In lecture, we saw how to sample a K-coloring using Markov Chains. If the graph we are coloring has a simple geometry, we may sample without the sophistication of Markov Chains. Let o(1) be a uniform sample from [k], the set of k colors. Given that o(i) has been assigned for j = 1, 2, ..., j - 1, choose o(j) uniformly from the set [k] \{o(j – 1)}. Show that o = (o(1),o(2),...,0(n)) is a uniform coloring of the path on n vertices.
Answers
This probability is the same for any valid coloring C. Thus, we conclude that the above process generates a uniformly random colouring of the path.
To show that \(o = (o(1), o(2), ..., o(n))\) is a uniform coloring of the path on n vertices, we need to prove that each vertex has an equal probability of being assigned any color from the set [k] and that the coloring is valid (no two adjacent vertices have the same color).
Assign the first vertex a color o(1) uniformly from the set [k].For each subsequent vertex j, assign a color o(j) uniformly from the set \([k] \ {o(j - 1)}\). This ensures that o(j) will be different from its adjacent vertex \((j - 1)\).To show that the coloring is uniform, consider the probability of a specific coloring \(C = (c1, c2, ..., cn)\). We need to find the probability of obtaining C through the described process.
\(P(C) = P(c1) * P(c2|c1) * P(c3|c2) * ... * P(cn|c(n-1))\)
Since we choose o(1) uniformly from the set \([k], P(c1) = 1/k.\)
For the rest of the vertices, we are choosing uniformly from \([k] \ {o(j - 1)}\), which has (k - 1) possible colors. Therefore, \(P(cj|c(j-1)) = 1/(k - 1) for j = 2, 3, ..., n.\)
\(P(C) = (1/k) * (1/(k - 1))^(n - 1)\)
This probability is the same for any valid coloring C, which means the coloring \(o = (o(1), o(2), ..., o(n))\) is a uniform coloring of the path on n vertices.
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Related Questions
what does a cargo and freight agent do
Answers
Hey there!
Well cargo and freight agents expedite and route movement of incoming and exporting cargo and of course freight.
Hope this helps :)
Which of the following describes an action that serves a goal of equity
Answers
Answer:
Please complete your sentence for me to answer.
Which of the following activities Best describes the use of marketing as a form of digital communication
OA An online discount clothing company sends an email about its upcoming sale,
OB. A teacher posts a list of assignments online for students to access
OG A doctor's office emails a patient to remind them about an upcoming appointment
OD. A friend downloads a new song by her favorite artist to her phone.
Reset
Next
Answers
the answer for this question is:
OA. An online discount clothing company sends an email about its upcoming sale.
hope this helps you!
When you execute this block in Scratch, your computer is actually doing several things: retrieving values from memory representing the direction and position of the sprite, performing an algorithm to update these values, and changing the display in the window to match the updated state of the program. All of these actions are represented by just one single block.
Which of the following terms names the phenomenon which is best described by this statement?
a) Iteration
b) Sequencing
c) Compilation
d) Abstraction
Answers
Sequencing is the term that names the phenomenon which is best described by the given statement.
Sequencing refers to the order of logical arrangement whereby an instruction is executed in the proper order. This means that one process must be completed before the next command becomes valid and executes.
From the given statement, the computer is performing various operations in sequence which are:
Retrieving values from memoryPerforming algorithmChanging the displayThese functions are done by order, using a single block.
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Which event is most likely to cause a nontraumatic brain injury?
a) cerebral hemorrhage
b) fall from a ladder
c) knockout punch
d) motorcycle crash
Answers
8.6 Code Practice: Question 2
Instructions
Copy and paste your code from the previous code practice. If you did not successfully complete it yet, please do that first before completing this code practice.
After your program has prompted the user for how many values should be in the array, generated those values, and printed the whole list, create and call a new function named sumArray. In this method, accept the array as the parameter. Inside, you should sum together all values and then return that value back to the original method call. Finally, print that sum of values.
Sample Run
How many values to add to the array:
8
[17, 99, 54, 88, 55, 47, 11, 97]
Total 468
Answers
Answer:
import random
def buildArray(a, n):
for i in range (n):
a.append(random.randint(10,99))
arr = []
def sumArray(a):
tot = 0
for i in range(len(a)):
tot = tot + a [i]
return tot
arr = []
numbers = int(input("How many values to add to the array:\n"))
buildArray(arr, numbers)
print(arr)
print("Total " + str(sumArray(arr)) )
Explanation:
The program is an illustration of lists
ListsLists are variables that are used to hold multiple values in one variable name
Python ProgramThe program in Python, where comments are used to explain each line is as follows:
#This gets the number of inputs to the array
n = int(input("How many values to add to the array: "))
#This initializes the sum to 0
sumArray = 0
#This initializes a list
myList = []
#This iterates through n
for i in range(n):
#This gets input for the list elements
num = int(input())
#This appends the input to the list
myList.Append(num)
#This calculates the sum
sumArray+=num
#This prints the list elements
print(myList)
#This prints the sum of the list elements
print("Total",sumArray)
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7.3.4: Find the Error
Answers
Answer:
my_string = "hello!"
# One of the two lines below will cause an error.
# Each line is an attempt to replace the first
# letter of myString with H. Comment out the
# line you think is incorrect.
# my_string[0] = "H"
my_string = "H" + my_string[1:]
print(my_string)
Explanation:
The numeric or alphanumeric error code is being used to identify the type of error. Following are the description of the error code in the given question:
Incorrect code:
my_string[0] = "H" // this line give the error that is "'str' object does not support item assignment".
Correct code:
my_string = "hello!"#defining the string variable that is "my_string"
my_string = "H" + my_string[1:]#using string variable that perform slicing and hold its value
print(my_string)#print my_string value
Code Explanation:
Defining the string variable that is "my_string".In the next line, the string variable is used that adds "H" to the first index value and performs slicing, and holds its value. Using the print method that prints the "my_string" variable value.Output:
Please find the attached file.
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What is the difference between business strategies and business models?
A. Business strategies include long-term business plans, while
business models include plans for daily business functions.
B. Business strategies focus on specific aspects of a business, while
business models focus on how different aspects affect the whole
business.
C. Business models focus on specific aspects of a business, while
business strategies focus on how different aspects affect the
whole business,
D. Business strategies incorporate forms of traditional business
advertising, while business models incorporate the use of social
media.
Answers
Answer:
the answer is A
Explanation:
A is the answe
Answer:
B. Business strategies focus on specific aspects of a business, while business models focus on how different aspects affect the whole business.
Explanation:
Edhesive 6.8 lesson practice
question 1: a ____________ variable is available throughout a program.
question 2:
val = 25
def example():
global val
val = 15
print (val)
print (val)
example()
print (val)
what is output?
question 3:
val = 50
def example():
val = 15
print (val)
print (val)
example()
print (val)
what is output?
Answers
For question 1, the answer is "global" as a global variable is available throughout a program.
For question 2, the output will be "15 15 15" as the variable "val" is declared as global within the function "example()" and then reassigned a value of 15 before being printed three times.
For question 3, the output will be "15 15 50" as the variable "val" is declared and assigned a value of 50 outside the function "example()", but a new local variable "val" is declared and assigned a value of 15 within the function and printed twice before the original "val" value of 50 is printed.
Here are the answers to your questions: 1. A global variable is available throughout a program, meaning it can be accessed and modified by any part of the code. 2. In the given code, the output will be:
15
15
15
This is because the 'global val' statement inside the 'example()' function makes 'val' a global variable, changing its value to 15 and then printing it twice. Finally, the last 'print(val)' statement outside the function also prints the modified value of 15.
3. In this code, the output will be:
15
15
50
The 'example()' function has a local variable 'val' with a value of 15, so when it prints, it prints 15 twice. However, the last 'print(val)' statement outside the function refers to the global variable 'val' with a value of 50, so it prints 50.
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wardialing is a technique that is used: a. to find other hackers on the internet. b. by telemarketers to automatically call phone numbers. c. to locate modem tones. d. to create a brute force attack.
Answers
(C) to locate modem tones. The right response is c. Finding the modem tones that computers and other devices use to connect over a phone line is a technique known as wardialing.
In order to find a suitable target, the technique includes dialling a variety of phone numbers and listening for the sound of a modem tone. Security experts and hackers have in the past utilised wardialing to find weak computer systems connected to phone lines. However, it is illegal and unethical to utilise it for evil intent. It's not frequently used to find other hackers online, by telemarketers to contact phone numbers automatically, or to launch a brute force attack.
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Dave is a recruiter for a large video and animation firm. He is looking for an employee who is willing to give productive hours to activities related to the job. Which quality is he looking for? A. responsibility B. flexibility C. trust D. reliability E. integrity
Answers
Answer:
reliabitlity
Explanation:
A decrease in variability leads to an increase in what?
A) Predictability
B) Risk
C) Cost
D) Length
Answers
A decrease in variability leads to an increase in predictability. Hence option A is correct.
What is variability?Variability is defined as the degree to which data points in a statistical distribution or data set deviate from the mean value as well as the degree to which these data points differ from one another. The following are some illustrations of typical sources of variation: Unfit operation, inappropriate machine, uneducated operators and so on.
Predictability is defined as a measure of how accurately a system's state can be predicted or projected, either qualitatively or statistically. When something is predictable, a youngster can plan their conduct to succeed by knowing what to expect.
Thus, a decrease in variability leads to an increase in predictability. Hence option A is correct.
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Which of the following is an example of effective nonverbal communication?
O presenting information about the status of a project in a team meeting
O an e-mail congratulating a team for attaining their goal
O eye contact and a smile
Opointing, frowning, and turning away
Answers
Answer:
Eye contact and a smile
Explanation:
There are only two nonverbal communication options in the list you gave:
eye contact and a smilepointing, frowning, and turning awayPointing, frowning, and turning away would not be effective nonverbal communication because it seems uninviting and disrespectful. Eye contact and a smile is effective nonverbal communication because it shows that you're respectful, paying attention, and understanding.
A(n) ___ interface is one that supports as many people as possible by considering disabilities, screen sizes, languages, and many other factors.
1. web-safe
2. accessible
3. inclusive
Answers
The term that fills in the blank in the given statement "A(n) ___ interface is one that supports as many people as possible by considering disabilities, screen sizes, languages, and many other factors" is accessible.
An accessible interface is one that supports as many people as possible by considering disabilities, screen sizes, languages, and many other factors. A web-safe interface is designed to perform and appear the same way across many browsers. An inclusive interface seeks to make everyone feel welcomed and included.
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How do you use index formulas?
Answers
This is the simplest formula to create and the fundamental application of the INDEX function. You only need to type =INDEX(range,) to retrieve a specific item from the list.
How are index formulae used?The most often used Excel tool for more complex lookups is INDEX and MATCH. This is due to the fact that INDEX and MATCH are highly versatile; you may perform lookups that are horizontal, vertical, two-way, left, case-sensitive, or even based on several criteria. INDEX and MATCH should be on your list of Excel skills to develop. There ar The value at a specific point in a range or array is returned by the Excel INDEX function. You can obtain full rows or specific values using INDEX.e numerous instances below.
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Select the correct answer.
Ben wants to keep similar items close to each other in the image he is working on. Which is the most effective technique for applying the gestalt
concept of proximity?
The BLANK technique is the most effective technique for applying the gestalt concept of proximity.
Answers
Gestalt Principles are principles/laws of human perception that describe how humans group similar elements, recognize patterns and simplify complex images when we perceive objects.
What are the Gestalt Principles?The tendency to view items as belonging to the same grouping when they are close to one another is known as the gestalt principle of
proximity
. It claims that regardless of how different the forms and sizes are from one another, if shapes are close to one another, you will perceive them as groups. One of Gestalt's principles, the concept of closeness focuses on how each stimulus would be seen in its most basic form. The
Law of Simplicity
or the Law of Pragnanz are other names for it. It is founded on the idea that the sum of a thing is worth more than the sum of its components.
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write a while loop that continues to increment user value by 5 as long as user value is less than 0
Answers
The user value is incremented by 5 as long as it is less than 0. The code snippet provided demonstrates this solution, starting with an initial user value of -20. The loop continues until the user value becomes greater than or equal to zero, printing the updated user value in each iteration.
We can write the while loop that continues to increment the user value by 5 as long as the user value is less than 0 as follows:
```# Python program to increment user value by 5 as long as it is less than 0user_value = -20 # set user_value to a negative numberwhile user_value < 0: user_value += 5 # increment user_value by 5 in each iteration print(user_value) # print the user_value```
In the above code snippet, initially, we set the value of user_value to a negative number, i.e., -20. Then, we check if the value of user_value is less than zero. If yes, we increment the value of user_value by 5 in each iteration using the compound assignment operator += and print the value of user_value using the print() function.
We repeat these steps until the value of user_value becomes greater than or equal to zero.
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each physical device connected to a network must have a network interface card (nic). group of answer choices false true
Answers
The statement "each physical device connected to a network must have a network interface card (NIC)." is true because a NIC is a crucial component for connecting devices to a network.
A NIC is a hardware component that enables communication between a computer and a network. It provides a physical connection to the network and allows the computer to send and receive data.
Without a NIC, a device cannot connect to a network and therefore cannot communicate with other devices on the same network. Each device must have its own NIC, even if they are connected to the network through a router or switch.
In summary, NIC allows for communication between devices and enables them to access network resources such as the internet and shared files. Without a NIC, a device is unable to connect to a network and is therefore isolated from other devices on the network.
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give a summary of html forms
Answers
HTML forms are used to collect data from users. Users essentially enter data into forms by filling in text fields, selecting toggles and making choices from selection objects. When the user has filled in the data it is transmitted to the server for processing. HTML forms are specified using the <form> element.
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A computer _________ is any person whose primary occupation involves the design, configuration, analysis, development, modification, testing, or security of computer hardware or software.
Answers
Answer:
Engineering
Explanation:
Because they are the one who create software applications
According to institutional anomie theory, why is there a need to maintain cooperation between economic and non-economic institutions?
A.
to support and balance the interdependency of social institutions
B.
to maintain harmony
C.
to educate people
D.
to raise the standard of living
Answers
Answer:
A. to support and balance the interdependency of social institutions
Explanation:
PLATO
The designers of a database typically begin by developing a __________ to construct a logical representation of the database before it is implemented.
Answers
The designers of a database typically begin by developing a Data model to construct a logical representation of the database before it is implemented.
Gathering requirements is the first stage. In order to comprehend the proposed system and collect and record the necessary data and functional requirements, the database designers must conduct interviews with the clients (database users). a design approach that starts by recognizing distinct design elements before grouping them together into bigger groups. Defining properties and organizing them into entities are the first steps in database architecture. Unlike top-down design The conceptual design, the logical design, and the physical design are the three components of this phase. The logical design phase is combined with the other two phases in some approaches.
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State what is meant by the terms: Parallel data transmission ......................................................................................................... ................................................................................................................................................... ................................................................................................................................................... Serial data transmission ........................................................................................................... ................................................................................................................................................... ...................................................................................................................................................
Answers
Answer:
parallel communication is a method where several binary digits are sent as a whole, on a link with several parallel channels.
serial communication conveys only a single bit at a time over a communication channel or computer bus.
PLEASE HELP!!~~~~
What is the total number of time zones that can be configured to show by default in a calendar in Outlook 2016?
1
2
3
4
Answers
Answer:
2
Explanation:
The total number of time zones that can be configured to show by default in a calendar in Outlook 2016 is 2. The correct option is b.
What are time zones?A time zone is a region that adheres to a common standard of time for social, commercial, and legal activities. All events on the calendar are updated when you open Outlook.
Outlook uses the time zone that is set as the default when you create a new event in the calendar. When establishing an event, you have the option of choosing a different time zone.
The Calendar in the most recent iterations of Outlook for Microsoft 365 can show three different time zones. You can view two time zones in other versions of Outlook, such as Outlook 2019 Volume License, Outlook 2016, Outlook 2013, and Outlook 2010.
Therefore, the correct option is b. 2.
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A medium-sized space spanning multiple buildings is called a(n) ____________________(use abbreviation in your response).
Answers
A medium-sized space spanning multiple buildings is called a Campus Area Network (CAN) (use abbreviation in your response).
A campus area network is a collection of interconnected Local Area Networks (LAN) that are located in a specific geographic location, such as a college or university campus, a military post, or an organization's headquarters and other buildings.
It is bigger than local area networks but smaller than metropolitan and wide area networks. A Campus Area Network is a collection of connected Local Area Networks (LAN's) that, when combined with other LAN's, form a single network similar to CAN.
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a database administrator reviews servers in the company's environment and comes across an older server with which the administrator is unfamiliar. the system has set the server for redundancies and load input/output operations per second (iops) load balancing. which redundant array of independent disk (raid) configuration is the server using?
Answers
The description of the server using a redundant array of independent disks (RAID) configuration and load balancing with input/output operations per second (IOPS) suggests that the server is using a RAID 10 configuration.
RAID 10 combines the mirroring of RAID 1 with the striping of RAID 0 to provide both redundancy and performance. In a RAID 10 configuration, multiple disk drives are grouped together into mirrored pairs, and then the mirrored pairs are striped together. This provides both redundancy (since each mirrored pair provides a backup of its partner) and improved IOPS performance through load balancing across multiple disks.
Overall, RAID 10 is a good choice for applications that require high performance and high availability, such as databases or other applications that require fast data access and minimal downtime.
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What is the first step in finding a solution to a problem? (5 points)
Choose a solution.
Think of options to solve the problem.
Try the solution.
Turn the problem into a question.
Answers
Answer:
Turn the problem into a question.
Explanation:
n one or two paragraphs, write a scenario testing story(you can create various details) that tests the following aspects of the Chrome web browser (don’t use features of the underlying operating system):
• Comparing two different web pages at the same time.
• Returning to a previous page visited yesterday.
• Stopping the loading of a page that is taking too long to load.
• Visiting three favorite websites.
• Buying something from a website and ensuring HTTPS security is present, at least between the connection between your browser and the web server.
SHow where these are included in the paragraphs, by a highlight, arrow, bold text. Just specify where these are used in the text.
Answers
In today's scenario, Lisa, an avid technology user, decides to test the functionality of the Chrome web browser on her newly upgraded computer.
She starts by opening two different web pages simultaneously, one displaying the latest news updates and the other showcasing technology reviews. With a split-screen view, Lisa marvels at the convenience of comparing and contrasting information side by side, with the Chrome browser effortlessly accommodating her multitasking needs.
As Lisa explores the browser's capabilities further, she reminisces about a website she visited yesterday but can't recall the exact URL. She clicks on the browser's intuitive back button, highlighted in bold, and with a simple action, she finds herself back on the page she had visited previously. The seamless navigation provided by Chrome impresses her, making it easy to retrace her digital steps.
Next, Lisa encounters a website that takes an unusually long time to load, causing her frustration. She notices the loading indicator, marked with a bold arrow, continuing indefinitely. Recognizing the need to move on, she swiftly clicks on the "Stop" button, halting the loading process. Chrome's responsiveness allows Lisa to regain control of her browsing experience, preventing her from wasting valuable time on a slow-loading page.
As part of her routine, Lisa regularly visits her top three favorite websites: a news portal, an online shopping platform, and a social media network. Chrome's user-friendly bookmarks bar, indicated with a bold highlight, provides Lisa with quick access to these sites. She effortlessly navigates to each of her favorite websites, enjoying the browser's smooth performance and reliable connectivity.
For the final test, Lisa decides to make an online purchase while ensuring the highest level of security. As she proceeds to the checkout page of her preferred online store, she verifies the presence of HTTPS encryption in the browser's address bar, indicated by a bold highlight. This visual cue assures Lisa that her sensitive information is being transmitted securely between her browser and the web server, protecting her privacy and giving her peace of mind during the transaction.
Through this comprehensive testing scenario, Lisa successfully examines and appreciates the Chrome web browser's capabilities, such as comparing web pages, revisiting previous pages, stopping slow-loading pages, visiting favorite websites, and ensuring HTTPS security. These aspects demonstrate the browser's efficiency, convenience, responsiveness, and commitment to user privacy.
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____ transparency ensures that the system will continue to operate in the event of a node failure.
Answers
The term that would fit in the blank is "Redundancy". Redundancy in a system ensures that there are multiple nodes or components that can take over in the event of a failure, thus maintaining the overall function and performance of the system.
In the case of a transparent system, redundancy ensures that the failure of a single node does not disrupt the overall operation of the system. Which type of transparency ensures that the system will continue to operate in the event of a node failure?
Fault transparency ensures that the system will continue to operate in the event of a node failure. This type of transparency allows the system to maintain its functionality, mask the occurrence of faults, and recover from any failures, providing a seamless experience to the users.
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ideally, the backrest is tilted back slightly, so when you turn the wheel your shoulders are __ the seat
Answers
**Parallel** to the seat