answer:1. Rectified Linear Unit (ReLU) Function: The ReLU function is given by: f(x) = max(0, x). It can also be rewritten as: f(x) = x for x > 0, 0 for x ≤ 0. The derivative of the function is:f'(x)= 1 for x > 0, 0 for x ≤ 0.This derivative turns zero for x ≤ 0 due to the fact that for values less than or equal to zero, the function is constant and does not change; hence its slope, captured by the derivative, is zero. For values of x > 0, the function is linear with a slope of 1; hence the derivative is 1.2. Sigmoid Function: The Sigmoid function is given by: σ(x) = 1/(1 + e^-x). Differentiating it, we get:σ'(x) = e^-x/ (1 + e^-x)^2 = σ(x).(1 - σ(x))Now σ(x) always lies between 0 and 1, so the maximum of σ(x).(1 - σ(x)) happens at σ(x) = 1/2 where its value is 1/4. This is why the derivative of the sigmoid function never exceeds 1/4 for all x.3. Continuity of derivative:Derivative of Sigmoid function is continuous for all real values, since e^-x and (1 + e^-x) are both continuous and differentiable for all real numbers, and the derivative of the sigmoid function involves only these parts.On the other hand, the derivative of ReLU function is undefined at x = 0. At x = 0, the function transitions from a constant 0 to a linear function with slope = 1. Hence, the ReLU function doesn't have a defined derivative at x = 0, which leads to some issues in gradient-based optimization algorithms. This issue points out the broken nature of the derivative of the ReLU function as it's not defined for x = 0.

answer:Here is an example in Python that should fulfill your requirements.```pythonclass DictList: def __init__(self): self.dict_list = [] # Insertion of a new dictionary def insert(self, new_dict): self.dict_list.append(new_dict) # Deletion of an existing dictionary def delete(self, del_dict): if del_dict in self.dict_list: self.dict_list.remove(del_dict) return True else: return False # Searching for a specific key across all dictionaries and returning its associated value def search(self, key): results = [] for d in self.dict_list: if key in d.keys(): results.append(d[key]) return results # Modification of an existing value attached to a key def modify(self, key, value): mod_count = 0 for d in self.dict_list: if key in d.keys(): d[key] = value mod_count += 1 return mod_countmyDictList = DictList()myDictList.insert({"key1": "value1", "key2": "value2", "key3": "value3"})myDictList.insert({"key2": "new_value2", "key4": "value4", "key5": "value5"})print(myDictList.search("key2"))print(myDictList.modify("key2", "modified_value2"))print(myDictList.search("key2"))print(myDictList.delete({"key1": "value1", "key2": "modified_value2", "key3": "value3"}))```This code creates a list of dictionaries and defines methods for insertion, deletion, searching and modifying. Please note that if multiple dictionaries contain the same key, the search function will return a list of all associated values and the modify function will modify the value for that key in all dictionaries. The delete function deletes an entire dictionary if it exists in the list.

answer:Below is the JavaScript function that fulfills the given requirements:```JavaScriptfunction complexOperation(inputString) { if(inputString === null || inputString === '') { // Check for null or empty string return ''; } let result = ''; let countObj = {}; for(let i = 0; i < inputString.length; i++) { let char = inputString[i]; if(countObj[char]) { // If character is already encountered countObj[char] += 1; } else { // If character encounter for the first time countObj[char] = 1; // Append character to result string result += char; } } let output = ''; for(let i = 0; i < result.length; i++) { let char = result[i]; // Append character along with its count output += char + countObj[char]; } return output;}```This function first checks if the input string is null or empty and returns an empty string in such a case. It then records the unique characters present in the string and for each character, counts the number of its occurrences. Finally, it generates the output string in which each unique character is followed by its count of occurrences.Example execution:```JavaScriptcomplexOperation('google'); // Returns: 'g2o2l1e1'```

answer:Creating a comprehensive guide that outlines the complexities and applications of lattice-based cryptography demands an interdisciplinary approach. This endeavor will necessitate a firm grasp on advanced cryptanalysis, complex number theory, data-driven strategies, and problem-solving skillsets. 1. Foundations in Lattice-Based Cryptography and Learning With Errors: The understanding and implementation of LWE-based cryptographic relations are fundamental. With roots in complex number theory, they leverage the hardness of decoding random linear codes and harness the power of lattice constructions for formulating robust cryptographic protocols. Understanding the basic building blocks of LWE is pivotal before delving into specific methodologies.2. Securing LWE and Identifying Breaches: Ensuring the security of cryptographic applications using LWE involves monitoring for vulnerabilities and breach attempts. This process includes maintaining surveillance on the vulnerabilities in the public key and shared secret exchanges besides checking for abnormalities commonly known in the context of LWE applications. Breach attempts might involve adversarial attempts to decode the LWE problem. Identification and rectification of these security breaches are key.3. Analytical Skills and Problem-Solving Proficiencies: LWE-based cryptanalysis often presents complicated challenges. Tackling these issues necessitates analytical skills that not only spot the problems but assist in their rectification. Skills range from basic cognitive skills, such as understanding a problem to advanced-level skills like formidable complex number theory and abstract algebra, with potential applications in real-time problem-solving.4. Cryptographic Effectiveness and Data Dependability: The accuracy and reliability of the encrypted data are primary factors for assessing the effectiveness of any cryptographic implementation. Review procedures guaranteeing the encrypted data's integrity and dependability are essential, and any issues detected should promptly be attended to and resolved.5. Integration and Deployment Strategies: Successful implementation and ongoing integration of LWE-based cryptographic applications require effective strategies. This involves consolidating new cryptographic updates with existing infrastructure smoothly and seamlessly. A profound understanding of the lattice-based cryptographic realm is required to ensure this continuous implementation.6. Performance Constraints and Enhancement Techniques: As cryptographic systems scale, they are likely to face performance constraints. To ensure the smooth propagation of LWE frameworks, it's important to identify potential constraints, which can range from computational power to the hardness assumptions of the LWE problem, and find effective solutions to these possible issues.Drawing from theoretical knowledge and practical expertise, this guide will dissect and present the different dimensions of LWE-based cryptography. Adhering to this guide will provide a structured pathway to deciphering the complexities of lattice-based cryptography.

answer:You can use the JavaScript built-in method `toUpperCase()` to convert a string to uppercase. Here's a simple function that does this:```javascriptfunction convertToUpper(str) { if (typeof str === 'string') { return str.toUpperCase(); } else { return "Provided parameter is not a string!"; }}var string = 'Hello World';console.log(convertToUpper(string)); // Outputs: HELLO WORLD```In this function, we first check if the input is a string by using the JavaScript `typeof` operator. If the input is a string, it is converted to uppercase and returned. If the input is not a string message "Provided parameter is not a string!" is returned.

answer:First, you need to install packages called BeautifulSoup and requests. You can do this via pip install requests and pip install BeautifulSoup4 commands in your terminal or command prompt.Here's an example of a Python function using the BeautifulSoup and requests packages for web scraping. This function scrapes an HTML page for the most frequent textual terms. You would just need to replace the passed url with the url of the web page you wish to scrape.```pythonfrom bs4 import BeautifulSoupimport requestsfrom collections import Counterimport redef web_scraper(url): # Make a request to the website r = requests.get(url) r.raise_for_status() # Parse the page soup = BeautifulSoup(r.text, 'html.parser') # Find the text text = soup.get_text() # Split the text into words words = re.findall('w+', text.lower()) # Count the words c = Counter(words) # Find the most common words most_common = c.most_common(10) return most_common# Use it like thisprint(web_scraper('http://example.com'))```This will return the 10 most common words in the text on the page, along with how many times each word appears.Note: Web scraping should be done in compliance with the terms of service of the website being scraped. It's also important to respect the server's resources and not overload the server with requests. It's also ethical (and in many cases, legally required) to make sure you're not harvesting personal information without consent. Finally, this technique is useful for simple HTML pages and may not work on pages with more advanced technologies like JavaScript rendering.