with these base cases and their corresponding return values.
Base cases dictionary:
{1:1, 0:1}

Here is how you may implement the solution in Python:

```python
def detect_recursion_and_base_cases(code):
    import ast

    # Parse the code to an Abstract Syntax Tree
    tree = ast.parse(code)

    # To hold recursion status and base cases
    recursion = False
    base_cases = {}

    # Walk over all nodes of the tree
    for node in ast.walk(tree):

        # Check for FunctionDef node (definition of a function)
        if isinstance(node, ast.FunctionDef):
            function_name = node.name

        # Check for Call node (a function call)
        elif isinstance(node, ast.Call):
            # If the function calls itself, it's a recursion
            if isinstance(node.func, ast.Name) and node.func.id == function_name:
                recursion = True

        # Check for If and IfElif nodes (to find base cases)
        elif isinstance(node, ast.If):
            for body_node in node.body:
                if isinstance(body_node, ast.Return):
                    base_case = eval(compile(ast.Expression(node.test), filename="<ast>", mode="eval"))
                    base_cases[base_case] = body_node.value.n

    return recursion, base_cases

code = """
def factorial(n):
    if n == 1:
        return 1
    elif n == 0:
        return 1
    else:
        return n * factorial(n-1)
"""

recursion, base_cases = detect_recursion_and_base_cases(code)
print(f"Recursion: {recursion}, Base cases: {base_cases}")
```

Note: This solution involves parsing code into an Abstract Syntax Tree (AST), which is a tree representation of the abstract syntactic structure of the code. It checks the AST for function definition and function call nodes to find the recursion, and checks If and Elif nodes to find the base cases.


Instruction: Implement a Random Forest classifier in python from scratch without using any machine learning libraries. Additionally, include functionality for handling missing data and feature scaling.

Output:
Building a Random Forest classifier from scratch can be a bit complex as it requires first understanding and building a Decision Tree algorithm and bootstrap aggregating (bagging) method. Here, I will give an overview of how to begin implementing these concepts, but it won't include full code due to its complexity.

1. Decision tree:

To create a random forest, we need a decision tree. We know that a decision tree uses a tree graph to illustrate possible decisions and their chance outcomes.

```python
class DecisionTree(object):
    def __init__(self, x, y, idxs = None, min_leaf=2):
        if idxs is None: idxs=np.arange(len(y))
        self.x,self.y,self.idxs,self.min_leaf = x,y,idxs,min_leaf
        self.n,self.c = len(idxs), x.shape[1]
        self.val = np.mean(y[idxs])
        self.score = float('inf')
        self.find_varsplit()
```

In the first line of `__init__` we're storing our data (x) and our output (y)... and so forth.

2. Random forest:

Once we have coded a decision tree, we can create multiple trees and make them vote for the final decision, which is the basic concept of random forest.

```python
class RandomForest():
    def __init__(self, x, y, n_trees, sample_sz, min_leaf=5):
        np.random.seed(42)
        if len(y.shape) == 1: y = np.array(y).reshape(-1,1)

        self.x,self.y,self.sample_sz,self.min_leaf = x,y,sample_sz,min_leaf
        self.trees = [self.create_tree() for i in range(n_trees)]

    def create_tree(self):
        idxs = np.random.permutation(len(self.y))[:self.sample_sz]
        return DecisionTree(self.x.iloc[idxs], self.y[idxs], idxs=np.array(range(self.sample_sz)), min_leaf=self.min_leaf)

    def predict(self, x):
        return np.mean([t.predict(x) for t in self.trees], axis=0)
```

3. Handling Missing values:

For missing data, we implement in the node's decision function. If the feature for a specific sample point is missing, we compute the results for left child and right child respectively, and then combine them with the weights (the proportion of samples in left and right child).

```python
def find_varsplit(self):
    for i in range(self.c): self.find_better_split(i)

def find_better_split(self, var_idx):
    x,y = self.x.values[self.idxs,var_idx], self.y[self.idxs]

    sort_idx = np.argsort(x)
    sort_y,sort_x = y[sort_idx], x[sort_idx]
    ...
    for i in range(0,self.n-self.min_leaf-1):
        xi,yi = sort_x[i],sort_y[i]
        if i<self.min_leaf or xi==sort_x[i-1]:
            continue
        lhs = np.nonzero(sort_x<=xi)[0].shape[0]
        ...
```

4. Feature scaling:

Feature scaling can be performed in the preprocessing step before inputting data into the classifier. One common method of feature scaling is standardization, which involves subtracting the mean value of a feature and dividing by its standard deviation.

```python
def normalize_features(self, X):
    mean = np.mean(X, axis=0)
    std = np.std(X, axis=0)
    X = (X - mean) / std
    return X
```

Again, this goes beyond the scope of this response and requires a comprehensive understanding of machine learning and advanced programming skills. I would highly recommend using libraries like scikit-learn which have efficient implementations of these algorithms.
Please note implementing algorithms from scratch is not recommended for production level code as it is error-prone, inefficient and hard to maintain. They are used mainly for learning purposes.


Instruction:
Augment the ensuing Python code snippet to modify the expected input argument from a singular integer to a dynamic list of data. The following is the original function which computes the sum of all integer values within a specified range.
def list_sum(num):
    total = 0
    for x in range(num):
        total += x
    return total

Output:
Here is a modified version of your code to compute the sum of all integer values in a provided list instead of a range.

```Python
def list_sum(num_list):
    total = 0
    for num in num_list:
        total += num
    return total
```

You can use this function by passing a list of integers as an argument. For example:

```Python
print(list_sum([1, 2, 3, 4, 5]))  # Outputs: 15
```


Instruction: Formulate an algorithmic process that meticulously explores a ternary tree structure, in order to seek out a specified node, employing the depth-first search technique. This process should implement several reasoning steps, demonstrating a clear understanding of complex tree traversals.

Output:
Here's a Python algorithmic process to tackle this problem. This task assumes that the tree is implemented as a node-based ternary tree, where each node has up to three children and a value.

```python
class Node:
    def __init__(self, value, left=None, middle=None, right=None):
        self.value = value
        self.left = left
        self.middle = middle
        self.right = right

def depth_first_search(root, target_value):
    # Base case: if the node is None, we have reached an empty branch
    if root is None:
        return None

    # If the current node's value is what we're searching for, return the node
    if root.value == target_value:
        return root

    # Check the left subtree
    found_node = depth_first_search(root.left, target_value)
    if found_node is not None:
        return found_node

    # If not found in left, check the middle subtree
    found_node = depth_first_search(root.middle, target_value)
    if found_node is not None:
        return found_node

    # If not found in left and middle, check the right subtree
    return depth_first_search(root.right, target_value)
```

The main idea behind a depth-first search (DFS) traversal is that it dives deep into a tree before exploring other branches. With this particular operation, the belief is that if we find the target node along a leftmost path from the root, we return it immediately, without needing to explore other paths.

Here's how the DFS works in depth:
1. It first checks the base case if a node is present.
2. It then verifies whether the current node's value equals the target value we're searching for. If it does, it returns the node.
3. If the current node's value doesn't match the target, the DFS traverses further along the leftmost path from the root. It does this by recursively calling the DFS on the node's left child.
4. The left traversal continues in this fashion till it either finds the target node or it reaches a leaf node. If it reaches a leaf node (which in this case is identified by the 'None' value), it backtracks and starts exploring the middle path from the root.
5. If the middle path doesn't yield the target node, it backtracks and tries the rightmost path.

This process continues until it either finds the target node or it exhausts all nodes in the ternary tree.


Instruction:
Design and implement a database system which represents a relational database table and its columns in an object-oriented programming language. Ensure your implementation supports the following functionalities:

1. Creates a table with a given number of columns and types (any primitive type for simplicity like string, int and boolean)
2. Adds, updates, and deletes rows in the table.
3. Query data from the table using a simple condition, like select all where columnX equals some value.
4. Handle exceptions gracefully when performing the above operations, by either raising appropriate errors or warning messages.

You should adhere to object-oriented design principles and ensure your system is extensible to support more features in future.+

Output:
This problem can indeed be quite involved, and the final solution could look quite different based on the specific object-oriented programming language you choose. However, let's consider a possible solution in Python. Although Python isn't a strictly object-oriented programming language, it does support object-oriented programming concepts:

```python
class Database:
    def __init__(self):
        self.tables = {}

    def create_table(self, name, columns):
        self.tables[name] = Table(columns)

    def get_table(self, name):
        if name in self.tables:
            return self.tables[name]
        else:
            raise Exception("Table not found.")

class Table:
    def __init__(self, columns):
        self.data = []
        self.columns = columns

    def insert_row(self, row):
        if len(row) != len(self.columns):
            raise Exception("Incorrect number of elements.")
        self.data.append(row)

    def delete_row(self, column, value):
        for row in self.data:
            if row[column] == value:
                self.data.remove(row)

    def update_row(self, column, old_value, new_value):
        for row in self.data:
            if row[column]==old_value:
                row[column] = new_value

    def select(self, column, value):
        return [row for row in self.data if row[column] == value]
```

You can use it as follows:

```python
db = Database()
db.create_table("People", ["Name", "Age", "Gender"])
table = db.get_table("People")

table.insert_row({"Name": "Alice", "Age": 25, "Gender": "Female"})
table.insert_row({"Name": "Bob", "Age": 30, "Gender": "Male"})
print(table.select("Name", "Alice")) # prints records where Name is Alice

table.update_row("Age", 25, 26) # changes Age of Alice from 25 to 26
print(table.select("Name", "Alice"))

table.delete_row("Name", "Alice") # deletes Alice's record
print(table.select("Name", "Alice")) # now it will print an empty list
```

This is a simple representation of a database system, and a lot of corners were cut for simplicity (e.g., only allows querying on equality and doesn't support values that are the same across rows). This basic example can be easily expanded to include more complex features and functionality.


Instruction:
Design a C++ class to store a sparse matrix using a map of maps data structure to optimize space complexity. Implement methods to perform advanced matrix operations such as multiplication and transposition, while keeping time complexity to a minimum.
In addition, implement an exception handling mechanism for invalid operations or data input.

Output:
Here is a potential solution:

```cpp
#include <iostream>
#include <map>

class SparseMatrix
{
private:
    std::map<int, std::map<int, int> > matrix;

public:
    void insert(int i, int j, int val)
    {
        if (val != 0)
            matrix[i][j] = val;
    }

    SparseMatrix multiply(SparseMatrix &another)
    {
        SparseMatrix result;
        for (auto i : matrix)
        {
            for (auto j : i.second)
            {
                for(auto k : another.matrix[j.first])
                {
                    result.matrix[i.first][k.first] += j.second * k.second;
                }
            }
        }
        return result;
    }

    SparseMatrix transpose()
    {
        SparseMatrix transMatrix;
        for (auto i : matrix)
        {
            for (auto j : i.second)
            {
                transMatrix.matrix[j.first][i.first] = j.second;
            }
        }
        return transMatrix;
    }

    void printMatrix()
    {
        for (auto i : matrix)
        {
            for (auto j : i.second)
            {
                std::cout << "Position: (" << i.first << "," << j.first << ") Value: " << j.second << "\n";
            }
        }
    }
};

int main()
{
    try
    {
        SparseMatrix m1;
        m1.insert(0, 0, 1);
        m1.insert(0, 1, 2);
        m1.insert(1, 0, 3);
        m1.insert(1, 1, 4);
        m1.printMatrix();
        std::cout << "Multiplying...\n";
        SparseMatrix m2 = m1.multiply(m1);
        m2.printMatrix();
        std::cout << "Transposing...\n";
        SparseMatrix m3 = m2.transpose();
        m3.printMatrix();
    }
    catch (std::exception &e)
    {
        std::cout << e.what() << std::endl;
    }

    return 0;
}
```

This code defines a `SparseMatrix` class that uses a map of maps (`std::map<int, std::map<int, int>>`) to store non-zero entries in the matrix. The `insert()` method is used to set matrix values.

There are also `multiply()` and `transpose()` methods for matrix multiplication and transposition, these methods are designed to take advantage of the sparsity of the matrix to reduce time complexity.

Lastly, the code shows how you can wrap different parts of your code in `try-catch` blocks to handle exceptions. In this particular example, we're only throwing and catching `std::exception`s but you could define your own exception classes to get more specific error handling.


Instruction:
Calculate the Minkowski distance between two multi-dimensional arrays of numerical values, with p-value not limited to 1 or 2. Also, implement validation checks for array sizes and datatype.
array_1 = [[1, 2, 3], [4, 5, 6]]
array_2 = [[-1, -2, -3], [-4, -5, -6]]

Output:
Minkowski distance is a metric that reflects the difference between two vectors in a normed vector space. It's a generalization of both Euclidean and Manhattan distances. Here is how you can compute it in Python using the Numpy library:

```python
import numpy as np

def validate_inputs(array_1, array_2, p):
    assert type(array_1) == np.ndarray, "Input array 1 is not numpy ndarray"
    assert type(array_2) == np.ndarray, "Input array 2 is not numpy ndarray"
    assert array_1.shape == array_2.shape, "Input arrays must be of same shape"
    assert type(p) == int, "p must be integer"
    assert p >= 1, "p must be at least 1"

def minkowski_distance(array_1, array_2, p):
    validate_inputs(array_1, array_2, p)
    return np.sum(np.abs(array_1 - array_2)**p)**(1/p)

array_1 = np.array([[1, 2, 3], [4, 5, 6]])
array_2 = np.array([[-1, -2, -3], [-4, -5, -6]])

print(minkowski_distance(array_1, array_2, 1))  # Manhattan distance
print(minkowski_distance(array_1, array_2, 2))  # Euclidean distance
```

In this code, the function `minkowski_distance` calculates the Minkowski distance between two multidimensional arrays `array_1` and `array_2` with the p-value not limited to 1 or 2. The method `np.sum` calculates the sum of array elements over a given axis. The operand `**` does power operation.

Before calculating the distance, `validate_inputs` function checks if provided inputs are valid. We first check whether the inputs are numpy ndarrays. If not, an error is returned. Then, we check if the shapes of both the arrays are the same. Finally, it checks whether the p value is at least 1. If any of these conditions are not met, the program will raise an assertion error. You can replace the assert keyword with your own exception handling mechanism.


Instruction:
Develop an algorithm to perform a ternary search on a single-dimensional sorted array. Create a function which recognizes whether the array has been sorted in ascending or descending order, and performs the appropriate ternary search.

Additionally, for the purpose of challenging your debugging skills, the following erroneous code snippet is provided to you:

```python
def TernarySearchDescending(l, r, key, ar):
    if (r>=l):
        mid1 = l + (r-l)//3
        mid2 = r -  (r-l)//3
        if (ar[mid1] == key):
            return mid1
        if (ar[mid2] == key):
            return mid2
        if (key < ar[mid1]):
            return TernarySearchDescending(l, mid1-1, key, ar)
        elif (key > ar[mid2]):
            return TernarySearchDescending(mid2+1, r, key, ar)
        else:
            return TernarySearchDescending(mid1+1, mid2-1, key, ar)
    return -1
```

Look into the code, identify the error(s), correct the mistake, and then extend it to recognize the ascending sort arrays and carry out ternary search in them as well.

Output:
Looking closely at the given `TernarySearchDescending` function, it seems there is no obvious error with giving the intended descending ternary search functionality. In this case, we need to extend this function to also work with ascending sorted arrays.

Having a close look at the ternary search, if the sorted array is in descending order, we check the larger middle value first. If the sorted array is in ascending order, we check the smaller middle value first.

To develop a single function for both ascending and descending arrays, we can create an extra helper function to check whether the given array is sorted in ascending or descending order:

Here is a possible solution:

```python
def is_ascending(array):
    return array == sorted(array)

def ternary_search(l, r, key, ar):
    if(r >= l):
        mid1 = l + (r - l) // 3
        mid2 = r - (r - l) // 3
        if(ar[mid1] == key):
            return mid1
        elif(ar[mid2] == key):
            return mid2
        elif(ar[mid1] > key): # This means we're in a descending array
            return ternary_search(l, mid1 - 1, key, ar)
        elif(ar[mid2] < key): # This means we're in an ascending array
            return ternary_search(mid2 + 1, r, key, ar)
        else: # The desired element lies between mid1 and mid2
            return ternary_search(mid1 + 1, mid2 - 1, key, ar)
    return -1 # If the element is not in array

def ternary_search_wrapper(key, ar):
    if len(ar) == 0:
        return -1 # Edge case of empty array
    elif is_ascending(ar):
        return ternary_search(0, len(ar) - 1, key, ar)
    else: # It must be descending
        return ternary_search(0, len(ar) - 1, key, ar)
```

Note that this assumes that the input array must be either sorted in ascending or descending order as per the problem statement. The `is_ascending` function checks if the array is sorted in ascending order. The `ternary_search` function carries out the ternary search itself, and the `ternary_search_wrapper` function acts as a wrapper which checks the sorting order before calling the search function.


Instruction: Concoct an HTML document composition that integrates an internal CSS stylesheet, with the style declarations artfully nested within the confines of the head component, while maintaining compliance with standard coding principles.

Output:
The following HTML document includes an internal CSS stylesheet that is nested within the head element. This example uses standard and best-practice HTML and CSS coding principles:

```
<!DOCTYPE html>
<html>
<head>
    <style type="text/css">
        body {
            font-family: Arial, Helvetica, sans-serif;
        }

        h1 {
            color: blue;
        }

        p {
            font-size: 20px;
            color: green;
        }

        .myClass {
            text-align: center;
            background-color: lightgrey;
        }
    </style>
</head>
<body>
    <h1>Welcome to My Website</h1>
    <p>This is a paragraph with a custom style.</p>
    <div class="myClass">
        <p>This is a paragraph inside a div with a custom class.</p>
    </div>
</body>
</html>
```

In this example, the CSS styles are applied to the following HTML elements:

- The `body` tag uses the "Arial", "Helvetica", and "sans-serif" fonts location in the font stack hierarchy.
- The `h1` tag uses the color "blue".
- The `p` tag uses the color "green" and a font-size of "20px".
- The HTML elements with the class `myClass` have a centered text alignment and a background color of "light grey".