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What Year Is Leap
How to Know if Certain Year is a Leap Year.
What year is leap. What is leap year for Class 9. Any year that is evenly divisible by 4 is a leap year. But here we will write a leap year C program to ask the user to input a range and print all
the leap years between the range.
The century year is a leap year only if it is perfectly divisible by 400. If the year is divisible by 100 years ending in two zeros it is not a leap except if. Leap years have 366 instead of.
For the sculpture see The Quantum Leap. Leap years are years where an extra or intercalary day is added to the end of the shortest month February. The 3 conditions for a given year be a leap year
A leap year is a year containing one additional day in order to keep the calendar year in sync with the astronomical year. 22 rows A leap year is a year with 366 days instead of 365. Leap years have
366 days instead of the usual 365 days and occur almost every four years.
However there is still a small error that must be accounted for. Quantum Leap is an American science-fiction television series created by Donald P. For example 1988 1992 and 1996 are leap years.
The intercalary day February 29 is commonly referred to as leap day. Leap years are years where an extra or intercalary day is added to the end of the shortest month February. Leap years refer to
those years where an extra or intercalary day is added to the end of the shortest month that is February. | {"url":"https://angry-mestorf.netlify.app/what-year-is-leap","timestamp":"2024-11-09T09:32:26Z","content_type":"text/html","content_length":"38089","record_id":"<urn:uuid:cff266ea-429c-4fa8-924b-8679638d3f2e>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00353.warc.gz"} |
Property D Cyclic Neofields
Graduation Semester and Year
Document Type
Degree Name
Doctor of Philosophy in Mathematics
First Advisor
Minerva Cordero-Epperson
In 1948 L. J. Paige introduced the notion of a neofield (N,\oplus,\cdot) as a set N with two binary operations, generally referred to as addition (\oplus) and multiplication (\cdot) such that (N,\
oplus) is a loop with identity 0 and (N-\{0\},\cdot) is a group, with both left and right distribution of multiplication over addition. The neofield was considered a generalization of a field and its
application was for the coordinatizing of projective planes and related geometry problems. In 1967 A.D. Keedwell introduced the notion of property D cyclic neofields in relation to his study of latin
squares and their application to projective geometry. In particular, the existence of a property D cyclic neofield guarantees the existence of a pair of orthogonal latin squares. Keedwell provides a
theorem for the existence of property D cyclic neofields with a set of conditions on a sequence of integers.We provide an alternate condition for Keedwell's existence theorem that requires only one
criteria for each condition in contrast to Keedwell's two criteria. We then establish a set of conditions for the existence of commutative property D cyclic neofields that require a sequence half as
long as for Keedwell's existence theorem. We also examine subneofields of property D cyclic neofields and consider their application to extending known neofields to higher order property D cyclic
Mathematics | Physical Sciences and Mathematics
Degree granted by The University of Texas at Arlington
Recommended Citation
Lacy, Scott, "Property D Cyclic Neofields" (2015). Mathematics Dissertations. 45. | {"url":"https://mavmatrix.uta.edu/math_dissertations/45/","timestamp":"2024-11-02T05:18:42Z","content_type":"text/html","content_length":"36126","record_id":"<urn:uuid:d03c81e8-cc9f-48b5-8a46-94c72d60ae4b>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00328.warc.gz"} |
The word pan rhyme with -Turito
Are you sure you want to logout?
The word pan rhyme with
A. Fan
B. Log
C. Cake
Rhyming words are words that have the same ending sounds.
The correct answer is: Fan
OPTION 1 is the correct answer.
The picture given in option 1 is of a fan which rhymes with pan.
Get an Expert Advice From Turito. | {"url":"https://www.turito.com/ask-a-doubt/English-2-the-word-pan-rhyme-with-cake-log-fan-electric-fan-cartoon-stock-illustrations-images-and-vectors-shutters-qacc43c","timestamp":"2024-11-15T00:41:08Z","content_type":"application/xhtml+xml","content_length":"1052464","record_id":"<urn:uuid:c2aff2b3-1dd9-47dd-9a9c-d7b194bbb54b>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00608.warc.gz"} |
Plant selection
The program generates a plant list with plants that thrive best in that water.
This is according to the method described by SCHWARZER & SCHWARZER*, from the measured value of the dissolved reactive Phophors a value for the nutrient supply (P) in the ecosystem and the total
hardness a value for the reaction of water (R). The resulting R-and P-values correspond to the values described by ELLENBERG for vascular plants of central Europe. In short, the program converts the
input of water values into so called Ellenberg values.
This indicator values were determined as ecological preferences among others for all types of aquatic plants in Central Europe by ELLENBERG and colleagues. So it is known that the pondweed
(Potamogeton perfoliatus) has the R-value of 7 and the P-value of 6. Should the program, for example, for the tested water determine values of 8, 7 or 6, while for P 5, 6 or 7, it will propose this
pondweed for the water adding this species to the list of suitable plants. It is evident that the program is performing with a deviation of 1 up and 1 down, as the indicator values of Ellenberg
always represent only an approximation. Plants thus have an ecological amplitude (tolerance) in which they find their optimal growth conditions.
* further information at »help« | {"url":"http://pondanalyst.com/pa/website/en/cms?cms_knuuid=e0ee3a7f-f910-48a1-aae3-7078c9e748be&cms_f4=","timestamp":"2024-11-10T11:41:05Z","content_type":"application/xhtml+xml","content_length":"11346","record_id":"<urn:uuid:007f137d-6762-4a4d-a48b-c4807b379986>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00679.warc.gz"} |
Post Office 1 year FD Interest Rate Calculator - GEGCalculators
Post Office 1 year FD Interest Rate Calculator
Post Office 1 year FD Interest Rate Calculator
What is the interest of 1 lakh FD in the post office? The interest on a 1 lakh FD (Fixed Deposit) in the post office would depend on the prevailing interest rate. As of my last knowledge update in
January 2022, the interest rate for a 1-year FD in the Post Office was around 5.5% to 6.7%. So, you could estimate the interest to be between ₹5,500 to ₹6,700 for one year.
How much interest does the post office give for 1 year? The interest rate for a 1-year FD in the Post Office can vary. As mentioned earlier, it was around 5.5% to 6.7% as of 2022. You would need to
check the current rates for 2023.
What is the interest rate for post office FD in 2023? I cannot provide the exact interest rate for 2023. You should contact your local Post Office or visit their official website for the most current
How do you calculate FD for one year? You can calculate FD interest using the following formula: Interest = Principal Amount × Rate of Interest × Time (in years) / 100
What is the interest on a 5 lakh FD for 1 year? Assuming an interest rate of 6% (as of 2022), the interest on a 5 lakh FD for one year would be approximately ₹30,000.
What is the monthly interest on 1 lakh FD? Assuming an interest rate of 6% (as of 2022), the monthly interest on a 1 lakh FD would be approximately ₹500.
What if I deposit $5,000 per month in the post office? Depositing $5,000 per month in a Post Office Savings Account would accumulate interest based on the prevailing rates for each month. The
interest is usually compounded annually.
Is post office interest monthly or yearly? The interest on Post Office FDs is generally compounded annually. However, Post Office Savings Accounts may provide interest on a monthly basis.
Which is the best account in the post office? The best account in the Post Office depends on your financial goals and needs. Common Post Office savings schemes include Public Provident Fund (PPF),
Senior Citizens Savings Scheme (SCSS), and Post Office Monthly Income Scheme (POMIS), among others. Choose the one that aligns with your financial objectives.
Which bank is best for a fixed deposit for 1 year? The best bank for a 1-year fixed deposit can vary based on interest rates, terms, and your preferences. Popular banks for FDs in India include State
Bank of India (SBI), HDFC Bank, ICICI Bank, and others. Compare the rates and terms offered by different banks to make an informed decision.
What is the difference between bank FD and post office FD? Bank FDs and Post Office FDs are similar in that they offer fixed returns on your deposits. However, interest rates, lock-in periods, and
terms may vary between the two. Post Office FDs are backed by the government, which some people find more secure. Banks often offer more flexibility and a wider range of FD products.
Which is the best FD scheme in the post office? The best FD scheme in the Post Office depends on your financial goals. PPF and SCSS are popular options, but it depends on factors like your age,
investment horizon, and risk tolerance.
Is FD for 1 year good? A 1-year FD can be a good option for short-term savings or when you want to keep your money safe and earn a fixed return. However, the suitability of a 1-year FD depends on
your financial goals and circumstances.
How to calculate FD interest for 12 months? To calculate FD interest for 12 months, you can use the formula mentioned earlier. Interest = Principal Amount × Rate of Interest × Time (in years) / 100.
What is the monthly interest on a 50,000 FD? Assuming an interest rate of 6% (as of 2022), the monthly interest on a 50,000 FD would be approximately ₹250.
How much will I get if I put 10 lakhs in FD? The final amount you will get from a 10 lakh FD depends on the interest rate and the tenure of the FD. You can use the FD interest formula to calculate
What is the monthly interest on 20 lakhs? Assuming an interest rate of 6% (as of 2022), the monthly interest on 20 lakhs would be approximately ₹10,000.
What is 5% interest on 10,000 for 1 year? 5% interest on 10,000 for 1 year would be ₹500.
What is the highest FD rate in India for one year? The highest FD rate in India can vary and is subject to change. As of my last update in 2022, it was around 6.5% to 7.5%. Check with banks for
current rates.
How do I calculate my Fixed Deposit? You can calculate the maturity amount of your Fixed Deposit using the formula mentioned earlier: Interest = Principal Amount × Rate of Interest × Time (in years)
/ 100.
How much will I get monthly from FD? The monthly interest from your FD depends on the FD amount and the interest rate. It is calculated based on the annual interest rate and then divided by 12 for
monthly payouts.
What happens if I deposit $50,000 in cash? Depositing $50,000 in cash may trigger certain reporting requirements to comply with anti-money laundering regulations. Your bank or financial institution
will provide guidance on the process.
How much money can I deposit in a year without being flagged? The threshold for cash deposits without being flagged can vary by country and financial institution. To avoid potential issues, it’s best
to check with your specific bank or financial authority for their regulations.
Is it safe to keep money in a post office account? Money kept in a Post Office account is generally considered safe, as it is backed by the government. However, you should still be aware of the
prevailing interest rates and any applicable fees.
Which scheme is best in post office for senior citizens? The Senior Citizens Savings Scheme (SCSS) is a popular choice for senior citizens in the Post Office. It offers higher interest rates and tax
What is the FD rate for senior citizens? The FD rate for senior citizens can vary depending on the bank or institution. Typically, senior citizens may receive slightly higher interest rates compared
to regular FDs.
How many years will FD double in the post office? In the Post Office, the time it takes for an FD to double depends on the interest rate. As a rough estimate, you can use the Rule of 72: Divide 72 by
the annual interest rate to approximate the number of years it takes for your investment to double.
What are the disadvantages of post office savings? Disadvantages of Post Office savings can include lower interest rates compared to some banks and limited online banking services. Additionally,
certain Post Office schemes may have restrictive terms.
Is a post office bank account good or bad? A Post Office bank account can be a good option for certain individuals, especially those seeking government-backed safety and simplicity. However, its
suitability depends on your financial goals and preferences.
Which bank gives 8% interest? The availability of a bank offering 8% interest can vary, and interest rates change over time. You should check with various banks to find the current rates.
Which bank is giving 7% interest on FD? The bank offering 7% interest on FD can vary, and interest rates change over time. You should check with different banks to find the current rates.
Which bank gives 9 percent interest? The availability of a bank offering 9% interest can vary, and such high rates may be subject to specific terms and conditions. You should check with banks for the
current rates and offers.
How do I double my money at the post office? To double your money at the Post Office, you can calculate the time it takes using the Rule of 72, as mentioned earlier. Alternatively, you can choose
higher-yielding Post Office schemes, such as the Senior Citizens Savings Scheme (SCSS), which offers competitive interest rates.
How much is a fixed deposit at the post office? The minimum and maximum deposit amounts for fixed deposits at the Post Office can vary depending on the specific scheme. You should check with your
local Post Office for current details.
How do I keep a fixed deposit in the post office? To open a fixed deposit in the Post Office, you will need to visit your local Post Office branch, fill out the required forms, provide the necessary
documents, and deposit the desired amount. The Post Office staff will guide you through the process.
Which bank is safe for FD? Most well-established banks in India are considered safe for FDs, as they are regulated by the Reserve Bank of India (RBI) and insured by the Deposit Insurance and Credit
Guarantee Corporation (DICGC). Popular choices include State Bank of India (SBI), HDFC Bank, and ICICI Bank, among others.
Which is better, saving in a bank or post office? The choice between saving in a bank or post office depends on your preferences, financial goals, and the specific offerings of each institution. Both
banks and post offices have their advantages and disadvantages, so it’s important to consider your individual needs.
Which bank is paying the highest FD rates? The bank offering the highest FD rates can vary, and it’s essential to compare rates from different banks to find the best option. Rates can change over
time, so check with banks for the most current rates and offers.
GEG Calculators is a comprehensive online platform that offers a wide range of calculators to cater to various needs. With over 300 calculators covering finance, health, science, mathematics, and
more, GEG Calculators provides users with accurate and convenient tools for everyday calculations. The website’s user-friendly interface ensures easy navigation and accessibility, making it suitable
for people from all walks of life. Whether it’s financial planning, health assessments, or educational purposes, GEG Calculators has a calculator to suit every requirement. With its reliable and
up-to-date calculations, GEG Calculators has become a go-to resource for individuals, professionals, and students seeking quick and precise results for their calculations.
Leave a Comment | {"url":"https://gegcalculators.com/post-office-1-year-fd-interest-rate-calculator/","timestamp":"2024-11-15T02:46:54Z","content_type":"text/html","content_length":"179342","record_id":"<urn:uuid:60c29118-e603-4eea-9097-7861d700aaba>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00268.warc.gz"} |
Rhombic tilings of (n,k)-Ovals, (n,k,λ)-cyclic difference sets, and related topics
Creative Commons Attribution Non-Commercial No Derivatives License
Each fixed integer nnhas associated with it ⌊n2⌋ rhombs: ρ1,ρ2,…,ρ⌊n2⌋, where, for each 1≤h≤⌊n2⌋, rhomb ρ[h]ρh is a parallelogram with all sides of unit length and with smaller face angle equal
toh×πn radians.
An Oval is a centro-symmetric convex polygon all of whose sides are of unit length, and each of whose turning angles equalsℓ×πn for some positive integer ℓℓ. A (n,k)(n,k)-Oval is an Oval with 2k2k
sides tiled with rhombsρ1,ρ2,…,ρ⌊n2⌋; it is defined by its Turning Angle Index Sequence, a kk-composition of nn. For any fixed pair (n,k)(n,k) we count and generate all (n,k)(n,k)-Ovals up to
translations and rotations, and, using multipliers, we count and generate all (n,k)(n,k)-Ovals up to congruency. For odd nn if a (n,k)(n,k)-Oval contains a fixed number λλ of each type of
rhombρ1,ρ2,…,ρ⌊n2⌋ then it is called a magic (n,k,λ)(n,k,λ)-Oval. We prove that a magic (n,k,λ)(n,k,λ)-Oval is equivalent to a (n,k,λ)(n,k,λ)-Cyclic Difference Set. For even nn we prove a similar
result. Using tables of Cyclic Difference Sets we find all magic (n,k,λ)(n,k,λ)-Ovals up to congruency for n≤40n≤40.
Many related topics including lists of (n,k)(n,k)-Ovals, partitions of the regular 2n2n-gon into Ovals, Cyclic Difference Families, partitions of triangle numbers, uu-equivalence of (n,k)(n,k)-Ovals,
etc., are also considered.
Recommended Citation
McSorley, John and Schoen, Alan. "Rhombic tilings of (n,k)-Ovals, (n,k,λ)-cyclic difference sets, and related topics." Discrete Mathematics 313, No. 1 (Jan 2013): 129-154. doi:10.1016/
Link to publisher version | {"url":"https://opensiuc.lib.siu.edu/math_articles/115/","timestamp":"2024-11-07T18:26:19Z","content_type":"text/html","content_length":"36829","record_id":"<urn:uuid:4f5b1c83-4cd8-4e49-9a03-83f730601cd8>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00246.warc.gz"} |
steel rolling mill motor design calculations
WEBRolling load calculation: Properties of Material to be used for Hot Rolling: Material – A36 Mild Steel UTS – 400 Mpa Yield Strength – 250 Mpa Elongation – 20% Carbon – Density – 7800 kg/m^3
Poisons ratio – Shear Modulus – Gpa Table 1: Effect of Temp on UTS PASSES TEMPARATURE ( ̊C) ULTIMATE TENSILE STRENGTH ...
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WEBWhat Is A Rolling Mill? In metalworking, rolling is a metal forming process in which metal stock is passed through one or more pairs of rolls to reduce the thickness and to make the thickness
uniform. The concept is similar to the rolling of dough. Rolling is classified according to the temperature of the metal rolled. If the temperature of the ...
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WEBCASTE. CASTE LLC (Consulting in Advanced Steel Technologies and Engineering) is a company formed to provide full service consulting and engineering solutions to steel companies around the
world. CASTE's consulting team, has years of experience in all phases of Rolling Mill projects from project development all the way through mill design ...
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WEB[7] Akhil khajuria, "Improvment in productivity by appliion of slat conveyor design in steel rolling mill," International journal for research in mechanical and civil engineering, vol 4, issue
1, ISSN:, jan 2018, Conveyor chain 3. CONCLUSIONS 1.
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WEBDESIGN CALCULATIONS Abstract Rolling is the process of reducing the thickness or 4 changing the cross section of a long work piece by compressive force applied through set of rolls. ... A two
stage belt drive is used to run the mill with a 1 HP motor. Conceptual Design Key Words: Roll force, Draft, Flow stress, Belt drive, Adjustment ...
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WEBMar 26, 2020 · The main factor influencing the rolling force required to reduce the thickness of strip in a rolling mill is the yield strength of the material being rolled. The calculation of
yield strength depends upon a wide range of factors. These are: composition; previous work done on the material; thermal history; speed of rolling; .
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WEBAug 21, 2022 · Abstract All the enterprises of metallurgical industry produce and use crushed materials obtained by crushing. The share of produced energy spent on crushing is more than 5% in
the global energy balance. In this paper, we consider the schematics of a crushing machine with stops on the roll, the design of which forms a complex stress .
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WEBNov 1, 2014 · On the Op miza on Procedure of Rolling Mill Design – a Combined Applica on of Rolling Models, R. Guo 10/19 Figure 6: Average Natural Crowns for Various WR and BU Roll Diameters
Work Roll ...
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WEBFeb 14, 2002 · The average flow stress of the material was taken as 550 MPa, so that a wide variety of steel materials may be already discussed, the maximum strip width (b) is 100 mm and
minimum inlet thickness (h 1) is 2 mm. Considering these values of b and h 1 as crisp, the parameters v, r and P were treated as construct the .
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WEBAug 10, 2023 · Li 7 found in the daily maintenance of the four high rolling mill that ... integrates the design of a servo motor and a ball or roller screw. ... power calculation of four roll
plate rolling ...
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WEBApr 8, 2022 · Subject Drives and controlTopic Steel Rolling MillChapter Industrial appliion of DrivesFaculty Prof. Parmanand PawarUpskill and get Placements wit...
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WEBSpeeds and feeds are based off of stub, standard or neck relieved lengths only. Flood coolant recommended. Check back often as we're continually adding new product speeds and feeds
calculations. Step 1: Material. Step 2: Cutting Method. Step 3: Depth. Step 4: Tool. Step 5: Tool Diameter.
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WEBMay 31, 2023 · Your Capacity and Production Requirements. The first step in selecting a rolling mill is assessing your production requirements. Determine the desired capacity and volume of
steel you need to process. Consider factors such as the thickness and width of the steel sheets or bars and the desired output speed.
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WEBJan 4, 2024 · Cold rolling is a process that operates at room temperature or slightly below it. It involves passing the steel through a set of rollers to reduce its thickness and improve its
surface finish. Cold rolling mills are often used to produce thinner gauges of steel sheets, strips, and foils. The process can also enhance the mechanical properties of ...
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WEBFeb 6, 2020 · its calculation procedure for rolling forces and bending forces. Rolling is a process of reducing thickness of work piece by a. compressive force. The force is applie d through
set of rolls. In ...
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WEBOct 27, 2022 · The looper control of hot strip finishing mill is one of the most critical control items in hot strip rolling mill process. It is a highly complex nonlinear system, with strong
states coupling and uncertainty that present a difficult control challenge. Loopers are placed between finishing mill stands not only to control the mass flow of the two stands but also .
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WEBTechnical information on our threephase roller table motors. Threephase roller table motors with squirrel cage motors. Voltage: up to 1,000 V. Dimensions: up to shaft height 400. Gilled
design. Suitable for grid and inverter operation. Motor housing: standard design in gray cast iron, optionally in steel. Thermal utilization: Thermal class ...
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WEBDec 1, 2014 · 1. Introduction. Roll force is a key parameter in the process control of hot strip rolling, and its computational accuracy directly determines thickness precision, strip shape
quality and rolling stability [1], [2].Therefore, the online calculation model of roll force with high accuracy is taken as the core for substantial studies at home and abroad [3], [4].
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WEBMay 24, 2022 · It is employed to reduce large thicknesses in a single pass of a steel strip. Its rolling capacity is higher than a cluster machine but less than a tandem rolling machine. 6.
Tandem or Continuous Mill. In this tandem mill types of rolling mills, It includes a number of nonreversing twohigh rolling mills provide one after other. So .
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WEBYou would then divide .250" by two (2), which would be a .125" thick shim to be placed under the bottom bearing block of this reworked pass. We use this same common denominator (reworked/
original throat diameters) as we did for the metal line, for the motor speed calculation. See sample "Calculating Drive RPM's" formula below:
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WEBNov 25, 2019 · Traditional mathematical modelling of metal rolling process was used to design mill equipment, ensure productivity and product quality. ... The appliion of software calculation
in steel rolling is mainly reflected in three aspects. (1) On the basis of mathematical model, the finite element method is used to simulate the rolling .
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WEBAug 1, 2016 · This paper describes the design and the implementation of a selftuning integralproportional (IP) speed controller for a rolling mill DC motor drive system, based on a 32bit
floating point ...
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WEBJan 1, 2019 · A grain size reduction hammer mill for crushing corn (Zea mays L.) was designed depending on variety characteristics and by using computer aided design "ANSYS" software.
Suitability of ...
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WEBTMEIC designs and manufactures two types of AC solutions for this purpose. Salient pole synchronous motors that meet the high power and torque demands of a hot strip mill, as well as roughing
and finishing stands. Squirrel cage rotor motor applied to medium power requirements of reels and stands. Meets NEMA MG1 and JEM 1157 standards.
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WEBFeb 1, 2005 · The rolling of M47 grade of CRNO steel having Si in the range of to % was troublesome as it led to generation of higher mill loads leading to high output gauge.
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WEBMay 26, 2019 · Fig 1 Components of a roll stand. Housing – Housing creates a framework of the rolling mill stand and for absorbing the total metal pressure on rolls during the process of
rolling. Hence, the housing is to be solid and its structure is to enable easy and fast roll changing. Also, there need to be easy access to all parts of the housing and .
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WEBJul 1, 2017 · However, rolling mills are major resource consumers; thus, urgent rationalisation is required in the relevant industrial systems. Roll pass design (RPD) is a principal factor
that determines ...
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WEBMar 1, 2021 · values of κ = N for the roller made of steel and for κ = N for the roller made. of cast iron were received for the roller's angular speed ω1 = rad·s−1. In Figure 5, the ...
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WEBJun 19, 2015 · The approximate horsepower HP of a mill can be calculated from the following equation: HP = (W) (C) (Sin a) (2π) (N)/ 33000. where: W = weight of charge. C = distance of centre
of gravity or charge from centre of mill in feet. a = dynamic angle of repose of the charge. N = mill speed in RPM. HP = A x B x C x L. Where.
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WEBA 1000 mm wide and 2mm thick mild steel sheet is cold rolled to mm thickness. The mean yield strength of the material of sheet is 25 kgf/mm 2. The working roll diameter is 500 mm. Determine
the rolling load on the rolling stand if the coefficient of friction is Also determine the rolling torque.
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WEBMetal Rolling. Metal rolling is one of the most important manufacturing processes in the modern world. The large majority of all metal products produced today are subject to metal rolling at
one point in their manufacture. Metal rolling is often the first step in creating raw metal forms. The or is hot rolled into a bloom or a slab, these are ...
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What is 4/1 as a Mixed Number?
Here we will show you how to convert the improper fraction 4/1 to a mixed number (aka mixed fraction). To find the answer, we simply divide 4 by 1 and get the answer:
4/1 = 4
The definition of a mixed number is that it has an integer (whole number) and a proper fraction.
Technically, the answer above only has an integer. To make the answer so it has an integer AND a fraction, you could write it like this:
Improper Fraction To Mixed Number Converter
4/1 as a mixed number is not the only problem we solved. Go here to convert another improper fraction to a mixed number.
What is 4/2 as a Mixed Number?
Here is the next improper fraction on our list that we converted to a mixed number.
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Improving Mr. Miyagi’s Coaching Style: Teaching Data Analytics with Interactive Data Visualizations
In the 1984 movie, The Karate Kid, a teenager named Daniel LaRusso triumphs in a local martial arts tournament after being coached by his apartment’s handyman, Mr. Miyagi.
Mr. Miyagi used a unique coaching style that developed Daniel’s fundamental skills in martial arts before teaching their context and application. Initially, this confused Daniel as he went to Mr.
Miyagi’s home expecting to learn standard karate moves (e.g., how to punch), but ended up doing repetitive household chores, such as painting fences and waxing cars. The only instructions Mr. Miyagi
offered pertained to the chores themselves: “Left hand, right hand.” “Up, down.” “Wax on, wax off.” “Breath in, breath out.” Although Mr. Miyagi knew his motives and felt gratified in his teachings,
Daniel was frustrated. Ultimately, he lost his cool and the following conversation insued:
Daniel: “I’m being your #!$@ slave … We made a deal … You’re supposed to teach, and I’m supposed to learn … I haven’t learned a #!$@ thing.”
Mr. Miyagi: “You learn plenty.”
Daniel: “I’m going home, man!”
Employing considerable—and entertaining—artistic license, Mr. Miyagi subsequently demonstrated how the mundane chores translated to practicing karate. In a controlled setting, Mr. Miyagi punched and
Daniel blocked using the arm motion from painting; Mr. Miyagi kicked and Daniel blocked again using the arm motion from waxing. It then became clear to Daniel that each chore had a purpose and taught
defensive arm movements. From that point onward, Daniel trusted Mr. Miyagi’s coaching and eventually applied what he learned in a tournament to become a karate champion!
Today, many of us teach introductory statistics, or more broadly, introductory data analytics in a way that is similar to Mr. Miyagi’s coaching style. Like Mr. Miyagi, we think we are serving the
students well by first teaching quantitative methods or tools for assessing data out of context. For example, we insist students master how to solve systems of equations or optimize functions before
we give them an opportunity to summarize a data set. Also, the tools we use are demonstrated in a controlled setting. The data sets provided to students often come from contrived textbook problems
and do not include technicalities or issues that real, modern data sets present. This means we do not require students to develop data-based, critical thinking skills, including the ability to:
1. Compartmentalize large problems into manageable pieces
2. Formulate and evaluate solutions with both quantitative and qualitative rigor
3. Make judgments that assimilate current information with new
4. Reflect upon such judgments
Yet, like Mr. Miyagi, we expect students to perform well and implement unpracticed skills when faced with tough, real-world problems.
Unlike in the movies, our students do not benefit from artistic license. Thus, many of our students miss having an “a-ha” moment in that they fail to connect classroom concepts to real-world
applications. In particular, students who receive a Miyagi-like data analytics education may get caught up in mundane analytical calculations and not grasp how data analytics serves in real-world
contexts. As professors of introductory data analytics classes, we can do better.
Here, we demonstrate how the use of interactive data visualizations (IDVs) may enable students to think critically about tough real-world problems before, during, and after they learn quantitative,
analytical tools. IDVs rely on 1) mathematical models such as weighted multidimensional scaling (MDS), as introduced by Kruskal and Wish in 1978, to display complex, high-dimensional data sets in two
dimensions and 2) methods that can reparameterize the models in response to user (e.g., student) interactions (with the current display) to create new displays. As a result, the new displays are
based on data, a model, and judgments (as communicated by interactions) of students.
Crucially, when students have access to interpretable, mathematically driven displays of data and experience how the displays change in response to their judgments, the students have the potential to
gain simultaneously an intuitive understanding for both the analytical methods underlying the displays and information available in the data. In other words, while students are thinking critically
with data, as defined by Linda Elder and Richard Paul’s eight “Elements of Thought” (EoT) (see Figure 1), published in A Thinkers Guide to Analytic Thinking, they also are developing insight about
mathematical or data analytics concepts underlying IDVs. The data analytics course we develop here exploits this “simultaneous learning” to emphasize both quantitative methods and critical thinking
with data jointly. In particular, we show how one may teach critical thinking with weighted MDS using IDVs.
A New Teaching Approach for Weighted MDS
Contrary to standard practice, a course that relies on IDVs may emphasize both data analytics methodology and critical thinking within the context of realistic case studies. While addressing problems
in the case studies, the students experience using their current knowledge base with new, technical methods to extract information from data and master data analytics concepts. Our proposed teaching
approach is similar in spirit to that described in the Change Agent for Teaching and Learning Statistics (CATALST) project. In response to the initiatives of CATALST, using model-eliciting
activities (MEAs) is suggested for teaching both statistical concepts and thinking. These activities provide open-ended research questions and satisfy requirements to enable students to develop
thoughtful, transferable problemsolving skills. In effect, our case studies could be considered examples of MEAs. However, we encourage students to take advantage of data visualizations to emphasize
the role of intuition, personal judgment, assessment, and reflection in every data analysis.
Consider weighted-MDS a data visualization scheme that seeks to find a low-dimensional (e.g., two-dimensional) representation or map of data that portrays how the data spread in the high-observations
in the high-dimensional space is preserved in a weighted-MDS map (see Figure 2). The coordinates of the observations in the weighted-MDS map are determined by minimizing a stress function that, to
some, is hard to conceptualize. Typical approaches for teaching weighted-MDS are Miyagi-like in that they first rely on explaining the abstract stress function and showing how to minimize it. Only
after the students master the minimization scheme do they have an opportunity to apply weighted-MDS to a high-dimensional data set. Since the data sets often lack relevance to real-world scenarios,
it is clear that the emphasis in typical teaching approaches is on only the method. Successful students are often those who memorize the weighted-MDS procedure and not necessarily those who can apply
weighted-MDS effectively in nontraditional problems.
In a course that relies on IDVs, the focus shifts from data analytics methodology to solving real-world problems. We recommend teaching weighted-MDS by presenting an open-ended, real-world case study
and progressing through the following four phases:
1. Assess and explore
2. Methods
3. Implement
4. Reflect
During these phases, the students use IDVs to assess the case study, learn a data analytics technique (e.g., weighted-MDS, principal component analysis), implement a technique computationally, and
reflect upon results and implications.
We define these phases so they correlate strongly with the EoT. The EoT is comparable to Chris Wild and Maxine Pfannkuch’s 1999 model of statistical thinking, called PPDAC, that appeared in the
International Statistical Review. PPDAC is an initialism for five components of statistical thinking: Problem, Plan, Data, Analysis, and Conclusions. Relative to PPDAC, the EoT is more refined and
general in that it describes eight quantitative and qualitative aspects of critical thinking that may apply to all problems, not just those with solutions that rely on statistics. By using the EoT as
our compass, students have the potential to develop critical thinking skills that may transfer to decisiomaking problems outside a data analytics classroom.
Weighted-MDS is an extension of multi-dimensional (MDS). Thus, to explain weighted-MDS, we start with MDS. As is weighted-MDS, MDS is a data visualization scheme that preserves pairwise distances in
high-dimensional observations within a low-dimensional data representation (e.g., in two dimensions). To explain by example, consider the well-known “Iris” data set that was analyzed by Sir R. A.
Fisher in 1936 (and available in R). This data set includes four continuous variables, including Sepal Length, Sepal Width, Petal Length, and Petal Width (three of these variables are plotted in
Figure 2), and one categorical variable, Species. One application of this data set is to learn how iris species differentiate based on sepal and petal measurements.
MDS is not a clustering nor predictive algorithm. Rather, it is a dimension-reduction method that can enable us to plot high-dimensional data sets and identify clusters (if they are present)
visually. For this example, we use MDS to reduce the dimension of the Iris data set from four to two. Let d[i] = (d[i][,1];…, d[i][,p]) denote each high-dimensional (in this case, four-dimensional)
observation i (for i ∈; {1, …, n}, n = 150) so that D = [d[1], …, d[n]]ʹ. MDS solves for R = [r[1], …, r[n]]ʹ, where each r[i] = (r[i][,1], r[i][,2]), represents a reduced, two-dimensional version of
d[i]. The solution R minimizes a stress function that calculates the difference in corresponding pairwise distances within D and R. That is, for points a and b, the low-dimensional distance between r
[a] and r[b], ||r[a] − r[b]||, approximates the high-dimensional distance between d[a] and d[b], denoted δ[a,b]. Mathematically, we write
The metric used to define δ[i,j] is application specific and typically relies on a univariate distance function Dist(·), such as euclidean distance, so that
where, . Given a definition for δ[i,j], solving Equation (1) 1s an
optimization problem for which closed form expressions exist under certain mathematical constraints.
Weighted-MDS extends MDS by including a p-vector of weights w = [w[1],…, w[p]] (where, ∑[d]w[d] = 1) to redefine δ[i,j], e.g.,
Based on w, weighted-MDS may emphasize (or de-emphasize) some dimensions in data D over others in the solution for R. When w[i] = w[j] for all {i,j} ∈; {1,…,p}, weighted-MDS and MDS solve for the
same values of R. To portray the impact that specifications for w may have on data visualizations, we plot in Figure 3 three weighted-MDS maps of the Iris data that rely on different specifications
for w. Figure 3a) sets each weight to 0.25; Figure 3b) sets w = [0.3, 0.4, 0.3, 0.0]; and Figure 3c) sets w = 0.2, 0.06, 0.0, 0.74]. Notice that each weight specification provides a different
spatialization of the data.
For figures a, b, and c, w = [0.25,0.25,0.25,0.25], w = [0.3,0.4,0.3,0.0], and w = [0.2,0.06,0.0,0.74], respectively.
To interpret weighted-MDS displays, the important metric is relative distance between observations; arguably, the observation coordinates can be considered irrelevant. Data points that appear close
in proximity (or distant) are similar (or different) in the dimensions that are weighted heavily. For example, observations in Figure 3c) separate the species fairly well. This suggests that
observations within the same species are comparable in the dimensions that are weighted heavily in the display; these dimensions include Petal Width (w[4] = 0.74) and Sepal Length (w[1] = 0.2).
Since the interpretation of weighted-MDS displays is straightforward, students do not need to understand the technicalities of weighted-MDS to use the displays and tackle tough data-driven problems.
Additionally, if we make weighted-MDS displays interactive, we can let students change the weights, assess the data from different perspectives, and discover weight specifications that result in
revealing structure in the data. To change the weights, students could specify them directly. However, for high-dimensional data, manual adjustments to parameters can be cumbersome or confusing. How
would a student know which weights to adjust in the presence of, say, 100 variables?
We developed a method to interpret certain data display adjustments as suggestions for reweighting variables. Namely, if students move observations together or apart, the variables for which these
observations are similar or different, respectively, are up-weighted. We refer to the process of quantifying display interactions to adjust parameters as visual to parametric interaction (V2PI). The
mathematics we use for V2PI within the context of weighted-MDS is provided in “Visual to Parametric Interaction (V2PI).” We refer to a display that relies on an interactive form of weighted-MDS as an
“IDV based on weighted-MDS.”
An important point to make is that, by using V2PI methods, students (again) do not need to understand mathematical technicalities to assess data from different perspectives that are based on
weighted-MDS. Rather, students can explore the data based on conjectures they make about the similarities and differences among a subset of observations. Additionally, V2PI can serve as a motivator
to learn the limitations of static or deterministic data summary methods.
Critical Thinking with Weighted-MDS and IDVs
As we mentioned previously, IDVs enable us to shift the focus from data analytics methodology to solving real-world case studies. In doing so, we can alleviate student frustration, motivate students,
and provide realistic practice for students within the classroom. In this section, we develop a four-phase weighted-MDS unit based on the following case study from Endert et al. [2011]:
To construct informed economic, health, and educational policies, the U.S. Census Bureau attempts to survey every individual living within the United States. We have access to a subset of the
1990 census that includes 2.5 million observations and p = 68 features (i.e., variables), including salary, education, marital status, employment status, occupation, family details, driving
patterns, etc. The U.S. president (in 1992) would like to implement policy that will help those with low socio-economic status. What would you (the students) recommend? Use census data to support
the recommendations.
Across the phases, we address the elements of EoT, in addition to the mathematics and computation of weighted-MDS. We highlight the elements of EoT at the end of each phase description and provide
Table 1 to bullet the phase objectives, categorize the objectives as either quantitative and qualitative aspects of problemsolving, and state (again) which elements of EoT are covered.
Phase I. Assess and Explore the Data
The way in which the case study is phrased suggests there are multiple recommendations for the president. Thus, Phase I requires that the students 1) state in their words the goal of their endeavors,
2) hypothesize what they will learn from the data, and 3) explore the data. For the exploration, the students may look directly at an Excel file that contains the data, use quantitative methods they
currently know to summarize the data, and assess the data visually using weighted-MDS.
Figure 4a plots an initial MDS (weighted-MDS with equal weights) display of a random sample (n = 3000) from the census data set. During Phase I, we do not explain the quantitative method used to
display the data. Rather, we provide information about how to interpret and use Figure 4a to explore the data. In this case, each data point in Figure 4 represents an individual’s completed survey.
Although the axes of the visualization do not have an explicit physical meaning, the distance between any pair of surveys conveys the degree to which they are similar (e.g., surveys that appear in
clusters are more similiar to one another (according to the 68 data features) than surveys that appear in different clusters). However, the display, as currently plotted, does not convey how the
surveys differ. That is, the mathematical method (MDS) used to create Figure 4a weighted the data features equally. Thus, to learn the features that differentiate the surveys, the students must
explore the data and interact with the display (e.g., students may highlight observations according to requested criteria and/or change the perspective of the visualization by taking advantage of the
display’s interactive machinery, V2PI).
For example, suppose some students focus on the word “socioeconomic” in the case study description and want to learn whether there are features that correlate with the variable salary. Given the
obvious structure in Figure 4a, these students might first identify three clusters and use highlighting to discover that Group 1 represents surveys from working-class people, Group 2 includes surveys
from unemployed adults, and Group 3 includes surveys from adults under 20 years of age. Since none of the clusters are based purely on salary, the students may next highlight surveys based on two
salary ranges: “less than $15k” or “within $30k and $60k.” Figure 4b marks the surveys with the respective salary ranges by “X” or “◻.” The marked observations do not present a clear clustering
structure. This means the display does not rely heavily on salary to differentiate observations. To change the perspective of the display and up-weight the role of salary in the display, the students
may drag the marked observations from each group apart. (The arrows in Figure 4b depict dragging.) Using V2PI, the visualization reconfigures, as shown in Figure 4c. Now, the data appear in several
small clusters and salary, in part, explains the spatialization of the clusters. We add a line to Figure 4c to show that the marked observations from Figure 4b separate perfectly; those above and
below the line have surveys with salaries within $30k and $60k and less than $15k, respectively.
One advantage of using the IDVs based on weighted-MDS is that, unlike Figure 4a, Figure 4c weights some data features more than others in response to the students’ feedback in Figure 4b. The data
features with the highest weights are the following: Salary (0.29), Have a reliable form of transportation to work (0.20), Whether or not employed (0.25), and Years of education (0.10). With this
information, students may assess which variables work jointly with salary to create the observed cluster structure in Figure 4c. In particular, students may mark observations in Figure 4c to discover
that 1) all observations for which r[1] < −0.2 represent employed individuals, 2) clusters 1 and 2 include individuals who make within $30k and $60k, but do or do not have reliable modes of
transportation to work, 3) clusters 3 and 4 include individuals who make less than $15k and either drive themselves to work or take public transportation, respectively. Now, students may conjecture
that people with low incomes need transportation assistance.
We expect students to make several conjectures about the data based on their visual explorations. The students report their findings in journals and, at the end of phase I, during oral presentations.
In the next phase, the students learn the mathematical and computational methods driving the visualization. An understanding of these methods may (or may not) affect their interpretations of the
EoT #1-5: The students assess their points of view, state the goal, and ask questions; gain an appreciation for the need of information/data to address questions; and interpret data visualizations to
infer relationships in the data.
Phase II. Learn Mathematical Methods
Phase I does not require students to master mathematical concepts for data exploration. Now, in the second phase, students learn the mathematical theory of MDS and its constraints. Students complete
standard problem sets to reinforce the mathematical concepts. At the conclusion of the phase, students conjecture and formulate mathematically how displays based on MDS may change, given changes in
its theory.
EoT # 5,6,7: The students learn the mathematical formulations of visualizations that rely on assumptions and result in interpretations that may lead to inference.
Phase III. Implement Computation
In Phase I, students use software that implements the V2PI machinery based on the mathematics of Phase II. Now, the students program one or more modules within the software to reimplement V2PI. The
software is coded in a way that includes self-contained modules which, when removed, can be replaced by code created by students. By replacing modules, students are shielded from high-level coding.
The modules that the students will replace include those that 1) read large high-dimensional data sets and 2) solve for coordinates R using a variety of techniques.
Since some students may not have computer programming in their backgrounds, computer lab assignments are important and Phase III may last longer than other phases. Note that those experiencing
programming for the first time have the benefit of a clear motivation to learn tedious (arguably), fundamental concepts, including, variable initialization, if/then statements, and loops.
EoT #5,6: Phase III reinforces the importance of summarizing and interpreting data using mathematical and computational concepts and models.
Phase IV. Reflect
Now that the students have explored the data, learned the mathematics of MDS, and programmed it, they have an opportunity to assess both the technical methods used to visualize the data and their
personal thoughts while assessing and interpreting information in the data.
In regard to methods, the students experience in Phase I the need to adjust data displays, but only learn during phases II and III a deterministic approach for summarizing data. Thus, in Phase IV,
the students hypothesize, formulate mathematically, and implement how the visualization can adjust to their data interactions. Effectively, the students construct an understanding of weighted-MDS and
implement it by replacing the appropriate module. With the right guidance from professors, students may realize the dimensions for which the observations are similar or different, respectively, are
more important than the remaining dimensions when they drag observations together or apart; the weights of the important dimensions (as determined by the dragging) should be higher than the remaining
During Phase IV, students also reflect upon what they gained from the data. They address the goals of the case study, state whether they validated their hypotheses or corrected any misconceptions,
and discuss any personal or analytical constraints. At the conclusion of Phase IV, students share their reflections and present their findings during an oral presentation and within a paper.
EoT #6,7,8,1: The students 1) evaluate the model and its interpretation given certain assumptions and 2) reflect upon implications (based on their points of view) of what they learned from the data
and the role data served in making recommendations to the president.
At the end of the fourth phase, students will have not only obtained the mathematical skills emphasized by traditional—or Miyagi—methods for teaching, but also the practice of applying weighted-MDS
in both contrived and realistic scenarios. For some students, this approach for teaching data analytics will dramatically affect their understanding of weighted-MDS.
Of course, data analytics classes should include other technical methods, in addition to weighted-MDS. We envision teaching at least four modules (with the same phases) during one semester-long,
undergraduate data analytics course. The additional modules may rely on data analytics techniques that are preferable to the instructor, but crucially, an IDV is needed for each technique chosen. In
work from Leman et al. [2011] and House et al. [2011], V2PI has been developed for principal component analysis (PCA), mixture PCA, and isomap. None of these data analytics approaches is ideal for
instructors, so we encourage instructors to develop their own V2PI method; V2PI is not specific to the data analytics techniques mentioned.
V2PI is, broadly, a process to consider for quantifying feedback in visualizations that may update model parameters. In fact, a mapping of the process is included within Figure 5: Step 1) Model or
summarize the data quantitatively based on estimates unknowns θ; Step 2) Display the summary in a visualization v; Step 3) Prompt students (or users) to assess v and adjust it as desired; Step 4)
Parameterize the adjustments; and Step 5) Update the original data summary to repeat the loop. We refer to the adjustments in Step 3) as “cognitive feedback” ƒ^(c) in that it represents visually what
the students think. Whereas “parametric feedback” ƒ^(p) is a quantified version of ƒ^(c) that transforms it to the parametric space of the data and enables model updating in Step 5).
Additionally, a data analytics course with IDVs may include probabilistic data analysis techniques as well. If the original data summarizing method in Step 1) is probabilistic, it is possible to
parameterize feedback and update the model while maintaining the model’s probabilistic integrity. To differentiate probabilistic from deterministic versions of V2PI, House et al. in their 2011
technical report refer to the former as Bayesian visual analytic (BaVA) methods.
Using data analytics (e.g., statistics) as a platform to emphasize critical thinking is not a new idea. However, the way by which we propose to integrate critical thinking with complex mathematical
and computational methods is new and similar in spirit to ideas from CATALST. This article discusses a way to reconsider the “wax on, wax off” teaching style invoked in many data analytics courses so
that students may practice and develop skills in the classroom that are directly applicable to realistic scenarios. Students have opportunities in the data analytics course that we propose to tackle
tough problems while they develop insight and master mathematical data summarizing techniques. In particular, we use IDVs as instructional tools for students to construct their understanding of 1)
how to think critically, 2) the role of data in critical thinking, and 3) the mathematical and computational methods needed to summarize high-dimensional data. Based on the Census case study, we
exemplified one approach for students to construct their understanding of thinking critically with data and the utility of weighted-MDS.
Because each course module begins with a case study, students have a clear purpose for learning data analytics. Unlike Daniel in the Karate Kid, students—from the beginning—have the potential to
assess how each lesson fits into a larger scheme of learning from data. They are motivated by an interesting problem and may avoid the frustration that Daniel experienced when he did not understand
the purpose of the household chores. With this in mind, we hope that students not only conclude our data analytics course enlightened by technical methods and critical thinking skills, but also with
a level of satisfaction that will inspire them to continue their education in data analytics.
Further Reading
Endert, A., C. Han, D. Maiti, L. House, S. Leman, and C. North. 2011. Observation-level interaction with statistical models for visual analytics (PDF download). Technical Report. Virginia Tech.
House, L., S. Leman, and C. Han. 2011. Bayesian visual analytics (BaVA) (PDF download). Technical Report. 10-2, FODAVA.
Leman, S., L. House, D. Maiti, A. Endert, and C. North. 2011. The bidirectional visualization pipeline and visual to parametric interaction (PDF download). Technical Report. Virginia Tech.
1 Comment
1. “Improving Mr. Miyagi’s Coaching Style: Teaching Data Analytics with Interactive
Data Visualizations | CHANCE” was indeed a superb posting.
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the word wide web. Well, thanks for your time, Coy | {"url":"https://chance.amstat.org/2012/04/teaching-data-analytics/","timestamp":"2024-11-11T20:29:11Z","content_type":"application/xhtml+xml","content_length":"77298","record_id":"<urn:uuid:12295a0d-d554-4911-8777-4121171eefe4>","cc-path":"CC-MAIN-2024-46/segments/1730477028239.20/warc/CC-MAIN-20241111190758-20241111220758-00246.warc.gz"} |
Take-up and the Inverse-Square Rule for Power Calculations Revisited: When does power not fall quite so drastically with take-up, and when does lower take-up increase power?
One of the earliest posts I wrote on this blog was about how to do power calculations with incomplete take-up. There I described the inverse-square rule for power calculations: if p is the difference
in take-up rates between your treatment and control groups, then the sample size you need to attain a given power is inversely proportional to the square of p. For example, if no one takes the
program in the control group, and 50% do in the treatment group, you need 1/(0.5^2) = 4 times the sample as with 100% take-up; and with 10% take-up, you would need 100 times the sample.
In revising my paper with Gabriel Lara and Claudia Ruiz on a financial education experiment with only 0.8% take-up (yes you sadly read that right, we blogged previously about why and what we did
instead), the editor asks the very useful question of how this rule changes if there is treatment effect heterogeneity. The revised paper, now forthcoming at the World Bank Economic Review, explores
this issue in some detail, and I thought I’d summarize some key ideas here.
Treatment Heterogeneity, Take-up, and Statistical Power
Let s be a dummy variable denoting whether or not subject i receives (takes-up) a given treatment, and gamma(i) the treatment effect of actually receiving this treatment. With treatment
heterogeneity, this effect will differ across individuals, and we can assume an underlying distribution of treatment effects with some mean mu(gamma) and variance sigma(gamma) squared. Assume that no
one in the control group receives the treatment. Then we show in the paper that the expected value of the standard ITT estimator takes the form:
There are two terms here, which describe how the average treatment effect changes as the take-up rate changes. The first term is the product of the take-up rate in the treatment group, and the mean
treatment effect conditional on getting treated. This term falls as the take-up rate falls, making it harder to detect an effect of your intervention. If there is no treatment heterogeneity, this is
the only term, and then the inverse-square rule applies.
The second term is the new part, and depends on the take-up rate, how much treatment heterogeneity there is, and the key term of the correlation between an individual’s treatment effect and their
likelihood of taking the treatment. If those individuals who expect to gain more from the treatment are more likely to take it up (what Heckman et al. call essential heterogeneity), then this
correlation will be positive, and the more heterogeneity there is, the stronger the effect of this second term. In contrast, in many cases individuals may have no clue as to their treatment effect (
even after taking part in a program), and take-up may instead reflect a range of factors like transport distance, who program officials could reach, etc. that are not strongly correlated with
treatment effects. Then this correlation may be zero, and power will be the same as in the no heterogeneity case.
What difference does this make to power? Figure 1 provides an example, calibrated to the outcome mean and sample size in our financial education experiment. With no treatment heterogeneity, or
take-up uncorrelated with treatment heterogeneity, the LATE is the same regardless of the take-up rate, but power falls dramatically as take-up does – so power drops from 99.7 percent with 100
percent take-up to 64.7 percent with 50 percent take-up, and only 4.3 percent with 5 percent take-up. If, instead, people partially or fully sort into taking up treatment based on their treatment
effect, then the LATE increases as the take-up rate falls (since the sample of compliers becomes those with bigger and bigger treatment effects), and power falls much less dramatically with take-up.
If, we were in the extreme case where individuals perfectly order themselves into taking up the intervention by what their treatment effect would be (correlation of 1), power would only fall to 90.4
percent with 50 percent take-up, a huge gain. However, notice from the equation above that this treatment heterogeneity effect is maximized at 50% take-up, and so as take-up gets to rates of 5%,
power is still really low, regardless of the correlation.
Figure 1: With Treatment Effect Heterogeneity, Power Falls Less Steeply with Take-up the More Positively Correlated Take-up is with Individual Treatment Effects
When might lower take-up increase power?
Suppose treatment heterogeneity is very large, with the program actually having negative effects for some individuals and positive effects for others. This could be the case for a vocational training
program, for example, where some individuals are hurt by more time out of the labor market while training, while others gain lots of valuable skills; or perhaps in a loan program, where some take on
debts they cannot manage and others use this credit to grow. Then, if take-up is strongly correlated with treatment, it can be possible for power to actually increase at first as take-up falls from
100%, since those with large negative effects no longer take-up treatment, and thus do not drag down the average. Figure 2 illustrates this case, showing the distribution of treatment effects for
those who take-up and do not take-up treatment at different take-up rates (assuming a correlation of 0.75 with take-up). You can see that with a take-up rate of 90%, the 10% who do not take-up
treatment are heavily drawn from those with negative treatment effects – and so by not giving them treatment, power is higher than with 100% take-up. But as the take-up rate falls, you still end up
excluding many people with positive treatment effects, which causes power to then start falling.
Figure 2: In the Extreme Case, Moving from 100% Take-up to Lower Take-up Rates Can Increase Power, so Long as Take-up is not too low
What does this mean for my power calculations and for my efforts to encourage take-up?
My take-aways from this analysis are that:
1. Unless you have a program with extreme heterogeneity, that is only useful to a small subset of people and hurts almost everyone else, you should be trying to encourage take-up to at least levels
of 75 or 80%.
2. If you are in a situation where people have a good idea of what the treatment is, and people can select into take-up on their anticipated treatment effect, you may not want to push too hard to
boost take-up from 90% to 100%, since the power gains may be less than you think, or even negative.
3. There are some programs where we think the people that it might help best may be least likely to take it up (e.g. badly managed firms may not know they are badly managed), which would result in a
negative correlation, and so pushing for higher take-up in those cases will be particularly useful.
4. When preparing power calculations, the conservative approach will be to typically apply the inverse-square rule still, but you may not lose as much power as you expect if sorting on treatment
heterogeneity is possible.
ee2e6d53e6117866ae305b8dfe77934b https://webapi.worldbank.org/comments/api/comment/post https://webapi.worldbank.org/comments/api/comment https://webapi.worldbank.org/comments/api/comment/count
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A Trip Back To High School: Solve this math riddle!
Home Lifestyle A Trip Back To High School: Solve this math riddle!
A Trip Back To High School: Solve this math riddle!
Take a look at the math puzzle below and see what you make of it. Also, check the clock before you start. How fast can you do this?
Ready to solve the equation?
Mull it over a few minutes and then write down your answer. Don’t cheat by scrolling down, however!
Alright, pencils down. Have you reached a solution? How fast did you get it?
Here is how we can break it down: 7(7-2×3) =?
– First of all, we need to start with solving the multiplication in the brackets
7 (7- 6)
– Then you solve the equation within the brackets
7 (1)
– Now you can continue with solving the multiplication:
7 x 1 =
– Now you have the solution to the equation: It’s 7
Comment your answer below 👇 | {"url":"https://ilovemylifeandiloveyou.teachmelife.net/a-trip-back-to-high-school-solve-this-math-riddle/","timestamp":"2024-11-07T20:00:08Z","content_type":"text/html","content_length":"104679","record_id":"<urn:uuid:22ca2ba5-0558-4e4d-95c2-efd472697b65>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00654.warc.gz"} |
Get first word from some text
To extract the first word from some text in Excel, you can use a formula with built-in functions like FIND and LEFT.
Today’s tutorial is a part of our definitive guide on Excel Formulas.
How to extract the first word from text in Excel?
Here are the steps to get the first word from the text:
1. Open Excel
2. Type =LEFT(text,FIND(” “,text)-1)
3. Press Enter.
4. The formula will extract the first word.
First, place the initial data set. The main point of the formula is the following:
The FIND function locates and gets the position of the first occurrence of a space (“ “) character in the given text string. The inner part of the formula returns the position as a number. Finally,
starting from the first character, the LEFT function extracts the characters until the length of the first word – 1. We have to cut the last character because it’s the space.
In the example, the formula looks like this:
=LEFT(B3,FIND(” “,B3)-1)
How do you get the first word if the cell contains only one word? Error handling is important to show that something went wrong. Using the formula mentioned above, we’ll get a #VALUE! Error. It is
important to prevent formula errors by using the IFERROR function.
=IFERROR(LEFT(B3,FIND(” “,B3)-1),B3) or
=IFERROR(LEFT(B3,FIND(” “,B3)-1),”The cell contains one word”)
In this case, the formula returns the first word:
=IFERROR(LEFT(B3,FIND(” “,B3)-1),B3)
Explanation: When an error occurs, the IFERROR expression returns with a user-specified message or the first word. Furthermore, it’s a smart way to handle the error: Add an extra space to the cell
value before running the FIND function.
=LEFT(B3,FIND(” “,B3&” “)-1)
Known limitation: The above-demonstrated formula works only with the first space.
Get the first word using a user-defined function
If you want to combine more than one built-in Excel into a formula, be careful; sometimes, it is not easy. In the example, we will use the GETWORDS user-defined function.
=GETWORDS(text, n, delimiter)
• text: cell reference
• n: position
• delimiter: define a separator
The solution looks like this:
=GETWORDS(B5,1,” “)
We strongly recommend using our free Excel add-ins if you have to clean data using Excel. In addition, the productivity suite contains a custom function library.
Related Formulas and Examples | {"url":"https://exceldashboardschool.com/get-first-word-from-some-text/","timestamp":"2024-11-11T16:33:07Z","content_type":"text/html","content_length":"157620","record_id":"<urn:uuid:54b47431-c736-4159-9b0f-dde93b78c539>","cc-path":"CC-MAIN-2024-46/segments/1730477028235.99/warc/CC-MAIN-20241111155008-20241111185008-00544.warc.gz"} |
In this fourth lesson of the "What Is a Wave?" unit, students will learn how electromagnetic radiation is related to common items, understand how electromagnetic radiation is a form of energy, and
create electromagnetic spectrum charts.
Essential Question(s)
What are waves? How do waves behave differently from particles?
Students construct images and summarize how those images relate to waves.
Students infer how common items are related to electromagnetic radiation.
Students compile Cornell Notes related to the electromagnetic spectrum.
Students create electromagnetic spectrum charts.
Students’ electromagnetic spectrum charts serve as the evaluation.
• Lesson Slides (attached)
• Puzzled Photos (attached, one set)
• Painting a Picture Images (attached, one set)
• Painting a Picture Chart (attached, one per student)
• Cornell Notes handout (attached, one per student)
• EM Spectrum Chart Rubric (attached, one per student)
• Copy paper
• Markers or colored pencils
Use the attached Lesson Slides to guide the lesson. You can review the essential questions and lesson objectives with students on slides 3 and 4 before beginning the lesson.
Begin by showing slide 5 and introducing students to the Puzzled strategy. Give each student a random piece from the Puzzled Photos. Tell students to move around the room to locate the other pieces
of their image, assemble the pieces to complete the image, and stay together as a group. When students believe they have correctly assembled the pieces to form an image, check to make sure it is
Ask students to discuss with their groups how their image relates to the Waves unit content that they have been learning about. After the discussion, show the complete puzzled images on slides 6-10
and ask each group to share what their image represents and how it relates to waves.
Pass out copies of the Painting a Picture Chart. Show slide 11 and introduce students to the Painting a Picture strategy. As students view each image posted in the classroom, they should record their
observations about each image in the first column of the chart and how each image relates to electromagnetic radiation in the second column of the chart.
After giving students time to view and record their observations for each image, show slides 12-16 and provide frequency and wavelength range information to students. Have students add this
information to the third column of their charts. Use this time to allow students to share their observations and inferences and correct any misconceptions they may have.
Show slide 17 and play the "Electromagnetic Spectrum" video.
Instruct your students to think about how heat-sensing snakes relate to the electromagnetic spectrum as they watch the "Heat Sensing Pit Vipers" video on slide 18.
Ask for volunteers to share their thoughts after the video.
Pass out copies of the Cornell Notes handout or have your students set up a page in their science notebook, share the instructional strategy Cornell Notes System, and use slides 19-24 to explain the
electromagnetic spectrum. Show slide 25 and ask students to write a summary at the bottom of their note sheet.
Move to slide 26 and ask students to compare their summaries with a student nearby. Then, ask for volunteers to share their summaries.
Show slide 27 and provide each student with a piece of copy paper and markers or colored pencils. Tell students to create an electromagnetic spectrum chart that includes the information listed. Pass
out copies of the EM Spectrum Chart Rubric and tell students that you will use the rubric to assess their understanding of the lesson.
The Electromagnetic Spectrum chart serves as the evaluation activity for this lesson. | {"url":"https://learn.k20center.ou.edu/lesson/1686","timestamp":"2024-11-06T14:29:13Z","content_type":"text/html","content_length":"36009","record_id":"<urn:uuid:360599d0-22b8-4cd4-9e82-128ae0c06fe8>","cc-path":"CC-MAIN-2024-46/segments/1730477027932.70/warc/CC-MAIN-20241106132104-20241106162104-00387.warc.gz"} |
What is Value?
The most fundamental concept in the social sciences is value. Value determines what we do. Value is that ‘thing’ that needs to be created, preserved, maximized, communicated, transferred, and shared.
Value is ever-present and ever-changing. The pervasiveness of value can easily lead to the conclusion that our lives revolve around value.
But what is value exactly?
Value is often described using synonyms such as importance, benefit, quality, usefulness, or appreciation. This isn’t very helpful because these notions are as vague as the common understanding of
value. Some would argue that such a grand concept as value cannot be defined. Accordingly, value is supposed to be something that can only be recognized.
Fortunately, it turns out that there’s something special about value. A very precise and useful definition of value exists that is barely known:
Value: the maximum amount that you’re prepared to give up
This definition has four interesting properties, and the following combination of properties provides the foundation to understand, measure, and analyze value.
• Value is quantifiable (“the maximum amount”)
• Value is about potential (“maximum … prepared”)
• Value is subjective (“you’re”)
• Value is expressed in terms of sacrifice (“to give up”).
Value Example
How much would you be prepared to walk to get freshly baked bread from a friend? Whatever the distance, that is your valuation of getting that bread. Some might go very far to get that bread. Maybe
because your friend’s bread is known to be really good, you promised someone to get it, or there is no more bread at home. Whatever the reasons, your willingness to walk a distance of x to get it
reflects the bread’s value to you. This is quantifiable; it’s about what you’re potentially willing to do, and it is expressed in walking distance, which requires effort.
The more valuable the bread becomes to you, the greater the distance you’re prepared to walk. Of course, not everyone is willing to walk the same distance. This shows that there’s no such thing as
objective or intrinsic value. Value cannot be separated from people; people determine value — without people, there’s no value.
I didn’t need to use money to express value in the bread example. You can get something edible (the object of value); to get it, you must walk (the sacrifice). In fact, most decisions in life
actually don’t involve any money. How much time are you willing to spend on reading that article? Or how much effort are you willing to exert to fix that nasty hole in the wall? Or how much noise are
you willing to endure to stay in a bar? These are all ways to express value.
The easiest way to express value is in terms of money. Specifically, your monetary valuation of anything is simply the maximum amount that you’re willing to pay for it. Knowing people’s willingness
to pay is powerful because it lets you predict what people will purchase.
The price of a product shouldn’t be confused with one’s maximum willingness to pay. The price of a product doesn’t necessarily reflect its value. The moment of purchase does, however, reveal a bit of
information about one’s valuation. If you order a cup of espresso for $3, that decision implies that your valuation of a cup of espresso at that moment is at least $3. Your valuation might be much
higher than $3, which can be considered a great deal. Or your valuation is only a little bit higher than $3, which means that if the cup was a little bit more expensive, you wouldn’t have bought it.
So, knowing how much people spent can only reveal what they were at least willing to pay, not their actual valuation.
Having a precise understanding of what value is isn’t merely a philosophical exercise. It provides a logical framework to understand what makes people tick. Knowing what people value most provides us
with the information to create as much value as possible. The more value we create, the more value we can capture in return, tangible or intangible. To be aware of what value is is in and of itself | {"url":"https://veylinx.com/blog/what-is-value","timestamp":"2024-11-12T23:49:37Z","content_type":"text/html","content_length":"102071","record_id":"<urn:uuid:25607495-a484-4828-abd3-90bf920ee331>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00557.warc.gz"} |
Elementary algebra for college students. No. 2/E. By Irving Drooyan, & William Wooton
Elementary algebra
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Elementary algebra for college students. By Irving Drooyan and William Wooton.
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Ryan Hynd (MIT/University of Pennsylvania), Analysis Seminar - Department of Mathematics
Ryan Hynd (MIT/University of Pennsylvania), Analysis Seminar
September 28, 2016 @ 4:00 pm - 5:00 pm
Title: Extremal functions for Morrey’s inequality in convex domains
Abstract: A celebrated result in the theory of Sobolev spaces is Morrey’s inequality, which establishes the continuous embedding of the continuous functions in certain Sobolev spaces. Interestingly
enough the equality case of this inequality has not been thoroughly investigated (unless the underlying domain is R^n). We show that if the underlying domain is a bounded convex domain, then the
extremal functions are determined up to a multiplicative factor. We will explain why the assertion is false if convexity is dropped and why convexity is not necessary for this result to hold.
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OP Malhotra ISC Class-11 S Chand Publication Maths Solutions - ICSEHELP
OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
OP Malhotra ISC Class-11 S Chand Publication Maths Solutions Chapter Wise . Step by Step All Exercise Solution with Chapter Test Questions is very help full for ISC student preparing Board exam.
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OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
Class: 11th
Subject: Mathematics
Topics: Chapter Wise Solutions
Board ISC
Writer OP Malhotra
Publications S.Chand Publications 2020-21
How To Solve ISC Class-11 Maths All Publication
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• Solved Specimen Paper of ISC Class-11 Maths
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These exercises are formulated by our expert tutors in order to assist you with your exam preparation, to attain good marks in Maths.
Chapter-wise solutions are available , which can be view for free .
Problems are solved step by step with detailed explanations with formula’s use for better and easy understanding.
Apart from clearing doubts, these solutions also give in-depth knowledge about the respective topics.
OP Malhotra ISC Class-11 S Chand Publication Maths Solutions
1.-Sets Page- 1.1 – 1.32
2-.Relations and Functions Page 2.1 – 2.61
3.-Angles and Arc Length Page- 3.1 -3.10
4.-Trigonometrical Function Page- 4.1 -4.29
5.- Compound and Multiple Angles Page 5.1 – 5.34
6.-Trigonometric Equations Page 6.1 – 6.16
7.- Properties of Triangle Page-7.1 – 7.11
8.- Mathematical Induction Page 8.1 – 8.14
9.- Complex Numbers Page 9.1 – 9.61
10.-Quadratic Equation Page 10.1 – 10.32
11. Inequalities Page 11.1 – 11.28
12.-Permutations and Combinations Page 12.1- 12.37
13.-Binomial Theorem Page 13.1 -13.16
14.-Sequence and series Page 14.1 – 14.42
15.- Basic Concept of Points and Their Coordinate Page 15.1 – 15.16
16.- The Straight Line Page 16.1 -16.38
17.- Circles Page 17.1 -17.18
18.- Limits Page 18.3 – 18.40
19.- Differentiation Page 19.1 – 19.27
20.- Measure of Central Tendency Page 20.1 -20.15
21. –Measure of Dispersion Page 21.1 -21.25
22.- Probability Page 22.1 -22.48
23.- Parabola Page 23.1 -23.20
24.- Ellipse Page 24.1 -24.18
25.-Hyperbola Page 25.1-25.22
26. Point and their Coordinate in Three Dimensional Page 26.1 – 26.12
27. Mathematical Reasoning Page 27.1 -27.30
SECTION – C
28.- Statistics (Continue from chap-20) Page 28.1-28.28
29.- Correlation Analysis Page 29.1 – 29.27
30.- Index Numbers Page 30.1 -30.25
31.-Moving Averages Page 31.1 -31.26
Multiple Choice Questions MCQ-1 –MCP-18
Model Test Paper MTP-1 — MTP-30
FAQ on OP Malhotra SChand Publication ISC Class-11 Maths
Who is OP Malhotra ?
Mr. O.P. Malhotra was one of the best students of Professor Shanti Narayan during the years (1941-1943). He has won accolades for his books on Mathematics throughout the length and breadth of India.
His teaching experience is simply unsurpassable. Before writing books on Mathematics
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The Argument From Marginal Cases
The argument from marginal cases
claims that you can't both think that humans
morally and that animals don't, because no reasonable set of criteria for moral worth cleanly separates all humans from all animals. For example, perhaps someone says that suffering only matters when
it happens to something that has some bundle of capabilities like linguistic ability, compassion, and/or abstract reasoning. If livestock don't have these capabilities, however, then some people such
as very young children probably don't either.
This is a strong argument, and it avoids the noncentral fallacy. Any set of qualities you value are going to vary over people and animals, and if you make a continuum there's not going to be a place
you can draw a line that will fall above all animals and below all people. So why do I treat humans as the only entities that count morally?
If you asked me how many chickens I would be willing to kill to save your life, the answer is effectively "all of them". [1] This pins down two points on the continuum that I'm clear on: you and
chickens. While I'm uncertain where along there things start getting up to significant levels, I think it's probably somewhere that includes no or almost no animals but nearly all humans. Making this
distinction among humans, however, would be incredibly socially destructive, especially given how unsure I am about where the line should go, and so I think we end up with a much better society if we
treat all humans as morally equal. This means I end up saying things like "value all humans equally; don't value animals" when that's not my real distinction, just the closest schelling point.
[1] Chicken extinction would make life worse for many other people, so I wouldn't actually do that, but not because of the effect on the chickens.
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Lesson 5
Negative Exponents with Powers of 10
Let’s see what happens when exponents are negative.
5.1: Number Talk: What's That Exponent?
Solve each equation mentally.
\(\frac{100}{1} = 10^x\)
\(\frac{100}{x} = 10^1\)
\(\frac{x}{100} = 10^0\)
\(\frac{100}{1,\!000} = 10^{x}\)
5.2: Negative Exponent Table
Complete the table to explore what negative exponents mean.
1. As you move toward the left, each number is being multiplied by 10. What is the multiplier as you move right?
2. How does a multiplier of 10 affect the placement of the decimal in the product? How does the other multiplier affect the placement of the decimal in the product?
3. Use the patterns you found in the table to write \(10^{\text -7}\) as a fraction.
4. Use the patterns you found in the table to write \(10^{\text -5}\) as a decimal.
5. Write \(\frac{1}{100,000,000}\) using a single exponent.
6. Use the patterns in the table to write \(10^{\text -n}\) as a fraction.
5.3: Follow the Exponent Rules
1. Match each exponential expression with an equivalent multiplication expression:
\(\left(10^2\right)^{\text -3}\)
\(\left(10^{\text -2}\right)^3\)
\(\left(10^{\text -2}\right)^{\text-3}\)
│\(\frac{1}{(10 \boldcdot 10)} \boldcdot \frac{1}{(10 \boldcdot 10)} \boldcdot \frac{1}{(10 \boldcdot 10)}\) │
│\(\left(\frac{1}{10} \boldcdot \frac{1}{10}\right)\left(\frac{1}{10} \boldcdot \frac{1}{10}\right)\left(\frac{1}{10} \boldcdot \frac{1}{10}\right)\) │
│\(\frac{1}{ \frac{1}{10} \boldcdot \frac{1}{10} }\boldcdot \frac{1}{ \frac{1}{10} \boldcdot \frac{1}{10} } \boldcdot \frac{1}{ \frac{1}{10} \boldcdot \frac{1}{10} }\)│
│\((10 \boldcdot 10)(10 \boldcdot 10)(10 \boldcdot 10)\) │
2. Write \((10^2)^{\text-3}\) as a power of 10 with a single exponent. Be prepared to explain your reasoning.
1. Match each exponential expression with an equivalent multiplication expression:
\(\frac{10^2}{10^{\text -5}}\)
\(\frac{10^{\text -2}}{10^5}\)
\(\frac{10^{\text -2}}{10^{\text -5}}\)
│\(\frac{ \frac{1}{10} \boldcdot \frac{1}{10} }{ \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\boldcdot \frac{1}{10}\boldcdot \frac{1}{10} }\)│
│\(\frac{10 \boldcdot 10}{10 \boldcdot 10 \boldcdot 10 \boldcdot 10 \boldcdot 10}\) │
│\(\frac{ \frac{1}{10} \boldcdot \frac{1}{10} }{ 10 \boldcdot 10\boldcdot 10\boldcdot 10\boldcdot 10 }\) │
│\(\frac{ 10 \boldcdot 10 }{ \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\boldcdot \frac{1}{10}\boldcdot \frac{1}{10}}\) │
2. Write \(\frac{10^{\text -2}}{10^{\text -5}}\) as a power of 10 with a single exponent. Be prepared to explain your reasoning.
1. Match each exponential expression with an equivalent multiplication expression:
\(10^4 \boldcdot 10^3\)
\(10^4 \boldcdot 10^{\text -3}\)
\(10^{\text -4} \boldcdot 10^3\)
\(10^{\text -4} \boldcdot 10^{\text -3}\)
│\((10 \boldcdot 10 \boldcdot 10 \boldcdot 10) \boldcdot ( \frac{1}{10} \boldcdot \frac{1}{10}\boldcdot \frac{1}{10})\) │
│\(\left(\frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\right) \boldcdot \left( \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\right)\)│
│\(\left(\frac{1}{10}\boldcdot \frac{1}{10} \boldcdot \frac{1}{10} \boldcdot \frac{1}{10}\right) \boldcdot \left(10 \boldcdot 10 \boldcdot 10\right)\) │
│\((10 \boldcdot 10 \boldcdot 10 \boldcdot 10) \boldcdot (10 \boldcdot 10 \boldcdot 10)\) │
2. Write \(10^{\text-4} \boldcdot 10^3\) as a power of 10 with a single exponent. Be prepared to explain your reasoning.
Priya, Jada, Han, and Diego stand in a circle and take turns playing a game.
Priya says, SAFE. Jada, standing to Priya's left, says, OUT and leaves the circle. Han is next: he says, SAFE. Then Diego says, OUT and leaves the circle. At this point, only Priya and Han are left.
They continue to alternate. Priya says, SAFE. Han says, OUT and leaves the circle. Priya is the only person left, so she is the winner.
Priya says, “I knew I’d be the only one left, since I went first.”
1. Record this game on paper a few times with different numbers of players. Does the person who starts always win?
2. Try to find as many numbers as you can where the person who starts always wins. What patterns do you notice?
When we multiply a positive power of 10 by \(\frac{1}{10}\), the exponent decreases by 1: \(\displaystyle 10^8 \boldcdot \frac{1}{10} = 10^7\)This is true for any positive power of 10. We can reason
in a similar way that multiplying by 2 factors that are \(\frac{1}{10}\) decreases the exponent by 2: \(\displaystyle \left(\frac{1}{10}\right)^2 \boldcdot 10^8 = 10^6\)
That means we can extend the rules to use negative exponents if we make \(10^{\text-2} = \left(\frac{1}{10}\right)^2\). Just as \(10^2\) is two factors that are 10, we have that \(10^{\text-2}\) is
two factors that are \(\frac{1}{10}\). More generally, the exponent rules we have developed are true for any integers \(n\) and \(m\) if we make \(\displaystyle 10^{\text-n} = \left(\frac{1}{10}\
right)^n = \frac{1}{10^n}\)
Here is an example of extending the rule \(\frac{10^n}{10^m} = 10^{n-m}\) to use negative exponents: \(\displaystyle \frac{10^3}{10^5} = 10^{3-5} = 10^{\text-2}\) To see why, notice that \(\
displaystyle \frac{10^3}{10^5} = \frac{10^3}{10^3 \boldcdot 10^2} = \frac{10^3}{10^3} \boldcdot \frac{1}{10^2} = \frac{1}{10^2}\)which is equal to \(10^{\text-2}\).
Here is an example of extending the rule \(\left(10^m\right)^n = 10^{m \boldcdot n}\) to use negative exponents: \(\displaystyle \left(10^{\text-2}\right)^{3} = 10^{(\text-2)(3)}=10^{\text-6}\)To see
why, notice that \(10^{\text-2} = \frac{1}{10} \boldcdot \frac{1}{10}\). This means that \(\displaystyle \left(10^{\text-2}\right)^{3} =\left( \frac{1}{10} \boldcdot \frac{1}{10}\right)^3 = \left(\
frac{1}{10} \boldcdot \frac{1}{10}\right) \boldcdot \left( \frac{1}{10} \boldcdot \frac{1}{10}\right)\boldcdot \left(\frac{1}{10}\boldcdot \frac{1}{10}\right) = \frac{1}{10^6} = 10^{\text-6}\)
• base (of an exponent)
In expressions like \(5^3\) and \(8^2\), the 5 and the 8 are called bases. They tell you what factor to multiply repeatedly. For example, \(5^3\) = \(5 \boldcdot 5 \boldcdot 5\), and \(8^2 = 8 \
boldcdot 8\). | {"url":"https://curriculum.illustrativemathematics.org/MS/students/3/7/5/index.html","timestamp":"2024-11-02T21:09:01Z","content_type":"text/html","content_length":"81140","record_id":"<urn:uuid:42ed0e0e-a289-4a9a-a238-586a8dbb3eb0>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00645.warc.gz"} |
Polygons | Orchids International School
Polygon Shapes for Class 5 Math
A polygon shape is a 2d shape that contains straight lines. Here students will learn about polygons.
In this learning concept, the students will also learn to
• Classify the types of polygons.
• Identify a regular polygon and an irregular polygon.
• Distinguish the different regular polygon shapes.
• Choose examples of polygons and the number of diagonals in a polygon.
Each concept is explained to class 5 maths students using illustrations, examples, and mind maps. Students can assess their learning by solving the two printable worksheets given at the page’s end.
Download the polygon shapes worksheet for class 5 and check the solutions to the polygon shapes question for class 5 provided in PDF format.
What Is a Polygon?
• A polygon is defined as a two-dimension closed figure formed by joining three or more straight lines.
• Few examples of polygons are:
• Every polygon is a closed figure but not every closed figure is a polygon.
• Look into the figures below:
• Each figure is a closed figure but not every side is made up of straight lines. Therefore, these are not polygons.
Types of Polygons
There are two types of polygons:
• Regular Polygon
• Irregular polygon
What Is a Regular Polygon?
A polygon is said to be a regular polygon if all its side is of equal length and all the angles are equal.
What Is an Irregular Polygon?
A polygon is said to be an irregular polygon if all its sides and angles are unequal.
Polygonal Shape Names
Triangle Polygon
• A triangle is a three-sided closed figure.
• The three-line segments that join to make a triangle is called the sides of the triangle.
• The point where the line segments meet each other is called the vertices of the triangle.
• The angle formed at the vertices of the triangle is called the angles of the triangles.
• The sum of the angles of a triangle is equal to 180°.
• A triangle has 3 vertices, 3 sides, and 3 angles.
• In the figure above ABC is the triangle.
□ Sides of the triangle = AB, AC, and BC
□ Vertices of the triangle = A, B, and C.
□ Angles of the triangle = ∠A, ∠B, and ∠C.
□ ∠A + ∠B + ∠C = 180°
Types of Triangles
• Equilateral triangle
• Isosceles triangle
• Scalene triangle
Equilateral Triangle
• In an equilateral triangle, each angle and the length of each side of the triangle are equal.
• Each angle of an equilateral triangle is equal to 60°.
• An equilateral triangle is also called a regular triangle.
• Triangle ABC,
□ Side: AB = BC = AC
□ Vertices: A, B, and C
□ Angles: ∠A = ∠B = ∠C = 60°
Isosceles Triangle
• In an isosceles triangle, two angles and the length of two sides of the triangle are equal.
• Triangle AOB,
□ Side: AO, AB, OB and AO = AB
□ Vertices: A, O and B
□ Angles: ∠O = ∠B and ∠A +∠O + ∠B = 180°
Scalene Triangle
• In a scalene triangle every angle and side of the triangle are unequal.
• Triangle ABC,
□ Side: AB ≠ AC ≠ BC
□ Vertices: A, B and C
□ Angles: ∠A ≠ ∠B ≠ C and ∠A +∠B + ∠C = 180°
Square Polygon
• A square is a four-side closed.
• It is made of two equal triangles.
• It is also known as a regular quadrilateral.
• It has 4 equal sides and the opposite sides are parallel to each other.
• It has 4 vertices.
• It has 4 interior angles and each interior angle of a square is equal to 90°.
• In the above figure, ABCD is a square.
□ Side: AB = BC = CD = AB
□ Vertices: A, B, C, and D.
□ Angles: ∠A = ∠B = ∠C = ∠D = 90°.
□ Sum of the angle of the square is 360°.
Rectangle Polygon
• A rectangle is a four-side closed.
• It is made of two equal triangles.
• It has 4 sides and the opposite sides are parallel and equal to each other.
• It has 4 vertices.
• It has 4 interior angles and each interior angle of a rectangle is equal to 90°.
• In the above figure, ABCD is a rectangle.
□ Side: AB = CD and AD = BC
□ Vertices: A, B, C, and D.
□ Angles: ∠A = ∠B = ∠C = ∠D = 90°.
□ Sum of the angle of the square is 360°.
Number of Diagonals in a Polygon
• The line segments that join the opposite vertices is called the diagonal.
Fun facts:
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Net best-ball team composition in golf
This paper proposes simple methods of forming two-player and four-player golf teams for the purposes of net best-ball tournaments in stroke play format. The proposals are based on the recognition
that variability is an important consideration in team composition; highly variable players contribute greatly in a best-ball setting. A theoretical rationale is provided for the proposed team
formations. In addition, simulation studies are carried out which compare the proposals against other common methods of team formation. In these studies, the proposed team compositions lead to
competitions that are more fair.
One of the compelling features of golf is that players of vastly different abilities can compete against one another and have a “fair” match. This is accomplished by the handicapping system which has
a long history of refinements extending back to the 1600’s (Yun 2011a, 2011b, 2011c, 2011d).
There is a considerable literature on golf handicapping, and the consensus is that most handicapping systems provide a modest advantage to the stronger player in both stroke and match play formats
involving two players (Chan, Madras and Puterman 2018, Kupper et al. 2012, Bingham and Swartz 2000, Scheid 1977 and Pollock 1974). In fact, Section 10-2 of the United States Golf Association (USGA)
Handicap System Manual (USGA 2016) states that the handicap formula provides an “incentive for players to improve their golf games” whereby a small bonus for excellence advantage is given to the
stronger player.
However, in competitions involving multiple players, varying rules and team formats, fairness may be greatly violated. For example, Bingham and Swartz (2000) suggested that weaker golfers have a
considerable advantage winning a tournaments based on net scores. Grasman and Thomas (2013) investigated scramble competitions and provided suggestions for assigning teams. And of particular
relevance to this paper, Hurley and Sauerbrei (2015) demonstrated that team net best-ball matches are not generally fair.
Handicapping in golf takes different forms depending on the governing body. In this paper, we focus on the handicapping system used by the USGA and the Royal Canadian Golf Association (RCGA). And
although golf is a stochastic game, the USGA/RCGA handicapping system was not developed using the tools of probability theory. On the other hand, we make use of the stochastic nature of golf to
provide team compositions in net best-ball competitions that are more fair than the status quo. For the purposes of this paper, we define a fair system involving n teams as one where the probability
of each team finishing in jth place is 1/n, j = 1, …, n. Surprisingly, although fairness in golf is a much discussed topic, the above definition does not appear to exist in the golf literature.
There are two related papers that concern the problem of team formation in net best-ball competitions. Siegbahn and Hearn (2010) studied fourball; a two-player versus two-player event where
handicapping is used. Like Bingham and Swartz (2000), golfer variability was a prominent focus of their study where the variability of golfer performance was parametrized and estimated as a function
of handicap. Siegbahn and Hearn (2010) concluded that high handicap golfers (i.e., weak golfers) have an advantage in fourball, and they suggested tie-breaking rules to reduce the unfairness. As
discussed in Siegbahn and Hearn (2010), previous studies on fairness in fourball matches focused on the difference in handicaps between teammates as a predictor of fourball success.
Pavlikov, Hearn and Uryasev (2014) built on the results of Siegbahn and Hearn (2010) to specifically address team composition in net best-ball tournament settings. They developed a sophisticated
search algorithm over the combinatorial space of potential team compositions. Optimal team formations were sought in the sense that all teams have nearly the same probability of winning. When the
number of golfers n < 40, it was asserted that the program can be run in reasonable computational times. A feature of the approach proposed by Pavlikov, Hearn and Uryasev (2014) is that the algorithm
is applicable to any prescribed team size. A drawback of the approach involves the reliance on tables that provide average scoring distributions for players of a given handicap. An implication of the
use of the tables is an imposed monotonicity between handicap and performance variability. That is, the table exhibits increasing scoring variability with increasing handicap. Whereas it is generally
the case that high handicap golfers tend to be more variable, there are clearly instances of high handicap golfers who are consistent. For example, imagine a senior golfer who does not hit the ball
far, is straight off the tee and rarely gets into trouble (i.e., does not land in the rough, hazards, water, etc.). It is the third author’s experience that such golfers do exist. Moreover, the
dataset which we consider in Section 4.2 suggests there is not a strictly monotonic relationship between handicap and variability. Following Swartz (2009), we estimate variability individually for
golfers, and this forms the critical component for our team formation proposals in net best-ball tournaments. And importantly, the proposed estimation of golfer specific variability is a
straightforward side calculation of handicap.
In Section 2, we review various background material that is related to the development of team composition. This includes details concerning the rules related to net best-ball tournaments, the
current handicapping system and related literature. In Section 3, our proposals for team composition are developed. They are based on the recognition that variability is an important consideration in
terms of player performance in net best-ball competitions. The basic idea is that golfers of high variability are matched up with golfers of low variability. Matching procedure are developed for both
two-man and four-man team competitions. A noteworthy aspect of the procedures is that they do not require sophisticated software and are simple to implement. A theoretical justification is given for
the proposed methods of team formation. In Section 4, two simulation studies are provided. The first study is based on a theoretical model for golf scores and investigates the performance of all
possible team compositions. The second study is based on a resampling procedure of actual golf scores and investigates common practices involving team composition. In both studies, it is demonstrated
that the proposed methods of team composition lead to competitions that are more fair. We conclude with a short discussion in Section 6.
Although the paper is written in a theoretical style, the results can be condensed into some straightforward non-technical advice that has wide applicablity. For example, in golf, it is common for
foursomes of friends to meet on the first tee and decide to play net best-ball matches, two players versus two players. In this case, how should the teams be formed? The simple answer is that matches
are fairest if the most consistent player is paired with the least consistent player. Friends often know who is consistent and who is not.
There is also a strategic aspect to our results. For example, suppose that in an important competition (e.g. the Ryder Cup or the Presidents Cup) there is a four ball component to the event. Of
course, in such competitions, there is no handicapping involved. However, if the players on a team are of nearly equal ability, then issues of consistency may be taken into account. In some
circumstances, it may be thoughtful to pair a long hitter capable of many birdies (e.g. Bubba Watson) with a shorter hitter who is known for “grinding” (e.g. Jim Furyk). Alternatively, a captain may
want to pair two players who are inconsistent but are “birdie machines” to form a formidable pairing.
2Background material
Although the proposed method for net best-ball team composition is easy to describe and to implement, some background material needs to be introduced. The background material provides the theoretical
structure for the proposal.
2.1Net best-ball competitions
Net best-ball competitions are typically based on teams of size m = 2 or teams of size m = 4. And in such competitions, we denote that there are n ≥ 2 teams.
On the jth hole of the course, j = 1, …, 18, the ith player on a given team has a gross score X[ij] which represents the number of strokes that it took to hole out. Associated with the ith player on
the jth hole is a handicap allowance h[ij] = 0, 1, 2 which is related to the quality of the player. The larger the value of h[ij], the weaker the player. Under this framework, the ith player has the
resultant net score
on hole
. The player’s team then records their
net best-ball score
on the
th hole
and the team’s overall performance is based on their aggregated net best-ball score
The teams in the competition are then ranked according to (3) where the winning team has the lowest value of
. Various procedures exist for breaking ties. For example, with multiple ties, the team having done best on the 18th hole may be determined the winner. If a tie still exists, the criteria may then be
applied to the 17th hole, then the 16th hole, etc, until the tie is broken.
The above format is known as stroke play which is the focus of our investigation. When there are only n = 2 teams, then match play competitions are possible. In match play, T[j] is calculated as in
(2), and the team with the lower value of T[j] is said to have won the jth hole. The team with the greatest number of winning holes is the match play winner. Match play typically involves a
competition between two teams. In this paper, we focus on the stroke play format.
2.2The current handicapping system
Section 10 of the USGA Handicap System Manual (USGA 2016) provides the intricate details involving the calculation of handicap. However, for ease of exposition, we provide a description of the
standard calculation which applies to most golfers.
Consider then a golfer’s most recent 20 rounds of golf where each round is completed on a full 18-hole golf course. The kth round yields the differential D[k] which is obtained by
Dk=(adjusted gross score-course rating)*113/(slope rating).
In (4), the
adjusted gross score
is the player’s actual score reduced according to
equitable stroke control
(ESC) which is a mechanism for limiting high scores on individual holes. The intuition is that handicap reflects potential and should not be distorted by unusually poor results. The
course rating
describes the difficulty of the course from the perspective of a
(expert) golfer. Typically, course ratings are close to the
score of the course where values less than (greater than) par indicates less (more) difficult courses. Course ratings are reported to one decimal place. The
slope rating
describes the difficulty of the course from the perspective of non-scratch golfers where a slope rating less than (greater than) 113 indicates an easier (more difficult) course than average. Slope
ratings are integer-valued and lie in the interval (55, 155). The main takeaway from (4) is that large differentials correspond to poor rounds of golf and small differentials correspond to good
rounds of golf. It is even possible for differentials to be negative which correspond to excellent rounds of golf. Differentials are rounded to the first decimal place.
Given a golfer’s scoring record, the golfer’s handicap index is calculated by taking 96% of the average of the 10 best (lowest) differentials and truncating the result to the first decimal place. In
Section 2.3, we will see that it is instructive to write the handicap index as
denotes the
th order statistic of the differentials. The handicap index is the summary statistic that is used in USGA handicapping; strong golfers have small handicap indices whereas weak golfers have large
handicap indices. It is possible that a golfer holds a handicap index
< 0, and these golfers (mostly professionals) are referred to as
golfers. The maximum allowable handicap index for men is 36.4. For many golfers, the calculation of the handicap index
is viewed as a black-box procedure. Under the RCGA jurisdiction (Golf Canada 2016), handicap index is referred to as
handicap factor
Recognizing that courses are of varying difficulty, the last step for the implementation of handicap involves converting the handicap index to strokes for a particular course. For a course with slope
rating S, the course handicap for a golfer with handicap index I is given by C = I × S/113 rounded to the nearest integer.
In the context of net best-ball competitions, the course handicaps C of the players in the tournament are then used to determine the hole-by-hole handicap allowances h[ij] in (1). It is at this point
where there is some variation in how h[ij] is obtained. According to Section 9-4(bii) of the USGA Handicap System Manual (USGA 2016), the recommended way is to first reduce the individual course
handicaps C by a factor of 90%, rounding to the nearest integer. An adjustment is then made to the reduced course handicaps where the course handicap for a given golfer is set to the offset between
their course handicap and the lowest (best) course handicap in the competition. For example, suppose that the best golfer in the competition has a reduced course handicap C[i[1]] = 3 and that some
other golfer has a reduced course handicap C[i[2]] = 24. Then the two course handicaps are converted to C[i[1]] = 3 -3 = 0 and C[i[2]] = 24 - 3 =21, respectively. Then, we note that the holes on a
golf course are assigned a hole handicap according to a stroke allocation table. The table consists of a permutation of the integers 1 to 18 where it is typically thought that increasing numbers
correspond to decreasing difficulty of the holes. Denote the hole handicap on the jth hole by HDCP[j]. Under the complicated framework described above, h[ij] is determined as follows:
Although (6) may be difficult to digest, the idea is that relative to the strongest player, an individual with
≤ 18 receives a single stroke on the most difficult holes up to his handicap offset. If his handicap offset exceeds 18, then he receives two strokes on the more difficult holes and one stroke on the
remaining holes. For example, if
= 21, the weaker player receives two shots on handicap holes #1, #2 and #3, and one shot on the remaining 15 holes.
Chan, Madras and Puterman (2018) investigated how alternative permutations of HDCP and other innovations affect the fairness of net match play events between two players.
2.3Related literature and ideas
In consultation with the RCGA, Swartz (2009) proposed an alternative handicapping system with the following features:
• • the system retains the well-established concepts of course rating and slope rating
• • the system provides a modified handicap index/factor referred to as the mean which has a clear interpretation in terms of actual golf performance; this is contrasted with the index/factor whose
interpretation is allegedly related to potential
• • the system was developed using probability theory, leading to net competitions that are more fair
The key component of the system developed by Swartz (2009) was that it incorporated variability in handicapping. And in the context of net best-ball tournaments, it is clear that amongst two golfers
with the same handicap index, a highly variable golfer is more valuable to a team than a consistent golfer. For example, the highly variable golfer will obtain more net birdies which contribute
positively to the overall net score of his team. On the other hand, when this highly variable golfer scores net double bogeys, these poor scores are not likely to penalize his team in the best-ball
As an alternative to the handicap index/factor, Swartz (2009) defined two statistics that characterize player performance. These statistics are referred to as the mean μˆ and the spread σˆ , and
their calculation is analogous to (5). Specifically,
where the weights
in (7) and
in (8) provide best linear unbiased estimators (BLUEs) of the mean and the standard deviations of the differentials where the differentials are assumed to be realizations of independent and
identically distributed normal random variables. Whereas (5) is based on 10 order statistics, (7) and (8) are based on 16 order statistics; the rationale was that data is informative and it is
wasteful to discard observations. On the other hand, there is evidence that the largest differentials may not arise from a normal distribution as the true underlying distribution may be positively
skewed (
Siegbahn and Hearn 2010
For the purposes of this paper, the spread σˆ in (8) plays a primary role and we record the weights q[i] in Table 1. Alternative weights are recorded in Swartz (2009) when a golfer has played fewer
than 20 complete rounds. When the spread calculation σˆ falls outside of the interval (1.5,8.0), it is set equal to the corresponding endpoint.
Table 1
q[1] q[2] q[3] q[4] q[5] q[6] q[7] q[8]
–0.1511 –0.1006 –0.0792 –0.0632 –0.0500 –0.0384 –0.0277 –0.0178
q[9] q[10] q[11] q[12] q[13] q[14] q[15] q[16]
–0.0082 0.0011 0.0103 0.0196 0.0291 0.0389 0.0492 0.3880
A point that is worth emphasizing is that the calculation of σˆ in (8) is simple and is directly analogous to the calculation of (5) which is part of the current handicapping system. In Section 3, we
assume that the values σˆ are available for each golfer in the net best-ball competition. Moreover, the values σˆ are the only values that are needed to form teams according to our proposal. Thus,
teams are formed based on the basis of individual performance variability σˆ , and this is the main message of Section 2.
3Team composition
Suppose that the number of golfers in a net best-ball tournament is an even number. The task with teams of size m = 2 is to pair players in a fair manner. Following (1), we let Y[ij] denote the net
score of golfer i on hole j. Although golf scores are discrete, we assume
The essence of handicapping is to create fair matches. Therefore, we make the assumption that all golfers have the same mean net score, i.e. μ[ij] = μ[j]. In addition, we are going to make the
clearly false assumptions that μ[j] = μ and τ[ij] = τ[i], that the mean net scores and the net score variances are the same on all holes. However, this assumption is not problematic as the same
analysis can be undertaken on a hole-by-hole basis leading to the same proposal for team compositions. Without loss of generality, we also set μ = 0 as it is only comparative golf scores that are
relevant. Accordingly, we simplify (9) whereby the net score for golfer i on each hole is given by
With a two-man team consisting of players i[1] and i[2], the quantity of interest is the distribution of the net best-ball result
It is shown by Nadarajah and Kotz (2008) that
is nearly normal if
do not vary greatly. Using (10), assuming that
do not vary greatly and assuming the independence between
, the moment expressions (11) and (12) from Nadarajah and Kotz (2008) lead to the approximate distribution
If we pair golfers such that every pair has the same probability distribution, then each pair has the same probability of finishing in any position in a tournament. Therefore, if the i[1]’s and i[2]
’s are paired such that τi12+τi22=c for some constant c, then the objective is achieved as each distribution in (11) is Normal(-c1/2/2π,c(π-1)/(2π)) .
Therefore, we have a prescription for pairing golfers in two-man net best-ball tournaments. We use σˆ in (8) as a proxy for τ, and we simply match the golfer with the highest σˆ with the golfer with
the lowest σˆ , we match the golfer with the second highest σˆ with the golfer with the second lowest σˆ , and so on. Given the σˆ values, the forming of two-man teams is an easy task for the golf
In the case of four-man net best-ball tournaments, the investigation of team composition ought to consider the distribution of Z[ijkl] = min(Y[i], Y[j], Y[k], Y[l]). However, the distribution theory
for Z[ijkl] appears intractable and we therefore propose an expedient approach. Our heuristic begins with the optimal two-man teams described above, and we then combine pairs of the two-man teams
based on the mean values in (11). Our procedure ranks the two-man teams according to σˆi12+σˆi22 . We then match the two-man team with the highest σˆi12+σˆi22 with the two-man team with the lowest
σˆi12+σˆi22 , and so on. Again, given the σˆ values, this is a simple task for the golf director.
There may be alternative approaches for forming four-man teams. For example, one could stratify the golfers into four groups according to increasing σˆi and then form a four-man team by randomly
selecting a golfer from each group. In the simulation study of Section 4.2, it turns out that a slight variation of our approach (which we refer to as WCS[Z]) gives even better results.
3.1The normality assumption
Whereas the normality of golf scores is frequently assumed in the literature (e.g. Pollock (1977), Scheid (1990), Berry (2010)), these papers assume normality on 18-hole scores. However, in (10),
normality is assumed on individual holes. This strong assumption does not strike us as problematic for several reasons. First, the development that follows (10) does not utilize the full
distributional properties of the normal. Rather, only the first two moments are used in determining team composition. Second, instead of defining Y[i] as the net score of the ith golfer, we could
have alternatively defined Y[i] as the latent net skill or performance of the ith golfer. Net skill/performance is a continuous variable that is clearly concave and better resembles normality.
Although not as clean, such a formulation would have led to the same approach for team composition. We can therefore think of golf scores as a discretized version of skill/performance. But the main
point is that the normality argument is provided only as a heuristic for forming teams, and we use actual golf data and simulation to establish that the approach improves upon traditional practice.
In Section 4, we supplement the theoretical underpinnings with simulation studies.
4Simulation studies
A rationale for the proposed team composition was provided using statistical theory in Section 3. However, given that the statistical theory was based on some approximations, it is good to supplement
the theory via simulation. We first generate golf scores from a theoretical model for scoring. We then use a resampling scheme to generate golf scores from a dataset of actual golf scores.
An aspect of our evaluation procedure which differs from the literature concerns our definition of fairness. The typical definition of a fair tournament involving n teams is that each team wins a
tournament with probability 1/n (Pavlikov et al. 2014 and Benincasa et al. 2017). Imagine a pathological example involving four teams where a particular team ends up in first, second, third and
fourth place 25%, 0%, 0% and 75% of the time. By strictly considering win probabilities, the competition is fair for this team. However, it is not fair in the sense that 3/4 of the time, the team
will end up in last place. This would be problematic if there is prize money for first place, second place, third place and fourth place. This is a motivating example for our matrix definition of
fairness where a fair tournament involving n teams is one where for each team
Prob(finishing in jth place)=1/n,j=1,…,n.
4.1Simulation via a theoretical scoring model
In Table 2, we provide probability distributions for 8 fictitious golfers corresponding to their performance on each hole. The distributions are not entirely realistic as we only permit the four net
scores of birdie (-1 relative to par), par, bogey (+1 relative to par) and double-bogey (+2 relative to par). However, the probability distributions have been constructed such that each golfer has
the same mean net score which is consistent with the desiderata of the handicapping system. The most noteworthy aspect of Table 2 is that the performance of the golfers is variable with increasing
standard deviations as we go down the rows of the table. Therefore, golfer 1 is the most consistent and golfer 8 is the most variable.
Table 2
Golfer Net Score Mean SD
Probability Distribution
–1 0 1 2
1 0.02 0.96 0.02 0.00 0.00 0.200
2 0.06 0.88 0.06 0.00 0.00 0.346
3 0.10 0.80 0.10 0.00 0.00 0.447
4 0.14 0.72 0.14 0.00 0.00 0.529
5 0.18 0.64 0.18 0.00 0.00 0.600
6 0.20 0.61 0.18 0.01 0.00 0.648
7 0.26 0.51 0.20 0.03 0.00 0.762
8 0.32 0.41 0.22 0.05 0.00 0.860
Imagine that these 8 golfers are competing in teams of size m = 2. Therefore, the number of possible tournament constructions is (28)(26)(24)/4!=105 . Consider one such tournament construction. For
each team, we first generate 18 holes for each golfer in the pair according to their probability distributions in Table 2. We then determine the team’s aggregate net best-ball score T according to
(3). For this particular round of 18 holes and for the particular tournament construction, we determine the finishing order of the four teams. We repeat the simulation procedure for 1,000 tournaments
to obtain frequency tables for the finishing positions. Note that if a tie exists for a particular round, we randomly break ties.
According to our proposed team composition developed in Section 3, the optimal tournament construction in terms of fairness is 1&8, 2&7, 3&6 and 4&5. We denote this tournament construction as WCS (an
acronym based on the authors’ surnames). We are interested in how WCS performs compared to the other 104 potential tournament constructions. Table 3 provides the percentage of time in the WCS
simulation corresponding to the four finishing positions for each of the four teams. If the competition were completely fair, the table entries would all be equal (i.e., 25.0%). For WCS, we observe
that Team 1&8 is clearly the strongest team finishing in the top two positions nearly 66% of the time.
Table 3
1&8 2&7 3&6 4&5
Finish 1st 37.4 24.7 17.7 20.2
Finish 2nd 28.5 25.4 20.6 25.5
Finish 3rd 21.5 27.0 27.8 23.7
Finish 4th 12.6 22.9 33.9 30.6
However, whether WCS is meritorious can only be determined in the context of the other potential tournament constructions. And each tournament construction has a corresponding Table 3 resulting from
the simulation procedure. For each tournament construction, it is natural to assess fairness via the Chi-Square test statistic
= 250 and the frequency
is the (
)th entry obtained from its corresponding
Table 3
matrix. Under the null hypothesis that the tournament construction is fair,
has a Chi-Square distribution on 9 degrees of freedom. Large values of
provide evidence against the null hypothesis.
Table 4 lists the best performing and worst performing tournament constructions based on the Chi-Square test statistic (12). Although none of the team constructions are fair (i.e., they all have
p-values that are statistically significant), we observe that our proposed team formation WCS is the best possible tournament construction. It is the best construction that can be achieved given the
characteristics of the 8 golfers and the rules of net best-ball tournaments. We also note that the best five tournament constructions are similar in the sense that golfers with high variability are
paired with ones with low variability.
Table 4
Ranking Team A Team B Team C Team D Chi-Square test statistic
1 (WCS) 1 &8 2 &7 3 &6 4 &5 221.4
2 1 &8 2 &7 3 &5 4 &6 270.4
3 1 &7 2 &8 3 &6 4 &5 371.2
4 1 &8 2 &6 3 &7 4 &5 420.8
5 1 &7 2 &8 3 &5 4 &6 433.0
... ... ... ... ... ...
101 1 &2 3 &6 4 &5 7 &8 3705.0
102 1 &2 3 &4 5 &7 6 &8 3738.7
103 1 &2 3 &4 5 &8 6 &7 3851.5
104 1 &2 3 &5 4 &6 7 &8 3919.3
105 1 &2 3 &4 5 &6 7 &8 4047.0
4.2Simulation via actual golf scores
This simulation study is based on a dataset obtained from Coloniale Golf Club in Beaumont, Alberta collected over the years 1996 through 1999.
After restricting scores to male golfers who have played at least 40 rounds, we are left with a dataset consisting of 10,470 rounds collected on 80 golfers. Therefore, the average number of rounds
played per golfer in the restricted dataset is approximately 131. In Figure 1, we provide a histogram and density plot of the handicap differentials corresponding to the 10,470 rounds. The mean
handicap differential is approximately 13 and is marked by the dashed vertical line. The data correspond to a large pool of golfers with varying skill levels. It should therefore have the required
generality for testing our proposed method of team formation in net best-ball tournaments.
Our simulation procedure is based on a resampling scheme. In this exercise, suppose that we investigate a particular team construction heuristic where we form n = 20 teams of size m = 4. For each
golfer, our first step involves randomly selecting 20 of his rounds of golf. These rounds will form his 20 differentials from which his handicap index I in (5) and his spread statistic σˆ in (8) can
be calculated. These two statistics are sufficient for determining all of the common methods of team composition including our proposed method. Therefore, based on the particular team construction
heuristic, the 20 teams of four players are identified. For each of these 80 golfers, we next generate one of their remaining rounds of golf for which we have hole-by-hole scores. In golf, detailed
hole-by-hole data is rare and is a feature of the Coloniale dataset. Using the generated round of golf for each of the 80 golfers, each team’s aggregate net best-ball score T can be calculated
according to (3), and we obtain the finishing order of the 20 teams composed by the particular team construction heuristic. This resampling procedure is repeated over 40,000 hypothetical tournaments.
Frequency tables are obtained as in Table 3 where finishing order corresponds to the rows and team compositions correspond to the columns. In this simulation exercise we therefore have matrices of
dimension 20 × 20.
We now compare two common team constructions against our proposed method WCS and a variation of WCS. Recall from Section 3 that our method of team formation first ranks golfers according to σˆ , and
then pairs golfers 1&80, 2&79, and so on. Then, these 40 pairs are ranked according to σˆi12+σˆi22 where i[1] and i[2] are in the same pair. We then pair the pairs as before with high values of
σˆi12+σˆi22 matched with low values. This algorithm determines the 4-man teams.
We refer to the most common method of team formation as “High-Low” where High-Low is very similar in construction to WCS. The only difference is that orderings are based on the handicap index I in
(5) rather than spread statistic σˆ in (8). The High-Low heuristic is that strong golfers are matched with weak golfers in the first pairing, and then strong teams (based on cumulative handicap
indices) are matched with weak teams in the subsequent pairing.
We refer to the third method of team formation as “Zigzag” which is less common than High-Low. Pavlikov, Hearn and Uryasev (2014) provide an illustrative example of Zigzag. For simplicity, consider
the formation of 16 golfers into four teams of four players as shown in Table 5. For example, Team 1 consists of golfers 1, 8, 9 and 16. The intuition behind Zigzag is that the summation of handicap
indices should be nearly constant across teams.
Table 5
Golfers ordered by handicap index from the lowest to highest
Team 1 x x x x
Team 2 x x x x
Team 3 x x x x
Team 4 x x x x
The fourth method which we refer to as “WCS[Z]” is a “Zigzag” variation of WCS. In WCS[Z], we carry out the Zigzag team formation procedure but instead of using handicap indices, we use the spread
statistic σˆ .
In Table 6, we provide the results of the comparison using the simulated frequency tables based on High-Low, Zigzag, WCS and WCS[Z]. In this exercise, the Chi-Square statistic (12) is used to assess
the four methods of team formation where the summations in (12) extend over the 20 × 20 cells and E[ij] = 2, 000. We observe that WCS[Z] outperforms the other three methods in terms of giving the
lowest Chi-Square statistic. The High-Low method is clearly the worst of the three methods in terms of fairness.
Table 6
Method χ˜2
High-Low 4049.09
Zigzag 2136.88
WCS 2034.99
WCS[Z] 1742.38
Another way of assessing the four methods is via heatmaps. In Figure 2, we produce heatmaps corresponding to the simulated frequency tables based on High-Low, Zigzag, WCS and WCS[Z]. It is evident
that the new approaches (WCS and WCS[Z]) have more constant coloring; this indicates that they are fairer methods of team composition than both High-Low and Zigzag.
In most sports, it is only reasonable for players of comparable abilities to compete. For example, it is difficult to imagine any basketball related competition where an average person is matched up
against Lebron James.
However, in golf, a comprehensive handicap system has been devised to allow players of different abilities to compete fairly against one another. Unfortunately, the handicap system can be far from
fair in particular competitions, and there are many types of competitions in golf. For example, golf can be played according to match play or stroke play, golf can be played 1v1, 2v2 or in tournament
settings, and golf can be played in various formats such as best-ball, foursomes, aggregate, scrambles, etc.
In this paper, we have devised simple proposals where teams of sizes two and four are formed in net best-ball competitions. Using both statistical theory and simulation studies, we have demonstrated
that the proposals are more fair than standard procedures for team composition.
One golfing format which is rarely used is a “worst-ball” competition where in two-man teams (for example), the higher of the two scores is the recorded team score. Following the development of the
distribution of the minimum in (11) and using the moment expressions in (9) and (10) from Nadarajah and Kotz (2008), the distribution of the maximum is approximately Normal(12π(τi12+τi22)1/2(π-12π)
(τi12+τi22)) . Therefore, as previously argued, the prescription for optimal pairing golfers would be the same as before where the most variable golfer is matched with the least variable golfer, and
so on.
The key component of our proposal is the recognition of variability in golf performance. Perhaps the variability aspect can be introduced to improve fairness in other types of golf competitions.
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20 Yun,H. , 2011c History of handicapping, part III: USGA leads the way. Available at http://www.usga.org/content/usga/home-page/articles/2011/10/
history-of-handicapping-part-iii-usga-leads-the-way-21474843686.html (Accessed: 21 August 2017).
21 Yun,H. , 2011d History of handicapping, part IV: The rise of the slope system. Available at http://www.usga.org/content/usga/home-page/articles/2011/10/
history-of-handicapping-part-iv-the-rise-of-the-slope-system-21474843751.html (Accessed: 21 August 2017). | {"url":"https://content.iospress.com/articles/journal-of-sports-analytics/jsa190311","timestamp":"2024-11-14T08:39:27Z","content_type":"text/html","content_length":"141561","record_id":"<urn:uuid:213aec9b-bbba-4f2e-9958-a4b4fbd8c1c5>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00619.warc.gz"} |
The Omnitruncated 120-cell
The omnitruncated 120-cell, also known as the omnitruncated 600-cell, is the largest member in the 120-cell/600-cell family of uniform polychora. It has 14400 vertices, 28800 edges, 17040 polygons
(10800 squares, 4800 hexagons, and 1440 decagons), and 2640 cells (120 great rhombicosidodecahedra, 720 decagonal prisms, 1200 hexagonal prisms, and 600 truncated octahedra).
The omnitruncated 120-cell may be constructed by radially expanding the great rhombicosidodecahedral cells of the cantitruncated 120-cell outwards, and filling the gaps with decagonal prisms,
hexagonal prisms, and truncated octahedra.
We shall explore the structure of the omnitruncated 120-cell by its parallel projections into 3D, centered on one of its great rhombicosidodecahedral cells.
First Layer
The above image shows the nearest great rhombicosidodecahedron to the 4D viewpoint. For the sake of clarity, we have rendered all the other cells in a light transparent color.
The decagonal faces of this nearest cell are joined to 12 decagonal prisms, as shown in the next image:
The square faces of the nearest cell are joined to 30 hexagonal prisms, shown below in blue:
Finally, the hexagonal faces of the nearest cell are joined to 20 truncated octahedra, shown next in green:
Second Layer
On top of the truncated octahedra from the previous layer are another 20 hexagonal prisms:
Fitting into the valleys between these hexagonal prisms are 30 more decagonal prisms:
Capping the hexagonal prisms and straddling these decagonal prisms are another 20 truncated octahedra:
The bowl-shaped depressions that are becoming obvious are the seats of 12 more great rhombicosidodecahedral cells:
Third Layer
The pattern of alternating hexagonal prisms and truncated octahedra continues from the previous layer between the great rhombicosidodecahedral cells last seen. The following image shows 60 more
hexagonal prisms:
These hexagonal prisms are capped by another 30 truncated octahedra:
The little inlets between these alternating cells are where 60 more decagonal prisms fit:
The alternating cells actually encircle these decagonal prisms; for example, there are 60 more hexagonal prisms that fit between them:
The other side of these prisms are, of course, attached to more truncated octahedra, another 60 of them:
These truncated octahedra converge on 12 more decagonal prisms:
The truncated octahedra are also bridged by 60 more hexagonal prisms:
The bowl-shaped depressions that are starting to form from these alternating cells are where 20 more great rhombicosidodecahedra are joined:
Fourth Layer
The great rhombicosidodecahedra from the previous layer are linked to each other by 30 decagonal prisms:
On either side of these prisms, 60 more hexagonal prisms continue the pattern of alternating hexagonal prisms and truncated octahedra:
It may not have been obvious before, but these hexagonal prisms also form an alternating pattern with the decagonal prisms, 60 more of which are shown below:
The truncated octahedra also alternate with these decagonal prisms, and the three types of cells form an interlocking network. The next image shows 60 of these truncated octahedra in alternating
formation with the decagonal prisms:
These circles of truncated octahedra are linked to each other via 30 more hexagonal prisms:
The obvious bowl-shaped depressions are where another 12 great rhombicosidodecahedra are fitted:
Fifth Layer
Of course, at the base of these great rhombicosidodecahedra there are also more hexagonal prisms emanating from the truncated octahedra within their five-fold circles, for a total of another 120
hexagonal prisms:
These hexagonal prisms converge on another 60 truncated octahedra:
Alternating with these truncated octahedra are another 60 decagonal prisms:
These decagonal prisms, in turn, alternate with yet another 60 hexagonal prisms:
On the other side of the truncated octahedra are some obvious gaps where 60 more decagonal prisms fit:
Straddling these decagonal prisms and touching the truncated octahedra are another 60 hexagonal prisms, the last before we reach the “equator” of the omnitruncated 120-cell:
Finally, these hexagonal prisms converge on 20 truncated octahedra:
These are all the cells that lie on the near side of the omnitruncated 120-cell. Past this point, we reach the limb, or “equator”, of the polytope.
The Equator
Now we come to the equator of the omnitruncated 120-cell. There are 30 great rhombicosidodecahedra on the equator:
For clarity, we have omitted the other cells that we have seen so far. These cells appear flattened into irregular dodecagons; this is because they are being seen at a 90° angle from the 4D
viewpoint. In 4D, they are perfectly uniform great rhombicosidodecahedra.
There are 20 hexagonal prisms where each three of these cells meet:
These hexagonal prisms have been foreshortened into hexagons because of the 90° view angle.
They aren't the only hexagonal prisms on the equator; there are 60 others that touch the great rhombicosidodecahedra:
These hexagonal prisms have a different orientation from the previous ones, hence they appear foreshortened into rectangles instead of hexagons. They alternate with 60 truncated octahedra:
As with the other equatorial cells, these truncated octahedra appear flattened into hexagons because they lie at a 90° angle to the 4D viewpoint. In 4D, they are perfectly uniform truncated
These hexagonal prisms and truncated octahedra meet at 12 decagonal prisms:
These decagonal prisms appear foreshortened into decagons due to their 90° angle with the 4D viewpoint. They are not the only decagonal prisms on the equator; the remaining rectangular gaps are
filled by another 60 decagonal prisms:
These decagonal prisms are in a different orientation from the previous ones; hence, they appear foreshortened into rectangles instead of decagons.
These are all the cells that lie on the equator of the omnitruncated 120-cell. Past this point, we reach the far side of the polytope, where the arrangement of cells exactly mirrors that of the near
side that we have seen, repeating in reverse order until we reach the antipodal great rhombicosidodecahedron.
The following table shows the summary of the cell counts in each layer of the omnitruncated 120-cell:
Region Layer
Near side 3 20 60 + 12 = 72 60 + 60 + 60 = 180 30 + 60 = 90
4 12 30 + 60 = 90 60 + 30 = 90 60
5 0 60 + 60 = 120 120 + 60 + 60 = 240 60 + 20 = 80
Subtotal 45 324 560 270
Equator 30 12 + 60 = 72 20 + 60 = 80 60
Far side 3 20 72 180 90
Subtotal 45 324 560 270
Grand total 120 720 1200 600
The coordinates of an origin-centered omnitruncated 120-cell with edge length 2 are all permutations of coordinates and changes of sign of:
• (1, 1, 1+6φ, 7+10φ) • (2φ^2, 4+2φ, 4φ^3, 4φ^3)
• (1, 1, 3+8φ, 7+8φ) • (3+2φ, 3+2φ, 3+8φ, φ^6)
• (1, 1, 1+4φ, 5+12φ) • (1+4φ, 3+4φ, 3+8φ, 3+8φ)
• (1, 3, φ^6, φ^6) • (2φ^3, 2φ^3, 2+8φ, 4φ^3)
• (2, 2, 4φ^3, 6+8φ)
along with all even permutations of coordinate and all changes of sign of:
• (1, 5φ^2, 4+7φ, 6φ^2)
• (1, 2φ^4, 5+7φ, 6+5φ) • (2+φ, 4φ, 7+10φ, 3φ^2)
• (1, 2, 1+5φ, 6+11φ) • (2+φ, 4+2φ, φ^6, 5+7φ)
• (1, φ^2, 6+9φ, 2+8φ) • (2+φ, 2φ^3, 7+8φ, 5φ^2)
• (1, φ^2, 8+9φ, 2+6φ) • (φ^3, 4+5φ, 2+8φ, 5+7φ)
• (1, 2φ, 7+9φ, 2+7φ) • (φ^3, 5φ^2, 2+7φ, 4φ^3)
• (1, φ^3, 5+12φ, 3+2φ) • (3+φ, 3φ, 7+10φ, 2φ^3)
• (1, 3+φ, 4+9φ, 4φ^3) • (3+φ, 3+2φ, 6+8φ, 4+7φ)
• (1, 1+3φ, 8+9φ, 4φ^2) • (3+φ, φ^4, 7+8φ, 2φ^4)
• (1, 1+3φ, 6+11φ, 4+2φ) • (3φ, 4φ^2, 3+8φ, 5+7φ)
• (1, 4φ, 7+9φ, 4+5φ) • (3φ, 2+6φ, φ^6, 5φ^2)
• (1, 3φ^2, 4+9φ, 6φ^2) • (2φ^2, 1+4φ, 8+9φ, 3φ^2)
• (1, 2φ^3, 5+9φ, 6+5φ) • (2φ^2, 1+5φ, 7+8φ, 4+5φ)
• (2, φ^2, 5+12φ, φ^4) • (1+3φ, 1+6φ, 6+8φ, 4+5φ)
• (2, 2+φ, 5+9φ, 3+8φ) • (1+3φ, 3φ^3, 2+8φ, 4+7φ)
• (2, φ^3, 8+9φ, φ^5) • (1+3φ, 2+7φ, 3+8φ, 2φ^4)
• (2, 3φ, 7+9φ, 3φ^3) • (1+3φ, 3+2φ, 2φ^3, 8+9φ)
• (2, 1+3φ, 7+10φ, 4+3φ) • (1+3φ, 4+3φ, 3+8φ, 4φ^3)
• (2, 3+2φ, 4+9φ, 5+7φ) • (3+2φ, 1+4φ, 7+8φ, 3φ^3)
• (2, 1+4φ, 6+9φ, 5φ^2) • (3+2φ, 2φ^3, 7+9φ, 4+3φ)
• (φ^2, 4+5φ, 3+8φ, 6φ^2) • (3+2φ, 1+5φ, 6+9φ, 4φ^2)
• (φ^2, 3φ^3, 4φ^3, 6+5φ) • (4φ, φ^5, 3+8φ, 4+7φ)
• (φ^2, 3, 2φ^3, 6+11φ) • (4φ, 2+6φ, 4φ^3, 2φ^4)
• (φ^2, 3φ, 5+12φ, 2φ^2) • (φ^4, 4φ^2, 1+6φ, 5+9φ)
• (φ^2, 3+2φ, 4φ, 6+11φ) • (φ^4, 4+2φ, 3+4φ, 7+9φ)
• (φ^2, 4+3φ, φ^6, 6φ^2) • (φ^4, 3φ^2, 2+8φ, φ^6)
• (φ^2, 3+4φ, 6+8φ, 6+5φ) • (4+2φ, 1+4φ, 6+9φ, φ^5)
• (3, φ^3, 7+10φ, 3+4φ) • (1+4φ, 1+6φ, φ^6, 3φ^3)
• (3, 2φ^2, 5+9φ, 4+7φ) • (1+4φ, 3φ^2, 2+7φ, 6+8φ)
• (3, 1+3φ, 6+9φ, 2φ^4) • (1+4φ, 4+3φ, 2+6φ, 5+9φ)
• (2φ, 4φ^2, 4φ^3, 6φ^2) • (2φ^3, 1+6φ, 4+9φ, φ^5)
• (2φ, φ^5, φ^6, 6+5φ) • (2φ^3, 1+5φ, φ^6, 2+7φ)
• (2φ, 2+φ, 1+3φ, 5+12φ) • (1+5φ, 3+4φ, 2+6φ, 4+9φ)
• (2φ, 3+φ, 1+4φ, 6+11φ)
where φ=(1+√5)/2 is the Golden Ratio. | {"url":"http://www.qfbox.info/4d/omni120cell","timestamp":"2024-11-07T21:44:15Z","content_type":"text/html","content_length":"26051","record_id":"<urn:uuid:00f8cfb1-21d0-4237-905f-e2bafdcd281f>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00330.warc.gz"} |
ALEKS Placement, Preparation & Learning | Mathematics | ESU
Congratulations on being accepted to East Stroudsburg University (ESU)!
We are excited to have you join our community. Everyone on campus wants you to succeed. A first step in that process is making sure you are registered for the correct classes for your major and
background. One of the most challenging issues is “which math class should I take?” ESU uses ALEKS to help answer that question.
ALEKS is a web-based program that will ask you math questions. It will adjust the difficulty of the questions as it “learns” about your mathematical ability. Early on, you may get some questions that
are too hard for you. Don’t panic, it means you got the previous question(s) right and the program is seeing how you perform on harder questions.
At the end you will receive two types of information:
(1) A score out of 100 that will indicate which math class would be most suitable for you and (2) a pie chart that will indicate the types of questions you answered on the assessment. There will also
be a recommended Prep and Learning Module you can complete to help prepare you for your college class or to prepare you to retake the assessment to improve your score and place into a different math
Approach this assessment thoughtfully. Choose a comfortable environment where you can really focus and concentrate. Make the ALEKS assessment a priority and give it your best effort. It's important
not to overlook your existing knowledge – we wouldn't want you spending unnecessary time and money on material you're already familiar with. Similarly, resist the temptation to reach out for help or
use unauthorized resources during the assessment. We want to ensure you're placed in a class that matches your readiness. Remember, having to retake classes can be both frustrating and costly.
The ALEKS assessment will include about 30 open-ended questions. You will have 24 hours to complete the assessment. Most students spend 60 – 90 minutes on the assessment. We recommend finding a quiet
place to take the assessment and giving yourself two hours to work on it.
You will need only scrap paper and a pencil or pen. The program has a built-in calculator for questions that need a calculator. You should not use a calculator other than the one provided by ALEKS.
When no calculator is provided, you should answer the question without using a calculator.
Got your score?
Use the table below to see which course(s) your ALEKS score shows you are ready to attempt. Note that most courses don’t have an upper limit. Any student who meets the minimum threshold can take
those courses. The courses with upper limits are designed for students who might benefit from extra support in their math classes.
Course number and name Minimum Score Maximum Score if applicable
MATH 090 Intermediate Algebra 0 30
MATH 100 Numbers Sets and Structures 30
MATH 101 Excursions in Mathematics 30
MATH 105 Problem Solving for Pre-K
to Grade 8 Education Majors 30
(education majors only)
MATH 110 General Statistics 46
MATH 111 General Statistics with 22 45
Introductory Mathematics
MATH 129 Applied Algebraic Methods 22 45
with Foundational Mathematics
MATH 130 Applied Algebraic Methods 46
MATH 135 Pre-calculus 61
MATH 140 Calculus I 76
Want more Information?
Contact Us
For more information on the programs offered in the Mathematics department, please contact cgetz@esu.edu.
Contact Information
Campus Address
Science & Technology 118
(570) 422-3899 (Fax)
Title of Department Leader
Interim Department Chair
N. Paul Shembari | {"url":"https://www.esu.edu/mathematics/aleks/index.cfm","timestamp":"2024-11-14T23:54:49Z","content_type":"text/html","content_length":"48901","record_id":"<urn:uuid:035224a2-6e34-4617-9567-027ec12863d9>","cc-path":"CC-MAIN-2024-46/segments/1730477397531.96/warc/CC-MAIN-20241114225955-20241115015955-00393.warc.gz"} |
Degree Course in
PHYSICS LABORATORY I A - L
Academic Year 2017/2018
- 1° Year
Teaching Staff: Silvio CHERUBINI Credit Value:
Scientific field:
FIS/01 - Experimental physics
Taught classes:
42 hours
90 hours
Term / Semester:
Learning Objectives
This is the first class that teaches the students Laboratory techniques and Statistics after they enroll in the undergraduate Physics course.
The aim of the course is to provide students with the basics for learning the experimental method and experimental data analysis techniques. It is divided into frontal lessons (42 hours) and
laboratory exercises (90 hours).
At the end of the course the successful student will be able to perform measurements of physical quantitites and report the results in a scientifically correct way.
Detailed Course Content
The course is accredited by 12 CFUs, corresponding to 132 hours of classroom and laboratory lectures. In particular, 42 hours of classroom lessons and 90 hours of guided laboratory experiences are
Experimental data analysis (22 hours).
- The Scientific Method. - Measurement of physical quantities. Operational determination of a physical quantity and its measurement. Fundamental and derived quantities. Units of measure and systems
of units of measure: the international system and CGS system. - Presentation of Significant Measures and Figures. Dimensional analysis of a formula and verification of its correctness -
Characteristics of a measuring instrument - Errors and / or uncertainties. Systematic and random errors. - Total error in measurements, relative error, precision degree. - Single and / or multiple
measurements. The best estimate of error (fashion, median and average) - Scarcity, mean square deviation, standard population, sample and mean deviation - Error propagation. - Representation of data:
tables, histograms and graphs. - Histograms: from discrete to limit distribution. - Gauss distribution as a limit distribution for ff measurements and not random errors. - Measurement of a magnitude
fl uenced by random phenomena and estimation of expected value. - Measurement in probabilistic terms. probability theory.- The criterion of maximum likelihood.- Probability distributions: Gaussian,
Binomial, Poisson.- Chi-quadro test.- Graphics and functional relations- Description of laboratory experiences
Statistics (20 hours)
Random events, random variables - classical, frequent and axiomatic probability of probability - total probability, probability conditional, composite probability - Bayes theorem - statistical
convergence - statistical independence and covariance - statistical population - sampling - large number law - mathematical hope for variables discrete and continuous randoms - probability density -
moments - generating functions of the moments and characteristic function - Bernoulli distribution • Poisson distribution • Gauss distribution • Student distribution • distribution χ2 • central limit
theorem • Statistical indices and their sample estimates
Laboratory Experiences (90 Hours)
a) Dynamics of the material point and the rigid body
Length Measurements: Nio, Caliber, Palmer • Sloping Plane • Fletcher Device • Atwood Machine • Simple Pendulum • Composite Pendulum, Kater Reversible Pendulum • Spherical Pendulum, Spherometer •
Arched Pendulum • Twist Pendulum • Maxwell Needle • Springs • Inertia moment of a flywheel • Kinetic rotation energy.
b) Mechanism of deformable continuous
Picnometer • Mohr-Westphal scale • Ostwald viscometer - Stalagmometer • Tensiometer • Venturi tube • Sedimentation.
c) Thermodynamics
Regnault mixing calorimeter • Heat propagation in a homogeneous bar • -Equipment of perfect gas status • Desormes and Clement's experience • Kundt tube
d) Verify the probability distribution
Galton Machine - Verification of probability distribution of a sample size of standard industrial production objects.
Google Traduttore per le aziende:Translator ToolkitTraduttore di siti web
Informazioni su Google TraduttoreCommunityPer cellulari | {"url":"https://www.dfa.unict.it/courses/l-30/course-units?cod=7465","timestamp":"2024-11-04T07:19:55Z","content_type":"text/html","content_length":"27936","record_id":"<urn:uuid:d31a6267-a0e2-42f4-90ef-3a2ddf0df0bf>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00770.warc.gz"} |
Belfast, Aug-Sep 2010
Saturday 28 August
Still dark when I left the house, though the city was not asleep; a couple walking down the road talking loudly; drivers chatting in Dell Cars; cleaners in a fast food place.
The bus came on time and was not crowded, but picked up a lot of people on the way. I sat upstairs at the front for the view; after a while, a well-dressed young man sat next to me, and proceeded to
fall asleep and loll over me. When the other front seat came free, he moved there.
Not long to wait for the train. It started on time but I had been put in one of the seats with no view and no room in the luggage rack, and travelled backwards to Glasgow. Also, sad to say, the
coffee machine was broken and so my first cup of coffee came rather late.
As we pulled out of Euston, the sun rose, and the carriage was filled with orange light.
By the end of the journey, I was quite sleepy; but no chance of a nap, the carriage was filled with noisy children.
We were on time at Glasgow, despite a ten-minute delay at Carlisle. I bought lunch and a paper, and waited for the platform for the Stranraer train to be announced. This happened rather late, and the
train was fairly crowded; fortunately I had a reservation. We pulled out on time for the two-and-a-quarter hour journey.
The rain came on to spatter, and Ailsa Craig looked decidedly rainwashed. It is a pretty train journey, but I described it last year and won't do so again. I was near the front, and saw the driver
handing the token (a large ring) to the signalman at the end of the downhill stretch. There was a lot of Himalayan balsam in flower by the track. Two girls went to the toilet together (what do they
do?), but forgot to lock the door; we had high-pitched screams when a man burst in on them.
Getting onto the ship was a slow process, since the two people checking tickets and handing out boarding cards seemed not to understand what they were doing. Eventually I was through, and a long walk
down dark winding corridors brought me to the car deck, from where narrow stairs took me to the passenger deck. I was on in good time, and we were away heading out through the sea loch. Out of the
heads, the open sea was a bit rough, and the ship rolled a bit; but soon enough we were in the calm of Belfast Lough.
My bag came quickly and I was out. I had a taxi to myself; the driver took me by a roundabout route so it was relatively expensive. But no problems with check-in this time, and I know that they think
"internet access" means "web access", so I won't even try to get proper internet access. Anyway, the web access does at least work.
At 7 I went out to meet Natalia. She and her husband Stanislav and son Sasha were already there. We set off on foot. The first restaurant they tried was full, so we went to another, "Deanes at
Queens", run by the University. We had a good meal and a very good talk. Stanislav wanted an example of an abelian topological group with no non-trivial proper closed subgroups. I suggested the
abelian group structures on the Urysohn space constructed by Anatoly Vershik and me. (They at least have the property that no proper closed subgroup contains any power of the generating isometry.) I
played with Sasha a bit until he started getting a bit manic, so we left.
They walked me back to Elms Village, where I went straight to bed and slept soundly.
Sunday 29 August
With the prospect of an empty day in Belfast, I was in no hurry to get up, so lay in bed and read yesterday's paper.
Because of refurbishment of the student centre, I have to go for breakfast to a small café in a University building about ten minutes walk from my room. It was drizzling when I set out, but soon
turned to serious rain. Fortunately I was passing a bus shelter, so waited out the worst of the rain before continuing on my way.
The road in which the breakfast place is located has no sign, so I overshot and had to backtrack. When I got there, it was pleasant. Breakfast is standard enough but good: juice, cereal, yoghurt,
cooked breakfast (bacon, sausage, beans, scrambled egg, hash browns, toasted soda bread), and decent coffee. The only glitch came when the waiter asked me if I was vegetarian, and I mis-heard him and
thought he asked if I was a visitor.
Back in my room, the prospect of sightseeing on a rainy Sunday in Belfast was not appealing, so I decided to have a lazy day, with maybe some work on my Indian diary. I spent the day editing pictures
and putting them in, and reading the rest of the paper. Ironically, the weather turned nice, though there was a cold wind.
By late afternoon I was finished, and I decided I'd better go for a walk. Just past the University, I passed the Crescent Church: not an attempt to reach out to Muslims, but a church in a street
called The Crescent.
I headed into town (I knew I was in the centre when I passed the City Hall) and out the other side. Coming back, I went down the road past the City Hall and found the river Lagan. Crossing over a
pedestrian bridge beside the railway line, I found a nice wide footpath by the river, so I followed it.
A little way along, I passed a man, and remarked on how unexpectedly lovely the day had turned out. (The sun was now sparkling on blue water.) He answered me in a German accent, and told me that a
steam train was about to come down the line (or, at least, sometime in the next hour or two).
I decided not to wait, so continued on my way. The path came up onto a very wide and busy road, but with some difficulty I crossed it and found that it continued on the other side of the river. As I
passed the station, I heard the train whistling and puffing, and saw the smoke rising.
I continued along a very nice towpath until I saw a cycle track sign to "Botanic Station". There is no station now, but I thought I could cut through the botanic gardens. But when I approached the
invitingly open gate of the gardens, two guards came out from behind bushes and started shouting at me that the gardens were closed. So I turned off and found myself in the back of the University.
There were many big trucks and vans advertising marquees, catering, etc. parked near the mathematics department, so I guessed that some event was happening in the park.
I went out through the University court and into the street. People were jumping over the low fence and urinating in the rose garden. Across the street, a huge queue had formed outside the Students
Union building.
I went down Stranmillis Road looking for a place to eat. The first two places were packed out; the third had spare seats but when I went in I was firmly told they were closed. Eventually I found a
Chinese takeaway that had a few tables, and ate there. It was not a very nice meal. After that I walked back to Elms Village. On the way I passed Adam Bohn and stopped for a quick word.
On the way in to the village, I was challenged by a security guard. After I had passed muster, he said "We always check people coming in here", even though he must have known that I knew it was a lie
(like the terminal manager in Cochin).
Monday 30 August
The water in the shower was just above lukewarm; the room still cold. It is clear and sunny outside.
At breakfast, there were several familiar faces; I sat with Robert Wisbauer, with whom I shared an umbrella in one of the worst downpours last year, and David Jordan was at the next table.
Since registration began at 9:30 but the opening ceremony only at 10:30, we were in plenty of time. I sat down and, to my delight, Nik Ruskuc came in and sat down next to me. In the pack was an
e-ticket for a concert in the Ulster Hall, to be recorded for the BBC, on my last night; thus the problem of what to do then is solved.
The first talk was a learned oddity by Arnfinn Laudal; though he is from Oslo, his accent seemed South African to me. He was explaining some applications of non-commutative deformation theory; since
I am not really at home even with the commutative case, the details were lost on me. He claims that it "explains" something that puzzled him about physics at school, why position and momentum suffice
to determine all future behaviour of a particle (somehow his formalism churns out things corresponding to higher derivatives). He began the talk with an appeal for us to help the Abdus Salaam School
of Mathematical Sciences in Lahore, which he claims is the only high-quality mathematics institute in Pakistan, and which is threatened with a 50 to 70 percent cut in funding.
At the coffee break, Michael and Tara Brough had arrived. I see from my programme that Tara is giving a talk (and that I am chairing the session).
Then a really lovely talk from David Jordan, moving from mutation of quivers to iteration to Poisson algebras to skew polynomial rings. His recurrence was a fascinating one:
a[n+4] = (a[n+1]a[n+3]+1)/a[n]
(try it with the first four numbers all 1).
Finally for the morning, Vladimir Bavula talked about the algebra of polynomials with differential and integral operators. He has managed to describe its automorphism group (this has not been
achieved for just polynomials and differential operators). One feature is that there are n height-1 prime ideals; any prime ideal is the sum of a subset of these; and any ideal is the product of its
minimal\ prime ideals. So the number of prime ideals is the nth Dedekind number (the number of antichains of subsets of {1,...,n}).
At lunch (as usual at this conference, rather late, 14:10) I didn't feel like eating (I think the result of last night), so I went looking for birthday cards. The convenience store near the
University had none; the selection in the Mace at the BP service station was unbelievably naff, but with little choice, I took the least objectionable. Then I sat in the Botanic Gardens until it was
time to go.
There were only two talks in the afternoon. Abdenacer Makhlouf was constructing twisted versions of everything you could think of. The main feature of his talk was the large number of questions,
which often led to discussions between four or five members of the audience; so he only got through half of the large amount of material he'd prepared.
Then Robert Wisbauer told us how, although it is essential for a ring to have an identity and modules to be unital (and analogous statements in categories) for many purposes, notably adjoints, he was
going to show us how to do without them, to some extent.
After the talk, Nik and I decided to go to dinner. We went to the Giraffe (a one-off, not part of a chain), which did us a pretty nice meal, and had a good talk about mathematics, its history and
philosophy, and many other things. Nik told me that, as a native speaker of a Slavic language, he had had trouble with articles in English, and had formed the impression that they were unnecessary,
until he saw a sign above a hospital receptionist's desk: "Please be patient".
Then home to work for a while before bedtime. I did a small search for news about the funding cut at ASSMS and found nothing, though it is clear that the rest of the story is true: it is a very good
institute, and both the University and the country seem proud of it.
Tuesday 31 August
This morning, when I woke, there were five magpies outside my window.
There was a huge quantity of information in the morning talks; let me single out the best two.
Tom Lenagan talked about Grassmannians. I don't believe he is capable of giving a lecture without explaining clearly what he is talking about. In this case, after a brief and lucid discussion of the
ordinary Grassmannian, its decomposition into Schubert cells, and their parametrisation by Young diagrams, he went on to an extraordinary relationship between the totally non-negative Grassmannian
(all minors non-negative) and the quantum Grassmannian: prime ideals of the latter invariant under scalar multiplications of coordinates are bijective with non-empty cells of the former.
Then Peter Jørgenson talked about cluster algebras and cluster categories. It was clear that his work (which he would have liked to have talked about) was on the infinitely generated case, but he was
too honest not to give us a very clear explanation of the general case first. I never really understood this stuff before, and I have to say that, while I find the cluster algebras absolutely
fascinating, the motivation for cluster categories completely escapes me: it seems to be an attempt to replace straightforward combinatorics with complicated algebra.
For lunch I got a sandwich from the Hope Café and sat in the sunshine (with my coat on – it is still very cold, even in the sun) to eat it.
Then I got to thinking about clusters. The mutation transformations are involutions, one for each vertex; so, when the Dynkin diagrams made an appearance, I confidently expected the groups generated
by these involutions to be the corresponding Coxeter groups. But they are not! In the case A[2] (two vertices joined by an edge), the Coxeter group is dihedral of order 6, but the mutation group is
dihedral of order 10. What's going on?
This problem took up much of my attention during the afternoon. I don't think I missed too much. The first talk was by Travis Squires, who was trying to replace something conceptually simple but with
complicated equations by something conceptually much harder, but he ran out of time. I learned that the terms "semi-strict" and "hemi-strict", applied to 2-vector spaces, are not the same. (A
2-vector space is like a category but sets are replaced by vector spaces and the various maps such as source, target and composition are linear.)
After tea, Natalia talked. She really has developed well; she has something to say, says it well, deals with questions well, and is master of the material.
The final talk was cancelled since Vladimir Dotsenko hadn't been able to get a visa in time. So we had the conference photograph, after which Nik and I decided to go to the pub. Soon Adam came in,
and the three of us had a nice talk. The others didn't really believe me when I said that 7:15 for 7:30 meant that we should sit down at 7:15, so the three of us got the last three seats and were
forced to continue our discussion. It was a very nice dinner, but we didn't stay late since both Nik and I have talks to prepare.
Wednesday 1 September
The day dawned cloudy, but the water in the shower was decently hot. I wrote the birthday cards, and then thought about the mutation group for A[3] until breakfast. It acts on the 14 quivers
imprimitively with 7 blocks of 2, and is 2^6.S[7] (if I am not mistaken). The blocks correspond to reversing all the arrows.
Without sunlight to beguile the eye, it was clear that the floral display in the Botanic Garden was past its best (especially the marigolds). A leaf detached itself from a tree as I passed, and
drifted ever so slowly down to the lawn. A very autumnal start to September!
It was nice to have some real group theory for a change. Shou-Jen Hu told us about checking the Noether property (rationality of the invariants, connected with the inverse Galois property) for groups
of order 64; altogether, it was a very nice summary of the subject. Alexander Lichtman talked about non-abelian valuations, which he uses for non-standard purposes, such as describing the
multiplicative group of the skew field of fractions of a group algebra. Unfortunately he didn't write very much, and what he did write he almost immediately erased.
At coffee time I caught Peter Jørgensen and asked him my question. He said he had never thought about it and didn't know if anyone had. I think he was almost as surprised as I was.
Nik was going to use his own laptop, for reasons he didn't reveal, and offered me the use of it for my talk. Apart from the fact that the laser pointer gave out halfway through, it went well. I
wasn't expecting to talk about more than a small part of the material, and so it turned out.
Nik's talk was lovely. He had a clip from "Waiting for Godot" to describe the different types of growth rates for direct powers of algebraic structures that he was talking about. It was a very fine
summary, illustrated with lots of detail. After the talk, we got sandwiches and sat in the Botanic Garden to eat them, talking about things that are on his mind as he begins his stint as head of
school (research assessment, appointments, recalcitrant administrations, international reviews, etc.), until he had to go and work. I sat a bit longer before going back for the next lecture.
In the afternoon, we had a more or less completely incomprehensible lecture on vertex operator algebras from Alexander Zuevsky, followed by a session I was chairing. Tara Brough talked about her PhD
work under Derek Holt on groups whose word problem is a finite intersection of context-free languages. The conjecture is that such a group is virtually a direct product of k free groups, where k is
the number of languages. She is close to a proof in the soluble case (where the conjecture says that the group is virtually abelian). Then Stanislav Shkarin talked about dense orbits of linear
operators on Banach spaces (these cannot occur in finite dimension, but he has some strange infinite examples.)
After the talks, Nik and I decided to go and eat; Nik was being very encouraging to Tara, so we asked her and Michael to come along as well. We went back to the Giraffe, where we had been two days
ago, and had a pleasant meal. Tara does talk a lot!
On the way home, I stopped for cash at the BP service station. It was all in Northern Irish notes. Nik told me the story of a colleague who had tried to pay a taxi driver in London with a Scottish
note; the cabbie had complained, and eventually called the police, who fined him fifty pounds for wasting police time! He capped it with another story of an officious policeman in Perth, who did
things such as, on seeing a man drop a twenty pound note in the street, had picked it up and returned it to him, and proceeded to fine him for littering.
Thursday 2 September
I had breakfast with Peter Plaumann, a German now retired and living in Mexico. As natural for a pair of expats, we spent a long time swapping stories about visa and passport problems, of which we
both had a huge supply.
He was the first speaker. His talk included two classical theorems, the first of which I didn't know at all, the second not in this form:
• Ritt's Theorem: The set of complex polynomials, with the operation of composition, has a sort of unique factorisation: if two compositions of "prime" polynomials are equal, then the numbers of
polynomials in the two decompositions are the same, and the degrees are the same after a possible permutation of the polynomials.
• Schreier's Theorem (this is J. Schreier, not O. Schreier): If S(X) denotes the semigroup of all mappings on X, then any endomorphism from S(X) to S(Y) is induced by a map from X to Y. (In other
words, there is no phenomenon like the outer automorphism of S[6] for full transformation semigroups.)
Then Sergei Sylvestrov gave a talk at which he took the situation of topological dynamics (a map from a topological space to itself) and translated it into a sort of "skew polynomial ring" over the
ring of continuous functions of the space, so that properties of the dynamics translate into properties of the ring; this allows him to treat many questions in a purely algebraic manner.
After the break, a surprisingly nice talk by Lucas Fresse on Springer fibres. One of these is the set of fixed points of a nilpotent matrix u in the flag variety. Such matrices are determined (over
the complex numbers) by the sizes of their Jordan blocks, a partition of n; Springer showed that there is an action of S[n] on the cohomology of this space, so that the top cohomology group is the
Specht module corresponding to the partition (so all the representation theory of S[n] in characteristic 0 is here). Of course it all became very combinatorial; components of the Springer fibre are
parametrised by tableaux of the given shape. One striking puzzle emerged. They had found for which partitions it is the case that all components of the Springer fibre are smooth. They had also found
for which partitions the centraliser of u has a dense orbit in each component. The partitions in the second theorem are precisely the conjugates of those in the first. They don't know why; it is just
an observation!
Finally Miguel Ferrero talked about "partial actions" of groups on rings. I might think about this, but I would prefer to replace the rings by something simpler such as abelian groups.
Then it was over; we thanked Natalia, said our goodbyes, she took a copy of my tickets, and we left. Nik and I again got sandwiches and sat in the sun in the Botanic Garden. I told him I had to go
and read a Masters project, at which he came out with a wonderful story, which apparently happened to Victoria Gould at York. She got an email from a Masters student, attaching a project in applied
maths. The email said, "Dear Dr Gould, I believe you are the only reader in the department. Could you please read my project by the end of the week?"
He left to work (he is writing up a paper which contains some rather hand-waving geometric arguments which he is having trouble making rigorous), and I went back to read my email and Sigita's
After working for a while, I went for a walk. With some difficulty, after following a zigzag path, I found the cycle track, and walked out along the river Lagan. The river bank had lots of Himalayan
balsam, with some giant hogweed and other rank late summer growth; there were lots of gulls, ducks and crows and a solitary coot. The path left the river to follow a disused canal with reeds and
grass in it, cutting off a big loop of the river.
I had resisted two entrances to Lagan Meadows (a nature reserve), but just after rejoining the river came one I couldn't resist, up a steep wooded hill. I followed this path right around the reserve.
First it was pleasant, undulating mixed forest; then, passing two rowans with astonishing red berries shining in the sun, it went through grassland, fenced off by hedges of hawthorn, bramble, gorse
and honeysuckle.
Back to the river in plenty of time, I retraced my steps and crossed the disused canal into a small forest of poplars, with Himalayan balsam and nettles in the understory. The balsam pods were huge
but not yet ready to pop. Crossing back to the towpath, I decided the time had come to turn back.
The path took me right into Belfast, though I turned off into the gasworks area (now modern offices and shops with no street life) and had a bit of trouble finding my way through. Eventually I saw
the BBC building and, with a bit further meandering, found the Ulster Hall. It was just seven, and queues were already forming; but soon they let us in.
The Ulster Orchestra were practising (and recording) their Proms programme. It was typical Proms fare: some English pieces from the Henry Wood era (by Bliss, Bax, Dorothy Howell and Parry) and some
favourites (Rachmaninov's piano concerto, the Karelia suite, and some well-known excerpts from Eugene Onegin. The Bliss and Bax were mostly "sounding brass and tinkling cymbals", and the Parry not
really to my taste either (it could have been good but needed much more precision than it got) but Howell's Lamia was a pleasant Impressionist piece with Faun-like qualities. But the familiar pieces
were very well done.
On the programme, they were advertising some concerts featuring Roddy Williams. I noted this to tell Hester later.
Nine "survivors" were at the concert (Natalia and Stanislav, Tara and Michael, Sergei, Miguel, Abdenacer, Arnfinn and me), and we decided to look for a place to eat afterwards. A lot of watering
holes had closed at ten, but Italian restaurants continue until eleven, so we found one very near the University and had a good meal. (I had lasagne with garlic bread, very filling.) I ordered a beer
with mine, but Arnfinn, sitting opposite, got two bottles of rosé d'Anjou in the course of the evening and insisted on putting some in my glass.
After dinner, and some goodbyes, everybody walked very slowly to the Botanic, where more of the party peeled off for a last drink; Michael and Tara went to their B&B, and Arnfinn and I continued back
to Elms Village. It was well after midnight when I got to bed.
Friday 3 September
I woke at the usual time, showered, and went out for my last breakfast, an identical copy of all the others. On the way back I bought a paper, so I would have some puzzles to do while waiting round.
I packed, checked out, and waited for the taxi. Sergei and Miguel were taking a taxi to the airport a little before mine, so we had another round of goodbyes.
My taxi came a bit early, and I was at the ferry terminal in good time. After not too much waiting, we were allowed onto the ship, where I found a seat and took it. Nobody asked me to check in my
bag. Two truckers came to sit opposite me. One got out his laptop and started surfing the web. I've no idea what he was looking at.
Arriving in Stranraer, I found my way out of the docks and turned along the road towards the guesthouse. It was a little further than I had remembered from the map, but I found it before I had begun
to worry. The landlady Elaine showed me the room and gave me the key.
I stopped at the tourist office. They were very friendly, and gave me the new public transport timetable (out today) and a town map. I also picked up some leaflets about walks and gardens. One of
these was the Lochryan Coastal Path, so I decided to walk a bit of that; I had a bit less than two hours each way before Ro's train was to arrive. Had the bus timetable been different I could have
tried to walk the whole thing and get a bus back; but that was not to be.
The weather was beautiful, and the birds were astonishingly varied: wagtails, finches, crows; ducks and swans; small brown waders and larger black waders; gulls; large flocks of what may have been
curlews. There were many different wildflowers (and a few garden escapes) among the gorse and brambles. The sun sparkled on the water of the loch as the ferries came and went.
At Cairnryan, just beyond the P&O terminal, it was time to turn back. I bought a cold drink at the village store and carried the bottle four miles before finding a bin. When I did, five yards before
the bin someone had left a cider bottle.
Coming into Stranraer, a gull on the water swam through the sun's track, and left trailing fire. | {"url":"https://cameroncounts.github.io/web/travel/belfast10/index.html","timestamp":"2024-11-10T17:10:15Z","content_type":"text/html","content_length":"28595","record_id":"<urn:uuid:d2a04c43-2e6b-49d1-93d7-15889a82b495>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00687.warc.gz"} |
Correct Vastu Energy Zone Gridding Methodology
Today 95% of the Vastu Practitioner uses wrong Gridding tool called Shakti Chakra. Unfortunately, The zone degrees there are not correct. This Paper aims to bring the authentic gridding methodology
based on our ancient Vedas. We will use the correct approach of 81 padvinyaas to divide the house in different zones.
Post a Comment
Comments 7
1 week ago
After figure 6, Step 1 you simply said to extend the lines from Centre . But you have not explained the method to draw those lines . At how many degrees we take to draw etc.
1 week ago
I have an irregular flat with NE and SW cuts. How do I find direction for this house
1 month ago
The free app doesn’t work, besides what is meant by the angle, usually one calculates the rotation of north’s rotation either to the east or west. It’s confusing. Moreover after uploading the plan
the picture cannot be rotated. It’s frustrating. Perhaps, the generation of frustration is meant to seek the vastu consultant.
2 months ago
I cannot locate the transparent png file for zone division. Can you point where can I find it for downloading?
Kushal Makwana
3 months ago
I want to create a bar chart but did not understood what is horizontal and vertical length?
Sushaant Kumar Das
3 months ago
Share the article for rectangular plot with north not oriented properly (for example tilted towards west 25 degree).As you divided into two part and described only one one part where nort is exactly
0 degree.
8 months ago
How to calculate the grid for properties where the North is deviated to a greater extent ? | {"url":"http://shilaavinyaas.com/p/correct-vastu-energy-zone-gridding-methodology","timestamp":"2024-11-02T05:07:26Z","content_type":"text/html","content_length":"213856","record_id":"<urn:uuid:04717f1a-95bf-42ac-a619-e34be940282e>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00412.warc.gz"} |
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1. Energy-balanced unequal clustering protocol for wireless sensor networks Acta Metallurgica Sinica(English letters) 2010, 17 (4): 94-99. DOI: 10.1016/S1005-8885(09)60494-5
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Clustering provides an effective way to prolong the lifetime of wireless sensor networks. One of the major issues of a clustering protocol is selecting an optimal group of sensor nodes as the
cluster heads to divide the network. Another is the mode of inter-cluster communication. In this paper, an energy-balanced unequal clustering (EBUC) protocol is proposed and evaluated. By using the
particle swarm optimization (PSO) algorithm, EBUC partitions all nodes into clusters of unequal size, in which the clusters closer to the base station have smaller size. The cluster heads of these
clusters can preserve some more energy for the inter-cluster relay traffic and the ‘hot-spots’ problem can be avoided. For inter-cluster communication, EBUC adopts an energy-aware multihop routing
to reduce the energy consumption of the cluster heads. Simulation results demonstrate that the protocol can efficiently decrease the dead speed of the nodes and prolong the network lifetime.
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被引次数: Baidu(
2. Spreading behavior of SIS model with non-uniform transmission on scale-free networks Acta Metallurgica Sinica(English letters) 2009, 16 (1): 27-31. DOI: 10.1016/S1005-8885(08)60173-9
The non-uniform transmission and network topological structure are combined to investigate the spreading behavior of susceptible-infected-susceptible (SIS) epidemic model. Based on the mean-field
theory, the analytical and numerical results indicate that the epidemic threshold is correlated with the topology of underlying networks, as well as the disease transmission mechanism. These
discoveries can greatly help us to further understand the virus propagation on communication networks.
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被引次数: Baidu(
3. Survey of multi-channel MAC protocols for IEEE 802.11-based wireless Mesh networks Acta Metallurgica Sinica(English letters) 2011, 18 (2): 33-44. DOI: 10.1016/S1005-8885(10)60042-8
This paper reviews multi-channel media access control (MAC) protocols based on IEEE 802.11 in wireless Mesh networks (WMNs). Several key issues in multi-channel IEEE 802.11-based WMNs are
introduced and typical solutions proposed in recent years are classified and discussed in detail. The experiments are performed by network simulator version 2 (NS2) to evaluate four representative
algorithms compared with traditional IEEE 802.11. Simulation results indicate that using multiple channels can substantially improve the performance of WMNs in single-hop scenario and each node
equipped with multiple interfaces can substantially improve the performance of WMNs in multi-hop scenario.
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被引次数: Baidu(
4. An improved multilevel fuzzy comprehensive evaluation algorithm for security performance Acta Metallurgica Sinica(English letters) DOI: 1005-8885 (2006) 04-0048-06
It is of great importance to take various factors into account when evaluating the network security performance. Multilevel fuzzy comprehensive evaluation is a relatively valid method. However, the
traditional multilevel fuzzy comprehensive evaluation algorithm relies on the expert’s knowledge and experiences excessively, and the result of the evaluation is usually less accurate. In this
article, an improved multilevel fuzzy comprehensive evaluation algorithm, based on fuzzy sets core and entropy weight is presented. Furthermore, a multilevel fuzzy comprehensive evaluation model of
P2P network security performance has also been designed, and the improved algorithm is used to make an instant computation based on the model. The advantages of the improved algorithm can be
embodied in comparison with the traditional evaluation algorithm.
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被引次数: Baidu(
5. Energy-efficient relay selection and optimal relay location in cooperative cellular networks with asymmetric traffic Acta Metallurgica Sinica(English letters) 2010, 17 (6): 80-88. DOI: 10.1016/
Energy-efficient communication is an important requirement for mobile relay networks due to the limited battery power of user terminals. This paper considers energy-efficient relaying schemes
through selection of mobile relays in cooperative cellular systems with asymmetric traffic. The total energy consumption per information bit of the battery-powered terminals, i.e., the mobile
station (MS) and the relay, is derived in theory. In the joint uplink and downlink relay selection (JUDRS) scheme we proposed, the relay which minimizes the total energy consumption is selected.
Additionally, the energy-efficient cooperation regions are investigated, and the optimal relay location is found for cooperative cellular systems with asymmetric traffic. The results reveal that
the MS-relay and the relay-base station (BS) channels have different influence over relay selection decisions for optimal energy-efficiency. Information theoretic analysis of the
diversity-multiplexing tradeoff (DMT) demonstrates that the proposed scheme achieves full spatial diversity in the quantity of cooperating terminals in this network. Finally, numerical results
further confirm a significant energy efficiency gain of the proposed algorithm comparing to the previous best worse channel selection and best harmonic mean selection algorithms.
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被引次数: Baidu(
6. NHRPA: a novel hierarchical routing protocol algorithm for wireless sensor networks Acta Metallurgica Sinica(English letters) 2008, 15 (3): 75-81.
Considering severe resources constraints and security threat of wireless sensor networks (WSN), the article proposed a novel hierarchical routing protocol algorithm. The proposed routing protocol
algorithm can adopt suitable routing technology for the nodes according to the distance of nodes to the base station, density of nodes distribution, and residual energy of nodes. Comparing the
proposed routing protocol algorithm with simple direction diffusion routing technology, cluster-based routing mechanisms, and simple hierarchical routing protocol algorithm through comprehensive
analysis and simulation in terms of the energy usage, packet latency, and security in the presence of node compromise attacks, the results show that the proposed routing protocol algorithm is more
efficient for wireless sensor networks.
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被引次数: Baidu(
7. Joint power allocation and subcarrier pairing in OFDM-based cooperative relaying system Acta Metallurgica Sinica(English letters) 2012, 19 (1): 24-30. DOI: 10.1016/S1005-8885(11)60223-9
This paper proposes rate-maximized (MR) joint subcarrier pairing (SP) and power allocation (PA) (MR-SP&PA), a novel scheme for maximizing the weighted sum rate of the orthogonal-frequency-division
multiplexing (OFDM) relaying system with a decode-and-forward (DF) relay. MR-SP&PA is based on the joint optimization of both SP and power allocation with total power constraint, and formulated as
a mixed integer programming problem in the paper. The programming problem is then transformed to a convex optimization problem by using continuous relaxation, and solved in the Lagrangian dual
domain. Simulation results show that MR-SP&PA can maximize the weighted sum rate under total power constraint and outperform equal power allocation (EPA) and proportion power allocation (PCG).
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被引次数: Baidu(
8. Framed slotted ALOHA with grouping tactic and binary selection for anti-collision in RFID systems Acta Metallurgica Sinica(English letters) 2009, 16 (4): 47-52. DOI: 10.1016/S1005-8885(08)
In radio frequency identification (RFID) systems, tag collision arbitration is a significant issue for fast tag identification. This article proposes a novel tag anti-collision algorithm called
framed slotted ALOHA with grouping tactic and binary selection (GB-FSA). The novelty of GB-FSA algorithm is that the reader uses binary tree algorithm to identify the tags according to the collided
slot counters information. Furthermore, to save slots, tags are randomly divided into several groups based on the number of collided binary bits in the identification codes (IDs) of tags, and then
only the number of the first group of tags is estimated. Performance analysis and simulation results show that the GB-FSA algorithm improves the identification efficiency by 9.9%–16.3% compared to
other ALOHA-based tag anti-collision algorithms when the number of tags is 1 000.
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被引次数: Baidu(
9. Performance evaluation of new echo state networks based on complex network Acta Metallurgica Sinica(English letters) 2012, 19 (1): 87-93. DOI: 10.1016/S1005-8885(11)60232-X
Recently, echo state networks (ESN) have aroused a lot of interest in their nonlinear dynamic system modeling capabilities. In a classical ESN, its dynamic reservoir (DR) has a sparse and random
topology, but the performance of ESN with its DR taking another kind of topology is still unknown. So based on complex network theory, three new ESNs are proposed and investigated in this paper.
The small-world topology, scale-free topology and the mixed topology of small-world effect and scale-free feature are considered in these new ESNs. We studied the relationship between DR
architecture and prediction capability. In our simulation experiments, we used two widely used time series to test the prediction performance among the new ESNs and classical ESN, and used the
independent identically distributed (i.i.d) time series to analyze the short-term memory (STM) capability. We answer the following questions: What are the differences of these ESNs in the
prediction performance? Can the spectral radius of the internal weights matrix be wider? What is the short-term memory capability? The experimental results show that the proposed new ESNs have
better prediction performance, wider spectral radius and almost the same STM capacity as classical ESN’s.
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被引次数: Baidu(
10. WPANFIS: combine fuzzy neural network with multiresolution for network traffic prediction Acta Metallurgica Sinica(English letters) 2010, 17 (4): 88-93. DOI: 10.1016/S1005-8885(09)60493-3
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A novel methodology for prediction of network traffic, WPANFIS, which relies on wavelet packet transform (WPT) for multi-resolution analysis and adaptive neuro-fuzzy inference system (ANFIS) is
proposed in this article. The widespread existence of self-similarity in network traffic has been demonstrated in earlier studies, which exhibits both long range dependence (LRD) and short range
dependence (SRD). Also, it has been shown that wavelet decomposition is an effective tool for LRD decorrelation. The new method uses WPT as extension of wavelet transform which can decoorrelate LRD
and make more precisely partition in the high-frequency section of the original traffic. Then ANFIS which can extract useful information from the original traffic is implemented in this study for
better prediction performance of each decomposed non-stationary wavelet coefficients. Simulation results show that the proposed WPANFIS can achieve high prediction accuracy in real network traffic
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被引次数: Baidu(
11. Multi-policy threshold signature with distinguished signing authorities Acta Metallurgica Sinica(English letters) 2011, 18 (1): 113-120. DOI: 10.1016/S1005-8885(10)60036-2
Threshold signature plays an important role to distribute the power of a single authority in modern electronic society. In order to add functions and improve efficiency of threshold signatures, a
multi-policy threshold signature scheme with distinguished signing authorities is proposed. In the scheme two groups can sign and verify each other, so the scheme is two-way signing and verifying.
Moreover, the threshold values of the two groups can change with the security classification of the signing document, every discretionary signatory only signs a small part of the document instead
of the whole one, so the bandwidth of data transmission for group signature construction can be reduced and the size of group signature is equivalent to that of any individual signature.
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被引次数: Baidu(
12. Constacyclic and cyclic codes over finite chain rings Acta Metallurgica Sinica(English letters) 2009, 16 (3): 122-125. DOI: 10.1016/S1005-8885(08)60237-X
The problem of Gray image of constacyclic code over finite chain ring is studied. A Gray map between codes over a finite chain ring and a finite field is defined. The Gray image of a linear
constacyclic code over the finite chain ring is proved to be a distance invariant quasi-cyclic code over the finite field. It is shown that every code over the finite field, which is the Gray image
of a cyclic code over the finite chain ring, is equivalent to a quasi-cyclic code.
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被引次数: Baidu(
13. Resource scheduling in downlink LTE-advanced system with carrier aggregation Acta Metallurgica Sinica(English letters) 2012, 19 (1): 44-49. DOI: 10.1016/S1005-8885(11)60226-4
In this paper, we focus on the resource scheduling in the downlink of long term evolution advanced (LTE-A) assuming equal power allocation among subcarriers. Considering the backward compatibility,
the LTE-A system serves LTE-A and long term evolution (LTE) users together with carrier aggregation (CA) technology. When CA is applied, a well-designed resource scheduling scheme is essential to
the LTE-A system. Joint scheduling (JS) and independent scheduling (INS) are two resource scheduling schemes. JS is optimal in performance but with high complexity. Whereas INS is applied, the LTE
users will acquire few resources because they can not support CA technology. And the system fairness is disappointing. In order to improve the system fairness without bringing high complexity to
the system, an improved proportional fair (PF) scheduling algorithm base on INS is proposed. In this algorithm, we design a weigh factor which is related with the number of the carriers and the
percentage of LTE users. Simulation result shows that the proposed algorithm can effectively enhance the throughput of LTE users and improve the system fairness.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
14. Improved particle filter based on fine resampling algorithm Acta Metallurgica Sinica(English letters) 2012, 19 (2): 100-106. DOI: 10.1016/S1005-8885(11)60253-7
In order to solve particle degeneracy phenomenon and simultaneously avoid sample impoverishment, this paper proposed an improved particle filter based on fine resampling algorithm for general case,
called as particle filter with fine resampling (PF-FR). By introducing distance-comparing process and generating new particle based on optimized combination scheme, PF-FR filter performs better
than generic sampling importance resampling particle filter (PF-SIR) both in terms of effectiveness and diversity of the particle system, hence, evidently improving estimation accuracy of the state
in the nonlinear/non-Gaussian models. Simulations indicate that the proposed PF-FR algorithm can maintain the diversity of particles and thus achieve the same estimation accuracy with less number
of particles. Consequently, PF-FR filter is a competitive choice in the applications of nonlinear state estimation.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
15. Pseudo-random sequence generator based on the generalized Henon map Acta Metallurgica Sinica(English letters) 2008, 15 (3): 64-68.
By analysis and comparison of several chaotic systems that are applied to generate pseudo-random sequence, the generalized Henon map is proposed as a pseudo-random sequence generator. A new
algorithm is created to solve the problem of non-uniform distribution of the sequence generated by the generalized Henon map. First, move the decimal point of elements in the sequence to the right;
then, cut off the integer; and finally, quantify it into a binary sequence. Statistical test, security analysis, and the application of image encryption have strongly supported the good random
statistical characteristics, high linear complexity, large key space, and great sensitivity of the binary sequence.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
16. Optimal power allocation for two-way relaying over OFDM using physical-layer network coding Acta Metallurgica Sinica(English letters) 2011, 18 (1): 9-15. DOI: 10.1016/S1005-8885(10)60021-0
In this paper, a network scenario of two-way relaying over orthogonal frequency division multiplexing (OFDM) is considered, in which two nodes intend to exchange the information via a relay using
physical-layer network coding (PLNC). Assuming that the full channel knowledge is available, an optimization problem, which maximizes the achievable sum rate under a sum-power constraint, is
investigated. It is shown that the optimization problem is non-convex, which is difficult to find the global optimum solution in terms of the computational complexity. In consequence, a
low-complexity optimal power allocation scheme is proposed for practice implementation. A link capacity diagram is first employed for power allocation on each subcarrier. Subsequently, an
equivalent relaxed optimization problem and Karush-Kuhn-Tucker (KKT) conditions are developed for power allocation among each subcarrier. Simulation results demonstrate that the substantial
capacity gains are achieved by implementing the proposed schemes efficiently with a low-complexity computational effort.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
17. Zero-bit watermarking resisting geometric attacks based on composite-chaos optimized SVR model Acta Metallurgica Sinica(English letters) 2011, 18 (2): 94-101. DOI: 10.1016/S1005-8885(10)60050-7
The problem to improve the performance of resisting geometric attacks in digital watermarking is addressed in this paper. Based on the optimized support vector regression (SVR), a zero-bit
watermarking algorithm is presented. The proposed algorithm encrypts the watermarking image by using composite chaos with large key space and capacity against prediction, which can strengthen the
safety of the proposed algorithm. By using the relationship between Tchebichef moment invariants of detected image and watermarking characteristics, the SVR training model optimized by composite
chaos enhances the ability of resisting geometric attacks. Performance analysis and simulations demonstrate that the proposed algorithm herein possesses better security and stronger robustness than
some similar methods.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
18. Unequal clustering algorithm for WSN based on fuzzy logic and improved ACO Acta Metallurgica Sinica(English letters) 2011, 18 (6): 89-97. DOI: 10.1016/S1005-8885(10)60126-4
PDF 收藏
This paper proposes a novel energy efficient unequal clustering algorithm for large scale wireless sensor network (WSN) which aims to balance the node power consumption and prolong the network
lifetime as long as possible. Our approach focuses on energy efficient unequal clustering scheme and inter-cluster routing protocol. On the one hand, considering each node’s local information such
as energy level, distance to base station and local density, we use fuzzy logic system to determine one node’s chance of becoming cluster head and estimate the corresponding competence radius. On
the other hand, adaptive max-min ant colony optimization is used to construct energy-aware inter-cluster routing between cluster heads and base station (BS), which balances the energy consumption
of cluster heads and alleviates the hot spots problem that occurs in multi-hop WSN routing protocol to a large extent. The confirmation experiment results have indicated the proposed clustering
algorithm has more superior performance than other methods such as low energy adaptive clustering hierarchy (LEACH) and energy efficient unequal clustering (EEUC).
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
19. Full privacy preserving electronic voting scheme Acta Metallurgica Sinica(English letters) 2012, 19 (4): 86-93. DOI: 10.1016/S1005-8885(11)60287-2
Privacy is an important issue in electronic voting. The concept of ‘full privacy’ in electronic voting was firstly proposed, not only the privacy of voters is concerned, but also the candidates’.
Privacy preserving electronic election architecture without any trusted third party is presented and a general technique for k¬-out-of-m election based on distributed ElGamal encryption and
mix-match is also provided. The voters can compute the result by themselves without disclosing their will and the vote of the losing candidates. Moreover, whether the vote of winner candidate is
more than a half can be verified directly. This scheme satisfies ‘vote and go’ pattern and achieves full privacy. The correctness and security are also analyzed.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu(
20. Two schemes of perfect teleportation one-particle state by a three-particle general W state Acta Metallurgica Sinica(English letters) 2008, 15 (4): 60-62.
In teleportation, it can be seen that the probability of success is determined by Alice’s measurement and quantum channel. If the Alice’s measurement is appropriate, the teleportation can be
successfully realized with the maximal probability. In accordance with transformation operator, two schemes are proposed for teleportation of an unknown one-particle state via a general W state,
through which the successful probability and the fidelity of both schemes reach 1. Furthermore, two optimal matches of orthogonal complete measurement bases are given for teleporting an unknown
one-particle state.
参考文献 | 相关文章 | 多维度评价
被引次数: Baidu( | {"url":"https://jcupt.bupt.edu.cn/CN/article/showBeiyincishuTop.do","timestamp":"2024-11-07T23:45:37Z","content_type":"text/html","content_length":"145747","record_id":"<urn:uuid:e5e09c34-1d2a-43f7-a532-42fd4e3b8c52>","cc-path":"CC-MAIN-2024-46/segments/1730477028017.48/warc/CC-MAIN-20241107212632-20241108002632-00399.warc.gz"} |
Understanding the Flaws in Neoclassical Economics and Market Behavior
The aggregate demand function has no interesting properties, so assumptions need to be made to make it interesting.
Combining preferences of individuals to represent the entire region as a single economy is not possible.
The demand curve in standard microeconomics is not accurate as individuals cannot be utility maximizers.
The supply curve in standard microeconomics is only true for a horizontal demand curve.
Monopolies have a higher price and result in welfare loss. | {"url":"https://chattube.io/summary/education/E6Gb4tk-z_s","timestamp":"2024-11-05T16:35:26Z","content_type":"text/html","content_length":"41515","record_id":"<urn:uuid:af63b4e1-2bae-49f1-a119-751bdbf67e56>","cc-path":"CC-MAIN-2024-46/segments/1730477027884.62/warc/CC-MAIN-20241105145721-20241105175721-00809.warc.gz"} |
Solve multiplication equations using the break apart and distribute strategy
Curriculum>Grade 3> Module 3>Topic D: Multiplication and Division Using Units of 9
Learn to solve multiplication equations with units of 9 by using the break apart and distribute strategy. In this activity, students will label parts of a tape diagram to demonstrate the distributive
property of multiplication | {"url":"https://happynumbers.com/demo/cards/303054/","timestamp":"2024-11-08T10:40:02Z","content_type":"text/html","content_length":"13953","record_id":"<urn:uuid:e0d054f8-488e-4417-bc99-aba673a452b0>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00072.warc.gz"} |
Test your knowledge
Question 6 of 6 Intermediate
Happy with your answers?
Submit your current answers and get the final test result.
Test results
Congratulations. You have passed the test and completed the 7 - Chilled water systems for air conditioning
Q: What is FLOWLIMIT?
A: An external flow commissioning algorithm available from an app
01: An external flow commissioning algorithm available from an app Your answer
02: An intelligent control valve placed after the pump
03: An electronic flow commissioning functionality built into the pump
Q: What is FLOWLIMIT?
A: An intelligent control valve placed after the pump
01: An external flow commissioning algorithm available from an app
02: An intelligent control valve placed after the pump Your answer
03: An electronic flow commissioning functionality built into the pump
Q: What is FLOWLIMIT?
A: An electronic flow commissioning functionality built into the pump
Q: What affects a system’s total cost of ownership the most?
A: Investing to increase user comfort
01: Investing to increase user comfort Your answer
03: Low flow in the system
Q: What affects a system’s total cost of ownership the most?
A: Low Delta T syndrome
Q: What affects a system’s total cost of ownership the most?
A: Low flow in the system
01: Investing to increase user comfort
03: Low flow in the system Your answer
Q: How does the VPF design achieve energy and cost savings?
A: By keeping constant-flow chiller pumps in a separate system
01: By keeping constant-flow chiller pumps in a separate system Your answer
02: By eliminating the constant-flow chilled water pumps by variable-flow
03: It doesn’t – but reliability is greatly increased
Q: How does the VPF design achieve energy and cost savings?
A: By eliminating the constant-flow chilled water pumps by variable-flow
Q: How does the VPF design achieve energy and cost savings?
A: It doesn’t – but reliability is greatly increased
01: By keeping constant-flow chiller pumps in a separate system
02: By eliminating the constant-flow chilled water pumps by variable-flow
03: It doesn’t – but reliability is greatly increased Your answer
Q: Which of the following statements about VPF systems is true?
A: They are getting cheaper in installation and more energy efficient
Q: Which of the following statements about VPF systems is true?
A: They offer substantial energy savings, but are expensive compared to other system alternatives (like primary secondary)
01: They are getting cheaper in installation and more energy efficient
02: They offer substantial energy savings, but are expensive compared to other system alternatives (like primary secondary) Your answer
03: They need more space in buildings or facilities compared to other system alternatives
Q: Which of the following statements about VPF systems is true?
A: They need more space in buildings or facilities compared to other system alternatives
01: They are getting cheaper in installation and more energy efficient
02: They offer substantial energy savings, but are expensive compared to other system alternatives (like primary secondary)
03: They need more space in buildings or facilities compared to other system alternatives Your answer
Q: If the chilled water temperature range for which the system is designed is not maintained…
A: … you risk low Delta T syndrome
Q: If the chilled water temperature range for which the system is designed is not maintained…
A: …you need to install new control valves
01: … you risk low Delta T syndrome
02: …you need to install new control valves Your answer
03: …you need to increase flow through the chillers
Q: If the chilled water temperature range for which the system is designed is not maintained…
A: …you need to increase flow through the chillers
01: … you risk low Delta T syndrome
02: …you need to install new control valves
03: …you need to increase flow through the chillers Your answer
Q: By separating pump control from chiller design, what does the VPF design achieve?
A: Ensures the pumps keep the water sufficiently cold to satisfy the building load
01: Ensures the pumps keep the water sufficiently cold to satisfy the building load Your answer
02: A chiller and its primary pump typically operate in tandem
03: The pumps maintain a target differential pressure, Delta P, at a specific point in the system
Q: By separating pump control from chiller design, what does the VPF design achieve?
A: A chiller and its primary pump typically operate in tandem
01: Ensures the pumps keep the water sufficiently cold to satisfy the building load
02: A chiller and its primary pump typically operate in tandem Your answer
03: The pumps maintain a target differential pressure, Delta P, at a specific point in the system
Q: By separating pump control from chiller design, what does the VPF design achieve?
A: The pumps maintain a target differential pressure, Delta P, at a specific point in the system | {"url":"https://www.grundfos.com/ke/learn/ecademy/all-courses/air-conditioning/test-your-knowledge","timestamp":"2024-11-13T11:55:39Z","content_type":"text/html","content_length":"693924","record_id":"<urn:uuid:852d1306-b306-4ea3-a9ef-04520e17b4e6>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00009.warc.gz"} |
Root vector
From Encyclopedia of Mathematics
2020 Mathematics Subject Classification: Primary: 15A18 [MSN][ZBL]
of a linear transformation $A$ of a vector space $V$ over a field $K$
A vector $v$ in the kernel of the linear transformation $(A-\lambda I)^n$, where $\lambda \in K$ and $n$ is a positive integer depending on $A$ and $v$. The number $\lambda$ is necessarily an
eigenvalue of $A$. If, under these conditions, $(A - \lambda I)^{n-1}v \ne 0$, one says that $v$ is a root vector of height $n$ belonging to $A$.
The concept of a root vector generalizes the concept of an eigenvector of a transformation $A$: The eigenvectors are precisely the root vectors of height $1$. The set $V_\lambda$ of root vectors
belonging to a fixed eigenvalue $\lambda$ is a linear subspace of $V$ which is invariant under $A$. It is known as the root subspace belonging to the eigenvalue $\lambda$. Root vectors belonging to
different eigenvalues are linearly independent; in particular, $V_\lambda \cap V_\mu = 0$ if $\lambda \ne \mu$.
Let $V$ be finite-dimensional. If all roots of the characteristic polynomial of $A$ are in $K$ (e.g. if $K$ is algebraically closed), then $V$ decomposes into the direct sum of different root spaces:
$$\label{eq:a1} V = V_\alpha \oplus \cdots \oplus V_\delta \ .$$
This decomposition is a special case of the weight decomposition of a vector space $V$ relative to a splitting nilpotent Lie algebra $L$ of linear transformations: The Lie algebra in this case is the
one-dimensional subalgebra generated by $A$ in the Lie algebra of all linear transformations of $V$ (see Weight of a representation of a Lie algebra).
If the matrix of $A$ relative to some basis is a Jordan matrix, then the components of the decomposition \eqref{eq:a1} may be described as follows: The root subspace $V_\lambda$ is the linear hull of
the set of basis vectors which correspond to Jordan cells with eigenvalue $\lambda$.
[1] V.V. Voevodin, "Algèbre linéare" , MIR (1976) (Translated from Russian)
[2] A.I. Mal'tsev, "Foundations of linear algebra" , Freeman (1963) (Translated from Russian)
How to Cite This Entry:
Root vector. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Root_vector&oldid=42306
This article was adapted from an original article by V.L. Popov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098.
See original article | {"url":"https://encyclopediaofmath.org/index.php?title=Root_vector&oldid=42306","timestamp":"2024-11-03T00:58:45Z","content_type":"text/html","content_length":"17752","record_id":"<urn:uuid:ba7b24bc-2e10-4dca-8bbb-953385d5217f>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00360.warc.gz"} |
package version <= 1.2.3
User guide for speaq package version <= 1.2.3
Trung Nghia Vu, Charlie Beirnaert, et al.
This introduction was written for the speaq package up until version 1.2.3. Since version 2.0 a lot of functionality is added but the original functionality is maintained. This vignette can therefor
still be used as it describes one part of the package dealing with spectral alignment and quantitation.
We introduce a novel suite of informatics tools for the quantitative analysis of NMR metabolomic profile data. The core of the processing cascade is a novel peak alignment algorithm, called
hierarchical Cluster-based Peak Alignment (CluPA).
The algorithm aligns a target spectrum to the reference spectrum in a top-down fashion by building a hierarchical cluster tree from peak lists of reference and target spectra and then dividing the
spectra into smaller segments based on the most distant clusters of the tree. To reduce the computational time to estimate the spectral misalignment, the method makes use of Fast Fourier
Transformation (FFT) cross-correlation. Since the method returns a high-quality alignment, we can propose a simple methodology to study the variability of the NMR spectra. For each aligned NMR data
point the ratio of the between-group and within-group sum of squares (BW-ratio) is calculated to quantify the difference in variability between and within predefined groups of NMR spectra. This
differential analysis is related to the calculation of the F-statistic or a one-way ANOVA, but without distributional assumptions. Statistical inference based on the BW-ratio is achieved by
bootstrapping the null distribution from the experimental data.
We are going to introduce step-by-step how part of speaq works for a specific dataset, this includes
• automatically do alignment
• allow user intervening into the process
• compute BW ratios
• visualize results
For any issue reports or discussions about speaq feel free to contact us via the developing website at github (https://github.com/beirnaert/speaq).
Data input
We randomly generate an NMR spectral dataset of two different groups (15 spectra for each group). Each spectrum has two peaks slightly shifted cross over spectra. More details are described in the
manual document of function makeSimulatedData().
#Generate a simulated NMR data set for this experiment
Now, we draw a spectral plot to observe the dataset before alignment.
Landmark peak detection
This section makes use of MassSpecWavelet package to detect peak lists of the dataset.
cat("\n detect peaks....");
## detect peaks....
startTime <- proc.time();
peakList <- detectSpecPeaks(X,
nDivRange = c(128),
scales = seq(1, 16, 2),
baselineThresh = 50000,
SNR.Th = -1,
endTime <- proc.time();
cat("Peak detection time:",(endTime[3]-startTime[3])/60," minutes");
## Peak detection time: 0.02153333 minutes
Reference finding
Next, We find the reference for other spectra align to.
cat("\n Find the spectrum reference...")
## Find the spectrum reference...
resFindRef<- findRef(peakList);
refInd <- resFindRef$refInd;
#The ranks of spectra
for (i in seq_along(resFindRef$orderSpec))
cat(paste(i, ":",resFindRef$orderSpec[i],sep=""), " ");
if (i %% 10 == 0) cat("\n")
## 1:24 2:14 3:11 4:5 5:15 6:30 7:16 8:22 9:23 10:1
## 11:3 12:19 13:29 14:20 15:28 16:25 17:27 18:26 19:6 20:10
## 21:4 22:2 23:17 24:7 25:13 26:9 27:8 28:18 29:21 30:12
cat("\n The reference is: ", refInd);
## The reference is: 24
Spectral alignment
For spectral alignment, function dohCluster() is used to implement hierarchical Cluster-based Peak Alignment [1] (CluPA) algorithm. In this function maxShift is set by 100 by default which is
suitable with many NMR datasets. Experienced users can set select more proper for their dataset. For example:
# Set maxShift
maxShift = 50;
Y <- dohCluster(X,
peakList = peakList,
refInd = refInd,
maxShift = maxShift,
acceptLostPeak = TRUE, verbose=FALSE);
Automatically detect the optimal maxShift
If users are not confident when selecting a value for the maxShift, just set the value to NULL. Then, the software will automatically learn to select the optimal value based on the median Pearson
correlation coefficient between spectra. It is worth noting that this metric is significantly effected by high peaks in the spectra [2], so it might not be the best measure for evaluating alignment
performances. However, it is fast for the purpose of detecting the suitable maxShift value. This mode also takes more time since CluPA implements extra alignment for few maxShift values. If set
verbose=TRUE, a plot of performances of CluPA with different values of maxShift will be displayed. For example:
Y <- dohCluster(X,
peakList = peakList,
refInd = refInd,
maxShift = NULL,
acceptLostPeak = TRUE, verbose=TRUE);
## --------------------------------
## maxShift=NULL, thus CluPA will automatically detect the optimal value of maxShift.
## --------------------------------
## maxShift= 2
## Median Pearson correlation coefficent: -0.03154662 , the best result: -1
## maxShift= 4
## Median Pearson correlation coefficent: -0.02854745 , the best result: -0.03154662
## maxShift= 8
## Median Pearson correlation coefficent: 0.05644193 , the best result: -0.02854745
## maxShift= 16
## Median Pearson correlation coefficent: 0.8035346 , the best result: 0.05644193
## maxShift= 32
## Median Pearson correlation coefficent: 0.9339107 , the best result: 0.8035346
## maxShift= 64
## Median Pearson correlation coefficent: 0.9481311 , the best result: 0.9339107
## maxShift= 128
## Median Pearson correlation coefficent: 0.9481311 , the best result: 0.9481311
## maxShift= 256
## Median Pearson correlation coefficent: 0.9481311 , the best result: 0.9481311
## Optimal maxShift= 64 with median Pearson correlation of aligned spectra= 0.9481311
## Alignment time: 0.007416667 minutes
In this example, the best maxShift=32 which is highlighted by a red star in the plot achieves the highest median Pearson correlation coefficient (0.93).
Spectral alignment with selected segments
If users just want to align in specific segments or prefer to use different parameter settings for different segments. speaq allows users to do that by intervene into the process. To do that, users
need to create a segment information matrix as the example in Table 1.
Each row contains the following information corresponding to the columns:
• begin: the starting point of the segment.
• end: the end point of the segment.
• forAlign: the segment is aligned (1) or not (0).
• ref: the index of the reference spectrum. If 0, the algorithm will select the reference found by the reference finding step.
• maxShift: the maximum number of points of a shift to left/right.
It is worth to note that only segments with forAlign=1 (column 3) will be taken into account for spectral alignment.
Now, simply run dohClusterCustommedSegments with the input from the information file.
## begin end forAlign ref maxShift
## [1,] 100 200 0 0 0
## [2,] 450 680 1 0 50
Yc <- dohClusterCustommedSegments(X,
peakList = peakList,
refInd = refInd,
segmentInfoMat = segmentInfoMat,
minSegSize = 128,
Spectral plots
We could draw a segment to see the performance of the alignment.
We could limit the heights of spectra to easily check the alignment performance.
highBound = 5e+5,
lowBound = -100);
We achieved similar results with Yc but the region of the first peak was not aligned because the segment information just allows align the region 450-680.
Quantitative analysis
This section presents the quantitative analysis for wine data that was used in our paper [1]. To save time, we just do permutation 100 times to create null distribution.
N = 100;
alpha = 0.05;
# find the BW-statistic
BW = BWR(Y, groupLabel);
# create sampled H0 and export to file
H0 = createNullSampling(Y, groupLabel, N = N,verbose=FALSE)
#compute percentile of alpha
perc = double(ncol(Y));
alpha_corr = alpha/sum(returnLocalMaxima(Y[2,])$pkMax>50000);
for (i in seq_along(perc)){
perc[i] = quantile(H0[,i],1-alpha_corr, type = 3);
Now, some figures are plotting. Read the publication to understand more about these figures.
drawBW(BW, perc,Y, groupLabel = groupLabel)
drawBW(BW, perc, Y ,startP=450, endP=680, groupLabel = groupLabel)
[1] Vu, Trung Nghia, Dirk Valkenborg, Koen Smets, Kim A. Verwaest, Roger Dommisse, Filip Lemiere, Alain Verschoren, Bart Goethals, and Kris Laukens. "An Integrated Workflow for Robust Alignment and
Simplified Quantitative Analysis of NMR Spectrometry Data." BMC Bioinformatics 12, no. 1 (October 20, 2011): 405.
[2] Vu, Trung Nghia, and Kris Laukens. "Getting Your Peaks in Line: A Review of Alignment Methods for NMR Spectral Data." Metabolites 3, no. 2 (April 15, 2013): 259-76. | {"url":"https://cran.hafro.is/web/packages/speaq/vignettes/classic_speaq_vignette.html","timestamp":"2024-11-03T16:10:12Z","content_type":"text/html","content_length":"792372","record_id":"<urn:uuid:f4c9ce79-b76f-475a-a43e-dcca176fcb69>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00462.warc.gz"} |
ml.js Alternatives - JavaScript Machine Learning | LibHunt
This library is a compilation of the tools developed in the mljs organization. It is mainly maintained for use in the browser. If you are working with Node.js, you might prefer to add to your
dependencies only the libraries that you need, as they are usually published to npm more often. We prefix all our npm package names with ml- (eg. ml-matrix) so they are easy to find.
To include the ml.js library in a web page:
Monthly Downloads: 0
Programming language: JavaScript
License: MIT License
ml.js alternatives and similar libraries
Based on the "Machine Learning" category.
Alternatively, view ml.js alternatives based on common mentions on social networks and blogs.
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* Code Quality Rankings and insights are calculated and provided by Lumnify.
They vary from L1 to L5 with "L5" being the highest.
Do you think we are missing an alternative of ml.js or a related project?
Add another 'Machine Learning' Library
ml.js - Machine learning tools in JavaScript
This library is a compilation of the tools developed in the mljs organization.
It is mainly maintained for use in the browser. If you are working with Node.js, you might prefer to add to your dependencies only the libraries that you need, as they are usually published to npm
more often.
We prefix all our npm package names with ml- (eg. ml-matrix) so they are easy to find.
To include the ml.js library in a web page:
<script src="https://www.lactame.com/lib/ml/6.0.0/ml.min.js"></script>
It will be available as the global ML variable. The package is in UMD format.
List of included libraries
Unsupervised learning
Supervised learning
Artificial neural networks (ANN)
Functions dealing with an object containing 2 properties x and y, both arrays.
let result = ML.ArrayXY.sortX({ x: [2, 3, 1], y: [4, 6, 2] });
// result = {x: [1,2,3], y: [2,4,6]}
Data processing
*Note that all licence references and agreements mentioned in the ml.js README section above are relevant to that project's source code only. | {"url":"https://js.libhunt.com/ml-alternatives","timestamp":"2024-11-12T12:24:51Z","content_type":"text/html","content_length":"62083","record_id":"<urn:uuid:bc1d5b76-a713-461d-8258-cd43340925fa>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00063.warc.gz"} |
How to Plot A Histogram In Matplotlib In Python?
To plot a histogram in matplotlib in Python, you can use the hist function from the matplotlib.pyplot module. The hist function takes in an array of data as input and bins the data into intervals to
create a histogram. You can specify the number of bins, the range of values to include in the histogram, and other parameters to customize the appearance of the histogram. Once you have specified the
parameters, you can call the hist function with your data array as input to display the histogram. This will generate a plot showing the distribution of your data in the form of a histogram.
How to create a cumulative histogram in matplotlib?
To create a cumulative histogram in Matplotlib, you can use the hist function with the parameter cumulative=True. Here is an example code snippet to create a cumulative histogram:
1 import matplotlib.pyplot as plt
2 import numpy as np
4 # Generate some random data
5 data = np.random.randn(1000)
7 # Create a cumulative histogram
8 plt.hist(data, bins=30, cumulative=True, color='skyblue', edgecolor='black')
10 # Add labels and title
11 plt.xlabel('Value')
12 plt.ylabel('Frequency')
13 plt.title('Cumulative Histogram')
15 # Display the plot
16 plt.show()
This code will create a cumulative histogram of the random data using 30 bins. You can adjust the number of bins and customize the plot according to your preference.
How to create a horizontal histogram in matplotlib?
To create a horizontal histogram in matplotlib, you can follow these steps:
1. Import the necessary libraries:
1 import matplotlib.pyplot as plt
2 import numpy as np
1. Create some sample data for the histogram:
1 data = np.random.randn(1000)
1. Create the histogram using the hist function with the orientation parameter set to 'horizontal':
1 plt.hist(data, orientation='horizontal')
1. Customize the histogram as needed:
1 plt.xlabel('Frequency')
2 plt.ylabel('Value')
3 plt.title('Horizontal Histogram')
4 plt.grid(True)
5 plt.show()
This code will generate a horizontal histogram using the sample data with frequency on the x-axis and value on the y-axis. You can customize the plot further by adjusting the labels, title, grid, and
other properties as needed.
How to plot a matrix histogram in matplotlib?
To plot a matrix histogram in matplotlib, you can use the imshow function along with hist function. Here is a step-by-step guide on how to do this:
1. Import the necessary libraries:
1 import matplotlib.pyplot as plt
2 import numpy as np
1. Create a random matrix:
1 matrix = np.random.rand(10, 10)
1. Plot the matrix as an image using imshow:
1 plt.imshow(matrix, cmap='viridis', aspect='auto')
2 plt.colorbar()
1. Calculate the histogram of the matrix values:
1 hist, bins = np.histogram(matrix.flatten(), bins=20)
1. Plot the histogram using plt.bar:
1 plt.figure()
2 plt.bar(bins[:-1], hist, width=np.diff(bins))
3 plt.xlabel('Value')
4 plt.ylabel('Frequency')
5 plt.title('Matrix Histogram')
6 plt.show()
Running this code will display the matrix as an image with a colorbar, as well as the histogram of values in the matrix. You can customize the colormap, number of bins, and other parameters according
to your needs.
What is the significance of the weights parameter in the hist() function in matplotlib?
The weights parameter in the hist() function in matplotlib allows for the weighted histogram calculation and plotting. This means that you can assign different weights to each data point, which will
affect the height of the bars in the histogram. This can be useful when you have data points with different significances and want to give them different weights in the histogram representation. This
can help in emphasizing certain data points over others, depending on their importance. | {"url":"https://ubuntuask.com/blog/how-to-plot-a-histogram-in-matplotlib-in-python","timestamp":"2024-11-13T12:20:29Z","content_type":"text/html","content_length":"341762","record_id":"<urn:uuid:5b89ea6b-6799-4a2a-a7f5-f8c535e1f054>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00548.warc.gz"} |
Innumeracy by John Allen Paulos
John Allen Paulos's Innumeracy is one of those classics of the field that I've never gotten around to reading. I've been thinking more about these sorts of issues recently, though, so when the copy I
bought a few years ago turned up in our recent book-shuffling, I decided to give it a read.
Unfortunately, I probably would've been a lot more impressed had I read it when it first came out in 1988. Most of the examples used to illustrate his point that people are generally very bad with
numbers are exceedingly familiar. They appear in How to Lie With Statistics, and the recent The Drunkard's Walk by Leonard Mlodinow, and a bunch of other books and articles.
It's hard to beat Paulos's description of the core problem, though:
Innumeracy, an inability to deal comfortably with the fundamental notions of number and chance, plagues far too many otherwise knowledgeable citizens. The same people who cringe when words such
as "imply" and "infer" are confused react without a trace of embarrassment to even the most egregious of numerical solecisms. I remember once listening to someone at a party drone on about the
difference between "continually" and "continuously." Later that evening we were watching the news, and the TV weathercaster announced that there was a 50 percent chance of rain for Saturday and a
50 percent chance for Sunday, and concluded that there was therefore a 100 percent chance of rain that weekend. The remark went right by the self-styled grammarian, and even after I explained the
mistake to him, he wasn't nearly as indignant as he would have been had the weathercaster left a dangling participle. In fact, unlike other failing which are hidden, mathematical illiteracy is
often flaunted: "I can't even balance my checkbook." "I'm a people person, not a numbers person." Or "I always hated math."
Paulos clearly and concisely identifies all the major sources of innumeracy in dealing with probability and statistics, excessive personalization and a kind of misplaced romanticism chief among them.
He doesn't go into as much detail as some other treatments of the subject, opting for a more typically terse mathematician's approach, but there's a sort of spare elegance to his presentation.
I would've liked to see more documentation of the problems of innumeracy-- how many people have a functional grasp of numbers, what are the policy consequences, what are the solutions that might be
attempted-- but that's sort of ahistorical, based on reading other treatments of the same mathematical issues recently. I'd still like some good numbers on the subject, if anyone knows a source.
The other striking thing about this book is how little has changed. This was written when Reagan was President, and yet the concrete examples he gives still apply perfectly well. Despite twenty-odd
years of people pointing to the problem, nothing has gotten any better. Of course, it's not clear that things have gotten any worse, so there's that to cling to at least...
If you've read other books on the subject recently, you've probably already seen all the examples he uses covered in greater detail. If you haven't read about the problems of mathematical illiteracy
before, though, you won't find a more concise and readable outline of the basic problems.
More like this
If you're reading this shortly after it's posted, you may notice ads for this book popping up in the sidebar and on top of the page. This is probably not entirely a happy coincidence-- I was offered
a review copy in email from the author and his publisher, and I suspect that they had ScienceBlogs…
It's summed up nicely by the discussion at Cosmic Variance, and spelled out explicitly in comment #125 by Marty Tysanner: Sean coaxingly requested, Come on, string theorists! Make some effort to
explain to everyone why this set of lofty speculations is as promising as you know it to be. It won't…
Over in LiveJournal land, nwhyte just finished reading all the Hugo-winning novels, and provides a list of them with links to reviews or at least short comments. He also gives a summary list of his
take on the best and worst books of the lot. The obvious thing to do with such a list, particularly…
I receive a fair number of books to review each week, so I thought I should do what several magazines and other publications do; list those books that have arrived in my mailbox so you know that this
is the pool of books from which I will be reading and reviewing on my blog. Lost Land of the…
Of course, it's not clear that things have gotten any worse, so there's that to cling to at least...
I'd beg to differ here. Two words: negative amortization.
You and I are numerate, so we understand that taking out a loan where the payment does not cover the interest (let alone the principal) is likely to be a bad idea. A major factor in the real estate
bubble was the fact that banks and mortgage brokers started issuing such loans. They're usually called Option ARMs because they offer several payment level options (among them interest only, 30-year
amortizing, and 15-year amortizing), but by far the most commonly chosen option (and all too often the option used to determine that the borrower was "qualified" for the loan) was a negatively
amortizing payment. I've owned my present house for almost ten years (with a fixed rate mortgage, thank you), but had I been buying in the last few years, the only reason I would not have walked away
from such a loan would be that I would have been running. It's because of these idiotic loans that the credit crisis is likely to continue for at least another couple of years or so.
I have read it back in 1992 or so and like it very much at the time. I wonder if I'd still like it as much today. I often recommend it to people, though.
An amazing book by an amazing man. You might now try his other books. He is SO very right. Of course we like books by Leonard Mlodinow -- how to top doing Physics with Gell-Mann and Feynman, then
dropping out to write for Star Trek TNG?
Math below Calculus is a good thing for a teacher to experience. I taught Algebra 1, Algebra 2, and Geometry for 5 semesters at Woodbury University, and a year of those (plus pre-Algebra and
pre-Calculus and other courses) in middle schools and high schools in Pasadena. I am better for the experience. My wife has taught Algebra and Trigonometry to students there, to prepare them for the
Physics courses that she teaches. Math for Physics. And, by the way, Physics for Architects.
Your primary role is to balance instruction (which is usually all that the naive think that teachers do), assessment, and management (lesson planning and classroom management). The assessment is not
just about grading homework and exams; it is to determine the learning style of each unique student. What matters is NOT what you know, but what you can find out about what is going on in the head of
the student. Give at least half credit on homework and exams under my mantra: if you can't write the equation, draw me a picture, or write me an English paragraph, but show my what you think. What
the student knows that is right, build on, using their learning style.
What the student knows that is wrong, usually the result of a bad teacher in the past, you solve by regressing them to just before that mistake, and then rolling forwards on the right path. The
student usually knows where and when they went off-track, and still resents the teacher who did that.
Read papers on Dyscalculia -- Mathematics Disorder. It is real, it is insidious, and in only 1/3 of the clinical cases is the cause neurological; the rest can be cured by good teaching. This is your
chance to save lives!
Innumeracy is the tip of the iceberg. What kills is the resultant anti-Science worldview, and the muddled thinking plus plunging self-esteem of Dyscalculia. The minor flaws acknowledged, John Allen
Paulos's Innumeracy should be required reading in every teacher's college in the USA. The rest of the developed world already knows.
Innumeracy is analogous to illiteracy, but what do we have for ignorance of the world? I once watched a newsreader reading the teleprompter, informing me about the planet of Jupiter called 'ten'.
The idiot who wrote the teleprompter script had read in "Io" and wrote out "IO". It seems that all teleprompters use all-caps, which is designed-in stupidity.
I am barely numerate myself, and owe what little familiarity with math I have to an astounding woman who taught Grade ten algebra to a class of students in a rural highschool in which the school had
*forgotten* to include a grade nine algebra course for my year class - about 150 students.
She was the very stereotype of a middle aged math whiz, unable to keep her clothing straight, her hair under control (it was always wildly undone from its bun by the end of class), or chalk smears
from her face. Her enthusiasm about math and the wonderful things that could be learned through understanding and using it was boundless and infectious. She crammed two years worth of algebra into
one, and almost all of us did well in the finals.
Nevertheless, aware that the available teachers for the next two years were known to be unable to understand the subject they were supposed to be teaching, I opted to take another two years of Latin
and Biology.
Innumeracy starts with ill-taught teachers.
The reason people are innumerate and bad at statistics is not because of a flaw in Platonic logic off in the distance on some mythical hill. The reason is that, despite all the groovy trigonometry a
human uses to wave a multijointed limb around, there's no need for consciousness of numbers in evolution. The reason for innumeracy is biology. It may feel good to whinge away at Philistines, but the
thing is is that humans use lossy computation and don't have calculators in the cranium. Language good, engineering who needs it, math who needs it. Now there is a RS for numeracy, but only recently.
Moral: There are 3 kinds of people in the world: Those who are good at math and those who aren't.
Despite twenty-odd years of people pointing to the problem, nothing has gotten any better. Of course, it's not clear that things have gotten any worse, so there's that to cling to at least...
To be slightly puckish... do you have any numbers to back up either statement? That statement's a little odd, coming as it does right after your stated desire to have some more documentation of the
Who oh who gets to decide what the set of knowledge everyone needs to know is? Sure having numeracy skills and literacy skills are important, but so is customer service and knowing what blood sugar
means and what cholesterol can do to you. What about reading a contract and knowing how to unclog a drain? Where do you draw the line? What is sufficient numeracy? Whatever it is, scientists will say
it is not enough because they work with it. But most people aren't going to be scientists. The great huge majority aren't going to be. I'd hazard a guess that 90% of college students won't ever do
anything remotely related to science in the high math / high theory meaning of the term. R.N.s etc. need to compute. It's true. But I'd rather they use a calculator if in doubt. How much real
numeracy ought real people do in a world full of computers?
On the other hand, on3 of the fastest growing professions on the planet is the field of accountancy. They have no great trouble finding candidates to take the degree programs which are growing
rapidly. Accountants get paid. I see no one on the street corner selling "numeracy skills." If it is so important people can figure out how to reduce the coins in their pocket, why isn't anyone
seeking it out? Ever notice that drugs get dealt in areas where the math scores are horrible? I wonder why.
@ #10: The Onion would disagree with you on that last bit.
As for your question about numeracy in a world of computers, I don't think computers make all that much difference. A calculator can make computing a tip trivial, and allows people with essentially
zero math skill handle retail transactions; but it won't give somebody with no clue about statistics even a basic resistance to common forms of sloppy and/or evasive presentation. Computers can do
math for you; but they can't understand math for you. | {"url":"https://www.scienceblogs.com/principles/2008/07/07/innumeracy-by-john-allen-paulo","timestamp":"2024-11-03T10:45:25Z","content_type":"text/html","content_length":"60408","record_id":"<urn:uuid:8e9b15ab-570c-4343-a835-f5d2fa4e589f>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00765.warc.gz"} |
WinRAR 7.01 with Crack • CrackingCityWinRAR 7.01 with Crack
WinRAR is a powerful archive manager providing complete support for RAR and ZIP archives and is able to unpack CAB, ARJ, LZH, TAR, GZ, ACE, UUE, BZ2, JAR, ISO, 7Z, Z archives. Its RAR format may only
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How to Install and Crack:
1. Temporarily disable antivirus software until install the patch if needed (mostly not needed)
2. Install “WinRAR”
3. Close WinRAR if opened
4. Extract “winrar.5.xx-patch.zip” (Password is: 123)
5. Run “winrar.5.xx-patch.exe” and click the “Patch” button
6. Done!!! Enjoy!!!
Download Link
Password = 123
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KOS.FS - faculty addon
Fluid Dynamics (E121502)
Departments: ústav mech. tekutin a termodyn. (12112)
Abbreviation: FD Approved: 12.06.2018
Valid until: ?? Range: 3P+2C
Semestr: Z Credits: 5
Completion: Z,ZK Language: EN
The first course in Fluid Mechanics designed to provide the fundamental tools necessary to analyse a fluid systems and predict its behaviour.
Navid Aslfattahi Ph.D.
Zimní 2024/2025
Ing. Vladimir Kulish DrSc.
Zimní 2023/2024
Ing. Vladimir Kulish DrSc.
Zimní 2022/2023
Ing. Vladimir Kulish DrSc.
Zimní 2021/2022
01. Hydrostatics. Pascal's law. Basic equations. Archimedes' law. Absolute and relative balance. Euler equation of hydrostatics and its integration.
02. Wall forces. Methods of calculation. Determining location and direction.
03. Basic equation of fluid dynamics - equation of continuity, motion equations and energy. Link with concepts in the subject of Thermomechanics.
04. Flow of perfect fluid. Outflow from vessels. Real fluid discharge. Overflow. Flow through a flooded hole.
05. Flow of the perfect fluid through the pipe. Basic equations. Real fluid flow. Local and frictional losses.
06. Unsteady flow. Water stroke. Absolute and relative flow.
07. Dynamic effects of fluid flow. Propulsion power. Euler's pump and turbine equation.
08. Laminar flow, flow in circular tube. Analytically solvable cases of laminar flow. Turbulent flow. Turbulence characteristics. Flow around a flat plate, boundary layer. Drag.
09. Flow around cylindrical body, spherical body, wing section. Lift and drag. Flow separation. Aerodynamic characteristics of the wing.
10. Fundamentals of the theory of similarity. Dimensional analysis. Similarity numbers and laws.
11. Compressible fluid flow. One dimensional isotropic flow. Outlet and maximum speed. The speed of sound. Mach number. Critical conditions. Hugeniot's theorem.
12. Perpendicular adiabatic shock wave. Nozzle and diffuser flows. Flow under non-design conditions. Aerodynamic choking.
• White, F. M.: Fluid Mechanics, 3rd ed., New York, 1994,
• Munson,B.,Young,D.,Okiishi,T.:Fundamentals of Fluid Mechanics, 2nd ed., New York,1994,
• Douglas, J., Mathews, R.: Solving Problems in Fluid Mechanics, Vol. 1 and 2, Longman, Malaysia, 1998
• Jílek, M.: Thermomechanics, CTU Prague, 2006
The first course in Fluid Mechanics designed to provide the fundamental tools necessary to analyse a fluid systems and predict its behaviour.
fluid dynamics | {"url":"https://kos.fs.cvut.cz/synopsis/department/E121502/en","timestamp":"2024-11-13T12:11:00Z","content_type":"text/html","content_length":"8679","record_id":"<urn:uuid:971f56f9-f3b7-4526-9b4a-42717915bf4e>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00324.warc.gz"} |
Verify that (secx/sinx)*(cotx/cscx)=cscx is an identity. (x=theta BTW)
Verify that (secx/sinx)*(cotx/cscx)=cscx is an identity.
(x=theta BTW)
= (secx/cscx)(cotx/sinx)
= (sinx/cosx)*cotx*(1/sinx)
The last steps should be obvious
To verify whether (secx/sinx)*(cotx/cscx) = cscx is an identity, we need to simplify both sides of the equation and show that they are equal.
Let's start by simplifying each side of the equation separately:
Left-hand side (LHS):
To simplify this expression, we can simplify each fraction individually, and then multiply the resulting terms together. Recall the following trigonometric identities:
secx = 1/cosx
cotx = 1/tanx = cosx/sinx
cscx = 1/sinx
Using these identities, we can rewrite the LHS expression as:
(secx/sinx)*(cotx/cscx) = (1/cosx)*(cosx/sinx)*(1/sinx)
Now, we can cancel out the common terms:
(1/cosx)*(cosx/sinx)*(1/sinx) = (1/sinx) * (1/sinx)
Multiplying the two terms together:
(1/sinx) * (1/sinx) = 1/(sinx * sinx) = 1/sin^2(x) = csc^2(x)
Right-hand side (RHS):
To simplify the RHS, we can rewrite cscx as 1/sinx:
cscx = 1/sinx
Now that we have simplified both the LHS and RHS, we can compare them:
LHS = csc^2(x)
RHS = cscx
Since csc^2(x) and cscx are equivalent, we can conclude that (secx/sinx)*(cotx/cscx) = cscx is indeed an identity.
By simplifying both sides, we showed that the LHS and RHS are equal to each other, which validates the given identity. | {"url":"https://askanewquestion.com/questions/81871","timestamp":"2024-11-02T11:59:02Z","content_type":"text/html","content_length":"18885","record_id":"<urn:uuid:829281db-00d2-4f34-96c1-2a0797906889>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00825.warc.gz"} |
Data Representation in Computer Science
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Binary data representation uses a system of numerical notation that has just two possible states represented by 0 and 1 (also known as 'binary digits' or 'bits'). Grasp the practical applications of
binary data representation and explore its benefits.
Finally, explore the vast world of data model representation. Different types of data models offer a variety of ways to organise data in databases. Understand the strategic role of data models in
data representation, and explore how they are used to design efficient database systems. This comprehensive guide positions you at the heart of data representation in Computer Science.
Understanding Data Representation in Computer Science
In the realm of Computer Science, data representation plays a paramount role. It refers to the methods or techniques used to represent, or express information in a computer system. This encompasses
everything from text and numbers to images, audio, and beyond.
Basic Concepts of Data Representation
Data representation in computer science is about how a computer interprets and functions with different types of information. Different information types require different representation techniques.
For instance, a video will be represented differently than a text document.
When working with various forms of data, it is important to grasp a fundamental understanding of:
• Binary system
• Bits and Bytes
• Number systems: decimal, hexadecimal
• Character encoding: ASCII, Unicode
Data in a computer system is represented in binary format, as a sequence of 0s and 1s, denoting 'off' and 'on' states respectively. The smallest component of this binary representation is known as a
bit, which stands for 'binary digit'.
A byte, on the other hand, generally encompasses 8 bits. An essential aspect of expressing numbers and text in a computer system, are the decimal and hexadecimal number systems, and character
encodings like ASCII and Unicode.
Role of Data Representation in Computer Science
Data Representation is the foundation of computing systems and affects both hardware and software designs. It enables both logic and arithmetic operations to be performed in the binary number system,
on which computers are based.
An illustrative example of the importance of data representation is when you write a text document. The characters you type are represented in ASCII code - a set of binary numbers. Each number is
sent to the memory, represented as electrical signals; everything you see on your screen is a representation of the underlying binary data.
Computing operations and functions, like searching, sorting or adding, rely heavily on appropriate data representation for efficient execution. Also, computer programming languages and compilers
require a deep understanding of data representation to successfully interpret and execute commands.
As technology evolves, so too does our data representation techniques. Quantum computing, for example, uses quantum bits or "qubits". A qubit can represent a 0, 1, or both at the same time, thanks to
the phenomenon of quantum superposition.
Types of Data Representation
In computer systems, various types of data representation techniques are utilized:
Numbers can be represented in real, integer, and rational formats. Text is represented by using different types of encodings, such as ASCII or Unicode. Images can be represented in various formats
like JPG, PNG, or GIF, each having its specific rendering algorithm and compression techniques.
Tables are another important way of data representation, especially in the realm of databases.
Name Email
John Doe john@gmail.com
Jane Doe jane@gmail.com
This approach is particularly effective in storing structured data, making information readily accessible and easy to handle. By understanding the principles of data representation, you can better
appreciate the complexity and sophistication behind our everyday interactions with technology.
Data Representation and Interpretation
To delve deeper into the world of Computer Science, it is essential to study the intricacies of data representation and interpretation. While data representation is about the techniques through which
data are expressed or encoded in a computer system, data interpretation refers to the computing machines' ability to understand and work with these encoded data.
Basics of Data Representation and Interpretation
The core of data representation and interpretation is founded on the binary system. Represented by 0s and 1s, the binary system signifies the 'off' and 'on' states of electric current, seamlessly
translating them into a language comprehensible to computing hardware.
For instance, \[ 1101 \, \text{in binary is equivalent to} \, 13 \, \text{in decimal} \] This interpretation happens consistently in the background during all of your interactions with a computer
Now, try imagining a vast array of these binary numbers. It could get overwhelming swiftly. To bring order and efficiency to this chaos, binary digits (or bits) are grouped into larger sets like
bytes, kilobytes, and so on. A single byte, the most commonly used set, contains eight bits. Here's a simplified representation of how bits are grouped:
However, the binary system isn't the only number system pivotal for data interpretation. Both decimal (base 10) and hexadecimal (base 16) systems play significant roles in processing numbers and text
data. Moreover, translating human-readable language into computer interpretable format involves character encodings like ASCII (American Standard Code for Information Interchange) and Unicode.
These systems interpret alphabetic characters, numerals, punctuation marks, and other common symbols into binary code. For example, the ASCII value for capital 'A' is 65, which corresponds to \
(01000001\) in binary.
In the world of images, different encoding schemes interpret pixel data. JPG, PNG, and GIF, being common examples of such encoded formats. Similarly, audio files utilise encoding formats like MP3 and
WAV to store sound data.
Importance of Data Interpretation in Computer Science
Understanding data interpretation in computer science is integral to unlocking the potential of any computing process or system. When coded data is input into a system, your computer must interpret
this data accurately to make it usable.
Consider typing a document in a word processor like Microsoft Word. As you type, each keystroke is converted to an ASCII code by your keyboard. Stored as binary, these codes are transmitted to the
active word processing software. The word processor interprets these codes back into alphabetic characters, enabling the correct letters to appear on your screen, as per your keystrokes.
Data interpretation is not just an isolated occurrence, but a recurring necessity - needed every time a computing process must deal with data. This is no different when you're watching a video,
browsing a website, or even when the computer boots up.
Rendering images and videos is an ideal illustration of the importance of data interpretation.
Digital photos and videos are composed of tiny dots, or pixels, each encoded with specific numbers to denote colour composition and intensity. Every time you view a photo or play a video, your
computer interprets the underlying data and reassembles the pixels to form a comprehensible image or video sequence on your screen.
Data interpretation further extends to more complex territories like facial recognition, bioinformatics, data mining, and even artificial intelligence. In these applications, data from various
sources is collected, converted into machine-acceptable format, processed, and interpreted to provide meaningful outputs.
In summary, data interpretation is vital for the functionality, efficiency, and progress of computer systems and the services they provide. Understanding the basics of data representation and
interpretation, thereby, forms the backbone of computer science studies.
Delving into Binary Data Representation
Binary data representation is the most fundamental and elementary form of data representation in computing systems. At the lowermost level, every piece of information processed by a computer is
converted into a binary format.
Understanding Binary Data Representation
Binary data representation is based on the binary numeral system. This system, also known as the base-2 system, uses only two digits - 0 and 1 to represent all kinds of data. The concept dates back
to the early 18th-century mathematics and has since found its place as the bedrock of modern computers. In computing, the binary system's digits are called bits (short for 'binary digit'), and they
are the smallest indivisible unit of data.
Each bit can be in one of two states representing 0 ('off') or 1 ('on'). Formally, the binary number \( b_n b_{n-1} ... b_2 b_1 b_0 \), is interpreted using the formula: \[ B = b_n \times 2^n + b_
{n-1} \times 2^{n-1} + ... + b_2 \times 2^2 + b_1 \times 2^1 + b_0 \times 2^0 \] Where \( b_i \) are the binary digits and \( B \) is the corresponding decimal number.
For example, for the binary number 1011, the process will look like this: \[ B = 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 \]
This mathematical translation makes it possible for computing machines to perform complex operations even though they understand only the simple language of 'on' and 'off' signals.
When representing character data, computing systems use binary-encoded formats. ASCII and Unicode are common examples. In ASCII, each character is assigned a unique 7-bit binary code. For example,
the binary representation for the uppercase letter 'A' is 0100001. Interpreting such encoded data back to a human-readable format is a core responsibility of computing systems and forms the basis for
the exchange of digital information globally.
Practical Application of Binary Data Representation
Binary data representation is used across every single aspect of digital computing. From simple calculations performed by a digital calculator to the complex animations rendered in a high-definition
video game, binary data representation is at play in the background.
Consider a simple calculation like 7+5. When you input this into a digital calculator, the numbers and the operation get converted into their binary equivalents. The microcontroller inside the
calculator processes these binary inputs, performs the sum operation in binary, and finally, returns the result as a binary output. This binary output is then converted back into a decimal number
which you see displayed on the calculator screen.
When it comes to text files, every character typed into the document is converted to its binary equivalent using a character encoding system, typically ASCII or Unicode. It is then saved onto your
storage device as a sequence of binary digits.
Similarly, for image files, every pixel is represented as a binary number. Each binary number, called a 'bit map', specifies the colour and intensity of each pixel. When you open the image file, the
computer reads the binary data and presents it on your screen as a colourful, coherent image. The concept extends even further into the internet and network communications, data encryption, data
compression, and more.
When you are downloading a file over the internet, it is sent to your system as a stream of binary data. The web browser on your system receives this data, recognizes the type of file and accordingly
interprets the binary data back into the intended format.
In essence, every operation that you can perform on a computer system, no matter how simple or complex, essentially boils down to large-scale manipulation of binary data. And that sums up the
practical application and universal significance of binary data representation in digital computing.
Binary Tree Representation in Data Structures
Binary trees occupy a central position in data structures, especially in algorithms and database designs. As a non-linear data structure, a binary tree is essentially a tree-like model where each
node has a maximum of two children, often distinguished as 'left child' and 'right child'.
Fundamentals of Binary Tree Representation
A binary tree is a tree data structure where each parent node has no more than two children, typically referred to as the left child and the right child. Each node in the binary tree contains:
• A data element
• Pointer or link to the left child
• Pointer or link to the right child
The topmost node of the tree is known as the root. The nodes without any children, usually dwelling at the tree's last level, are known as leaf nodes or external nodes. Binary trees are fundamentally
differentiated by their properties and the relationships among the elements. Some types include:
• Full Binary Tree: A binary tree where every node has 0 or 2 children.
• Complete Binary Tree: A binary tree where all levels are completely filled except possibly the last level, which is filled from left to right.
• Perfect Binary Tree: A binary tree where all internal nodes have two children and all leaves are at the same level.
• Skewed Binary Tree: A binary tree where every node has only left child or only right child.
In a binary tree, the maximum number of nodes \( N \) at any level \( L \) can be calculated using the formula \( N = 2^{L-1} \). Conversely, for a tree with \( N \) nodes, the maximum height or
maximum number of levels is \( \lceil Log_2(N+1) \rceil \).
Binary tree representation employs arrays and linked lists. Sometimes, an implicit array-based representation suffices, especially for complete binary trees. The root is stored at index 0, while for
each node at index \( i \), the left child is stored at index \( 2i + 1 \), and the right child at \( 2i + 2 \).
However, the most common representation is the linked-node representation that utilises a node-based structure. Each node in the binary tree is a data structure that contains a data field and two
pointers pointing to its left and right child nodes.
Usage of Binary Tree in Data Structures
Binary trees are typically used for expressing hierarchical relationships, and thus find application across various areas in computer science. In mathematical applications, binary trees are ideal for
expressing certain elements' relationships.
For example, binary trees are used to represent expressions in arithmetic and Boolean algebra.
Consider an arithmetic expression like (4 + 5) * 6. This can be represented using a binary tree where the operators are parent nodes, and the operands are children. The expression gets evaluated by
performing operations in a specific tree traversal order.
Among the more complex usages, binary search trees — a variant of binary trees — are employed in database engines and file systems.
• Binary Heaps, a type of binary tree, are used as an efficient priority queue in many algorithms like Dijkstra's algorithm and the Heap Sort algorithm.
• Binary trees are also used in creating binary space partition trees, which are used for quickly finding objects in games and 3D computer graphics.
• Syntax trees used in compilers are a direct application of binary trees. They help translate high-level language expressions into machine code.
• Huffman Coding Trees, which are used in data compression algorithms, are another variant of binary trees.
The theoretical underpinnings of all these binary tree applications are the traversal methods and operations, such as insertion and deletion, which are intrinsic to the data structure.
Binary trees are also used in advanced machine-learning algorithms. Decision Tree is a type of binary tree that uses a tree-like model of decisions. It is one of the most successful forms of
supervised learning algorithms in data mining and machine learning.
The advantages of a binary tree lie in their efficient organisation and quick data access, making them a cornerstone of many complex data structures and algorithms. Understanding the workings and
fundamentals of binary tree representation will equip you with a stronger pillaring in the world of data structures and computer science in general.
Grasping Data Model Representation
When dealing with vast amounts of data, organising and understanding the relationships between different pieces of data is of utmost importance. This is where data model representation comes into
play in computer science. A data model provides an abstract, simplified view of real-world data. It defines the data elements and the relationships among them, providing an organised and consistent
representation of data.
Exploring Different Types of Data Models
Understanding the intricacies of data models will equip you with a solid foundation in making sense of complex data relationships. Some of the most commonly used data models include:
• Hierarchical Model
• Network Model
• Relational Model
• Entity-Relationship Model
• Object-Oriented Model
• Semantic Model
The Hierarchical Model presents data in a tree-like structure, where each record has one parent record and many children. This model is largely applied in file systems and XML documents. The
limitations are that this model does not allow a child to have multiple parents, thus limiting its real-world applications.
The Network Model, an enhancement of the hierarchical model, allows a child node to have multiple parent nodes, resulting in a graph structure. This model is suitable for representing complex
relationships but comes with its own challenges such as iteration and navigation, which can be intricate.
The Relational Model, created by E.F. Codd, uses a tabular structure to depict data and their relationships. Each row represents a collection of related data values, and each column represents a
particular attribute. This is the most widely used model due to its simplicity and flexibility.
The Entity-Relationship Model illustrates the conceptual view of a database. It uses three basic concepts: Entities, Attributes (the properties of these entities), and Relationships among entities.
This model is most commonly used in database design.
The Object-Oriented Model goes a step further and adds methods (functions) to the entities besides attributes. This data model integrates the data and the operations applicable to the data into a
single component known as an object. Such an approach enables encapsulation, a significant characteristic of object-oriented programming.
The Semantic Model aims to capture more meaning of data by defining the nature of data and the relationships that exist between them. This model is beneficial in representing complex data
interrelations and is used in expert systems and artificial intelligence fields.
The Role of Data Models in Data Representation
Data models provide a method for the efficient representation and interaction of data elements, thus forming an integral part of any database system. They provide the theoretical foundation for
designing databases, thereby playing an essential role in the development of applications.
A data model is a set of concepts and rules for formally describing and representing real-world data. It serves as a blueprint for designing and implementing databases and assists communication
between system developers and end-users.
Databases serve as vast repositories, storing a plethora of data. Such vast data needs effective organisation and management for optimal access and usage. Here, data models come into play, providing
a structural view of data, thereby enabling the efficient organisation, storage and retrieval of data.
Consider a library system. The system needs to record data about books, authors, publishers, members, and loans. All these items represent different entities. Relationships exist between these
entities. For example, a book is published by a publisher, an author writes a book, or a member borrows a book. Using an Entity-Relationship Model, we can effectively represent all these entities and
relationships, aiding the library system's development process.
Designing such a model requires careful consideration of what data is required to be stored and how different data elements relate to each other. Depending on their specific requirements, database
developers can select the most suitable data model representation. This choice can significantly affect the functionality, performance, and scalability of the resulting databases.
From decision-support systems and expert systems to distributed databases and data warehouses, data models find a place in various applications.
Modern NoSQL databases often use several models simultaneously to meet their needs. For example, a document-based model for unstructured data and a column-based model for analyzing large data sets.
In this way, data models continue to evolve and adapt to the burgeoning needs of the digital world.
Therefore, acquiring a strong understanding of data model representations and their roles forms an integral part of the database management and design process. It empowers you with the ability to
handle large volumes of diverse data efficiently and effectively.
Data Representation - Key takeaways
• Data representation refers to techniques used to express information in computer systems, encompassing text, numbers, images, audio, and more.
• Data Representation is about how computers interpret and function with different information types, including binary systems, bits and bytes, number systems (decimal, hexadecimal) and character
encoding (ASCII, Unicode).
• Binary Data Representation is the conversion of all kinds of information processed by a computer into binary format.
• Binary Trees in Data Structures are used to:
□ Express hierarchical relationships across various areas in computer science.
□ Represent relationships in mathematical applications, used in database engines, file systems, and priority queues in algorithms.
• Data Model Representation is an abstract, simplified view of real-world data that defines the data elements, and their relationships and provides a consistently organised way of representing
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Frequently Asked Questions about Data Representation in Computer Science
What is data representation?
Data representation is the method used to encode information into a format that can be used and understood by computer systems. It involves the conversion of real-world data, such as text, images,
sounds, numbers, into forms like binary or hexadecimal which computers can process. The choice of representation can affect the quality, accuracy and efficiency of data processing. Precisely, it's
how computer systems interpret and manipulate data.
What does data representation mean?
Data representation refers to the methods or techniques used to express, display or encode data in a readable format for a computer or a user. This could be in different forms such as binary,
decimal, or alphabetic forms. It's crucial in computer science since it links the abstract world of thought and concept to the concrete domain of signals, signs and symbols. It forms the basis of
information processing and storage in contemporary digital computing systems.
Why is data representation important?
Data representation is crucial as it allows information to be processed, transferred, and interpreted in a meaningful way. It helps in organising and analysing data effectively, providing insights
for decision-making processes. Moreover, it facilitates communication between the computer system and the real world, enabling computing outcomes to be understood by users. Finally, accurate data
representation ensures integrity and reliability of the data, which is vital for effective problem solving.
How to make a graphical representation of data?
To create a graphical representation of data, first collect and organise your data. Choose a suitable form of data representation such as bar graphs, pie charts, line graphs, or histograms depending
on the type of data and the information you want to display. Use a data visualisation tool or software such as Excel or Tableau to help you generate the graph. Always remember to label your axes and
provide a title and legend if necessary.
What is data representation in statistics?
Data representation in statistics refers to the various methods used to display or present data in meaningful ways. This often includes the use of graphs, charts, tables, histograms or other visual
tools that can help in the interpretation and analysis of data. It enables efficient communication of information and helps in drawing statistical conclusions. Essentially, it's a way of providing a
visual context to complex datasets, making the data easily understandable.
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model object produced by lm or glm.
A one-sided formula that specifies a subset of the regressors. One component-plus-residual plot is drawn for each term. The default ~. is to plot against all numeric predictors. For example, the
specification terms = ~ . - X3 would plot against all predictors except for X3. Factors and nonstandard predictors such as B-splines are skipped. If this argument is a quoted name of one of the
regressors, the component-plus-residual plot is drawn for that predictor only.
If set to a value like c(1, 1) or c(4, 3), the layout of the graph will have this many rows and columns. If not set, the program will select an appropriate layout. If the number of graphs exceed
nine, you must select the layout yourself, or you will get a maximum of nine per page. If layout=NA, the function does not set the layout and the user can use the par function to control the
layout, for example to have plots from two models in the same graphics window.
If TRUE, ask the user before drawing the next plot; if FALSE, the default, don't ask. This is relevant only if not all the graphs can be drawn in one window.
Overall title for any array of cerers plots; if missing a default is provided.
ceresPlots passes these arguments to ceresPlot. ceresPlot passes them to plot.
A quoted string giving the name of a variable for the horizontal axis
controls point identification; if FALSE (the default), no points are identified; can be a list of named arguments to the showLabels function; TRUE is equivalent to list(method=list(abs(residuals
(model, type="pearson")), "x"), n=2, cex=1, col=carPalette()[1], location="lr"), which identifies the 2 points with the largest residuals and the 2 points with the most extreme horizontal (X)
TRUE to plot least-squares line.
specifies the smoother to be used along with its arguments; if FALSE, no smoother is shown; can be a list giving the smoother function and its named arguments; TRUE, the default, is equivalent to
list(smoother=loessLine). See ScatterplotSmoothers for the smoothers supplied by the car package and their arguments. Ceres plots do not support variance smooths.
color for points; the default is the first entry in the current car palette (see carPalette and par).
a list of at least two colors. The first color is used for the ls line and the second color is used for the fitted lowess line. To use the same color for both, use, for example, col.lines=c
("red", "red")
labels for the x and y axes, respectively. If not set appropriate labels are created by the function.
plotting character for points; default is 1 (a circle, see par).
line width; default is 2 (see par).
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Formula Help - Average IF
Hi everyone. I am hoping you can help me. I am trying to average the time it takes individual case managers to complete a case between specific dates.
The reference cells are {CM Text} in the main sheet and it has to equal the name in [Case Manager]@row in the reference sheet
The average comes from the reference identified as {Days to Complete} in the main sheet
The specific date column is referenced as {GS Action Complete} and between the two dates shown in the [Week End]@row and the [Week Begin]@ row.
I keep getting errors on the below formula.
=AVERAGEIFS({Days to Complete}, {CM Text}, [Case Manager]@row, {GS Action Complete}, <=[Week End]@row, {GS Action Complete}, >=[Week Begin]@row)
Any help would be appreciated in getting this fixed.
Best Answers
• You have to create logic within the formula as AVERAGEIFS is not considered a function in Smartsheet.
You could collect the range first then do the average:
=AVG(COLLECT({Days to Complete}, CM Text}, [Case Manager]@row, {GS Action Complete}, <=[Week End]@row, {GS Action Complete}, >=[Week Begin]@row))
or put @cell
=AVG(COLLECT({Days to Complete}, CM Text}, [Case Manager]@row, {GS Action Complete}, @cell<=[Week End]@row, {GS Action Complete}, @cell>=[Week Begin]@row))
• You have to create logic within the formula as AVERAGEIFS is not considered a function in Smartsheet.
You could collect the range first then do the average:
=AVG(COLLECT({Days to Complete}, CM Text}, [Case Manager]@row, {GS Action Complete}, <=[Week End]@row, {GS Action Complete}, >=[Week Begin]@row))
or put @cell
=AVG(COLLECT({Days to Complete}, CM Text}, [Case Manager]@row, {GS Action Complete}, @cell<=[Week End]@row, {GS Action Complete}, @cell>=[Week Begin]@row))
• Leona you are awesome! This worked perfectly thank you so much!
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Class 7 Chapter 7: Linear Equations
Important Concepts and Formulas on Linear Equations
1. An equation is a statement of equality between two expressions.
2. An equation has two sides separated by the symbol (=). The two sides are LHS and RHS.
3. The value of the variable, which makes both sides of the equation same is called the solution of the equation. For example, x = 3 is the solution of equation 4x – 5 = 7.
4. If LHS and RHS are interchanged, the equation remains the same.
5. There are different methods for finding the solution of an equation. To solve an equation in one variable, we can
· add the same number to both sides.
· subtract the same number from both sides.
· multiply both sides by the same number.
· divide both sides by the same (non-zero) number.
6. The concept of algebraic equation can be utilized to solve problems related to real-life situations.
7. To solve an equation, we carry out a series of identical mathematical operations on two sides of the equation such that the unknown variable is on one side and its value is obtained on the other
8. When we transpose a number from one side of the equation to the other side, we change its sign.
Please do not enter any spam link in the comment box.
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Start Networking! - Activity
Quick Look
Grade Level: 9 (7-10)
Time Required: 45 minutes
Expendable Cost/Group: US $0.00
Group Size: 28
Activity Dependency:
Subject Areas: Biology, Life Science, Problem Solving, Science and Technology
To get a better understanding of complex networks, students create their own, real social network example by interacting with their peers in the classroom and documenting the interactions. They
represent the interaction data as a graph, calculate two mathematical quantities associated with the graph—the degree of each node and the degree distribution of the graph—and analyze how these
quantities can be used to infer properties of the social network at hand.
What can we learn about the characteristics of complex networks by analyzing graphs?
Engineering Connection
We are all members of social networks. Many of us use social networking websites—built by software engineers—to keep in touch and up to date with the people in our social circles. Our money changes
hands in exchange for goods and services, creating economic networks studied by financial engineers. Infectious diseases spread via contact networks and are studied by bioengineers and public health
researchers. Information flows over our friendship and acquaintance networks, often facilitated by technologies developed by electrical and computer engineers.
Learning Objectives
After this activity, students should be able to:
• Represent data as a graph.
• Calculate the degree of each node of a graph as well as the degree distribution of a graph.
Educational Standards
Each TeachEngineering lesson or activity is correlated to one or more K-12 science, technology, engineering or math (STEM) educational standards.
All 100,000+ K-12 STEM standards covered in TeachEngineering are collected, maintained and packaged by the Achievement Standards Network (ASN), a project of D2L (www.achievementstandards.org).
In the ASN, standards are hierarchically structured: first by source; e.g., by state; within source by type; e.g., science or mathematics; within type by subtype, then by grade, etc.
• Solve real-world and mathematical problems involving the four operations with rational numbers. (Grade 7) More Details
Do you agree with this alignment? Thanks for your feedback!
• Represent data with plots on the real number line (dot plots, histograms, and box plots). (Grades 9 - 12) More Details
Do you agree with this alignment? Thanks for your feedback!
• (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). (Grades 9 - 12) More Details
Do you agree with this alignment? Thanks for your feedback!
• Analyze the stability of a technological system and how it is influenced by all the components in the system, especially those in the feedback loop. (Grades 9 - 12) More Details
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• Explain how scientific knowledge and reasoning provide an empirically-based perspective to inform society's decision making. (Grades 9 - 12) More Details
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• use representations to model and interpret physical, social, and mathematical phenomena (Grades Pre-K - 12) More Details
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Suggest an alignment not listed above
Social networks are prolific and important to many branches of modern science and engineering. Money changes hands in exchange for goods and services, creating our economic networks. Infectious
diseases spread via contact networks. Information flows over our friendship and acquaintance networks.
Today we are going to build a real social network by collecting data on your interactions in the classroom. Then you'll represent this data as a graph and compute two mathematical quantities
associated with the graph so that we can learn how these quantities can be used to infer properties of the social network at hand.
Refer to the Teacher Background section of the associated Sets-Nodes-Edges: Representing Complex Networks in Graph Theory lesson for information on graphs, degree of nodes and degree distribution of
With the Students
1. Ask each student in the class to write his or her name at the top of a sheet of paper.
2. Instruct the students to move around the classroom and sign each other's papers if they agree to do so. For example, John and Ann meet and agree to sign each other's sheet of paper. In this case,
John's sheet of paper will have his and Ann's name written on it. Likewise, Ann's sheet of paper will have hers and John's name written on it.
3. Allow this activity to proceed long enough for students to collect a few signatures (perhaps two to three, on average). Avoid giving too much time because you do not want every student to collect
signatures from every other student—a situation that leads to non-interesting results.
4. Ask students to return back to their seats and ask one volunteer to collect all sheets of paper.
5. Ask one student to make a graph of the interaction data obtained from Step 3 on the classroom board. Represent each student by a node (labeled with his/her name or initials). Draw an edge between
two nodes if the students represented by those nodes have exchanged signatures (see Figure 1 for an example). It is easiest to draw the graph if the nodes are placed on a large circle around the
border of the board.
Figure 1. Example graph of interaction data.
The Figure 1 graph is an example of an outcome that might be drawn on the board. In this example, six students are in the class: Ann, Matt, Alex, John, Steve and Amy. An edge is drawn between
students who exchanged signatures. For example, John and Ann exchanged signatures, whereas Steve and Amy did not.
6. Ask another student to calculate the degree of each node and the degree distribution of the resulting graph. The degree of a node is given by counting the number of edges connected to the node.
Using Figure 1 example data, the results are shown in Table 1 (left). The degree distribution can be found by calculating how many nodes have a given degree and by dividing these numbers by the
total number of nodes in the network. Using Figure 1 example data, the results are shown in Table 1 (right). This data can also be plotted, resulting in the Figure 2 bar graph.
7. Conclude with a class discussion to analyze the graph. See the questions in the Assessment section.
Table 1. Example calculated degree of each node and degree distribution.
Figure 2. Example plotting of degree distribution data.
complex network: A set of individuals (students, neurons, molecules, computers, web pages) that interact with each other in a certain fashion.
degree distribution: A function telling what fraction of the nodes in a graph has a given degree.
degree of a node: The number of edges connecting to the node.
graph: A set of vertices and a set of edges that connect the vertices. Graphs are used as visual representations of complex networks.
Pre-Activity Assessment
Opening Questions: Before starting the activity, ask students a few questions to review what they have learned in the associated Sets-Nodes-Edges: Representing Complex Networks in Graph Theory
• What is a social network?
• What is a graph?
• Can you come up with examples of systems that can be represented as graphs?
• What is the degree of a node?
• What is the degree distribution of a graph?
Activity Embedded Assessment
Engagement: While students are networking, monitor them and observe who is participating.
Post-Activity Assessment
Concluding Discussion: After the activity is complete, gauge student comprehension by asking them the following analysis questions about the class social network and discussing as a class:
• Which fellow students are the most and least successful in collecting signatures? What are the degrees of the nodes associated with these two students? (Answer: Looking at the graph, student
nodes with the most signatures are the ones with the most edges from them and thus the highest degree numbers. Student nodes with the fewest signatures have the fewest edges and the lowest degree
numbers. High degree nodes represent "hubs'' that control many properties of the network as a whole and are important points of study by network scientists and engineers.)
• What does the calculated degree distribution indicate about the resulting social network? (Answer: The most likely number of signatures collected by an individual is given by the mode of the
distribution; that is, by the degree with the highest probability. If the distribution is narrow around the mode, then the students are more or less equally successful in collecting signatures. A
wide distribution indicates that some students are not as successful as other students in collecting signatures.)
• What happens to the graph if one student decides not to participate in the activity of collecting signatures from his/her classmates? What is the degree of the node associated with this student?
(Answer: The node assigned to this student will have no edges and will not be connected to other nodes in the network. Its degree will be zero.)
• What happens to the graph and its degree distribution if enough time is allowed so that each student can collect signatures from all other fellow students? (Answer: If every student obtains
signatures from every other student, then all nodes in the network would have edges to all other nodes. In this case, the degree distribution would take only one non-zero value, assigned to the
degree that equals the total number of nodes in the network. This value is one.)
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© 2013 by Regents of the University of Colorado; original © 2012 The Johns Hopkins University
Garrett Jenkinson and John Goutsias, The Johns Hopkins University, Baltimore, MD; Debbie Jenkinson and Susan Frennesson, The Pine School, Stuart, FL
Supporting Program
Complex Systems Science Laboratory, Whitaker Biomedical Engineering Institute, The Johns Hopkins University
The generous support of the National Science Foundation, Directorate for Computer and Information Science and Engineering (CISE), Division of Computing and Communication Foundations (CCF), is
gratefully acknowledged.
Last modified: April 15, 2024 | {"url":"https://www.teachengineering.org/activities/view/jhu_cnetworks_lesson01_activity1","timestamp":"2024-11-14T14:05:37Z","content_type":"text/html","content_length":"89756","record_id":"<urn:uuid:1b2bd48f-57f3-4bc6-b7dd-a760bfeef814>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00731.warc.gz"} |
Does the 5 number summary include outliers?
The Five Number Summary is a method for summarizing a distribution of data. The five numbers are the minimum, the first quartile(Q1) value, the median, the third quartile(Q3) value, and the maximum.
This is very different from the rest of the data. It is an outlier and must be removed.
What is not used in a five number summary?
2 Answers. Actually its the mean. The 25th percentile is Q1 which is used to calcualte inter-quartile range i.e. The mean has nothing to do with the five number summary or box and whisker plot.
What is the purpose of a 5 number summary?
Five-number summaries A five-number summary is especially useful in descriptive analyses or during the preliminary investigation of a large data set. A summary consists of five values: the most
extreme values in the data set (the maximum and minimum values), the lower and upper quartiles, and the median.
How do you find the five-number summary?
How to Find a Five-Number Summary: Steps
1. Step 1: Put your numbers in ascending order (from smallest to largest).
2. Step 2: Find the minimum and maximum for your data set.
3. Step 3: Find the median.
4. Step 4: Place parentheses around the numbers above and below the median.
5. Step 5: Find Q1 and Q3.
What type of plot is used to illustrate the five-number summary?
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. In a box plot, we draw a box from the first quartile to the third quartile. A vertical line goes
through the box at the median. The whiskers go from each quartile to the minimum or maximum.
What are the 5 numbers in the five-number summary?
The five number summary of a set of data is the minimum, first quartile, second quartile, third quartile, and maximum. The lower quartile, also known as Q1, is the median of the lower half of the
What is the five-number summary of the following box and whisker plot?
A box and whisker plot—also called a box plot—displays the five-number summary of a set of data. The five-number summary is the minimum, first quartile, median, third quartile, and maximum. The
whiskers go from each quartile to the minimum or maximum.
What is the five-number summary quizlet?
The five-number summary of a distribution consists of the minimum, quartile 1, median, quartile 3, and maximum. The IQR is the measure of spread we should use when using the median to measure center.
How do you find 5 number Summary?
How to calculate 5 number summary?
How to Find a Five-Number Summary: Steps Put your numbers in ascending order (from smallest to largest). Find the minimum and maximum for your data set. Now that your numbers are in order, this
should be easy to spot. Find the median. Place parentheses around the numbers above and below the median. Find Q1 and Q3. Write down your summary found in the above steps.
What is 5 number summary?
The five-number summary is a set of descriptive statistics that provide information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest
observation) the lower quartile or first quartile. the median (the middle value)
What is the five number summary in statistics?
A five number summary is a summary of a statistical dataset. The five number summary consists of the median, the first quartile (Q1), the third quartile (Q3), the minimum value, and the maximum value
of the dataset.
What is a five number summary in Excel?
The Five Number Summary is a method for summarizing a distribution of data. The five numbers are the minimum, the first quartile(Q1) value, the median, the third quartile(Q3) value, and the maximum. | {"url":"https://stw-news.org/does-the-5-number-summary-include-outliers/","timestamp":"2024-11-01T22:03:15Z","content_type":"text/html","content_length":"69293","record_id":"<urn:uuid:2d76ad97-7d8d-46f9-ad8b-893720bf3010>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00829.warc.gz"} |
What are some activities to do on Pi Day in 2024 ? - The Student's Palace
Table of Contents
1. Introduction to Pi Day
2. History and significance
3. Fun Pi Day activities for students
☆ π recitation contest
☆ Baking π-themed treats
☆ Pi-Day scavenger hunt
4. Educational Pi Day activities
☆ Exploring the history of Pi
☆ Hands-on Pi experiments
☆ π-related art projects
5. Virtual Pi Day celebration ideas
☆ Online Pi trivia quiz
☆ Virtual Pi bake-off
☆ Pi themed Zoom backgrounds
6. Incorporating Pi Day into the classroom
☆ Pi-Day lesson plans
☆ Math games and puzzles
☆ Collaborative Pi projects
7. Pi-Day challenges and competitions
☆ π digit memorization challenge
☆ π coding challenge
8. Pi Day outreach and community engagement
☆ Hosting a Pi-Day event
☆ Collaborating with local businesses
9. The impact of Pi-Day celebrations
10. Conclusion
Pi Day, celebrated on March 14th (3/14), is not just about indulging in delicious pie; it’s a day to commemorate the mathematical constant π (pi). Whether you’re a teacher looking to engage students
or someone simply eager to celebrate the wonders of mathematics, Pi-Day offers a plethora of activities. Let’s explore some exciting ways to make your Pi-Day memorable.
1. Introduction to Pi Day
Welcome readers into the fascinating world of Pi-Day. Explain the significance of celebrating π, the irrational number that represents the ratio of a circle’s circumference to its diameter.
2. History and significance
Delve into the history of Pi-Day, including its origin and the influence of physicist Larry Shaw. Highlight why π is a fundamental concept in mathematics and how celebrating it promotes a love for
the subject.
Pi Recitation Contest
Encourage friendly competition by organizing a π recitation contest. Students can challenge themselves to memorize and recite as many digits of π as possible.
Baking Pi-themed Treats
Combine education with culinary creativity. Students can engage in baking π-shaped cookies or pies, linking the celebration to a tasty learning experience.
Pi-Day Scavenger Hunt
Create an exciting Pi-Day scavenger hunt with clues related to mathematical concepts. This interactive activity fosters teamwork and problem-solving skills.
4. Educational Pi Day activities
Exploring the History of Pi
Take a deeper dive into the history of π, exploring ancient civilizations’ contributions to understanding this mathematical constant.
Hands-on Pi Experiments
Engage students with hands-on experiments that demonstrate the concept of π. This can include measuring circular objects and calculating their circumferences.
Pi-related Art Projects
Fuse mathematics with creativity through Pi-themed art projects. Students can create visual representations of the digits of π using various artistic mediums.
5. Virtual Pi Day celebration ideas
Online Pi Trivia Quiz
Host a virtual trivia quiz focusing on π-related facts. This can be a fun and educational way to involve participants from different locations.
Virtual Pi Bake-off
Encourage virtual participation by organizing a Pi-themed bake-off. Participants can showcase their creations through video calls.
Pi π Themed Zoom Backgrounds
Add a touch of Pi-Day to virtual meetings with themed Zoom backgrounds. This injects a sense of festivity into online interactions.
6. Incorporating Pi Day into the classroom
Pi-Day Lesson Plans
Provide teachers with ready-to-use lesson plans that integrate Pi-Day activities into the curriculum. This ensures a seamless infusion of π into the classroom.
Develop interactive math games and puzzles centered around π. This makes learning enjoyable while reinforcing mathematical concepts.
Collaborative Pi-Day Projects
Foster teamwork and collaboration with Pi-Day projects that involve group activities and presentations.
7. Pi Day challenges and competitions
Pi Digit Memorization Challenge
Challenge enthusiasts to memorize and recite as many digits of π as they can. Recognize and reward participants for their dedication and achievements.
Pi Day Coding Challenge
Appeal to tech-savvy individuals with a coding challenge related to π. This fosters interest in both mathematics and programming.
8. Pi Day outreach and community engagement
Hosting a Pi-Day Event
Organize a community-wide Pi-Day event, inviting local businesses and schools to participate. This strengthens community bonds and promotes a love for mathematics.
Collaborating with Local Businesses
Partner with local bakeries or restaurants to create π specials. This collaboration can generate excitement and attract more participants.
9. The impact of Pi Day celebrations
Examine the broader impact of Pi-Day celebrations on students, educators, and the community. Discuss how such events contribute to a positive perception of mathematics.
10. Conclusion
Summarize the diverse range of Pi-Day activities discussed and emphasize the importance of celebrating π in fostering a love for mathematics. Encourage readers to incorporate these ideas into their
Pi-Day celebrations for an unforgettable experience.
1. Q: Can I celebrate Pi-Day even if I’m not a math enthusiast? A: Absolutely! Pi-Day offers a variety of activities suitable for everyone, regardless of their level of interest in mathematics.
2. Q: How can I involve my community in Pi-Day celebrations? A: Organize events, collaborate with local businesses, and spread the word through social media to create a widespread community
3. Q: Are there virtual Pi-Day activities for those unable to gather in person? A: Yes, virtual trivia quizzes, online bake-offs, and Zoom backgrounds are great options for celebrating Pi Day
4. Q: Can businesses benefit from participating in Pi Day celebrations? A: Yes, businesses can attract customers by offering Pi Day specials and engaging in collaborative events, contributing to
community outreach.
5. Q: Is Pi Day only for students and educators? A: No, Pi Day is for everyone! Individuals of all ages and backgrounds can join the celebration and explore the fun side of mathematics.
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Two Search Algorithms - Programming Help
**Data Structure:** Vector <BR>
**Programming Focus:** Exposure to the Standard Template Library (STL) and review of C++
Two Search Algorithms
For this computer assignment, you are to write and implement a C++ program that uses two search algorithms (linear search and binary search) on randomly generated integers stored in a vector from
Put the definitions of all constants and the prototypes of your subroutines in your header file *twosort.h*, and complete the implementation of the `main()` routine in your source file *twosort.cc*,
along with the implementations of of your subroutines, as described below.
**Do the following in your `main()` routine:**
1) Define two vectors (`A` and `B`) with sizes `a_size` and `b_size`.
2) Pass the `A` vector to `init_vector(…)` with the coresponding seed value `a_seed`, `rand_low`, and `rand_high`.
3) Pass the `B` vector to `init_vector(…)` with the coresponding seed value `b_seed`, `rand_low`, and `rand_high`.
4) Print the elements of the `A` vector by calling the subroutine `print_vector(…)`.
5) Sort the elements of the `A` vector by calling the subroutine `sort_vector(…)`.
6) Print the elements of `A` vector after sorting its elements by calling the subroutine `print_vector(…)`.
7) Print the elements of the `B` vector by calling the subroutine `print_vector(…)`.
8) Search for each value in vector `B` in vector `A` using the *linear search algorithm* by calling the subroutine `search_vector(…)`.
9) Print the statistical values for the linear search by calling the subroutine `print_stat()`.
10) Search for each value in vector `B` (again) in vector `A` using the *binary search algorithm* by calling the subroutine `search_vector(…)`.
11) Print the statistical values for the binary search by calling the subroutine `print_stat()`.
**Implement the following subroutines:**
– `void init_vector(std::vector<int> &vec, int seed, int lo, int hi)`:
Assign random valued to the elements in `vec` by using the `seed` value. Initialize the random number generator by calling `srand(seed)` and then generate a random number between `lo` and `hi` by
using `rand()%(hi-lo+1)+lo`.
– `void print_vector(const std::vector<int> &v, int print_cols, int col_width)`:
Print the given vector `v` with `print_cols` elements on each line and with each numeric value padded out to `col_width` wide (use std::setw()). See the reference output for the formatting details
and alignment. Note that there is an aditional space printed after the element value and before the pipe character `|`.
– `void sort_vector(std::vector<int> &v)`:
Implement a sort algorithm to sort the elements of vector `v` in ascending order. For this function, use the `std::sort()` function from the STL.
– `int search_vector(const std::vector<int> &v1, const std::vector<int> &v2, bool (*p)(const std::vector<int> &, int))`:
Implement a generic search algorithm. This will take a pointer to the search routine `p()` that must be called once for each element that is in `v2` to be searched for in `v1`. It must count the
number of successful searches and return that value. (Note that this returned value is one of the parameters to be passed to `print_stat()` in your `main()`.
– `void print_stat(int found, int total)`:
Print the percent of successful searches as a floating-point number on stdout, where `found` is the total number of successful searches and `total` is the size of the test vector that is searched.
Note that the reference output includes test printed from `main()` that indicates the type of search and output from `print_stat()` that indicates portion of the output that is the same for both
searches and the percentage.
– `bool linear_search(const std::vector<int> &v, int x)`:
A linear search algorithm, where `x` is the value to search for in vector `v`. It simply starts searching for `x` from the beginning of vector `v` to the end, but it stops searching when there is a
match. If the search is successful, it returns `true`; otherwise, it returns `false`. To implement this routine, use the `std::find()` function from the STL: https://en.cppreference.com/w/cpp/
algorithm/find Note that `std::find()` requires the use of iterators to specify the range of values to check in `v`. See https://en.cppreference.com/w/cpp/container/vector for a discussion of how to
use `vector.begin()` and `vector.end()` to get the iterators needed for `std::find()`. Note that the example on page https://en.cppreference.com/w/cpp/container/vector/begin that shows how to call
`std::accumulate()` looks very similar to how you need to call `std::find()`!
– `bool binary_search(const std::vector<int> &v, int x)`:
A binary search algorithm, where `x` is the value to search for in vector `v`. If the search is successful, it returns `true`; otherwise, it returns `false`. To implement this routine, simply call
the `std::binary_search()` function from the STL: https://en.cppreference.com/w/cpp/algorithm/binary_search Note that the example showing how to call `std::binary_search()` is exactly the same way
you want to call `std::find()` in your `linear_search()` function!
**How The Reference Output Was Created:**
– ./twosearch > twosearch.out
– ./twosearch -w3 > twosearch-w3.out
– ./twosearch -l2 -h1002 > twosearch-l2-h1002.out
– ./twosearch -b 18 -c 9 > twosearch-b18-c19.out
– ./twosearch -a250 -b99 -c14 -h1234 -l21 -w5 -x9 -y7 > twosearch-a250-b99-c14-h1234-l21-w5-x9-y7.out
– ./twosearch -x &> twosearch-x.out
**Programming Notes:**
– Note that the last example reference output run used `&>` to save its output because it fails to run and prints to `cerr` which would not otherwise be saved into the output file for your reference!
**Assignment Notes:**
– Include any necessary headers and add necessary global constants.
– You are not allowed to use any I/O functions from the C library, such as scanf() or printf(). Instead, use the I/O functions from the C++ library, such as cin or cout.
– Add documentation to the appropriate source files as discussed in your class.
When your program is ready for grading, ***commit*** and ***push*** your local repository to remote git classroom repository and follow the _**Assignment Submission Instructions**_. | {"url":"https://www.edulissy.org/product/programming-focus-exposure-to-the-standard-template-library-stl-and-review-of-c/","timestamp":"2024-11-11T12:57:35Z","content_type":"text/html","content_length":"179001","record_id":"<urn:uuid:f36bae39-6016-40b9-a201-d8d08b392719>","cc-path":"CC-MAIN-2024-46/segments/1730477028230.68/warc/CC-MAIN-20241111123424-20241111153424-00611.warc.gz"} |
Issue 2735: std::abs(short), std::abs(signed char) and others should return int instead of
double in order to be compatible with C++98 and C
This page is a snapshot from the LWG issues list, see the Library Active Issues List for more information and the meaning of C++17 status.
2735. std::abs(short), std::abs(signed char) and others should return int instead of double in order to be compatible with C++98 and C
Section: 29.7 [c.math] Status: C++17 Submitter: Jörn Heusipp Opened: 2016-06-16 Last modified: 2017-07-30
Priority: 3
View all other issues in [c.math].
View all issues with C++17 status.
Consider this C++98 program:
#include <cmath>
#include <cstdlib>
int main() {
return std::abs(static_cast<short>(23)) % 42;
This works fine with C++98 compilers. At the std::abs(short) call, short gets promoted to int and std::abs(int) is called.
C++11 added the following wording on page 1083 §26.9 p15 b2 [c.math]:
Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double parameters are
effectively cast to double.
C++17 draft additionally adds on page 1080 §26.9 p10 [c.math]:
If abs() is called with an argument of type X for which is_unsigned<X>::value is true and if X cannot be converted to int by integral promotion (4.5), the program is ill-formed. [Note: Arguments
that can be promoted to int are permitted for compatibility with C. — end note]
It is somewhat confusing and probably even contradictory to on the one hand specify abs() in terms of integral promotion in §26.9 p10 and on the other hand demand all integral types to be converted
to double in §26.9 p15 b2.
Most compilers (each with their own respective library implementation) I tested (MSVC, Clang, older GCC) appear to not consider §26.9 p15 b2 for std::abs and compile the code successfully. GCC
4.5-5.3 (for std::abs but not for ::abs) as well as GCC >=6.0 (for both std::abs and ::abs) fail to compile in the following way: Taking §26.9 p15 b2 literally and applying it to abs() (which is
listed in §26.9 p12) results in abs(short) returning double, and with operator% not being specified for double, this makes the programm ill-formed. I do acknowledge the reason for the wording and
semantics demanded by §26.9 p15 b2, i.e. being able to call math functions with integral types or with partly floating point types and partly integral types. Converting integral types to double
certainly makes sense here for all the other floating point math functions. However, abs() is special. abs() has overloads for the 3 wider integral types which return integral types. abs() originates
in the C standard in stdlib.h and had originally been specified for integral types only. Calling it in C with a short argument returns an int. Calling std::abs(short) in C++98 also returns an int.
Calling std::abs(short) in C++11 and later with §26.9 p15 b2 applied to abs() suddenly returns a double. Additionally, this behaviour also breaks third-party C headers which contain macros or inline
functions calling abs(short). As per discussion on std-discussion, my reading of the standard as well as GCC's interpretation seem valid. However, as can be seen, this breaks existing code. In
addition to the compatibilty concerns, having std::abs(short) return double is also very confusing and unintuitive. The other (possibly, depending on their respective size relative to int) affected
types besides short are signed char, unsigned char and unsigned short, and also char, char16_t, char32_t and wchar_t, (all of these are or may be promotable to int). Wider integral types are not
affected because explicit overloads are specified for those types by §26.9 p6, §26.9 p7 and §26.9 p9. div() is also not affected because it is neither listed in §26.9 p12, nor does it actually
provide any overload for double at all. As far as I can see, the proposed or implemented solutions for LWG 2294^(i), 2192^(i) and/or 2086^(i) do not resolve this issue. I think both, §26.9 p10
[c.math] and §26.9 p15 [c.math] need some correction and clarification. (Note: These changes would explicitly render the current implementation in GCC's libstdc++ non-conforming, which would be a
good thing, as outlined above.)
Previous resolution [SUPERSEDED]:
This wording is relative to N4594.
1. Modify 29.7 [c.math] as indicated:
-10- If abs() is called with an argument of type X for which is_unsigned<X>::value is true and if X cannot be converted to int by integral promotion (4.5), the program is ill-formed. [
Note: Arguments that can be promoted to int are [DEL:permitted for:DEL] compatibility with C. — end note]
[…] -15- Moreover, there shall be additional overloads sufficient to ensure:
1. If any argument of arithmetic type corresponding to a double parameter has type long double, then all arguments of arithmetic type (3.9.1) corresponding to double parameters are
effectively cast to long double.
2. Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double
parameters are effectively cast to double.
3. Otherwise, all arguments of arithmetic type corresponding to double parameters have type float.
See also: ISO C 7.5, 7.10.2, 7.10.6.
[2016-07 Chicago]
Monday: Some of this has been changed in N4606; the rest of the changes may be editorial.
Fri PM: Move to Tentatively Ready
Proposed resolution:
This wording is relative to N4606.
1. Modify 29.7.1 [cmath.syn] as indicated:
-2- For each set of overloaded functions within <cmath>, there shall be additional overloads sufficient to ensure:
1. If any argument of arithmetic type corresponding to a double parameter has type long double, then all arguments of arithmetic type (3.9.1) corresponding to double parameters are
effectively cast to long double.
2. Otherwise, if any argument of arithmetic type corresponding to a double parameter has type double or an integer type, then all arguments of arithmetic type corresponding to double
parameters are effectively cast to double.
3. Otherwise, all arguments of arithmetic type corresponding to double parameters have type float.
See also: ISO C 7.5, 7.10.2, 7.10.6. | {"url":"https://cplusplus.github.io/LWG/issue2735","timestamp":"2024-11-02T19:03:32Z","content_type":"text/html","content_length":"12874","record_id":"<urn:uuid:f0fd8bba-e596-47f6-8f11-85fea7c33f0f>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00724.warc.gz"} |
Asymmetric maximum likelihood (AML) - Data Science Wiki
What is Asymmetric maximum likelihood (AML) ?
Asymmetric maximum
(AML) is a statistical method used to estimate
parameters in cases where the likelihood function is not symmetrical. This can occur when there is a significant difference in the
of the data for different values of the model parameters.
One example of when AML may be used is in financial modeling. In the case of a stock price, the likelihood function may be skewed to the right, with a higher variance for higher stock prices compared
to lower prices. In this case, using standard
maximum likelihood estimation
(MLE) would underestimate the true value of the model parameters, leading to biased results. AML can be used to account for this asymmetry and provide more accurate estimates.
Another example is in medical research, where AML may be used to model the efficacy of a new treatment. In this case, the likelihood function may be skewed to the left, with a higher variance for
lower efficacy rates compared to higher rates. Using MLE would again lead to biased estimates, and AML can be used to correct for this asymmetry.
The key difference between AML and MLE is that AML allows for different variances for different values of the model parameters. This is achieved by using a weighting function, which adjusts the
contribution of each data point to the likelihood function based on its position relative to the model parameters. This weighting function is determined through a process of iterative optimization,
in which the model parameters are updated based on the weighted likelihood function until a maximum likelihood estimate is reached.
Overall, AML provides a more flexible and accurate method for estimating model parameters in cases where the likelihood function is not symmetrical. This can lead to more reliable results in
applications such as financial modeling and medical research. | {"url":"https://datasciencewiki.net/asymmetric-maximum-likelihood-aml/","timestamp":"2024-11-13T15:48:00Z","content_type":"text/html","content_length":"41217","record_id":"<urn:uuid:9cc04c88-90cf-409c-b3a9-0f34099e4992>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00430.warc.gz"} |
Qualifier | UWCMT
top of page
Date: March 1st - March 11th (schools could choose any day out of these dates)
Location: Students around the world, online (proctored venue for registered schools if possible)
More info on the level please
Students are allowed to participate in the level for the grade which they are in or higher levels. For example, a grade 8 student could participate in the G9-10 level. It is important to note that
only G9-10 has the Finals for 2022.
How challenging is it?
Our tournament is meant to be suitable to many students. We encourage many students to try this tournament out. The majority of the questions in both the
🌐lympi(@^^)/~~~:D and the SDG round are meant to be able to be solved by most students. There are, however, some questions (like 2 per each section) which are challenging in order to keep the more
experienced students engaged.
15 Questions in total:
Around 10 should be something which most students could do with moderate to no difficulty.
Around 3 would be a challenge for regular students, but possible with effort.
Around 2 should be challenging questions for the more experienced students
Maximum points for this round is 90. Each of the questions are multiple choice with 5 choices. 6 points for correct, 1.5 points for blank and 0 points for incorrect. The expected result for randomly
guessing with no elimination is less than blank so guess at your own risk!
This round will reference mathematicians around the world and from a diverse backgrounds and cultures to make everyone feel more welcome towards mathematics.
Fun fact: The Olympiad Round in our first tournament in 2021 used to have 25 questions.
Olympiad Info
SDG for short. It focuses on UN's SDGs. Some of the questions could be on real world projects which focuses on the SDGs.
Maximum points for this round is 60. It contains two parts worth 30 marks each. Each section focuses on one of the SDG. Each question could give 1 to 7 points based on difficulty. The questions are
integer answers and the student gets the designated number of marks for correct or 0 marks for blank or incorrect.
This round is done in the Qualifier with the Olympiad.
Sustainable Development Goal
Nearly all of the 1 to 4 mark questions should be something which the average student should be able to do. 5 mark questions are also something many students could do, but requires effort. 6 and 7
mark questions are for the best students, but there is only one of these types of questions per section.
Fun fact 1: This round is in some ways an improvement of the Theme Round in the first UWCMT which took place in 2021.
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Computing Limits
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Section 2.5 : Computing Limits
In the previous section we saw that there is a large class of functions that allows us to use
\[\mathop {\lim }\limits_{x \to a} f\left( x \right) = f\left( a \right)\]
to compute limits. However, there are also many limits for which this won’t work easily. The purpose of this section is to develop techniques for dealing with some of these limits that will not allow
us to just use this fact.
Let’s first go back and take a look at one of the first limits that we looked at and compute its exact value and verify our guess for the limit.
Example 1
Evaluate the following limit. \[\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} + 4x - 12}}{{{x^2} - 2x}}\]
Show Solution
First let’s notice that if we try to plug in \(x = 2\) we get,
\[\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} + 4x - 12}}{{{x^2} - 2x}} = \frac{0}{0}\]
So, we can’t just plug in \(x = 2\) to evaluate the limit. So, we’re going to have to do something else.
The first thing that we should always do when evaluating limits is to simplify the function as much as possible. In this case that means factoring both the numerator and denominator. Doing this
\[\begin{align*}\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} + 4x - 12}}{{{x^2} - 2x}} & = \mathop {\lim }\limits_{x \to 2} \frac{{\left( {x - 2} \right)\left( {x + 6} \right)}}{{x\left( {x - 2} \
right)}}\\ & = \mathop {\lim }\limits_{x \to 2} \frac{{x + 6}}{x}\end{align*}\]
So, upon factoring we saw that we could cancel an \(x - 2\) from both the numerator and the denominator. Upon doing this we now have a new rational expression that we can plug \(x = 2\) into because
we lost the division by zero problem. Therefore, the limit is,
\[\mathop {\lim }\limits_{x \to 2} \frac{{{x^2} + 4x - 12}}{{{x^2} - 2x}} = \mathop {\lim }\limits_{x \to 2} \frac{{x + 6}}{x} = \frac{8}{2} = 4\]
Note that this is in fact what we guessed the limit to be.
Before leaving this example let’s discuss the fact that we couldn’t plug \(x = 2\) into our original limit but once we did the simplification we just plugged in \(x = 2\) to get the answer. At first
glance this may appear to be a contradiction.
In the original limit we couldn’t plug in \(x = 2\) because that gave us the 0/0 situation that we couldn’t do anything with. Upon doing the simplification we can note that,
\[\frac{{{x^2} + 4x - 12}}{{{x^2} - 2x}} = \frac{{x + 6}}{x}\hspace{0.25in}{\mbox{provided }}x \ne 2\]
In other words, the two equations give identical values except at \(x = 2\) and because limits are only concerned with that is going on around the point \(x = 2\) the limit of the two equations will
be equal. More importantly, in the simplified version we get a “nice enough” equation and so what is happening around \(x = 2\) is identical to what is happening at \(x = 2\).
We can therefore take the limit of the simplified version simply by plugging in \(x = 2\) even though we couldn’t plug \(x = 2\) into the original equation and the value of the limit of the
simplified equation will be the same as the limit of the original equation.
On a side note, the 0/0 we initially got in the previous example is called an indeterminate form. This means that we don’t really know what it will be until we do some more work. Typically, zero in
the denominator means it’s undefined. However, that will only be true if the numerator isn’t also zero. Also, zero in the numerator usually means that the fraction is zero, unless the denominator is
also zero. Likewise, anything divided by itself is 1, unless we’re talking about zero.
So, there are really three competing “rules” here and it’s not clear which one will win out. It’s also possible that none of them will win out and we will get something totally different from
undefined, zero, or one. We might, for instance, get a value of 4 out of this, to pick a number completely at random.
When simply evaluating an equation 0/0 is undefined. However, in taking the limit, if we get 0/0 we can get a variety of answers and the only way to know which one is correct is to actually compute
the limit.
There are many more kinds of indeterminate forms and we will be discussing indeterminate forms at length in the next chapter.
Let’s take a look at a couple of more examples.
Example 2
Evaluate the following limit. \[\mathop {\lim }\limits_{h \to 0} \frac{{2{{\left( { - 3 + h} \right)}^2} - 18}}{h}\]
Show Solution
In this case we also get 0/0 and factoring is not really an option. However, there is still some simplification that we can do.
\[\begin{align*}\mathop {\lim }\limits_{h \to 0} \frac{{2{{\left( { - 3 + h} \right)}^2} - 18}}{h} & = \mathop {\lim }\limits_{h \to 0} \frac{{2\left( {9 - 6h + {h^2}} \right) - 18}}{h}\\ & = \mathop
{\lim }\limits_{h \to 0} \frac{{18 - 12h + 2{h^2} - 18}}{h}\\ & = \mathop {\lim }\limits_{h \to 0} \frac{{ - 12h + 2{h^2}}}{h}\end{align*}\]
So, upon multiplying out the first term we get a little cancellation and now notice that we can factor an \(h\) out of both terms in the numerator which will cancel against the \(h\) in the
denominator and the division by zero problem goes away and we can then evaluate the limit.
\[\begin{align*}\mathop {\lim }\limits_{h \to 0} \frac{{2{{\left( { - 3 + h} \right)}^2} - 18}}{h} & = \mathop {\lim }\limits_{h \to 0} \frac{{ - 12h + 2{h^2}}}{h}\\ & = \mathop {\lim }\limits_{h \to
0} \frac{{h\left( { - 12 + 2h} \right)}}{h}\\ & = \mathop {\lim }\limits_{h \to 0} \,\, - 12 + 2h = - 12\end{align*}\]
Example 3
Evaluate the following limit. \[\mathop {\lim }\limits_{t \to 4} \frac{{t - \sqrt {3t + 4} }}{{4 - t}}\]
Show Solution
This limit is going to be a little more work than the previous two. Once again however note that we get the indeterminate form 0/0 if we try to just evaluate the limit. Also note that neither of the
two examples will be of any help here, at least initially. We can’t factor the equation and we can’t just multiply something out to get the equation to simplify.
When there is a square root in the numerator or denominator we can try to rationalize and see if that helps. Recall that rationalizing makes use of the fact that
\[\left( {a + b} \right)\left( {a - b} \right) = {a^2} - {b^2}\]
So, if either the first and/or the second term have a square root in them the rationalizing will eliminate the root(s). This might help in evaluating the limit.
Let’s try rationalizing the numerator in this case.
\[\mathop {\lim }\limits_{t \to 4} \frac{{t - \sqrt {3t + 4} }}{{4 - t}} = \mathop {\lim }\limits_{t \to 4} \frac{{\left( {t - \sqrt {3t + 4} } \right)}}{{\left( {4 - t} \right)}}\,\frac{{\left( {t +
\sqrt {3t + 4} } \right)}}{{\left( {t + \sqrt {3t + 4} } \right)}}\]
Remember that to rationalize we just take the numerator (since that’s what we’re rationalizing), change the sign on the second term and multiply the numerator and denominator by this new term.
Next, we multiply the numerator out being careful to watch minus signs.
\[\begin{align*}\mathop {\lim }\limits_{t \to 4} \frac{{t - \sqrt {3t + 4} }}{{4 - t}} & = \mathop {\lim }\limits_{t \to 4} \frac{{{t^2} - \left( {3t + 4} \right)}}{{\left( {4 - t} \right)\left( {t +
\sqrt {3t + 4} } \right)}}\\ & = \mathop {\lim }\limits_{t \to 4} \frac{{{t^2} - 3t - 4}}{{\left( {4 - t} \right)\left( {t + \sqrt {3t + 4} } \right)}}\end{align*}\]
Notice that we didn’t multiply the denominator out as well. Most students come out of an Algebra class having it beaten into their heads to always multiply this stuff out. However, in this case
multiplying out will make the problem very difficult and in the end you’ll just end up factoring it back out anyway.
At this stage we are almost done. Notice that we can factor the numerator so let’s do that.
\[\mathop {\lim }\limits_{t \to 4} \frac{{t - \sqrt {3t + 4} }}{{4 - t}} = \mathop {\lim }\limits_{t \to 4} \frac{{\left( {t - 4} \right)\left( {t + 1} \right)}}{{\left( {4 - t} \right)\left( {t + \
sqrt {3t + 4} } \right)}}\]
Now all we need to do is notice that if we factor a “-1”out of the first term in the denominator we can do some canceling. At that point the division by zero problem will go away and we can evaluate
the limit.
\[\begin{align*}\mathop {\lim }\limits_{t \to 4} \frac{{t - \sqrt {3t + 4} }}{{4 - t}} & = \mathop {\lim }\limits_{t \to 4} \frac{{\left( {t - 4} \right)\left( {t + 1} \right)}}{{ - \left( {t - 4} \
right)\left( {t + \sqrt {3t + 4} } \right)}}\\ & = \mathop {\lim }\limits_{t \to 4} \frac{{t + 1}}{{ - \left( {t + \sqrt {3t + 4} } \right)}}\\ & = - \frac{5}{8}\end{align*}\]
Note that if we had multiplied the denominator out we would not have been able to do this canceling and in all likelihood would not have even seen that some canceling could have been done.
So, we’ve taken a look at a couple of limits in which evaluation gave the indeterminate form 0/0 and we now have a couple of things to try in these cases.
Let’s take a look at another kind of problem that can arise in computing some limits involving piecewise functions.
Example 4
Given the function, \[g\left( y \right) = \left\{ \begin{align*}{y^2} + 5 & \hspace{0.25in}{\mbox{if }}y < - 2\\ 1 - 3y & \hspace{0.25in}{\mbox{if }}y \ge - 2\end{align*} \right.\]
Compute the following limits.
1. \(\mathop {\lim }\limits_{y \to 6} g\left( y \right)\)
2. \(\mathop {\lim }\limits_{y \to - 2} g\left( y \right)\)
Show All Solutions Hide All Solutions
\(\mathop {\lim }\limits_{y \to 6} g\left( y \right)\)
Show Solution
In this case there really isn’t a whole lot to do. In doing limits recall that we must always look at what’s happening on both sides of the point in question as we move in towards it. In this case \
(y = 6\) is completely inside the second interval for the function and so there are values of \(y\) on both sides of \(y = 6\) that are also inside this interval. This means that we can just use the
fact to evaluate this limit.
\[\begin{align*}\mathop {\lim }\limits_{y \to 6} g\left( y \right) & = \mathop {\lim }\limits_{y \to 6}( 1 - 3y)\\ & = - 17\end{align*}\]
\(\mathop {\lim }\limits_{y \to - 2} g\left( y \right)\)
Show Solution
This part is the real point to this problem. In this case the point that we want to take the limit for is the cutoff point for the two intervals. In other words, we can’t just plug \(y = - 2\) into
the second portion because this interval does not contain values of \(y\) to the left of \(y = - 2\) and we need to know what is happening on both sides of the point.
To do this part we are going to have to remember the fact from the section on one-sided limits that says that if the two one-sided limits exist and are the same then the normal limit will also exist
and have the same value.
Notice that both of the one-sided limits can be done here since we are only going to be looking at one side of the point in question. So, let’s do the two one-sided limits and see what we get.
\[\begin{align*}\mathop {\lim }\limits_{y \to - {2^ - }} g\left( y \right) & = \mathop {\lim }\limits_{y \to - {2^ - }} ({y^2} + 5)\hspace{0.25in}{\mbox{since }}y \to {-2^ - }{\mbox{ implies }}y < -
2\\ & = 9\end{align*}\] \[\begin{align*}\mathop {\lim }\limits_{y \to - {2^ + }} g\left( y \right) & = \mathop {\lim }\limits_{y \to - {2^ + }} (1 - 3y)\hspace{0.25in}{\mbox{since }}y \to {-2^ + }{\
mbox{ implies }}y > - 2\\ & = 7\end{align*}\]
So, in this case we can see that,
\[\mathop {\lim }\limits_{y \to - {2^ - }} g\left( y \right) = 9 \ne 7 = \mathop {\lim }\limits_{y \to - {2^ + }} g\left( y \right)\]
and so since the two one sided limits aren’t the same
\[\mathop {\lim }\limits_{y \to - 2} g\left( y \right)\]
doesn’t exist.
Note that a very simple change to the function will make the limit at \(y = - 2\) exist so don’t get in into your head that limits at these cutoff points in piecewise function don’t ever exist as the
following example will show.
Example 5
Evaluate the following limit. \[\mathop {\lim }\limits_{y \to - 2} g\left( y \right)\hspace{0.25in}{\mbox{where,}}\,\,g\left( y \right) = \left\{ \begin{align*}{y^2} + 5 & \hspace{0.25in}{\mbox{if }}
y < - 2\\ 3 - 3y & \hspace{0.25in}{\mbox{if }}y \ge - 2\end{align*} \right.\]
Show Solution
The two one-sided limits this time are,
\[\begin{align*}\mathop {\lim }\limits_{y \to - {2^ - }} g\left( y \right) & = \mathop {\lim }\limits_{y \to - {2^ - }} ({y^2} + 5)\hspace{0.25in}{\mbox{since }}y \to {-2^ - }{\mbox{ implies }}y < -
2\\ & = 9\end{align*}\] \[\begin{align*}\mathop {\lim }\limits_{y \to - {2^ + }} g\left( y \right) & = \mathop {\lim }\limits_{y \to - {2^ + }} (3 - 3y)\hspace{0.25in}{\mbox{since }}y \to {-2^ + }{\
mbox{ implies }}y > - 2\\ & = 9\end{align*}\]
The one-sided limits are the same so we get,
\[\mathop {\lim }\limits_{y \to - 2} g\left( y \right) = 9\]
There is one more limit that we need to do. However, we will need a new fact about limits that will help us to do this.
If \(f\left( x \right) \le g\left( x \right)\) for all \(x\) on \([a, b]\) (except possibly at \(x = c\)) and \(a \le c \le b\) then,
\[\mathop {\lim }\limits_{x \to c} f\left( x \right) \le \mathop {\lim }\limits_{x \to c} g\left( x \right)\]
Note that this fact should make some sense to you if we assume that both functions are nice enough. If both of the functions are “nice enough” to use the limit evaluation fact then we have,
\[\mathop {\lim }\limits_{x \to c} f\left( x \right) = f\left( c \right) \le g\left( c \right) = \mathop {\lim }\limits_{x \to c} g\left( x \right)\]
The inequality is true because we know that \(c\) is somewhere between \(a\) and \(b\) and in that range we also know \(f\left( x \right) \le g\left( x \right)\).
Note that we don’t really need the two functions to be nice enough for the fact to be true, but it does provide a nice way to give a quick “justification” for the fact.
Also, note that we said that we assumed that \(f\left( x \right) \le g\left( x \right)\) for all \(x\) on \([a, b]\) (except possibly at \(x = c\)). Because limits do not care what is actually
happening at \(x = c\) we don’t really need the inequality to hold at that specific point. We only need it to hold around \(x = c\) since that is what the limit is concerned about.
We can take this fact one step farther to get the following theorem.
Squeeze Theorem
Suppose that for all \(x\) on \([a, b]\) (except possibly at \(x = c\)) we have,
\[f\left( x \right) \le h\left( x \right) \le g\left( x \right)\]
Also suppose that,
\[\mathop {\lim }\limits_{x \to c} f\left( x \right) = \mathop {\lim }\limits_{x \to c} g\left( x \right) = L\]
for some \(a \le c \le b\). Then,
\[\mathop {\lim }\limits_{x \to c} h\left( x \right) = L\]
As with the previous fact we only need to know that \(f\left( x \right) \le h\left( x \right) \le g\left( x \right)\) is true around \(x = c\) because we are working with limits and they are only
concerned with what is going on around \(x = c\) and not what is actually happening at \(x = c\).
Now, if we again assume that all three functions are nice enough (again this isn’t required to make the Squeeze Theorem true, it only helps with the visualization) then we can get a quick sketch of
what the Squeeze Theorem is telling us. The following figure illustrates what is happening in this theorem.
From the figure we can see that if the limits of \(f(x)\) and \(g(x)\) are equal at \(x = c\) then the function values must also be equal at \(x = c\) (this is where we’re using the fact that we
assumed the functions were “nice enough”, which isn’t really required for the Theorem). However, because \(h(x)\) is “squeezed” between \(f(x)\) and \(g(x)\) at this point then \(h(x)\) must have the
same value. Therefore, the limit of \(h(x)\) at this point must also be the same.
The Squeeze theorem is also known as the Sandwich Theorem and the Pinching Theorem.
So, how do we use this theorem to help us with limits? Let’s take a look at the following example to see the theorem in action.
Example 6
Evaluate the following limit. \[\mathop {\lim }\limits_{x \to 0} {x^2}\cos \left( {\frac{1}{x}} \right)\]
Show Solution
In this example none of the previous examples can help us. There’s no factoring or simplifying to do. We can’t rationalize and one-sided limits won’t work. There’s even a question as to whether this
limit will exist since we have division by zero inside the cosine at \(x=0\).
The first thing to notice is that we know the following fact about cosine.
\[ - 1 \le \cos \left( x \right) \le 1\]
Our function doesn’t have just an \(x\) in the cosine, but as long as we avoid \(x = 0\) we can say the same thing for our cosine.
\[ - 1 \le \cos \left( {\frac{1}{x}} \right) \le 1\]
It’s okay for us to ignore \(x = 0\) here because we are taking a limit and we know that limits don’t care about what’s actually going on at the point in question, \(x = 0\) in this case.
Now if we have the above inequality for our cosine we can just multiply everything by an \(x^{2}\) and get the following.
\[ - {x^2} \le {x^2}\cos \left( {\frac{1}{x}} \right) \le {x^2}\]
In other words we’ve managed to squeeze the function that we were interested in between two other functions that are very easy to deal with. So, the limits of the two outer functions are.
\[\mathop {\lim }\limits_{x \to 0} {x^2} = 0\hspace{0.25in}\hspace{0.25in}\mathop {\lim }\limits_{x \to 0} \left( { - {x^2}} \right) = 0\]
These are the same and so by the Squeeze theorem we must also have,
\[\mathop {\lim }\limits_{x \to 0} {x^2}\cos \left( {\frac{1}{x}} \right) = 0\]
We can verify this with the graph of the three functions. This is shown below.
In this section we’ve seen several tools that we can use to help us to compute limits in which we can’t just evaluate the function at the point in question. As we will see many of the limits that
we’ll be doing in later sections will require one or more of these tools. | {"url":"https://tutorial.math.lamar.edu/classes/calci/computinglimits.aspx","timestamp":"2024-11-14T10:49:17Z","content_type":"text/html","content_length":"94487","record_id":"<urn:uuid:4e7e0ab8-1948-4512-bbf3-ebe0ee8d10a9>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00488.warc.gz"} |
Should I Vaccinate? A Mathematical Model.
Economists have long preoccupied themselves with trying to make rational decisions, especially when facing risk or uncertainty. From allocating your money between different asset classes, to choosing
whether or not to be vaccinated — such rational choice models can help you decide whether or not the risks of a decision are worth the expected payoffs.
In 2005, long before COVID-19, researchers from the City University of London’s economics department published a paper on how rational individuals can decide on whether to be vaccinated. I thought it
would be interesting to see how that might help us make some rational decisions about whether or not to take a COVID-19 vaccine.
But before we proceed — two things should be noted. Firstly, this model is a selfish one. It does not consider how the calculus would change if the majority behaved cooperatively, making it safer for
everyone in the group. So if you care about people other than yourself, this model does not account for that. Secondly, this model is highly dependent on the reliability of your input calculations.
Calculate the inputs wrongly, and you are likely to produce irrational outcomes. As with all models: garbage in, garbage out.
So assuming you are both (i) incredibly selfish, and (ii) incredibly good at accurately calculating probabilities and outcomes, here’s what you should do:
Step 1: Relative Risks
Calculate your expected risks (probability) of:
• being infected (ρ), and
• having adverse reactions from the vaccine you intend to take (φ)
Step 2: Estimated Losses
Calculate your expected losses:
• Due to vaccine side effects (S): Like nearly everything in life, taking a vaccine comes with risks such as adverse side effects. The losses from adverse side effects can be calculated by
estimating your expected income losses and attendant costs arising from negative side effects of the vaccine.
• Due to infection from not being vaccinated (I): Not getting vaccinated is not risk-free either. You can calculate the estimated losses you are likely to suffer by estimating your expected income
losses and attendant costs arising from infection.
Step 3: Vaccine Efficacy
Calculate the expected:
• efficacy rate of the vaccine you intend to take (e): This is readily available from the manufacturers’ data from their clinical trials.
Step 4: Should I Vaccinate?
Put the input variables you calculated above into the simplified decision rule below (relax, its just multiplying fractions):
This decision rule expresses four key ideas:
1. It is only rational to vaccinate when you expect the relative risk of infection to risk of side effects (left hand side) to be greater than the threshold probability level of expected losses
(right hand side).
2. The higher the expected losses from adverse side effects (S), the higher is the threshold probability on the right hand side of the model. A larger risk of adverse events means more expected
income losses arising from vaccine side effects, reducing your willingness to vaccinate.
3. The higher the expected losses from infection (I), the lower the threshold level of probability above which individual decides to get vaccinated.
4. The vaccine efficacy (e) has an inverse relationship with the threshold probability (right hand side). The higher the vaccine efficacy, the lower the possibility of infection, and therefore the
larger the propensity to accept vaccination; and vice versa.
However you feel about the vaccine, this model provides a handy way to think rationally about balancing both the risks and benefits of being vaccinated. It also encourages us to identify our key
assumptions more clearly, even if you arrive at a different conclusion from everyone else.
If you found this helpful, feel free to share it with anyone you know who may be undecided about getting vaccinated. | {"url":"https://askivan.medium.com/should-i-vaccinate-a-mathematical-model-e85dbb5554f1?responsesOpen=true&sortBy=REVERSE_CHRON&source=author_recirc-----b36ba5b4afba----2---------------------6321aaf0_ff3e_4a5e_a2e6_0eee8858c9a3-------","timestamp":"2024-11-09T11:12:01Z","content_type":"text/html","content_length":"110364","record_id":"<urn:uuid:af9a1477-f212-44d4-954e-4cb4c0b671e9>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00490.warc.gz"} |
Confusion Matrix
What is a Confusion Matrix?
A confusion matrix is a table that is often used to describe the performance of a classification model (or "classifier") on a set of test data for which the true values are known. It allows
visualization of the performance of an algorithm, and helps in understanding whether the system is confusing two classes (i.e., commonly mislabeling one as another).
The confusion matrix shows the ways in which your classification model is confused when it makes predictions. It gives insight not only into the errors being made by your classifier but, more
importantly, the types of errors that are being made.
Confusion Matrix Structure
A confusion matrix is a table with two dimensions ("Actual" and "Predicted"), and identical sets of "classes" in both dimensions. It compares the actual target values with those predicted by the
machine learning model.
The general structure of a confusion matrix for a binary classifier is as follows:
Actual Positive Negative
Positive True Positive (TP) False Negative (FN)
Negative False Positive (FP) True Negative (TN)
The four quadrants of the confusion matrix correspond to the following:
• True Positive (TP): Correctly predicted positive class.
• True Negative (TN): Correctly predicted negative class.
• False Positive (FP): Incorrectly predicted positive class (Type I error).
• False Negative (FN): Incorrectly predicted negative class (Type II error).
Confusion Matrix Example
Suppose we have a binary classification problem where we are predicting whether emails are "Spam" or "Not Spam". We test our classifier on a set of 100 emails:
• 50 emails are actually Spam, and 50 are Not Spam.
• Our classifier predicts 45 emails as Spam, and 55 as Not Spam.
Let's say that:
• Out of the 50 actual Spams, the classifier correctly predicted 40 as Spam (True Positives), and incorrectly predicted 10 as Not Spam (False Negatives).
• Out of the 50 actual Not Spams, the classifier incorrectly predicted 5 as Spam (False Positives), and correctly predicted 45 as Not Spam (True Negatives).
The confusion matrix would be:
Actual Spam Not Spam
Spam TP = 40 FN = 10
Not Spam FP = 5 TN = 45
Metrics Derived from the Confusion Matrix
The confusion matrix provides the foundation for calculating a variety of performance metrics. Some of the most commonly used metrics include:
Accuracy is the proportion of the total number of predictions that were correct.
Accuracy = (TP + TN) / (TP + TN + FP + FN)
Example Calculation:
Accuracy = (40 + 45) / (40 + 45 + 5 + 10) = 85 / 100 = 0.85
Precision is the proportion of positive identifications that were actually correct. It answers: "What proportion of predicted positives is actually positive?"
Precision = TP / (TP + FP)
Example Calculation:
Precision = 40 / (40 + 5) = 40 / 45 ≈ 0.8889
Recall (Sensitivity or True Positive Rate)
Recall is the proportion of actual positives that were correctly identified. It answers: "What proportion of actual positives was correctly classified?"
Recall = TP / (TP + FN)
Example Calculation:
Recall = 40 / (40 + 10) = 40 / 50 = 0.80
Specificity (True Negative Rate)
Specificity is the proportion of actual negatives that were correctly identified.
Specificity = TN / (TN + FP)
Example Calculation:
Specificity = 45 / (45 + 5) = 45 / 50 = 0.90
F1 Score
The F1 Score is the harmonic mean of Precision and Recall. It provides a balance between Precision and Recall.
F1 Score = 2 * (Precision * Recall) / (Precision + Recall)
Example Calculation:
F1 Score = 2 * (0.8889 * 0.80) / (0.8889 + 0.80) ≈ 0.8421
False Positive Rate (Fall-out)
The proportion of actual negatives that were incorrectly classified as positives.
False Positive Rate = FP / (FP + TN)
Example Calculation:
False Positive Rate = 5 / (5 + 45) = 5 / 50 = 0.10
Understanding Class Imbalance
In datasets where one class significantly outnumbers another (class imbalance), accuracy can be a misleading metric. For example, in a dataset where 99% of the instances belong to one class, a
classifier that always predicts that class will have 99% accuracy but will be ineffective.
The confusion matrix allows us to see the breakdown of correct and incorrect classifications for each class, which gives a more comprehensive view of a model's performance, especially in the presence
of imbalanced classes.
Confusion Matrix in Multi-Class Classification
For multi-class classification problems, the confusion matrix becomes a larger square matrix, with dimensions equal to the number of classes. Each cell in the matrix represents the number of
instances of class i that were classified as class j.
Suppose we have a classifier for three classes: A, B, and C. The confusion matrix would look like:
Actual A B C
A 50 2 1
B 5 45 5
C 0 3 47
This matrix shows how many instances of each actual class were classified into each predicted class.
Calculating Metrics for Multi-Class Classification
In multi-class classification, metrics like Precision, Recall, and F1 Score can be calculated for each class individually, and then averaged across classes using methods like micro-averaging or
Micro-averaging aggregates the contributions of all classes to compute the average metric.
Macro-averaging computes the metric independently for each class and then takes the average (unweighted) of the measures.
Applications of the Confusion Matrix
Model Evaluation and Selection
The confusion matrix is a valuable tool for evaluating classification models, especially in determining which model performs better on specific types of errors. It helps in selecting models based on
the trade-offs between different types of errors (e.g., deciding between higher precision or higher recall based on application requirements).
Medical Diagnosis
In medical testing, the confusion matrix helps in understanding how often tests correctly identify a condition (True Positives), incorrectly indicate a condition in a healthy person (False
Positives), incorrectly miss a condition (False Negatives), and correctly identify the absence of a condition (True Negatives). This is crucial for assessing the effectiveness of diagnostic tests.
Fraud Detection
In fraud detection, the confusion matrix can help in evaluating how effectively a model identifies fraudulent transactions (True Positives), misses fraudulent transactions (False Negatives), or
incorrectly flags legitimate transactions as fraudulent (False Positives). This aids in balancing customer satisfaction and fraud prevention.
Confusion Matrix vs ROC Curve
While a confusion matrix provides detailed insights into the performance of a classification model by showing the exact number of True Positives, False Positives, True Negatives, and False Negatives,
the ROC (Receiver Operating Characteristic) curve is a graphical representation that illustrates the diagnostic ability of a binary classifier system as its discrimination threshold is varied.
The ROC curve plots the True Positive Rate (Sensitivity) against the False Positive Rate (1 - Specificity) at various threshold settings. The area under the ROC curve (AUC) is a measure of how well
the model can distinguish between the two classes.
Both tools are useful, but they serve different purposes. The confusion matrix gives a detailed breakdown at a particular threshold, while the ROC curve shows how model performance varies across
Limitations of the Confusion Matrix
• It is only applicable to supervised learning where true values are known.
• In multi-class scenarios, the confusion matrix can become large and harder to interpret.
• Does not account for the severity or cost associated with different types of errors.
• Only provides information at a fixed threshold; cannot show performance changes over different thresholds.
Confusion Matrix in Machine Learning Libraries
Many machine learning libraries and tools provide built-in functions to compute and display confusion matrices. Examples include:
• In Python scikit-learn, the function confusion_matrix(y_true, y_pred) computes the confusion matrix.
• In R, the package caret provides the function confusionMatrix().
Confusion Matrix History
The confusion matrix has its origins in the field of classification and was first introduced by the British biologist and statistician Karl Pearson in the early 20th century. He used a matrix to
describe the errors made in mathematical tables.
Over time, the confusion matrix became a standard tool in machine learning and statistical classification, particularly for analyzing the performance of classification algorithms.
The term "confusion matrix" itself was popularized by the American statistician William H. Greene in his textbook on econometrics. Today, confusion matrices are a fundamental concept taught in data
science and machine learning courses.
• Fawcett, T. "An introduction to ROC analysis." Pattern Recognition Letters 27.8 (2006): 861-874.
• Powers, D.M.W. "Evaluation: From Precision, Recall and F-Measure to ROC, Informedness, Markedness & Correlation." Journal of Machine Learning Technologies 2.1 (2011): 37-63.
• Kohavi, R. and Provost, F., "Glossary of terms", Machine Learning, Special Issue on Applications of Machine Learning and the Knowledge Discovery Process, vol.30, no.2-3, pp. 271-274, 1998.
• Saito, T. and Rehmsmeier, M., "The precision-recall plot is more informative than the ROC plot when evaluating binary classifiers on imbalanced datasets." PloS one 10.3 (2015): e0118432. | {"url":"https://deepai.org/machine-learning-glossary-and-terms/confusion-matrix","timestamp":"2024-11-07T20:39:18Z","content_type":"text/html","content_length":"177152","record_id":"<urn:uuid:cf7c5f84-e70e-4612-99f8-15b3a3bd268a>","cc-path":"CC-MAIN-2024-46/segments/1730477028009.81/warc/CC-MAIN-20241107181317-20241107211317-00469.warc.gz"} |
Unsupervised Learning
Unsupervised Learning
It is possible to do unsupervised exploration of the datasets using PCA, tSNE, KMeans and UMAP. Before using these methods, it is necessary to featurize the data and scale it. If you don’t know how
to do it, please check the Featurization and Scaling sections.
from deepmol.scalers import MinMaxScaler
from deepmol.loaders import CSVLoader
from deepmol.compound_featurization import TwoDimensionDescriptors
# Load data from CSV file
loader = CSVLoader(dataset_path='../data/CHEMBL217_reduced.csv',
# create the dataset
data = loader.create_dataset(sep=',', header=0)
TwoDimensionDescriptors().featurize(data, inplace=True)
scaler = MinMaxScaler()
PCA (Principal Component Analysis) is a widely used technique in chemoinformatics, which is the application of computational methods to chemical data. In chemoinformatics, PCA is used to analyze
molecular descriptors, which are numerical representations of chemical structures.
Molecular descriptors can be used to represent various aspects of a molecule, such as its size, shape, polarity, or electronic properties. However, molecular descriptor sets can be quite large and
highly correlated, making it difficult to extract meaningful information from them.
PCA can help address this problem by reducing the dimensionality of the molecular descriptor space, while preserving as much of the information as possible. Specifically, PCA can identify the most
important descriptors that contribute to the variation in the data, and create a smaller set of descriptors that captures the majority of the information in the original data.
The reduced set of descriptors can then be used for various tasks, such as drug design, virtual screening, or molecular similarity analysis. PCA can also be used for visualization and exploration of
chemical data, by projecting the high-dimensional descriptor space onto a lower-dimensional space that can be easily visualized.
Overall, PCA is a powerful tool in chemoinformatics that can help extract meaningful information from complex chemical data sets, and facilitate the discovery and design of new drugs and materials.
from deepmol.unsupervised import PCA
pca = PCA(n_components=2)
pca_df = pca.run(data)
pca.plot(pca_df.X, path='pca_output_2.png')
pca = PCA(n_components=3)
pca_df = pca.run(data)
pca.plot(pca_df.X, path='pca_output_3.png')
pca = PCA(n_components=6)
pca_df = pca.run(data)
pca.plot(pca_df.X, path='pca_output_6.png')
t-SNE (t-distributed Stochastic Neighbor Embedding) is a popular technique in chemoinformatics for visualizing high-dimensional molecular data in a lower-dimensional space.
In chemoinformatics, t-SNE is often used to explore the structure-activity relationship (SAR) of chemical compounds, by visualizing how similar compounds are clustered in a lower-dimensional space
based on their molecular descriptors.
t-SNE works by first computing pairwise similarities between the high-dimensional data points, such as molecular descriptors. These similarities are then used to construct a probability distribution
that represents the likelihood of a data point being similar to other data points in the high-dimensional space.
Next, t-SNE creates a similar probability distribution in a lower-dimensional space, and iteratively adjusts the positions of the data points in this space to minimize the difference between the two
distributions. The result is a 2D or 3D visualization of the data points, where similar data points are located close to each other, and dissimilar data points are located far apart.
t-SNE is particularly useful for visualizing complex and non-linear relationships in chemoinformatics data, and for identifying clusters or patterns that may not be easily detectable in the original
high-dimensional space. However, it should be noted that t-SNE is a non-parametric technique, and its results may depend on the choice of parameters and the specific initialization of the algorithm.
Therefore, t-SNE should be used in combination with other techniques, such as PCA or hierarchical clustering, to gain a more comprehensive understanding of the chemical data.
from deepmol.unsupervised import TSNE
tsne = TSNE(n_components=2)
tsne_df = tsne.run(data)
tsne.plot(tsne_df.X, path='tsne_output_2.png')
from deepmol.unsupervised import TSNE
tsne = TSNE(n_components=3)
tsne_df = tsne.run(data)
tsne.plot(tsne_df.X, path='tsne_output_3.png')
from deepmol.unsupervised import TSNE
tsne = TSNE(n_components=4, method='exact')
tsne_df = tsne.run(data)
tsne.plot(tsne_df.X, path='tsne_output_4.png')
K-means clustering is a widely used unsupervised learning algorithm in chemoinformatics for identifying groups of similar chemical compounds based on their molecular descriptors.
The algorithm works by iteratively assigning each data point (i.e., chemical compound) to the closest cluster center (i.e., centroid), and updating the cluster centers based on the new assignments.
The process continues until the assignments no longer change, or until a maximum number of iterations is reached.
In chemoinformatics, k-means clustering is often used for tasks such as compound clustering, lead optimization, and hit identification. By identifying clusters of similar compounds, researchers can
gain insights into the structure-activity relationships (SAR) of the compounds, and identify potential candidates for further study.
However, k-means clustering has some limitations in chemoinformatics. One limitation is that the algorithm assumes that the clusters are spherical and of equal size, which may not always be the case
for chemical compounds. Another limitation is that the algorithm requires the number of clusters to be specified in advance, which may be difficult to determine for large and complex data sets.
from deepmol.unsupervised import KMeans
kmeans = KMeans(n_clusters=2)
kmeans_df = kmeans.run(data)
kmeans.plot(kmeans_df.X, path='kmeans_output_2.png')
from deepmol.unsupervised import KMeans
kmeans = KMeans(n_clusters=3)
kmeans_df = kmeans.run(data)
kmeans.plot(kmeans_df.X, path='kmeans_output_3.png')
from deepmol.unsupervised import KMeans
kmeans = KMeans(n_clusters=6)
kmeans_df = kmeans.run(data)
kmeans.plot(kmeans_df.X, path='kmeans_output_6.png')
UMAP (Uniform Manifold Approximation and Projection) is a dimensionality reduction technique that has gained popularity in chemoinformatics for visualizing and analyzing high-dimensional molecular
Like t-SNE, UMAP works by creating a lower-dimensional representation of the high-dimensional data, but it uses a different approach based on topology and geometry. UMAP constructs a high-dimensional
graph that captures the local relationships between the data points, and then uses a mathematical technique called Riemannian geometry to embed the graph into a lower-dimensional space.
In chemoinformatics, UMAP has been used for tasks such as compound clustering, lead optimization, and molecular visualization. UMAP can reveal complex and non-linear relationships in the data that
may not be easily visible in the original high-dimensional space, and it can provide insights into the structure-activity relationships (SAR) of the compounds.
One advantage of UMAP over other dimensionality reduction techniques is its scalability and speed. UMAP can handle large and complex data sets, and can produce visualizations in real-time. Moreover,
UMAP has a few parameters that can be tuned, making it easy to use and apply in various chemoinformatics applications.
from deepmol.unsupervised import UMAP
ump = UMAP(n_components=2)
umap_df = ump.run(data)
ump.plot(umap_df.X, path='umap_output_2.png')
from deepmol.unsupervised import UMAP
ump = UMAP(n_components=3)
umap_df = ump.run(data)
ump.plot(umap_df.X, path='umap_output_3.png')
from deepmol.unsupervised import UMAP
ump = UMAP(n_components=6)
umap_df = ump.run(data)
ump.plot(umap_df.X, path='umap_output_6.png')
Do your own analysis
You can always generate the data yourself for any of these unsupervised learning methods and plot them the way you want. Let’s try it out with PCA.
from deepmol.unsupervised import PCA
pca = PCA(n_components=2)
pca_df = pca.run(data)
The principal components are stored in the X attribute of the dataset object. So, one can access this information by typing:
array([[-0.5702929 , 0.34961516],
[ 0.4019284 , 0.25011715],
[ 0.4814127 , -0.29691637],
[-0.67021173, 0.7563012 ],
[-1.295675 , 0.05596984],
[-0.5351163 , -0.29156607]], dtype=float32)
Accordingly you can plot the data using matplotlib or any other plotting library of your choice.
import matplotlib.pyplot as plt
plt.scatter(pca_df.X[:, 0], pca_df.X[:, 1]) | {"url":"https://deepmol.readthedocs.io/en/latest/deepmol_docs/unsupervised_learning.html","timestamp":"2024-11-13T14:03:50Z","content_type":"text/html","content_length":"33567","record_id":"<urn:uuid:15875e2c-5291-4b3a-9d44-d444d8d6bae1>","cc-path":"CC-MAIN-2024-46/segments/1730477028369.36/warc/CC-MAIN-20241113135544-20241113165544-00561.warc.gz"} |
Find derivatives y=tanh sqrt 1+t^2 ? | Socratic
Find derivatives y=tanh sqrt 1+t^2 ?
1 Answer
$\frac{\mathrm{dy}}{d} = \frac{t \setminus {\sech}^{2} \sqrt{1 + {t}^{2}}}{\sqrt{1 + {t}^{2}}}$
We seek:
$\frac{\mathrm{dy}}{\mathrm{dt}}$, where $y = \tanh \sqrt{1 + {t}^{2}}$
Using the known result:
$\frac{d}{\mathrm{dt}} \tanh = {\sech}^{2} t$
In conjunction with the chain rule, we get:
$\frac{\mathrm{dy}}{\mathrm{dt}} = \left({\sech}^{2} \sqrt{1 + {t}^{2}}\right) \left(\frac{d}{\mathrm{dt}} \sqrt{1 + {t}^{2}}\right)$
$\setminus \setminus \setminus \setminus \setminus = {\sech}^{2} \sqrt{1 + {t}^{2}} \setminus \left(\frac{1}{2} {\left(1 + {t}^{2}\right)}^{- \frac{1}{2}} \frac{d}{\mathrm{dt}} \left(1 + {t}^{2}\
$\setminus \setminus \setminus \setminus \setminus = {\sech}^{2} \sqrt{1 + {t}^{2}} \setminus \left(\frac{1}{2 \sqrt{1 + {t}^{2}}}\right) \left(2 t\right)$
$\setminus \setminus \setminus \setminus \setminus = \frac{t \setminus {\sech}^{2} \sqrt{1 + {t}^{2}}}{\sqrt{1 + {t}^{2}}}$
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[Solved] Here is an interesting game presented and | SolutionInn
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Verified Expert Solution
Here is an interesting game presented and discussed by psychologists, mathematicians, philosophers, and people in business, risk management, and gambling. You start with $1, and
Here is an interesting game presented and discussed by psychologists, mathematicians, philosophers, and people in business, risk management, and gambling. You start with $1, and a die is rolled. You
"win" if the outcome is not a 6, in which case you double your amount. You "lose" if the outcome is a 6, in which you lose everything you have accumulated. At any point of this game, you can continue
or quit. Once you lose your money, there is no point in continuing since twice 0 is still 0. For example, on the first roll, say a 3 comes up. Now you have $2. You decide to continue, and the second
outcome is a 5. Now you have $4. You decide to continue, and the third outcome is a 4. Now you will have $8. You decide to continue, and the four outcome is a 3. You will now have $16. You decide to
continue, and the fifth outcome is a 6. You lose everything (your $16) and go down to $0.
(a) If no 6 comes up the first 5 rolls, how much would you have?
(b) Suppose no 6 comes up the first 10 rolls. How much would you have?
(c) If the first 6 comes up on the th roll, how much would you lose then?
(d) There is about a 93.5% chance that at least one 6 comes up during the first 15 rolls. If you have played this game 15 times, therefore, you have about a 93.5% chance that you have nothing, but
you still have a 6.5% chance (( 5/6 ) 15 0.0649) that you have money. How much would you have if no 6 comes up 15 times in a row?
(e) After playing this game times, how much do you expect to have?
(f) When would you stop playing this game? Put yourself in this situation and answer according to your personality. Then, find the "correct" answer using mathematics.
(g) Instead of sequentially rolling one die times, imagine rolling dice simultaneously, once. Would any of your answers change? Why or why not?
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How to Compute Distance from a Point to Three Points 3-D
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How to Compute Distance from a Point to Three Points 3-D
Assume that we have three points (
) in a 3-D space.
Those three points determine a plane.
How do I calculate the distance from a point
to those point,
given only the distances between four points
1 Reply
There's probably a ton of ways to do this. Are you looking for a clever answer to this by any chance?
A straightforward approach would be to use
the law of cosines
, which will give you all the angles in the triangles from their lengths. If you assume a is at the origin and that b is on the x axis an appropiate distance away from a, then you can use basic trig
to find vector coordinates of all the points in that embedding. Once you do this, you can find
the equation of the plane
and then
solve for the distance from point d to that plane
Alternatively, you could first find the volume of the tetrahedron ABCD using the Cayley-Menger determinant (I didn't know about this until I just read it). You can also find the are of the triangle
ABC using Heron's formula. The area of a tetrahedron relates these to each other using the distance between d and the triangle ABC:
(Volume of the tetrahedron ABCD) = 1/3 * (distance from d to triangle ABC) * (Area of Triangle ABC) | {"url":"https://community.wolfram.com/groups/-/m/t/203447","timestamp":"2024-11-06T12:14:52Z","content_type":"text/html","content_length":"94798","record_id":"<urn:uuid:aa2fbf99-0720-4125-8135-2787c3bfd555>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00291.warc.gz"} |
By: Imran Ahmed, Copyright 2004-2008
1.1: Overview
1.2: Multiplying Digital to Analog Converter (MDAC)
1.3: MDAC design considerations (matching, thermal noise, switch sizes)
1.4: Opamp design - gain requirement
1.5: Stage-ADC/Sub-ADC comparator design
1.6: Summary
his tutorial discusses circuit implementations and related design issues for 1.5 bit/stage pipeline ADCs. The key sub-blocks discussed are: the stage MDAC, the stage ADC, and the stage amplifier.
As pipeline stages operate on discrete time signals (since each stage has a sample and hold), switched capacitor circuits are used for pipeline ADCs. With switch capacitor circuits it is possible to
perform highly accurate mathematical operations such as addition, subtraction, and multiplication (by a constant), due to the availability of capacitors with a high degree of relative matching.
Switch capacitor circuits also facilitate multiple, simultaneous signal manipulations with relatively simple architectures. It is possible to combine the functions of sample and hold, subtraction,
DAC, and gain into a single switched capacitor circuit, referred to as the Multiplying Digital-to-Analog Converter (MDAC) as shown in Fig. 1.
Fig. 1: MDAC functionality in dashes
Fig. 2 shows a single ended circuit implementation of the MDAC of Fig. 1, using a switched capacitor approach.
Fig. 2: stage MDAC
The MDAC of Fig. 2 is shown single ended for simplicity, although in practice fully differential circuitry is commonly used to suppress common-mode noise [3]. A 1.5 bits/stage architecture has one
of three digital outputs, thus the DAC has three operating modes:
ADC output = 01: No over range error (stage input is between –Vref/4 and Vref/4.
During []: Q[C1]=C[1]V[in], Q[C2]=C[2]V[in]
During []: C[1] is discharged, thus by charge conservation: C[1]V[in] + C[2]V[in ]= C[2]V[out] (noting negative feedback forces node V[p] to a virtual ground). Thus
[] è if C[1]=C[2], then: V[out]=2V[in ](0.1)
[ ]
ADC output = 10: Over range error – Input exceeds Vref/4, thus subtract Vref/2 from input
During []: Q[C1]=C[1]V[in], Q[C2]=C[2]V[in]
During []: C[1 ]is charged to V[ref], thus by charge conservation
C[1]V[in] + C[2]V[in ]= C[1]V[ref] +C[2]V[out]
[] è if C[1]=C[2], then: V[out]=2V[in]-V[ref] =2(V[in]-V[ref]/2) (0.2)
ADC output = 00: Under range error – Input below -Vref/4, thus add Vref/2 to input
During []: Q[C1]=C[1]V[in], Q[C2]=C[2]V[in]
During []: C[1] is charged to -V[ref], thus by charge conservation
C[1]V[in] + C[2]V[in ]= C[1](-V[ref] )+C[2]V[out]
[] è if C[1]=C[2], then: V[out]=2V[in]+V[ref] =2(V[in]+V[ref]/2) (0.3)
Thus the switched capacitor circuit implements the stage sample-and-hold, stage gain, DAC, and subtraction blocks.
Signal dependent charge injection is minimized by using bottom plate sampling, where the use of an advanced clock [], makes charge injection signal independent [4]. A non-overlapping clock generator
is thus required for the MDAC.
From equations (3.1)-(3.3) it is clear stage gain is determined by the ratio of capacitors C[1 ]and C[2]. Thus to ensure a gain which is at least 10-bit accurate, C[1] and C[2] must match to at
least 10-bit accuracy or within 0.1% for the first stage in the pipeline. To obtain at least 0.1% matching a high quality capacitor such as a Metal-Insulator-Metal (MIM) capacitor must be used. If
properly designed in layout, MIM capacitors can achieve matching between 0.01-0.1% [5]. MIM capacitors however are often unavailable in purely digital processes, necessitating alternative capacitor
structures. Alternatively metal-finger capacitors, which derive their capacitance from the combination of area and fringe capacitance between overlapping metal layers can be used in digital
processes to achieve sub 0.1% matching. Metal-finger capacitors however can have large absolute variation (>20%), thus require a conservative design approach. Alternatively a digital calibration
algorithm can be employed to significantly minimize mismatch-induced gain errors (and finite opamp gain errors) [6], [7], [8], [9]. Due to additional design complexity, calibration schemes are
beyond the focus of this dissertation. We note however that calibration techniques are emerging as essential approaches for high-resolution pipeline ADCs due to the relaxed accuracy constraints
In addition to capacitor matching, it is essential the ratio of capacitors C[1] and C[2] be linear for the desired input range to minimize harmonic distortion. Thus non-linear parasitic gate
capacitance (MOS-caps), or other active capacitors should be avoided for C[1] and C[2] in high precision pipeline ADCs. Passive MIM, and metal-finger capacitors are linear well beyond the 10-bit
level, thus are typically used.
The MDAC shown in Fig. 2 is a popular MDAC architecture, as the capacitor sizes of C[1 ]and C[2] are equal. Since C[1]=C[2], identical layouts can be used for C[1] and C[2 ]- maximizing layout
symmetry and hence maximizing accuracy. As MIM capacitors only have a marginal matching for 10-bit accuracy, a high degree of capacitor matching is essential to minimize INL/DNL errors. Another
advantage of the architecture of Fig. 2 is a high beta value (feedback factor), which maximizes the bandwidth of the closed loop system [10].
Although capacitors are ideally noiseless elements, in a sampled system, sample and hold capacitors capture noise generated by noisy elements such as switch resistors, opamps, etc. Consider the
following noise analysis of a capacitor sampling resistor noise as shown in Fig. 3:
Fig. 3: RC noise model
from [1] it is shown equivalent noise bandwidth is [],
[] [1]
[] è [] (0.4)
From the above example it is clear increasing the size of the sampling capacitor reduces the power of thermal noise. As thermal noise represents a dynamic noise source that reduces ADC SNR, a
minimum capacitance (i.e. C[1], C[2]) must be driven to ensure a sufficient accuracy – thus thermal noise imposes a tradeoff between power and accuracy. For the MDAC of Fig. 2, the effective input
referred thermal noise, which includes switch, and opamp noise is derived in [11] and found to be
[] (0.5)
where[] is the equivalent output load capacitance, and C[opamp] the input capacitance to the opamp. The relationship between SNR and minimum capacitor size for a full scale signal swing of 0.8V, and
C[1]=C[2]=C[opamp]=0.5pF is shown in Fig. 4.
Fig. 4: Variation of SNR due to thermal noise (ignoring quantization error, full scale=0.8V, C[1]=C[2]=C[opamp]=0.5pF)
From Fig. 4 it is clear thermal noise can alone limit accuracy to less than 10-bits (SNR=62dB) if capacitors are not sufficiently sized. As thermal noise represents only one of several precision
limiting factors (others include: quantization noise, power supply noise, capacitor mismatch, etc.), it is desirable to place the noise floor beyond the 10-bit level (e.g.) for thermal noise less
than 1/4 LSB è thermal noise floor should be at least -72dB. The stage accuracy requirements are relaxed for subsequent pipeline stages. Thus it is possible to increase the noise floor for
subsequent stages by using smaller capacitors - maximizing opamp bandwidth and minimizing overall power.
When sizing a MOS switch two key issues should be considered: 1.) The desired RC time constant, and 2.) The maximum distortion tolerable through the switch.
As switched-capacitor circuits have a finite time to settle, it is essential the switches be sized large enough such that the sampled signal settle to the desired accuracy in the allotted time.
Since [], switch resistance can be minimized by increasing the MOS switch W/L ratio. However an increased W/L ratio implies a larger area, which imparts a larger parasitic capacitance to the
circuit. As described in [1], a sufficiently large parasitic capacitance can alter charge-sharing equations, and introduce harmonic distortion through charge injection. Thus switch transistors must
be carefully sized, where switches should be large enough to ensure a sufficient RC time constant, but small enough to minimize parasitic induced errors.
A consequence of the switch’s resistance dependency on V[eff] is an RC time constant that is signal dependent, hence non-linear. A non-linear RC time constant can lead to significant distortion if
the switch passes a continuous time signal, as is the case in front-end sample and hold inputs. Signal–dependent RC time constants also affect discrete time signals, as the MOS switch must be sized
sufficiently such that the worst-case RC time constant (i.e. when V[eff] is smallest) is sufficient for the desired sampling speed. Non-linear RC time constants can be significantly minimized
however using a bootstrapping approach [4], which maintains a constant and maximal V[eff], thereby minimizing signal dependent variations.
The charge transfer relations derived in equations (3.1)–(3.3) were based on the assumption of a perfect virtual ground at node V[p] in Fig. 2, which only occurs when the opamp gain is infinite. In
practice opamp gain is finite - introducing an error into the charge balance equations. As such opamp gain must be made sufficiently large to minimize finite gain error.
Consider the closed loop gain of a negative feedback system H(s), as shown in Fig. 5:
[] (0.6)
Fig. 5: basic linear feedback structure
Ideally as A(s) tends to infinity, H(s) è 1/b. Thus the relative error ([]) is
[] (0.7)
As switch capacitor circuits settle to DC values, DC gain affects charge transfer equations:
[] (0.8)
Hence for an error due to finite opamp gain to be less than ¼ LSB, i.e. 1/(4x1024)=1/(4096), with b=0.5 implies A > 8192, or A >78dB. Fig. 6 illustrates the variation of relative error with opamp
Fig. 6: gain error variation with opamp gain
Attaining 78dB of DC gain while maintaining a reasonable bandwidth is near impossible with a simple single stage configuration (e.g. differential pair) for sub-micron technologies. Thus two-stage or
gain-boosted configurations are necessitated for 10-bit pipeline ADCs (a detailed description of high gain opamps is given in [1], [12]). It is noted that stage accuracy requirements decrease along
the pipeline, thus latter stages may have less gain, allowing for simpler opamps (single stage, or no gain-boosting), thus reducing power.
It should be noted that alternative MDAC architectures exist which employ gain-error cancellation methods, facilitating much lower opamp gains [6], [7], [8], [9] than those required by (3.8). Such
approaches however introduce a design overhead, and increase design time, thus are not considered in this dissertation.
Switched capacitor circuits have a finite time in which to settle, thus to ensure a minimum settling accuracy, opamp bandwidth must be optimized. If the opamp is modeled as a first order system, the
opamp transfer function near the unity gain frequency is given by:[] [1]. Thus the MDAC step response, during [] is given by
[] (0.9)
where [], and slew rate is ignored. Since[], where x is the settling accuracy in bits, the available time to settle is
[] (0.10)
As the available time t to settle is half the clock period, []
[] , (0.11)
[] (0.12)
where for settling within ¼ LSB, [] for a 10-bit ADC. Figure Fig. 7 graphically illustrates the required opamp unity gain bandwidth to achieve a desired sampling rate and settling accuracy.
Fig. 7: required opamp unity gain frequency versus sampling frequency and settling accuracy
From Fig. 7 and equations (3.11)-(3.12), a unity gain frequency much larger than sampling frequency is required to obtain high accuracy settling. Since the MDAC opamps must drive large capacitive
loads (to minimize thermal noise), much power is consumed by the opamps. As such, the power consumption of opamps in a pipeline ADC often consumes 60-80% of the total ADC power. However, the
accuracy requirements decrease along the pipeline, thus the unity gain frequency of subsequent stages along the pipeline can be reduced, minimizing total power [2].
A flash architecture is commonly used for the stage ADCs, due to low accuracy required by the stage ADCs. Flash ADCs consist of comparators at the various thresholds of the ADC. For a 1.5-bit/stage
pipeline architecture stage flash ADCs require comparators at thresholds of +/-Vref/4 and 0. Digital error correction could be used to relax the tolerable offset on stage-ADC comparators (up to +/
-Vref/4). For Vref=0.8V, the comparator offset can be as high as 200mV, which allows for minimum size devices in the comparator (hence minimizing parasitic capacitance, thus minimizing power). The
relaxed offset constrains also afford simpler dynamic comparator architectures, which do not require pre-amp gain stages, or static comparators (e.g.: as used in. 6-bit flash ADCs [13], [14]). Like
digital logic, dynamic comparators only consume power on clock edges according to fCV^2 thus have a power that scales linearly with sampling frequency. For pipeline ADCs one of two dynamic
comparators are typically used [15]: the Lewis and Gray comparator [16] (Fig. 8), or the charge-distribution comparator (Fig. 9).
Fig. 8: Lewis and Grey comparator
Fig. 9: switched capacitor/charge distribution comparator
The Lewis and Gray comparator compares two fully differential signals [], and [] (Fully differential comparators are highly desirable to reduce common-mode noise which can be large in digital
environments). Comparators at Vref/4 and –Vref/4 are required to implement the 1.5bit/stage architecture, and comparators at Vref/2, and –Vref/2 for the 2-bit flash at the end of the pipeline.
Rather than supply multiple reference voltages for each unique threshold, it is possible using the architecture of Fig. 8 to derive an arbitrary threshold by appropriate device sizing. Transistors
M1-M4 operate in triode while the remaining transistors implement positive feedback to resolve the differential input [11]. The equivalent triode conductance of M1 and M2 from Fig. 8 are:
[] (0.13)
[] (0.14)
The comparator threshold occurs when the circuit is perfectly symmetric, i.e. when G[1]=G[2], thus if W[1]=W[4], and W[2]=W[3]
[] (0.15)
where V[in ]= V[in+ ]- V[in-], and V[ref ]= V[ref+ ] - V[ref-]
Thus it is possible to achieve thresholds at ±Vref/4, and ±Vref/2 by providing a common differential reference voltage to each comparator in the pipeline, but sizing each comparator to yield the
desired threshold (e.g.: W[2 ]= 4W[1] for a threshold of Vref/4, W[2] = 2W[1] for a threshold of Vref/2, etc.). As the comparator is fully differential, thresholds at –Vref/4 and –Vref/2 can be
realized by reversing the polarity to the reference voltage. Thus all required thresholds for a 1.5 bit/stage pipeline can be realized by only supplying only one fully differential reference
potential to the chip.
A drawback of the Lewis and Gray comparator is the threshold is a significant function of device symmetry. As the value resolved by the comparator operates by comparing the integral of the ratio of
current to node capacitance at nodes V[1] and V[2], circuit symmetry is crucial to reduce offset. Thus the layout of the Lewis and Gray comparator requires great care, and parasitic extraction for
full characterization of input-referred offset. In [15] the Lewis and Gray comparator is shown to have an offset of >200mV for a 0.35mm CMOS process,
Alternatively a charge distribution approach can be used to achieve a lower offset at the cost of increased power. As shown in Fig. 9, the charge distribution approach uses charge conservation to
derive a comparator threshold, which depends on the ratio of capacitors rather than the ratio of device widths and parasitic capacitances. Using a two-phase clock ([],[]), capacitors C[in] and C
[ref] are charged to [] and [] respectively (in a differential sense) on the first clock phase. The charge is forced to redistribute between both capacitors during the second clock phase, where
according to charge conservation the effective threshold of the comparator is found to be [15]
[] (0.16)
As the threshold is primarily a function of passive components and largely independent of parasitic capacitance, a lower offset can be achieved using the charge-distribution comparator. An analysis
in [15] compares fabricated implementations (in 0.35mm CMOS) of the Lewis and Gray, and charge distribution comparators, where the following silicon measured results were obtained:
Table 0‑1: Comparison of comparator area, offset, and power
│ Comparator │ Area │Power @ 100Msps│V[offset-max]│
│ Lewis and Grey │1200mm│ 0.32mW │ 290mV │
│Charge distribution │2800mm│ 0.81mW │ 75mV │
As other offsets besides device mismatch (e.g. noise) affect the stage transfer function, it is desirable to keep comparator offsets below Vref/4. It should be noted the reduced offset of the charge
distribution comparator comes at the cost of increased power (due to the dynamic charging of the sampling capacitors, and switches) and area. Thus the choice of which comparator architecture to use
requires a tradeoff between tolerable offset, desired power consumption and area.
In this chapter circuit level implementation and design related issued were discussed for key components in a 1.5 bit/stage pipeline ADC: the stage MDAC and stage ADC comparators. It was shown for a
desired settling accuracy, MDAC opamps require a minimum gain and unity gain bandwidth. Noise limitations due to thermal and opamp noise were shown limit minimum MDAC sampling and feedback capacitor
sizes. Two popular dynamic comparators were examined: the Lewis and Gray comparator, and the charge distribution comparator, where it was shown the optimal comparator was a tradeoff between power
and input referred offset.
. References
[1] Johns, David and Martin, Ken. Analog Integrated Circuit Design. John Wiley & Sons, Inc: New York, 1997.
[2] P.T.F. Kwok et al, “Power Optimization for Pipeline Analog-to-Digital Converters”, IEEE Transactions on Circuits and Systems--II: Analog and Digital Signal Processing, vol 36, May 1999, pp.
[3] Y. Park et al, “A low power 10 bit, 80MS/s CMOS pipelined ADC at 1.8V power supply”, 2001 IEEEE International Symposium on Circuits and Systems (ISCAS), vol 1, pp. 580-583
[4] A. Abo, “Design for Reliability of Low-voltage, Switched-capacitor Circuits”, Doctor of Philosophy in Electrical Engineering, University of California Berkeley, 1999
[5] C. Diaz et al, “CMOS Technology for MS/RF SoC”, IEEE Transactions on Electron Devices, vol 50, March 2003, pp. 557-566
[6] J. Li et al, “Background Calibration Techniques for Multistage Pipelined ADCs With Digital Redundancy”, IEEE Transactions on Circuits and Systems – II: Analog and Digital Signal Processing, vol
50, September 2003, pp. 531-538
[7] Y. Chiu et al, “Least Mean Square Adaptive Digital Background Calibration of Pipelined Analog-to-Digital Converters”, IEEE Transactions on Circuits and Systems – I: Regular Papers, vol 51,
Janurary 2004, pp. 38-46
[8] S. Chuang et al, “A Digitally Self-Calibrating 14-bit 10-MHz CMOS Pipelined A/D Converter”, IEEE Journal of Solid-State Circuits, vol 37, June 2002, pp. 674-683
[9] B. Murmann et al, “A 12-bit 75-MS/s Pipelined ADC Using Open-Loop Residue Amplification”, IEEE Journal of Solid-State Circuits, vol 38, December 2003, pp. 2040-2050
[10] W. Yang et al, “A 3-V 340-mW 14-b 75 Msample/s CMOS ADC with 85dB SFDR at Nyquist Input”, IEEE Journal of Solid State Circuits, Brief Paper, vol 36, December 2001, pp. 1931-1936
[11] T. Cho, “Low power Low voltage A/D conversion techniques using pipelined architecture”, Doctor of Philosophy in Engineering, University of California Berkeley, 1995
[12] Razavi, Behzad. Design of Analog CMOS Integrated Circuits. McGraw-Hill, New York, 2000
[13] Uyttenhove et al, “A 1.8-V 6-bit 1.3-GHz flash ADC in 0.25mm CMOS”, IEEE Journal of Solid-State Circuits, vol 28, July 2003, pp. 1115-1122
[14] M. Choi et al, “A 6-b 1.3-Gsample/s A/D converter in 0.35-mm CMOS”, IEEE Journal of Solid-State Circuits, vol 36, December 2001, pp. 1847-1858
[15] L. Sumanen et al, “CMOS dynamic comparators for pipeline A/D converters”, 2002 IEEE International Symposium on Circuits and Systems (ISCAS), vol 5, 2002, pp. 157-160
[16] L. Sumanen et al, “A mismatch insensitive CMOS dynamic comparator for pipeline A/D converters”, 2000 International Conference on Electronics, Circuits and Systems (ICECS), pp. 32-35 | {"url":"https://iadc.ca/Pipeline_ADC_tutorial.htm","timestamp":"2024-11-13T04:55:59Z","content_type":"text/html","content_length":"47256","record_id":"<urn:uuid:623cd6ba-8150-4232-8363-414e8f800aac>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00079.warc.gz"} |
Michael Klooß
Michael Klooß
Practical Blind Signatures in Pairing-Free Groups Abstract
Blind signatures have garnered significant attention in recent years, with several efficient constructions in the random oracle model relying on well-understood assumptions. However, this progress
does not apply to pairing-free cyclic groups: fully secure constructions over cyclic groups rely on pairings, remain inefficient, or depend on the algebraic group model or strong interactive
assumptions. To address this gap, Chairattana-Apirom, Tessaro, and Zhu (CTZ, Crypto 2024) proposed a new scheme based on the CDH assumption. Unfortunately, their construction results in large
signatures and high communication complexity. In this work, we propose a new blind signature construction in the random oracle model that significantly improves upon the CTZ scheme. Compared to CTZ,
our scheme reduces communication complexity by a factor of more than 10 and decreases the signature size by a factor of more than 45, achieving a compact signature size of only 224~Bytes. The
security of our scheme is based on the DDH assumption over pairing-free cyclic groups, and we show how to generalize it to the partially blind setting.
RoK, Paper, SISsors – Toolkit for Lattice-based Succinct Arguments Abstract
Lattice-based succinct arguments allow to prove bounded-norm satisfiability of relations, such as $f(\mathbf{s}) = \mathbf{t} \bmod q$ and $\|\mathbf{s}\|\leq \beta$, over specific cyclotomic rings $
\mathcal{O}_\mathcal{K}$, with proof size polylogarithmic in the witness size. However, state-of-the-art protocols require either 1) a super-polynomial size modulus $q$ due to a soundness gap in the
security argument, or 2) a verifier which runs in time linear in the witness size. Furthermore, construction techniques often rely on specific choices of $\mathcal{K}$ which are not mutually
compatible. In this work, we exhibit a diverse toolkit for constructing efficient lattice-based succinct arguments: \begin{enumerate} \item We identify new subtractive sets for general cyclotomic
fields $\mathcal{K}$ and their maximal real subfields $\mathcal{K}^+$, which are useful as challenge sets, e.g. in arguments for exact norm bounds. \item We construct modular, verifier-succinct
reductions of knowledge for the bounded-norm satisfiability of structured-linear/inner-product relations, without any soundness gap, under the vanishing SIS assumption, over any $\mathcal{K}$ which
admits polynomial-size subtractive sets. \item We propose a framework to use twisted trace maps, i.e. maps of the form $\tau(z) = \frac{1}{N} \cdot \mathsf{Trace}_{\mathcal{K}/\mathbb{Q}}( \alpha \
cdot z )$, to embed $\mathcal{R}$-inner-products as $\mathcal{R}$-inner-products for some structured subrings $\mathcal{R} \subseteq \mathcal{O}_\mathcal{K}$ whenever the conductor has a square-free
odd part. \item We present a simple extension of our reductions of knowledge for proving the consistency between the coefficient embedding and the Chinese Remainder Transform (CRT) encoding of $\vec
{s}$ over any cyclotomic field $\mathcal{K}$ with a smooth conductor, based on a succinct decomposition of the CRT map into automorphisms, and a new, simple succinct argument for proving automorphism
relations. \end{enumerate} Combining all techniques, we obtain, for example, verifier-succinct arguments for proving that $\vec{s}$ satisfying $f(\mathbf{s}) = \mathbf{t} \bmod q$ has binary
coefficients, without soundness gap and with polynomial-size modulus $q$.
Publicly Verifiable Zero-Knowledge and Post-Quantum Signatures From VOLE-in-the-Head Abstract
We present a new method for transforming zero-knowledge protocols in the designated verifier setting into public-coin protocols, which can be made non-interactive and publicly verifiable. Our
transformation applies to a large class of ZK protocols based on oblivious transfer. In particular, we show that it can be applied to recent, fast protocols based on vector oblivious linear
evaluation (VOLE), with a technique we call VOLE-in-the-head, upgrading these protocols to support public verifiability. Our resulting ZK protocols have linear proof size, and are simpler, smaller
and faster than related approaches based on MPC-in-the-head. To build VOLE-in-the-head while supporting both binary circuits and large finite fields, we develop several new technical tools. One of
these is a new proof of security for the SoftSpokenOT protocol (Crypto 2022), which generalizes it to produce certain types of VOLE correlations over large fields. Secondly, we present a new ZK
protocol that is tailored to take advantage of this form of VOLE, which leads to a publicly verifiable VOLE-in-the-head protocol with only 2x more communication than the best, designated-verifier
VOLE-based protocols. We analyze the soundness of our approach when made non-interactive using the Fiat-Shamir transform, using round-by-round soundness. As an application of the resulting NIZK, we
present FAEST, a post-quantum signature scheme based on AES. FAEST is the first AES-based signature scheme to be smaller than SPHINCS+, with signature sizes between 5.6 and 6.6kB at the 128-bit
security level. Compared with the smallest version of SPHINCS+ (7.9kB), FAEST verification is slower, but the signing times are between 8x and 40x faster.
Universally Composable Auditable Surveillance Abstract
User privacy is becoming increasingly important in our digital society. Yet, many applications face legal requirements or regulations that prohibit unconditional anonymity guarantees, e.g., in
electronic payments where surveillance is mandated to investigate suspected crimes. As a result, many systems have no effective privacy protections at all, or have backdoors, e.g., stored at the
operator side of the system, that can be used by authorities to disclose a user’s private information (e.g., lawful interception). The problem with such backdoors is that they also enable silent mass
surveillance within the system. To prevent such misuse, various approaches have been suggested which limit possible abuse or ensure it can be detected. Many works consider auditability of
surveillance actions but do not enforce that traces are left when backdoors are retrieved. A notable exception which offers retrospective and silent surveillance is the recent work on
misuse-resistant surveillance by Green et al. (EUROCRYPT’21). However, their approach relies on extractable witness encryption, which is a very strong primitive with no known efficient and secure
implementations. In this work, we develop a building block for auditable surveillance. In our protocol, backdoors or escrow secrets of users are protected in multiple ways: (1) Backdoors are
short-term and user-specific; (2) they are shared between trustworthy parties to avoid a single point of failure; and (3) backdoor access is given conditionally. Moreover (4) there are audit trails
and public statistics for every (granted) backdoor request; and (5) surveillance remains silent, i.e., users do not know they are surveilled. Concretely, we present an abstract UC-functionality which
can be used to augment applications with auditable surveillance capabilities. Our realization makes use of threshold encryption to protect user secrets, and is concretely built in a blockchain
context with committee-based YOSO MPC. As a consequence, the committee can verify that the conditions for backdoor access are given, e.g., that law enforcement is in possession of a valid
surveillance warrant (via a zero-knowledge proof). Moreover, access leaves an audit trail on the ledger, which allows an auditor to retrospectively examine surveillance decisions. As a toy example,
we present an Auditably Sender-Traceable Encryption scheme, a PKE scheme where the sender can be deanonymized by law enforcement. We observe and solve problems posed by retrospective surveillance via
a special non-interactive non-committing encryption scheme which allows zero-knowledge proofs over message, sender identity and (escrow) secrets.
Composable Long-Term Security with Rewinding Abstract
Long-term security, a variant of Universally Composable (UC) security introduced by Müller-Quade and Unruh (TCC ’07, JoC ’10), allows to analyze the security of protocols in a setting where all
hardness assumptions no longer hold after the protocol execution has finished. Such a strict notion is highly desirable when properties such as input privacy need to be guaranteed for a long time,
e.g. with zero-knowledge proofs for secure electronic voting. Strong impossibility results rule out so-called long-term-revealing setups, e.g. a common reference string (CRS), to achieve long-term
security, with known constructions for long-term security requiring hardware assumptions, e.g. signature cards. We circumvent these impossibility results with new techniques, enabling rewinding-based
simulation in a way that universal composability is achieved. This allows us to construct a long-term-secure composable commitment scheme in the CRS-hybrid model, which is provably impossible in the
notion of Müller-Quade and Unruh. We base our construction on a statistically hiding commitment scheme in the CRS-hybrid model with CCA-like properties. To provide a CCA oracle, we cannot rely on
super-polynomial extraction techniques and instead extract the value committed to via rewinding. To this end, we incorporate rewinding-based commitment extraction into the UC framework via a helper
in analogy to Canetti, Lin and Pass (FOCS 2010), allowing both adversary and environment to extract statistically hiding commitments. Our new framework provides the first setting in which a
commitment scheme that is both statistically hiding and universally composable can be constructed from standard polynomial-time hardness assumptions and a CRS only. We also prove that our CCA oracle
is k-robust extractable. This asserts that extraction is possible without rewinding a concurrently executed k-round protocol. Consequently any k-round (standard) UC-secure protocol remains secure in
the presence of our helper. Finally, we prove that building long-term-secure oblivious transfer (and thus general two-party computations) from long-term-revealing setups remains impossible in our
setting. Still, our long-term-secure commitment scheme suffices for natural applications, such as long-term secure and composable (commit-and-prove) zero-knowledge arguments of knowledge.
Fiat–Shamir Transformation of Multi-Round Interactive Proofs (Extended Version) Abstract
The celebrated Fiat–Shamir transformation turns any public-coin interactive proof into a non-interactive one, which inherits the main security properties (in the random oracle model) of the
interactive version. While originally considered in the context of 3-move public-coin interactive proofs, i.e., so-called $$\varSigma $$ Σ -protocols, it is now applied to multi-round protocols as
well. Unfortunately, the security loss for a $$(2\mu + 1)$$ ( 2 μ + 1 ) -move protocol is, in general, approximately $$Q^\mu $$ Q μ , where Q is the number of oracle queries performed by the
attacker. In general, this is the best one can hope for, as it is easy to see that this loss applies to the $$\mu $$ μ -fold sequential repetition of $$\varSigma $$ Σ -protocols, but it raises the
question whether certain (natural) classes of interactive proofs feature a milder security loss. In this work, we give positive and negative results on this question. On the positive side, we show
that for $$(k_1, \ldots , k_\mu )$$ ( k 1 , … , k μ ) -special-sound protocols (which cover a broad class of use cases), the knowledge error degrades linearly in Q , instead of $$Q^\mu $$ Q μ . On
the negative side, we show that for t -fold parallel repetitions of typical $$(k_1, \ldots , k_\mu )$$ ( k 1 , … , k μ ) -special-sound protocols with $$t \ge \mu $$ t ≥ μ (and assuming for
simplicity that t and Q are integer multiples of $$\mu $$ μ ), there is an attack that results in a security loss of approximately $$\frac{1}{2} Q^\mu /\mu ^{\mu +t}$$ 1 2 Q μ / μ μ + t .
Fiat-Shamir Transformation of Multi-Round Interactive Proofs Abstract
The celebrated Fiat-Shamir transformation turns any public-coin interactive proof into a non-interactive one, which inherits the main security properties (in the random oracle model) of the
interactive version. While originally considered in the context of 3-move public-coin interactive proofs, i.e., so-called $\Sigma$-protocols, it is now applied to multi-round protocols as well.
Unfortunately, the security loss for a $(2\mu + 1)$-move protocol is, in general, approximately $Q^\mu$, where $Q$ is the number of oracle queries performed by the attacker. In general, this is the
best one can hope for, as it is easy to see that this loss applies to the $\mu$-fold sequential repetition of $\Sigma$-protocols, but it raises the question whether certain (natural) classes of
interactive proofs feature a milder security loss. In this work, we give positive and negative results on this question. On the positive side, we show that for $(k_1, \ldots, k_\mu)$-special-sound
protocols (which cover a broad class of use cases), the knowledge error degrades linearly in $Q$, instead of $Q^\mu$. On the negative side, we show that for $t$-fold \emph{parallel repetitions} of
typical $(k_1, \ldots, k_\mu)$-special-sound protocols with $t \geq \mu$ (and assuming for simplicity that $t$ and $Q$ are integer multiples of $\mu$), there is an attack that results in a security
loss of approximately~$\frac12 Q^\mu /\mu^{\mu+t}$.
Efficient Range Proofs with Transparent Setup from Bounded Integer Commitments 📺 Abstract
We introduce a new approach for constructing range proofs. Our approach is modular, and leads to highly competitive range proofs under standard assumption, using less communication and (much) less
computation than the state of the art methods, and without relying on a trusted setup. Our range proofs can be used as a drop-in replacement in a variety of protocols such as distributed ledgers,
anonymous transaction systems, and many more, leading to significant reductions in communication and computation for these applications. At the heart of our result is a new method to transform any
commitment over a finite field into a commitment scheme which allows to commit to and efficiently prove relations about bounded integers. Combining these new commitments with a classical approach for
range proofs based on square decomposition, we obtain several new instantiations of a paradigm which was previously limited to RSA-based range proofs (with high communication and computation, and
trusted setup). More specifically, we get: - Under the discrete logarithm assumption, we obtain the most compact and efficient range proof among all existing candidates (with or without trusted
setup). Our proofs are 12% to 20% shorter than the state of the art Bulletproof (Bootle et al., CRYPTO'18) for standard choices of range size and security parameter, and are more efficient (both for
the prover and the verifier) by more than an order of magnitude. - Under the LWE assumption, we obtain range proofs that improve over the state of the art in a batch setting when at least a few dozen
range proofs are required. The amortized communication of our range proofs improves by up to two orders of magnitudes over the state of the art when the number of required range proofs grows. -
Eventually, under standard class group assumptions, we obtain the first concretely efficient standard integer commitment scheme (without bounds on the size of the committed integer) which does not
assume trusted setup.
On expected polynomial runtime in cryptography 📺 Abstract
A common definition of black-box zero-knowledge considers strict polynomial time (PPT) adversaries but expected polynomial time (EPT) simulation. This is necessary for constant round black-box
zero-knowledge in the plain model, and the asymmetry between simulator and adversary an accepted consequence. Consideration of EPT adversaries naturally leads to designated adversaries, i.e.
adversaries which are only required to be efficient in the protocol they are designed to attack. They were first examined in Feige’s thesis [Fei90], where obstructions to proving security are shown.
Prior work on (designated) EPT adversaries by Katz and Lindell (TCC’05) requires superpolynomial hardness assumptions, whereas the work of Goldreich (TCC’07) postulates “nice” behaviour under
rewinding. In this work, we start from scratch and revisit the definition of efficient algorithms. We argue that the standard runtime classes, PPT and EPT, behave “unnatural” from a cryptographic
perspective. Namely, algorithms can have indistinguishable runtime distributions, yet one is considered efficient while the other is not. Hence, classical runtime classes are not “closed under
indistinguishability”, which causes problems. Relaxations of PPT which are “closed” are (well-)known and used. We propose computationally expected polynomial time (CEPT), the class of runtimes which
are (computationally) indistinguishable from EPT, which is “closed”. We analyze CEPT in the setting of uniform complexity (following Goldreich (JC’93)) with designated adversaries, and provide
easy-to-check criteria for zero-knowledge protocols with blackbox simulation in the plain model, which show that many (all known?) such protocols handle designated CEPT adversaries in CEPT.
(R)CCA Secure Updatable Encryption with Integrity Protection Abstract
An updatable encryption scheme allows a data host to update ciphertexts of a client from an old to a new key, given so-called update tokens from the client. Rotation of the encryption key is a common
requirement in practice in order to mitigate the impact of key compromises over time. There are two incarnations of updatable encryption: One is ciphertext-dependent, i.e. the data owner has to
(partially) download all of his data and derive a dedicated token per ciphertext. Everspaugh et al. (CRYPTO’17) proposed CCA and CTXT secure schemes in this setting. The other, more convenient
variant is ciphertext-independent, i.e., it allows a single token to update all ciphertexts. However, so far, the broader functionality of tokens in this setting comes at the price of considerably
weaker security: the existing schemes by Boneh et al. (CRYPTO’13) and Lehmann and Tackmann (EUROCRYPT’18) only achieve CPA security and provide no integrity protection. Arguably, when targeting the
scenario of outsourcing data to an untrusted host, plaintext integrity should be a minimal security requirement. Otherwise, the data host may alter or inject ciphertexts arbitrarily. Indeed, the
schemes from BLMR13 and LT18 suffer from this weakness, and even EPRS17 only provides integrity against adversaries which cannot arbitrarily inject ciphertexts. In this work, we provide the first
ciphertext-independent updatable encryption schemes with security beyond CPA, in particular providing strong integrity protection. Our constructions and security proofs of updatable encryption
schemes are surprisingly modular. We give a generic transformation that allows key-rotation and confidentiality/integrity of the scheme to be treated almost separately, i.e., security of the
updatable scheme is derived from simple properties of its static building blocks. An interesting side effect of our generic approach is that it immediately implies the unlinkability of ciphertext
updates that was introduced as an essential additional property of updatable encryption by EPRS17 and LT18. | {"url":"https://www.iacr.org/cryptodb/data/author.php?authorkey=11010","timestamp":"2024-11-12T13:33:45Z","content_type":"text/html","content_length":"51473","record_id":"<urn:uuid:90ccd969-1bef-459e-bb64-58eabe753ca7>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00252.warc.gz"} |
Ergodic Theory
This is a development version of this entry. It might change over time and is not stable. Please refer to release versions for citations.
Ergodic theory is the branch of mathematics that studies the behaviour of measure preserving transformations, in finite or infinite measure. It interacts both with probability theory (mainly through
measure theory) and with geometry as a lot of interesting examples are from geometric origin. We implement the first definitions and theorems of ergodic theory, including notably Poicaré recurrence
theorem for finite measure preserving systems (together with the notion of conservativity in general), induced maps, Kac's theorem, Birkhoff theorem (arguably the most important theorem in ergodic
theory), and variations around it such as conservativity of the corresponding skew product, or Atkinson lemma.
Session Ergodic_Theory | {"url":"https://devel.isa-afp.org/entries/Ergodic_Theory.html","timestamp":"2024-11-12T03:19:39Z","content_type":"text/html","content_length":"12638","record_id":"<urn:uuid:1d7244cd-e18d-4ca1-8043-52bfb359a960>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00457.warc.gz"} |
Statistics for Data Science: Visualising Conditional Probability
Image by Author
I have been thinking of writing an article about the visual representation of the Bayes Theorem for some time. However, when I sat down to write it, I found that breaking the article into two is
better, as it was getting too long. In the first article here, I am giving a visual intuition about conditional probability, and then I will proceed to Bayes Theorem in the following article.
Before we start, let us go over a few definitions :
Sample Space
A sample space is the set of all possible outcomes of a random experiment. For example, in the throwing of a dice, the sample space will consist of the outcomes {1,2,3,4,5,6}. This article will
denote the sample space by rectangle U. As the sample space contains all the possible outcomes in any experiment, P(U) = 1, always.
An event in any random experiment is a subset of the sample space of that experiment. For example, in the dice roll experiment, an event A can denote that the outcome is an even number, written in
the set form as {2,4,6}. In this article, the events are represented by circles inside the sample space, shown as rectangles.
Image by Author
For this article, we will assume that we have drawn these figures so that, area of each of these figures is directly proportional to the number of possible outcomes inside that particular subset or
event. And also that the area of the rectangle representing the sample space U is 1 unit, that is,
i) Area(U) = 1
So in the dice roll example, as the number of outcomes possible in event A is half that of U,
ii) Area(A) = 1/2,
Also, by the definition of probability,
P(A) = no. of outcomes possible in event A/total no. of outcomes possible
And as the number of outcomes is directly proportional to the area as per our representation, we can write
P(A) = Area(A)/Area(U)
from 1 and 2 above,
P(A) = 1/2
Now using this formulation, let us arrive at the formula for conditional probability using geometric intuition :
Conditional Probability
The conditional probability of an event A, given that an event B has already occurred, is given by
P(A|B) = P(A∩B)/P(B)
where P(A∩B) is the probability that event A and B both occur together.
To derive the above formula geometrically, let us consider the dice roll example from above, with U and A same as before, while adding the event B, which is the event of the occurrence of numbers
less than equal to 4.
So, U~ {1,2,3,4,5,6},
A ~ {2,4,6}, and
B ~ {1,2,3,4}
This can be represented visually as :
Image by Author
Here, as before Area(U) = 1, and
iii) P(B) = Area(B)/Area(U) = Area(B), and
iv) P(A∩B) = Area(A∩B)/Area(U) = Area(A∩B) ,
which is shown as the shaded region between the 2 circles.
If we know that event B has already occurred, circle B becomes the sample space now, since all the possible outcomes are inside B.
Image By Author
Here, as before Area(U) = 1, and
iii) P(B) = Area(B)/Area(U) = Area(B), and
iv) P(A∩B) = Area(A∩B)/Area(U) = Area(A∩B) ,
which is shown as the shaded region between the 2 circles.
If we know that event B has already occurred, circle B becomes the sample space now, since all the possible outcomes are inside B.
Image By Author
And now the probability of A occurring, given B has occurred, is given by
P(A|B) = Area(A∩B)/Area(B)
from iii) and iv),
P(A|B) = P(A∩B)/P(B)
which is also the definition of conditional probability.
The geometrical proof for the conditional probability formula was quite simple enough, and we will build upon this to visualise Bayes Theorem in the next article.
Your comments and suggestion are welcome. Subscribe if you would like to read more articles like this in future. Thank you. | {"url":"https://psrivasin.medium.com/visualising-conditional-probability-735019933d08?source=post_page-----83c40e7c1bf7--------------------------------","timestamp":"2024-11-04T17:25:56Z","content_type":"text/html","content_length":"122944","record_id":"<urn:uuid:e98b3983-d49e-455a-8145-9cc2d7b30a15>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00891.warc.gz"} |
China's transport, tanker & heavy lift aircraft
If/when the advertised purchase of 30 il76 goes through it will greatly increase china's airlift abilities. With those new aircraft china's combined airlift capacities of its il76 fleet, y-8 fleet,
y-7 fleet and some calculated 250 units of its y-5 fleet would rise to 3570 tons of cargo or 16800 equipped troops in one run. That's calculated for under 1000 km range, as i don't see the need for
longer runs in taiwan scenario. Of course i'm not saying that a force of several hundred of transport planes can operate at the same time on an area size of taiwan, for example. I'm just talking
about potential.
I used the figure of 14 previously purchased il76, minus one that is reffited for AEW. 43 Il76s would give 2020 tons of cargo lift or 8170 equipped troops. If china has more previously bought IL76 (i
found a figure of up to 20) of course the airlift potential would be even greater.
48 y-8 fleet can carry 960 tons of cargo or some 4600 equipped troops. However, i don't know what number of these planes is used for roles other than transport.
80 y-7 can carry 440 tons of cargo or some 2000 equipped troops. Finally, figures for y-5 were extremely hard to find, some going into over 400 range. But given how it's an old airplane i went with a
conservative 250 fleet assumption. such a number would give ability to lift 250 tons or 2000 equipped troops.
All these airplanes can load/unload their cargo on their own, without any access ramps or additional airport equipment. There is also a number of commercial airliners in PLAF's service, combined able
to ferry at least additional 2000 troops at once. These, of course, need conventional runways and must have stairways and ramps to get the troops/cargo on and off the planes.
Finally, does anyone have data for cargo hold specs on the il76md? i know weight wise it could haul one tank based on t72/t80 design but is the cargo hold wide enough?
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The Last Jedi
VIP Professional
Re: China's transport plane capacities
That's interesting. When the purchase of the 30 il76 goes through that will be a big boost to the PLAAF. Could you post a link about the purchase of the new aircraft? Thanks
Personally I think the PLAAF needs to improve it's in air re-fueling capablity. I read in the old forum that the re-fueling probes are not compatiable with all their aircraft. Any more info on that?
Re: China's transport plane capacities
This site is normally quite good. It says china got 40 IL-76 and IL-78 for $1 billion. The commonly speculated breakdown is 30 IL-76 and 10 IL-78. Add that to the 10 to 20 IL-76 China already has,
the transport and aerial refueling capability has definitely been greatly enhanced.
Re: China's transport plane capacities
50 Il-76 and 20-Il-78..
All China needs is those bigger An-124?? An-250?? (like 10-20 of them to provide bigger and badder units) and China will be in VERY good shape
Just 1 problem... Does China have a license to built them or is China working on a new version to replace the old ones?
Re: China's transport plane capacities
the ones delivered to china will be new ones, but I'm not sure if China is getting the latest MF variant. Does anyone know what the price on the IL-76MD planes are?
Re: China's transport plane capacities
They are Purchasing 38 planes (most Il-76 tranports, some Il-78 refuelers, I don't know the exact mix) for a total purchase price of $1.5 billion.
If we treated the Il-76 and Il-78 has similarly priced, that comes out to $40 million per plane.
The Il-76MF is the newest version and has similar load capablilities to the C-17 Globemaster of America. They are both capable of utilizing shorter runways than the giant cargo planes like the
Antonov's or the C-5 Galaxy. As far as I know the C-17 is still superior in regards to the fact that it has truly global range (hence the name Globemaster). This is because it is capable of in-flight
refueling. The Il-76MF is still not capable of in-flight refueling.
Btw, the C-17 also costs $340 million per plane and has been sharply criticized by the General Accounting Office as a wasteful Pork program. I think the plane is needed, but that price tag is
Four Il-76MF's are already under construction for Russian clients. It is doubtful that these planes were displayed in the recent joint military maneuvers, but there is a good chance it is this model
that will be produced in the factory since the order is for brand new planes.
The refueling plane is comparable to America's KC-10 Extender. Forget about the Stratotanker (dated 1965), its limited range does not put it in the same league. The KC-10 costs $100 million apiece.
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Re: China's transport plane capacities
These, of course, need conventional runways and must have stairways and ramps to get the troops/cargo on and off the planes.
Are you telling me soldiers will not be able to board/leave planes without ramps? Why can't they can either jump or climb up on a rope!?!
Re: China's transport plane capacities
Fairthought said:
Btw, the C-141 also costs $340 million per plane and has been sharply criticized by the General Accounting Office as a wasteful Pork program. I think the plane is needed, but that price tag is
C-141 is no longer in production and is in fact being retired from service. Maybe you are refering to the C-17 GlobemasterIII? But $340 mil. still sounds steep to me.
Re: China's transport plane capacities
Thank you Walter,
I am mistaken. The price tag is for the C-17. The C-141 has not been in production in over ten years and the last one is set to retire in 2006. Yes, I meant to say the C-17 globemaster. Terribly
sorry about the mix up. The C-141 is not capable of the inflight refueling, the C-17 is.
Re: China's transport plane capacities
I did not realize the price tag ($340 mil.) was so high on the C-17--that sure is a lot of pork!
At that price i would almost prefer the US also buying the Il-76MF for $40 million a copy. | {"url":"https://sinodefenceforum.com/t/chinas-transport-tanker-heavy-lift-aircraft.197/","timestamp":"2024-11-09T09:09:06Z","content_type":"text/html","content_length":"78451","record_id":"<urn:uuid:9194571f-ac0e-4c73-8b4c-a983ea06c0f6>","cc-path":"CC-MAIN-2024-46/segments/1730477028116.75/warc/CC-MAIN-20241109085148-20241109115148-00812.warc.gz"} |
Relations and Functions-Tips-Maths Class 12 NCERT
This gives you a complete set of formulas for Sets, Relations and Functions needed for Class 12 maths. You will start with the definition of a set , properties of union and intersection of 2 sets.
Number of elements in A union B , number of elements in A union B union C .Concept of a Relation, Types of Relations, Reflexive, Symmetric, Transitive, Equivalence Relation and Equivalence Classes.
Functions, Injective and Surjective and other types. Composite functions and Binary Operations.
Class 12 Maths NCERT and ISC tool. | {"url":"https://www.mathmadeeasy.co/post/relations-and-functions-tips-maths-class-12-ncert","timestamp":"2024-11-04T17:03:04Z","content_type":"text/html","content_length":"1050594","record_id":"<urn:uuid:42d70e93-c6ad-4c67-94b6-316d39297418>","cc-path":"CC-MAIN-2024-46/segments/1730477027838.15/warc/CC-MAIN-20241104163253-20241104193253-00756.warc.gz"} |
620 research outputs found
The eigenvalue density of a quantum-mechanical system exhibits oscillations, determined by the closed orbits of the corresponding classical system; this relationship is simple and strong for waves in
billiards or on manifolds, but becomes slightly muddy for a Schrodinger equation with a potential, where the orbits depend on the energy. We discuss several variants of a way to restore the
simplicity by rescaling the coupling constant or the size of the orbit or both. In each case the relation between the oscillation frequency and the period of the orbit is inspected critically; in
many cases it is observed that a characteristic length of the orbit is a better indicator. When these matters are properly understood, the periodic-orbit theory for generic quantum systems recovers
the clarity and simplicity that it always had for the wave equation in a cavity. Finally, we comment on the alleged "paradox" that semiclassical periodic-orbit theory is more effective in calculating
low energy levels than high ones.Comment: 19 pages, RevTeX4 with PicTeX. Minor improvements in content, new references, typos correcte
The regularized vacuum energy (or energy density) of a quantum field subjected to static external conditions is shown to satisfy a certain partial differential equation with respect to two variables,
the mass and the "time" (ultraviolet cutoff parameter). The equation is solved to provide integral expressions for the regularized energy (more precisely, the cylinder kernel) at positive mass in
terms of that for zero mass. Alternatively, for fixed positive mass all coefficients in the short-time asymptotics of the regularized energy can be obtained recursively from the first nontrivial
coefficient, which is the renormalized vacuum energy.Comment: 8 pages, RevTeX; v.2 has minor updates and format change
Casimir pistons are models in which finite Casimir forces can be calculated without any suspect renormalizations. It has been suggested that such forces are always attractive. We present three
scenarios in which that is not true. Two of these depend on mixing two types of boundary conditions. The other, however, is a simple type of quantum graph in which the sign of the force depends upon
the number of edges.Comment: 4 pages, 2 figures; RevTeX. Minor additions and correction
Asymptotic expansions of Green functions and spectral densities associated with partial differential operators are widely applied in quantum field theory and elsewhere. The mathematical properties of
these expansions can be clarified and more precisely determined by means of tools from distribution theory and summability theory. (These are the same, insofar as recently the classic Cesaro-Riesz
theory of summability of series and integrals has been given a distributional interpretation.) When applied to the spectral analysis of Green functions (which are then to be expanded as series in a
parameter, usually the time), these methods show: (1) The "local" or "global" dependence of the expansion coefficients on the background geometry, etc., is determined by the regularity of the
asymptotic expansion of the integrand at the origin (in "frequency space"); this marks the difference between a heat kernel and a Wightman two-point function, for instance. (2) The behavior of the
integrand at infinity determines whether the expansion of the Green function is genuinely asymptotic in the literal, pointwise sense, or is merely valid in a distributional (cesaro-averaged) sense;
this is the difference between the heat kernel and the Schrodinger kernel. (3) The high-frequency expansion of the spectral density itself is local in a distributional sense (but not pointwise).
These observations make rigorous sense out of calculations in the physics literature that are sometimes dismissed as merely formal.Comment: 34 pages, REVTeX; very minor correction
A simple transformation converts a solution of a partial differential equation with a Dirichlet boundary condition to a function satisfying a Robin (generalized Neumann) condition. In the simplest
cases this observation enables the exact construction of the Green functions for the wave, heat, and Schrodinger problems with a Robin boundary condition. The resulting physical picture is that the
field can exchange energy with the boundary, and a delayed reflection from the boundary results. In more general situations the method allows at least approximate and local construction of the
appropriate reflected solutions, and hence a "classical path" analysis of the Green functions and the associated spectral information. By this method we solve the wave equation on an interval with
one Robin and one Dirichlet endpoint, and thence derive several variants of a Gutzwiller-type expansion for the density of eigenvalues. The variants are consistent except for an interesting subtlety
of distributional convergence that affects only the neighborhood of zero in the frequency variable.Comment: 31 pages, 5 figures; RevTe | {"url":"https://core.ac.uk/search/?q=author%3A(Fulling%20S%20A)","timestamp":"2024-11-12T06:39:30Z","content_type":"text/html","content_length":"109878","record_id":"<urn:uuid:f25ac65a-b3f2-437e-944b-9353698dbb8f>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.58/warc/CC-MAIN-20241112045844-20241112075844-00484.warc.gz"} |
Effective communication formula - Juan Damia
Effective communication formula
It’s pretty late at night and I just can’s sleep, so here I am trying to play a bit with some maths. The exercise is to finds out the formula for an effective communication. Well, finally I guess I
finds out the formula for an effective communication, and guess what, seems pretty simple. Even when is true that everything seems to be simple while you take humans behavior out from your plans,
lets take a look at it
EC = P(mm) x R Where:
EC = Effective Communication.
P = People.
mm = Mental Model.
R = Respect.
If we take into consideration that P(mm) or persons with their own mental models are constant the only variable is R.
When R = 0
EC = P(mm) x 0 and everything multiplied by 0 is 0. Then the Effective communication is null.
EC = 0
Finally as much the R (respect) tends to 0, as lower is the EC (Effective communication). Simple, Fast, and Very understandable but, how much prepared are humans for respecting each other? ;=)
This site uses Akismet to reduce spam. Learn how your comment data is processed. | {"url":"https://damia.me/web-analytics/effective-communication-formula","timestamp":"2024-11-12T11:55:06Z","content_type":"text/html","content_length":"39365","record_id":"<urn:uuid:33079a8a-622d-4cc0-9d4a-7922f1058df7>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00426.warc.gz"} |
Omics data integration with o2plsda
o2plsda: Omics data integration with o2plsda
o2plsda provides functions to do O2PLS-DA analysis for multiple omics integration.The algorithm came from “O2-PLS, a two-block (X±Y) latent variable regression (LVR) method with an integral OSC
filter” which published by Johan Trygg and Svante Wold at 2003. O2PLS is a bidirectional multivariate regression method that aims to separate the covariance between two data sets (it was recently
extended to multiple data sets) (Löfstedt and Trygg, 2011; Löfstedt et al., 2012) from the systematic sources of variance being specific for each data set separately. It decomposes the variation of
two datasets in three parts:
• a joint part that is correlated (predictive) to \(X\) and \(Y\) (i.e. variation related to both \(X\) and \(Y\)), denoted as \(X/Y\) joint variation in \(X\) and \(Y\): \(TW^\top\) and \(UC^\top
• a part contained inside \(X/Y\) that is uncorrelated (orthogonal) to \(X\) and \(Y\): \(T_{yosc} W_{yosc} ^\top\) and \(U_{xosc} C_{xosc}^\top\),
• A noise part for \(X\) and \(Y\): \(E_{xy}\) and \(F_{yx}\).
The number of columns in \(T\), \(U\), \(W\) and \(C\) are denoted by as \(nc\) and are referred to as the number of joint components. The number of columns in \(T_{yosc}\) and \(W_{yosc}\) are
denoted by as \(nx\) and are referred to as the number of \(X\)-specific components. Analoguous for \(Y\), where we use \(ny\) to denote the number of \(Y\)-specific components. The relation between
\(T\) and \(U\) makes the joint part the joint part: \(U = TB_U + H\) or \(U = TB_T'+ H'\). The number of components \((nc, nx, ny)\) are chosen beforehand (e.g. with Cross-Validation).
In order to avoid overfitting of the model, the optimal number of latent variables for each model structure was estimated using group-balanced Monte Carlo cross-validation (MCCV). The package could
use the group information when we select the best parameters with cross-validation. In cross-validation (CV) one minimizes a certain measure of error over some parameters that should be determined a
priori. Here, we have three parameters: \((nc, nx, ny)\). A popular measure is the prediction error \(||Y - \hat{Y}||\), where \(\hat{Y}\) is a prediction of \(Y\). In our case the O2PLS method is
symmetric in \(X\) and \(Y\), so we minimize the sum of the prediction errors: \(||X - \hat{X}||+||Y - \hat{Y}||\).
Here \(nc\) should be a positive integer, and \(nx\) and \(ny\) should be non-negative. The ‘best’ integers are then the minimizers of the prediction error.
The O2PLS-DA analysis was performed as described by Bylesjö et al. (2007); briefly, the O2PLS predictive variation [$TW^\top$, \(UC^\top\)] was used for a subsequent O2PLS-DA analysis. The Variable
Importance in the Projection (VIP) value was calculated as a weighted sum of the squared correlations between the OPLS-DA components and the original variable.
## Attaching package: 'o2plsda'
## The following object is masked from 'package:stats':
## loadings
# sample * values
X = matrix(rnorm(5000),50,100)
# sample * values
Y = matrix(rnorm(5000),50,100)
##add sample names
rownames(X) <- paste("S",1:50,sep="")
rownames(Y) <- paste("S",1:50,sep="")
## gene names
colnames(X) <- paste("Gene",1:100,sep="")
colnames(Y) <- paste("Lipid",1:100,sep="")
X = scale(X, scale = TRUE)
Y = scale(Y, scale = TRUE)
## group factor could be omitted if you don't have any group
group <- rep(c("Ctrl","Treat"), each = 25)
Do cross validation with group information
## nr_folds : cross validation k-fold (suggest 10)
## ncores : parallel paramaters for large datasets
cv <- o2cv(X,Y,1:5,1:3,1:3, group = group, nr_folds = 10)
## #####################################
## The best parameters are nc = 1, nx = 2, ny = 1
## #####################################
## The the RMSE is: 1.97990443734287
## #####################################
Then we can do the O2PLS analysis with nc = 1, nx = 2, ny =1. You can also select the best parameters by looking at the cross validation results.
fit <- o2pls(X,Y,1,2,1)
## ######### Summary of the O2PLS results #########
## ### Call o2pls(X, Y, nc= 1 , nx= 2 , ny= 1 ) ###
## ### Total variation
## ### X: 4900 ; Y: 4900 ###
## ### Total modeled variation ### X: 0.108 ; Y: 0.098 ###
## ### Joint, Orthogonal, Noise (proportions) ###
## X Y
## Joint 0.039 0.052
## Orthogonal 0.070 0.046
## Noise 0.892 0.902
## ### Variation in X joint part predicted by Y Joint part: 0.882
## ### Variation in Y joint part predicted by X Joint part: 0.882
## ### Variation in each Latent Variable (LV) in Joint part:
## LV1
## X 0.039
## Y 0.052
## ### Variation in each Latent Variable (LV) in X Orthogonal part:
## LV1 LV2
## X 0.036 0.034
## ### Variation in each Latent Variable (LV) in Y Orthogonal part:
## LV1
## Y 0.046
## ############################################
Extract the loadings and scores from the fit results and generated figures
Xl <- loadings(fit,loading="Xjoint")
Xs <- scores(fit,score="Xjoint")
plot(fit,type="score",var="Xjoint", group=group)
plot(fit,type="loading",var="Xjoint", group=group,repel=F,rotation=TRUE)
Do the OPLSDA based on the O2PLS results and calculate the VIP values
res <- oplsda(fit,group, nc=1)
plot(res,type="score", group=group,repel=TRUE)
vip <- vip(res)
plot(res,type="vip", group = group, repel = FALSE,order=TRUE)
If you like this package, please contact me for the citation.
For any questions please contact guokai8@gmail.com or https://github.com/guokai8/o2plsda/issues | {"url":"https://cran.itam.mx/web/packages/o2plsda/vignettes/o2plsda.html","timestamp":"2024-11-03T19:12:38Z","content_type":"text/html","content_length":"269951","record_id":"<urn:uuid:ca8ec59c-4d12-40d3-bef5-ab804bbc85e4>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00420.warc.gz"} |
Evolutionary biology and dangerous diseases - DocMartin
Evolutionary biology and dangerous diseases
Viewing 18 posts - 1 through 18 (of 18 total)
• Author
• 21 September 2005 at 10:08 am #3249
Evolutionary Biology Important re Bird and Human Flu
Interesting paper (to me!) by Professor Paul Ewald –
Guarding Against the Most Dangerous Emerging Pathogens: Insights from Evolutionary Biology
– covers pathogen characteristics that indicate they could cause dangerous diseases.
Has a checklist, to assess if a pathogen could be dangerous – it could be if answer is yes to any of the following:
Does it have a tendency for waterborne transmission?
Is it vector-borne with the ability to use humans as part of the life cycle?
If it is directly transmitted, is it durable in the external environment? Is it attendant-borne? Is it needle-borne?*
If it is sexually transmitted, is it mutation-prone with a tropism for critical cell types or does it have invasive or oncogenic tendencies?
Relevant to human and bird (poultry) flu:
With regard to the emergence of virulent variants from established pathogens, the influenza viruses circulating at the Western Front during World War I would be considered dangerous because
barriers to transmission from immobile hosts were removed by cultural practices and because influenza virus is mutation prone. It is, therefore, not surprising that the Western Front has been
identified as the source of the highly lethal variants of the 1918 influenza pandemic and that a pandemic of this severity has never recurred. More importantly, evolutionary considerations
suggest that such a lethal pandemic will not recur unless influenza viruses are again exposed to opportunities that allow transmission from immobile hosts, as they are on poultry farms where
highly lethal influenza outbreaks periodically emerge.
(I learned of this through an article in New Republic, by Wendy Orent, saying we are not facing a pandemic of highly lethal flu, as don’t have the necessary conditions [inc chance for people laid
low by flu to still readily transmit to others]; subscription needed to view article I believe.)
24 September 2005 at 3:43 pm #3826
Related article – mentioning flu evolution and comparisons with 1918 – argues Fear is more likely to get you than the avian flu
23 October 2005 at 11:58 am #3827
Article by Carl Zimmer – TAMING PATHOGENS: AN ELEGANT IDEA, BUT WILL IT WORK? – mentions some criticisms of evolutionary biology and pathogens, but doesn’t seem they are by any means watertight.
Ewald complains … the critics … leave out a crucial component of his work, for example, the mode by which a disease infects new hosts. If hosts become so sick they can’t move, a parasite can only
infect other people who come close, unless a vector such as a mosquito can transport it. This factor is crucial in Ewald’s explanation of Spanish flu. … "My argument was that at the Western Front
you had conditions in which people who were completely immobilized could contact hundreds or thousands of people." Sick soldiers were moved on stretchers to triage areas, then to makeshift
hospitals, then onto crowded trains. In these conditions, a flu virus could devastate its host but still infect vast numbers of people. "My argument was that we wouldn’t see a 1918 pandemic arise
unless we duplicated this situation which occurred on the Western Front," says Ewald.
– relevant to birds, too. Poultry farms can become "disease factories" (as Wendy Orent puts it); but in the wild, bird flus are mild, because Dead Ducks Don’t Fly.
4 November 2005 at 9:11 am #3828
Scientific American blogger (editor of the magazine) made post with sume criticisms of evolutionary biology and flu at:
Don’t Fear The (Bird) Reaper
led to detailed responses: Bird Reaper, Pt II: Wendy Orent replies
Bird Reaper, Pt III: Paul Ewald replies
Above replies give useful info re evolutionary biology. I just fired off something simpler:
C’mon, the post with the muddled stuff about H5N1 and evolutionary biology’s a red herring. The real issue’s surely the remarkable Lindsay Beyerstein – remarkable not so much for her blog posts
but because (from the photo), Dang, She’s Hot!
Otherwise, what with extensively citing an anonymous muddleheaded blogger who bandies big words about in sentences without clear conclusions (or, to demonstrate his belief in Unintelligent
Design?) would suggest you were making a contribution to what the November Esquire calls Idiot America. Toodlepip (from citizen but not currently resident of UK, which has faults but at least
doesn’t need Oprah to explain global warming)
8 November 2005 at 1:39 pm #3829
A blogger with the moniker Mike the Mad Biologist has written short critique of ideas from Ewald (and covered by Wendy Orent in several articles); seems to hinge largely on flu being
transmissible before symptoms.
Evolution, Tradeoffs, Ignoring Biology, and Influenza
Doesn’t seem arguments are real substantial; not helped by what seems to me a rather curious quote re a colleague referring to "those stupid fucking natural history facts." Main one of these
facts being again related to flu being transmissible before symptoms (tho as Orent notes, h5n1 is not transmissible – or darn near not transmissible – in humans). I’ve just added comment: Is flu
just as contagious during asymptomatic phase. as when symptoms evident (and those with bad cases become immobile)? What of 1918 flu? Just coincidence it evolved – Ewald argues – during Western
Front conditions? (And human flu otherwise not major problem; if it could readily evolve to high virulence, shouldn’t it do so more often, and even stay that way?) And why are regular bird flus
"mild", yet crowd poultry in "disease factories" and get a flurry of highly pathogenic flus evolving? To me – a birder not biologist – latter seem to be neatly explained by ideas Orent writes of.
(Any other theories able to explain these latter facts? Poultry farms would seem "good", accidental experiments that help confirm Ewald’s theory.)
24 January 2006 at 3:52 pm #3830
Just come across blog post by John Hawks, Assistant Professor of Anthropology at the University of Wisconsin—Madison; on the arguments between Ewald and Revere.
He notes:
1. Almost no mainstream press accounts of the bird flu threat discuss anything about the evolution of influenza. This is probably the most important public impact of evolutionary theory today,
but we hear almost nothing of the evolutionary modeling of how the virus may change.
2. Ewald is very well known for studying the evolutionary dynamics of disease. He is making an argument that is sound, as far as the dynamics of selection are concerned. Thus, there are good
reasons to think that the worst will not happen, and this is a perspective that has been underplayed.
3. So far, the theory has only been tested by a relatively small number of instances — there just haven’t been so many pandemics that we can infer accurately from past events what the future will
be like. It could certainly happen that some new influenza strain could violate the model in some unexpected way, and for this reason governments should play it safe rather than assume that no
high-virulence pandemic will emerge.
4. A lot of public health scientists are going to be well-employed for as long as the bird flu remains in the public perception. This doesn’t mean that they are wrong to convey alarm, but it does
mean that they don’t benefit by playing down the threat. It’s sort of like NASA and the asteroid impact threat — partly they are more concerned because they know more about the threat and its
terrible effects, partly because it’s their job to be concerned.
5. There are a lot of biologists who don’t use or understand selection.
Ewald bird flu spat
28 January 2006 at 12:37 pm #3831
from correspondent re point 4 in above post:
Perhaps I understand the background more correctly. The asteroid
impact threat was not a final target of the study, but it was more
important that the same research tools (wide-field automated telescopes
and pipeline analysis) can be applied to different targets of
academic interest. They will not be very appealing (at least for
the beginning) to the public. The NASA people needed a different,
more popular target in pursuit of their original scientific interest.
These telescopes are now being used to rapid follow-up observations of
gamma-ray bursts, recovery of dead comets, and other targets of current
popular astronomy problems. The “blue book” of the Hubble Space
Telescope was similar, but produced far greater results than originally
I don’t know whether influenza specialists are taking the similar
course, or they regard pandemic a real, foreseeable threat. But
as far as I read, top virologists look like to have been more
deliberate, and have warned the public against alarmism. I think
that these people regard it a real threat, and urge governments
to prepare for the “upper limit” disaster. They probably think it
insufficient to prepare for the “expected mean” (as might be derived
from evolutionary biology).
2 February 2006 at 8:44 am #3832
Had lengthy correspondence re natural selection and H5N1, with “a correspondent”; also led to comments from Wendy Orent.
> Indicates quoted text within the chunks of quoted text – gets a bit complex like this I’m afraid.
Lest of interest, here goes:
Again, the paper by Ewald, with predictions re evolution of pathogens including flu:
Yes, this is well-known. This is a famous piece in learning
ecology in terms of natural selection. This is a reason why experts
more fear a long-range transport (either by humans or birds) than
gradual geographical invasion.
But we can’t predict exactly, particularly when various species
are involved. We don’t even know why LPAIs are so “evolutionary
static” in wild ducks, while they can be so pathogenic to humans
when they happen to enter the human world. The only truth is
“natural selection works”, but we may not know or deal with all
factors of natural selection.
But again: Ewald makes predictions re flus becoming pathogenic entering human world.
Takes special conditions – very sick people able to readily transmit – to evolve a dangerous flu.
Most extreme in 1918: First World War.
Mao maybe helped cause 1957 and 1968 flus.
No such special conditions today; so Ewald argues that we won’t get a highly pathogenic human flu today.
His theory predicts avian flus will be mild in wild birds. Need to have birds flying to carry the flus, so evolution to mild strains. So, to me, we do know why LPAIs are “evolutionary static” in
wild birds.
High path strains into wild birds, and quickly to low path. Or extinction.
Quoting Ewald directly:
“With regard to the future I am predicting that such a highly lethal pandemic (i.e., 1 death per 50 infections) will not occur, not from H5N1 and not from any other influenza virus that will
arise unless regional conditions allow transmission from immobile hosts, as they did on the Western Front in 1918. This is not “speculation” as is claimed by our hooded critic with the
self-aggrandizing name. It is a prediction based on careful consideration of theory and evidence. The future will demonstrate whether it is accurate.”
Makes sense to me.
Can make analagous predictions for birds (Ewald does so for poultry):
– crowd together, indefinitely, so sick birds can readily transmit: and evolve dangerous flus
– wild situations, need birds to fly to transmit, and equilibrium when flus are mild
That is, predictions fit what we observe. Which to me is science; and not speculation.
Only mystery to me is why this is so widely ignored.
> No such special conditions today; so Ewald argues that we won’t get a
highly pathogenic human flu today.
As I have (indirectly) heard from flu experts, some argue the virus
will not enter the human world in the HP form, but others’ claim
is different — we (even virologists) don’t know how HPAI will behave.
“Most extreme in 1918: First World War”
> No such special conditions today
Wouldn’t airplanes, locomotion, population density be special?
We have never met a pandemic strain in such extremely globalized
world — we don’t really have an experience.
> His theory predicts avian flus will be mild in wild birds. Need to have
birds flying to carry the flus, so evolution to mild strains. So, to
me, we do know why LPAIs are “evolutionary static” in wild birds.
Yes, this explains “why”. We don’t exactly know “how”. This
means we don’t know exactly how selection pressure works. (Also
we don’t know how Zq strain retained high path to natural hosts).
As we haven’t seen LPAIs arising from Zq strain, we don’t know the
time-scale this process would require (may not be “very quickly”).
> High path strains into wild birds, and quickly to low path. Or
Most look like to be going extinction (i.e. R0 But planes, crowded conditions etc not enough to him; not so special.
Need to have very sick people – immobile with disease – able to readily
transmit the virus.
Crowding doesn’t matter here, if very sick people stay
But flu is already contagious during the incubation period.
Less traffic than in WW I? Less packed people? (imagine Tokyo
trains) Though I can’t figure out the effect, all present factors
seem to increase the risk of a more virulent pandemic.
> I’d figure that with wild birds, there’s always potential for virulent
flus to evolve.
Spectrum of virulence it seems to me (this from chemistry background,
not viruses): get some higher path, others lower path. Get an
equilibrium, depending on prevailing conditions.
As need flying birds to transmit flu in the wild, the equilibrium is
greatly towards non virulent forms. High path forms stay rare. (This
again from chemistry; some memories from when I did this re systems
reaching equilibrium.)
Thanks! This is much easier to understand. If “random” distribution
of mutated form is close to Gaussian, natural selection would work
in this way (for a specific species). If it is very far from Gaussian,
we can’t be sure (because there is no effective average — this might
explain some of social phenomena like Zipf’s law). What if some
populations (due to genetic diversity) are more resistant (not all
infected individuals die, but can excrete substantial amount of the
virus) — we probably need a more complex view. Natural selection on
incubation period may also occur.
> Could well be that doesn’t matter what bird species is: if cram into
captivity, infect with flu, and have substantial chance that birds with
high path forms can transmit flu, then will get evolution towards
higher pathogenic forms.
If this is population density-dependent, how can we be sure our
population density is below a threshold where high path strains can
be sustained for a meaningful (effective transmission to a next
cluster) time? What is the major difference from poultry chickens?
(Well, some of recent pandemic plans from various companies seem to
assume “forced working” of employees with milder symptoms — they
will mix healthy populations during movement or in taxis — we may
eventually be poultry chickens
One more on “equilibrium theory”, why we have never seen a human
pandemic strain eventually forming a non-pathogenic form (as in LPAIs
in wild ducks?) What would be the difference between ducks and humans?
(Why “evolutionary stasis” is never reached)
By the way, when considering selection pressure, won’t the extensive
use of Tamiflu in pandemic lead to a more virulent strain? Not
necessarily drug resistance, but won’t we be selecting a more neurotrophic
strain (since Tamiflu doesn’t effectively cross the blood-brain barrier),
I casted this question to a public health expert, but haven’t received
a reply. This might be another factor different from past pandemics.
Well, now you ask questions I wish I had all answers for! – should really go directly to Paul Ewald, as I have some understanding but relatively superficial (I’ll forward to science writer Wendy
Orent, who has written several articles based on his ideas, and with whom I’ve had some correspondence; she’s now in aiwatch).
The packed people, Tokyo trains or Hong Kong malls, not so important – if people who get sick, v quickly go to bed/hospital.
Seen re flu becoming infectious before symptoms; queried Wendy re this.
How infectious, I wonder, if not coughing/sneezing? How do you transmit virus without doing these things?
Gaussian curve: not sure, but it’s my way of understanding things, as noted based on (physical) chemistry.
Main thing w poultry farms, to Ewald, is that can have (ready) transmission from even very sick chickens – so dangerous forms can transmit, even intensify.
Wendy notes that 1918 flu did become non-virulent, and still circulates.
I also don’t know re Tamiflu; hadn’t known this re brain.
Doesn’t seem wise, to me, to use it extensively; cf antibiotics and resistance.
Rather as I’m also sceptical re vaccinations, perhaps helping sustain h5n1 (when vaccinations and surveillance less than near perfect).
> Seen re flu becoming infectious before symptoms; queried Wendy re this.
How infectious, I wonder, if not coughing/sneezing? How do you transmit
virus without doing these things?
If high path mechanism (replicate without trypsin) indeed works,
we don’t necessarily require respiratory organs. Virus replicates
everywhere in the body.
> Wendy notes that 1918 flu did become non-virulent, and still circulates.
The 1918 flu once disappeared (around 1950), reappeared later
(likely from a lab) and now circulating.
What if some
populations (due to genetic diversity) are more resistant (not all
infected individuals die, but can excrete substantial amount of the
virus) — we probably need a more complex view.
I’ve noticed that this possibility is a real concern. If such
individuals (or individuals of different species) are sporadic, we
don’t need to worry. But if chains of such individuals are
established? — This corresponds to the “percolation theory”.
(You may have read Simon Levin’s “Fragile Dominion” or Kauffman’s
“At Home in the Universe” in relation to percolation leading to
phase transition and its role in ecosystem).
> Well, not sure if water-borne disease should be more specialised to
this transmission route, between humans. Like cholera.
And like cholera, can’t imagine it becoming widespread, but more in few
places w bad sanitation.
Worst SARS outbreak outside hospital (that we know of) was evidently
from sewage (apparently from toilet, somehow reached people’s showers,
and several people infected in an apartment block). Looked scary, but
proved isolated.
Natural selection works as if a pathogen is seeking for a higher basic
reproduction number (not plainly necessarily less lethal). If a pathogen
has an ability to spread in a more efficient way, this would become
a primary route of transmission. If the virus replicates in intestines
or kidneys, sewage would be an efficient place for viral adaptation
(much resembling avian infections??).
> As discussed, I don’t believe Osterholm is correct re predictions.
> What may happen though, is that if get pandemic – and no matter if it’s
relatively mild – panic will lead to problems.
Already too many problems (such as worry, Tamiflu stocking etc), even
in US – where no H5N1, just fear of the disease.
As we know, our existence is dependent on the present biodiversity
— a product of ecosystem evolution, to which we best adapt.
We don’t know when our present existence is threatened how much and
how rapidly biodiversity is degraded, but there should be some number
(not easily predicted). The same is true for our society; our life
is dependent on the present social system — a product of social
evolution, to which we best adapt. We don’t know when our present
world is threatened how much and how rapidly social system is degraded.
These two problems are alike, both arising from a complex adaptive
system. Complex social systems could amplify the effect of a minor
Time-scales also play a role. If any change is slow enough, we
can, or ecosystem would adapt to a new form. If the change is rapid
enough, they may fail. There is a simple physical analogy; the
adaptation of gas is limited by the sound speed. If change goes
faster than the sound speed, the gas fails to adapt — the net result
is a well-known supersonic shock. The same would be true for our
society. If the spread of the pandemic is rapid enough, our system
would fail to adapt. Of course, with the advent of the internet,
we have a better chance of adaptation before the wave comes. But the
expected result of adaptation is so drastically different from the
current social system, the arrival of pandemic flu will trigger
a reaction that looks like to change the world overnight.
I’m skeptical about such a drastic change in social systems could be
done overnight (even officials declare “immediately”), since no one
is accustomed to the change, and expect the situations something
between adapted (with a drastic change) to less-adapted (little
reaction before the wave reaches, and an immediate panic is
Post edited by: martin, at: 2006/02/02 00:49
2 February 2006 at 8:52 am #3833
Right, time to break things up a little; still re the above correspondence, but here, some comments from Wendy Orent:
Dear Martin,
These are all good questions. I wish we could make it clear to
everyone that it isn’t crowding, per se, that is the crucial
condition. It’s the ability to transmit the germ repeatedly from
immobilized hosts to the well. People can be packed like sardines on
a train, subway, or plane, even for many hours, and not do anything
to advance the virulence of a respiratory pathogen like influenza. If
you’re that deathly ill, you are not getting on the plane, unless
you’re carried on. Even if that happened, and a number of people
caught a disease like that, whatever they caught would quickly lose
virulence – unless you kept people packed in together for weeks, or
months, or whatever it ttakes – no one knows. I.e., you’d need a
disease factory to develop virulence and transmissibility, and to
keep it going. I can’t think of any disease factory conditions on the
planet right not – World War One doesn’t happen frequently.
The whole plane thing is a red herring. We are not talking about
spreading a disease around the world; we’re talking about the
evolution of virulence. That is not going to happen on a plane in
normal circumstances – I mean, absent a plane getting hijacked with
someone deathly ill on board, and keeping people trapped on boared
with that person for weeks. Even then, it’s iffy…we don’t know how
long the evolution of virulence, or of transmissibility, takes.
As for contagiousness before symptoms: people love to trot that out.
But how does it work? You really can’t shed too much virus if there
isn’t a huge buildup in your upper respiratory tract. You might be a
little contagious, but only a little. It’s the symptoms that make you
contagious – the sneezing, the coughing – the virus’s little way of
making its host shed it into the world, where it hopes, so to speak,
someone else will pick it up. Anyway, the severest disease appears to
be that where the virus or bacterium replicates most quickly and
exploits the host’s tissues most thoroughly. It doesn’t give itself
the long window of being shed. Plague – the right sort of plague
(from marmots), not all plague – was pretty good at this – it’s
what’s been called a “stealth infection” – it suppresses the immune
response, inflammation, fever, everything – so the body doesn’t know
it’s under siege. That’s what people appear to keel over and die so
suddenly from pneumonic plague. They’re half dead while they’re still
walking around. But they aren’t shedding that much virulent bacteria
for all that time – their lungs have to get pretty destroyed before
they start coughing the blood-tinged sputum that’s infectious. That’s
plague – that’s not flu…you’d cough earlier in flu, but it’s just
not that deadly a disease – even 1918 killed 2-5% of its victims
(pneumonic plague kills 99.9% – it’s too lethal to people to exist
for long as a human-adapted disease.) So rule of thumb is –
contagiousness before symptoms is almost an oxymoron – you’d have to
be sneezing or coughing, at the least, to shed a lot of bugs. I
imagine that the deadlier the disease, the shorter the window of
contagiousness while you’re still up and walking around. Point being:
people with deadly flu aren’t going to be shedding it for very long
before they’re wiped off their feet.
You’re completely right about the wild birds, though I think the
Gaussian thing might be a red herring (though it’s also possible I
don’t clearly understand what you meant. It isn’t a question of the
mean in natural selection.) The thing is, wild birds can catch
high-path flu, die of it, even spread it a little, LOCALLY – but they
CAN’T maintain it. High-path flu can’t survive the sieve of natural
> Rather as I’m also sceptical re vaccinations, perhaps helping
sustain h5n1 (when vaccinations and surveillance less than near
A GOOD vaccine would be the way to go, if we had one – but for what
disease? Human-adapted H5N1 doesn’t exist yet, and no one knows what
it would look like if it did.
(I’d meant I was sceptical re vaccinations for poultry)
Equilibrium theory is for sure a red herring. Selection works on the
level of the individual organism or the individual strain or genetic
line – not on the population or species. A non-pathogenic strain in
people would mean that the virus wouldn’t get shed – it’s got to make
you sick to make you shed X;{ , or we’d all be infected with scads of
things we just pass around all the time, without ever getting sick
(some things, like staph epidermidis, do probably pass around this
way.) But wild birds just pass the bug in their feces – harmless
intestinal bugs, like most enteroviruses in people.
2 February 2006 at 9:18 am #3834
back to “a correspondent”:
We need a genetic explanation. Like Niman and ProMED, some people
regard the genetic similarity as evidence for migration theory.
My genetic interpretation is completely the reverse. The lack of
genetic variation is a result of “no natural selection” (evolutionary
stasis), i.e. the observed similarity is a genetic proof against wild
birds as vectors. Such a degree of “no natural selection” (as well as
the lack of reassortment) certainly requires artificial environment,
i.e. poultry. Wouldn’t that be a breakthrough? What we need is an
expert’s verification.
I have been just informed of a domestic TV program tonight,
highlighting “novel transmission ways” of flu. According to the
program, two new ways will be presented: mildly symptomatic people
(less immune reaction) and Tamiflu-treated people (I have read
numerous reports Tamiflu-treated mildly symptomatic people enter
crowds, spreading the virus). The can easily become “transmission
hubs”, making the spread easier and more preserving the virulence.
Wendy again:
Nah, this doesn’t work at all. Mildly symptomatic people will produce mild strains…the disease will move towards mildness. That’s the whole point of Ewald’s argument. I don’t know how much
Tamiful treatment changes this picture – very little, I would think. The “less immune reaction” is a complete red herring. Less immune reaction is caused by a less virulent strain. In all cases,
having people well enough to walk about will only decrease virulence, not maintain it or add to it. I suspect Tamiful-treated people will just recover more quickly and be less effective
transmitters – remember, the virus has got to make you sick – coughing and sneezing- to get itself out and into someone else.
and correspondent:
Not all individuals react to the same (or similar) strain in the
same way. While the virus is less virulent to some people, there
still remains a possibility of a higher virulence to the rest.
(We already know the present H5N1 has shown different reactions to
different ages, but the reason is unknown. An asymptomatic crow
infection, with systemic viral replication, is already experimentally
known, which excreted sufficient viral load to infect other birds.
This shows less symptomatic populations in the same species can emerge).
By the way, I am not trying to argue “how dangerous the virus is”,
but Ewald’s argument expects the “expected mean”, not clearly directed
to the “potential upper limit”. Predictions assuming some kind of
an equilibrium or “mean field approximation” would fail in certain
conditions, especially there is a background variation (different
responses in populations). This is the very point recently targeted
by the complex network theory or modern numerical ecology.
5 February 2006 at 5:52 pm #3835
From further email from Wendy Orent:
Natural selection works on a genetic and individual level, not a population level. When you are talking about viruses, think of a swarm of strains, some of which are going to be more effective
under the particular conditions they find themselves in (a host, or group of hosts, under particular ecological conditions.)
These influenza strains (say) are all madly jockeying, so to speak, to outreproduce each other (of course, this intentionality is strictly metaphorical.) Now, let’s say we are talking about a
population of wild ducks who are infested with low-path H5N1. If there is a wide range of strains within duck A, those strains best at exploiting that duck’s body will reproduce better and faster
and more effectively than milder strains. So, in the competition to use up the duck, so to speak, MORE virulent strains will win out.
Now, here’s the thing. That duck is dead – wiped out, gone. But duck B, which happened to get a smaller or a milder set of strains, doesn’t die; he lives to pass whatever virus he is dealing with
to ducks C and D. So those milder strains are going to win out – and spread through the duck population. It has nothing to do with equilibrium – only with the balance between within host and
outside-host competition. You sometimes do find dead ducks in the wild, because natural selection is blind as a cavefish and can’t see what’s going to happen a duck or so down the road. If you
get a mutant that increases virulence, that will put virulent strains at a temporary advantage. But that virulent strain won’t spread – that’s why Ewald speaks of the “sieve of natural selection”
when he talks about flu in wild migrating birds.
Change the conditions, and you change the equation – that’s the point of “disease factory” conditions – you remove the penalties on viruses for being virulent.
Post edited by: martin, at: 2006/02/06 00:13
5 February 2006 at 5:58 pm #3836
Perhaps useful article, originally in Fortune:
How disease evolves
natural selection doesn’t favor very vicious bugs when transmission from sick hosts is difficult, for the hosts literally become dead ends before the bugs can leap to others. In such cases,
milder strains tend to become the dominant ones in circulation.
Which in case of bird flu, is roughly summarised by Dead Ducks Don’t Fly
(Even though dead ducks n other birds said to be spreading H5N1)
9 February 2006 at 7:10 pm #3837
whew! – correspondence on this topic getting pretty long, but may be some useful guff within.
Another email from me, to Wendy Orent:
“Change the conditions, and you change the equation” looks to me like what I know of re equilibrium (from physical chemistry).
As you say, each strain (even indiv virus) responds to conditions: important here, what’s likelihood it can be passed to another host. Then, as many different strains/individual viruses, see an
overall picture, a population.
To me, seems similar to ensemble (I think that called – some time ago now!) in phys chem. Whole lot of possible states – perhaps of atoms or molecules; as change one or more important variables,
change likelihood of occurrence of each of them, and get shift in overall population.
So with ducks, being stubborn here (!), we see equilibrium for reasons you note: dead ones don’t fly/move, their virus populations go extinct (tho always latent potential for creating them in
numbers), and see population of low-path virus.
Shove ducks together, so v sick ones can more readily pass high-path strains, and the higher path strains can increase. See a shift in the equilibrium point – overall virus population moves to
higher path, tho still a mix, with potential to have lower path virus as well as higher path.
Move back to having ducks in wild conditions, needing to fly to transmit, and those higher path viruses will disappear again, the lower path ones will increase. Equilibrium point shifts back.
or am I talking codswallop; hazy thinking this morning for some reason
I hadn’t been aware re population biologists thinking on – err – population levels. Whole lot of giraffes growing longer necks, instead of some individuals born with longer, some shorter, and
longer more successful (as it looks to me like you’re saying). Curious; treating at population levels would just seem convenient way of achieving some simplification, which could be useful,
whilst surely should remain keenly aware of individuals.
Wenday again:
natural selection isn’t a population-level phenomenon. Evolution is – in the sense that individuals don’t evolve. But selection has everything to do with competition within populations.
Population biologists know this, in a sense, but they often don’t keep the levels of selection straight and they keep slipping.
The term “equilibrium” as you used it in the last e-mail is very slippery – I think the analogy to chemistry may not be helpful. You do get different strains within a population of hosts, which
is why, for example, you can’t just go get a marmot and hope to isolate from that marmot a killer strain of plague – or dig up any old anthrax spores from the soil and think you’re going to get a
bioweapon. But that doesn’t mean the strains are in any sort of balance, or that it’s in the least helpful to think of them that way. Viruses are continuously generating variation: some changes
will lead to greater virulence, some to less.
The reason many are so prone to copying error, which is what mutation is, is that they have to keep changing to meet changing conditions in their host population. (i.e. they might encounter
stronger or less-strong immune systems; their hosts might be in a greater or worse position to pass strains on, etc.) Some of these “errors” will benefit the virus in a particular line, and
they’ll be selected. That is what adaptation is.
You can see that process at work in one or two Turkish cases – scientists found that some of the swarms of strains in the host’s body showed some better adaptation to people. They were better
able to adhere to non-ciliated cells (human flu receptors), and they were able to grow higher up in the nasal passages – therefore at cooler temperatures. But the hosts were dead and the new
lineages died with them.
These results show that the H5N1 virus can adapt, at least a bit, to human beings. There was no reason to think it couldn’t. But you’d need a long chain of human beings passing on these changes
from one to another for any real adaptation to occur – i.e. before bird-adapted H5N1 flu became human-adapted H5N1. Could it happen? Yes – if governments keep covering up their bird flu cases. Is
it likely? Not very – but it is certainly possible.
Surveillance is the single best way to stop it – quarantine would work very well before the virus got very adapted to people. Once it is, you can’t control human-adapted flu with quarantine. But
you can BEFORE it gets there. That’s why the phrase “mutate to transmissibility” is so ridiculous. It implies that one or two chance mutations can produce adaptation – in the absence of natural
(translation: to “mutate to transmissibility” means that some chicken, somewhere, is carrying a strain that has somehow mutated to be adapted to people. It then infects a person, who passes it on
– and bingo. But selection does not and cannot work this way. A change that pre-adapts the strain for human infection and transmissbility cannot survive in chickens. Someone would have to catch
it before the miraculously-mutated human-adapted strain got pushed aside by selection for chicken flu within the chicken’s own body. Thinking probabilistically – this chance is, uh, vanishingly
small. Not to say non-existent.)
You can talke about “evolve to transmissibility” – but that’s a host/pathogen activity – it requires long chains of human beings (no one know how long – but more than a few, simply because so
many changes are obviously required.) This process can happen, and has happened, with earlier flus. That is not in doubt. But the human-adapted flu strains will lose virulence, or never evolve
it, because of the requirements imposed by transmission. Res ipsa locutor.
me again:
My equilibrium notions from now somewhat hazy memories of phase space, from lectures. Think I retain the gist, and not slippery.
Continuous variation – multitude of potential states – crucial here too. But overall picture not random.
Key, perhaps, would be:
With flu – would we expect overall virus to have different levels of virulence, which could be predicted if we have all the equations and numbers (surely impossible)?
Suppose had variations as follows – and only these variations (would be considerably more complex in practice):
Zero or effectively zero probability of spread by immobile carriers.
10% probability of spread by immobile carriers
30% probability of spread by immobile carriers
70% probability of spread by immobile carriers
If, over time, virus [as population] would evolve to a certain level of virulence, and maintain it while conditions persist, would surely have equilibrium. (Even though in each case, still
potential for individual viruses to replicate to different states. Equilibrium at macro level doesn’t mean that stopped the perpetual mutations etc to various states – it’s just that
probabilities individual states can persist/increase have changed.)
If levels of virulence of virus population would just fluctuate wildly, not settling over time, then indeed no equilibrium.
From all I’d seen before, I’d thought “miraculously-mutated human-adapted strain” was what all disease experts believed in; hadn’t really thought more re this – if WHO etc said it was so that
virus could mix in a pig, then go on to devastate humanity, maybe it was so.
Back to Wendy:
As for equilibrium, I think you make a reasonable argument – and that it is one way to look at what we’re seeing. The problem is that it is a species – or population-level argument – which is not
Darwinian. (translation: no traits can evolve or be maintained anywhere, under any circumstances, that are bad for the individual or individual genetic line, and good for the group. Darwin
himself that that if one such example could be found, it would destroy his entire theory.
Keeping a population at some sort of equilibrium suggests that there is an advantage to the population as a whole in having variants around. Sounds good, but evolution, if you will forgive my
putting it so bluntly, doesn’t work that way. Any traits that exist for the benefit of the group that jeopardizes its carrier’s fitness will be swiftly eliminated.
Only the traits that enhance their carrier’s fitness will be represented in the next generation – there are accidents, of course, like a tree falling on all the fittest members of the group, but
natural selection will zap the less fit in the next generation. Remember that natural selection is not “survival of the fittest” but rather “differential reproduction.” )
To say that, for instance, flu viruses in wild birds are essentially stable simply means, from the perspective of evolutionary biology, that the strategy of low virulence continues to work well,
and that the environmental conditions the bug finds itself in are stable. It doesn’t mean the bug isn’t just as mutagenic as ever; it’s just that low-pathogenic strains will continue to be at a
selective advantage, which keeps the phenotypic variability in check.
So from this perspective, “settling over time” just means that the environmental conditions are stable. Certainly viral evolution will occur more quickly as a virus adapts to a new host. The
mutation rate doesn’t change, so far as we know, though it might…we just don’t know if there is an actual viral mechanism to increase copying error; it sure sounds unlikely to me, but you never
know. But selection pressure is more intense. We could see intensive selection pressure to adapt to human beings – but you’d need a string of human beings, ad seriatum, for the virus to adapt to.
Have I misunderstood anything in your argument? Please let me know.
to which I added:
What you write doesn’t seem at variance with my picture, deluded as I may be!
Equilibrium at macro level doesn’t mean all is nice n stable for individual viruses.
Phase space, as I recall rather more dimly than i might wish, partly about probabilities for individual states.
So here with flu, there’s a host of probabilities for forms a virus might take – here, only worrying re those that are more or less virulent (but surely others that better for being passed on,
several that utterly useless).
All occurring – so with a virus, surely can have carriers lacking fitness for being passed on, for replicating. Not many of them, and as they are dead ends with normal conditions (virus that
could wipe out the planet, say), they remain tiny populations, so nigh on invisible when look at population as a whole.
Can get “sports” in larger animals – birds with oddly curved mandibles etc, but v few (large animal populations tiny compared to viruses), and not surviving long enough or well enough to
continue. So, see variations around some kind of mean.
But, one example known in UK is a moth: usually pale, resting on silver birch during day; a few dark variants. Add pollution, darken trees, get more predation of normal light form, and dark form
became dominant near factories etc.
Change the conditions w virus, here to immobile carriers, and those rare mutations leading to increased virulence can increase, as they are passed on, can multiply; so virus as a whole becomes
more virulent. Still all the mutations happening.
Reduce immobile carrier transmission, and these virulent forms become scarcer again, the virus back to low virulence.
HIV again: i saw re drug resistant strains appearing in people taking drugs. Again, surely v rare normally – maybe examine the virus population and wouldn’t notice them. But, when regular HIV
blocked, the resistant strains become dominant (which to me looks like shift in equilibrium point).
Stop the drugs with this person, and evolves back again, so that later can again use the drugs.
Post edited by: martin, at: 2006/02/09 12:26
9 February 2006 at 8:59 pm #3838
more from a correspondent:
Perhaps you know this “experimental” incidence (coevolution
of pathogens with hosts):
“Myxoma Virus and Rabbits”
This example was also referred to by our specialist in predicting
the future of H5N1, but he said “there is a tendency like this,
but uncertainties remain”. This myxoma virus (though it’a a vector-
mediated) once got less lethal, but regained half-lethal, perhaps
a result of some sort of host-pathogen equilibrium. A frequently
cited example in an ecology textbook.
Yet another – evolution of host-pathogen relation, and
possible emergence of virulence from population structure:
“Large Shifts in Pathogen Virulence Relate to Host Population
Here we show that rapid evolution of virulence can occur as
a consequence of bistability in the evolutionary dynamics of
pathogens associated with changes in host social structure.
7 March 2006 at 1:19 pm #3839
Article by Paul Ewald on website of the Edge Foundation, in answer to question re what’s his dangerous idea includes:
Today experts on infectious diseases and institutions entrusted to protect and improve human health sound the alarm in response to each novel threat. The current fears over a devastating pandemic
of bird flu is a case in point. Some of the loudest voices offer a simplistic argument: failing to prepare for the worst-case scenarios is irresponsible and dangerous. This criticism has been
recently leveled at me and others who question expert proclamations, such as those from the World Health Organization and the Centers for Disease Control.
These proclamations inform us that H5N1 bird flu virus poses an imminent threat of an influenza pandemic similar to or even worse than the 1918 pandemic. I have decreased my popularity in such
circles by suggesting that the threat of this scenario is essentially nonexistent. In brief I argue that the 1918 influenza viruses evolved their unique combination of high virulence and high
transmissibility in the conditions at the Western Front of World War I.
23 March 2006 at 10:02 am #3840
after I posted little info to a discussion group re H5N1 and conservation, this message from a virologist:
Just a little point about influenza in humans- transmission is largely before any illness, as the peak of viral shedding occurrs before interferon release and the specific immune response e.g.
T-cell response. This curtails viral replication and reduces shedding.
Any person admitted to hospital ill from influenza will have already transmitted the virus to another/s. The epidemic peak is very sharp in human influenza and it is probably the percentage of
immune individuals in the population that brings the epidemic to an end. Therefore I don’t agree with your evolutionary biology idea.
It may be that the number of immune persons in the population after the circulation of the virus for a year forced changes in the HA molecule to escape from neutralising antibody and this had an
effect on the virulence of H1N1 but the reason for the virulence of that virus and why it arose and then changed is I believe not known.
I sent a reply:
– evolutionary biology not my idea!
Is peak of shedding always before main symptoms? I know little of this, but some info from WHO suggests virus shedding peaks with symptoms.
How do asymptomatic people transmit virus – just by talking (if not coughing, sneezing)? – and if lower probability of transmission this way, might this have an impact on virus evolution? – to
evolve/sustain a virulent flu, maybe need fair percentage of those infected to be able to transmit to others?
Sadly, I’ve seen only fairly brief info from Paul Ewald, not his book, Evolution of Infectious Diseases.
also contacted Wendy Orent, who responded:
I believe she is incorrect about transmission before any illness. There may be (in human influenza after it is fully adapted to the human species) some slight transmission before symptoms set in.
But not much. It would have to be shed by breathing and talking – these are not efficient means of transmission. What are symptoms for? Why do we ccough and sneeze?/ Viruses settle in the upper
airways and irritate us precisely in order to get us to cough and sneeze. In certain diseases, measles for instance, you transmit fairly early in the course of the disease, before you’re
bed-ridden. Measles makes you sneeze. But you are still symptomatic!
Of course, before the disease has adapted to human beings, transmission tends to happen late in the illness, e.g. SARS. Had SARS continued to transmit, it would have adapted to people by becoming
a more efficient shedder and spreading earlier in the course of the infection – it would have evolved to mildness like all coronaviruses, which are just common colds in people. It didn’t have
that chance – it was wiped out before it became efficiently transmissible.
Just read your answer [after I’d sent in second email], and you are absolutely right – except for the bit about the “fair percentage” – I think you are still thinking in population terms.
She is also, I believe, incorrect about the “not known.” We have a very good idea why the virulence evolved, and why it diminished over time.
[As noted above hin this thread I believe, but I sent to discussion group, maybe useful as summary:] I learned of evolutionary biology and diseases thro Wendy; don’t know all about it by any
means (must read Ewald’s book!) – till then believed a monster human h5n1 pandemic flu was imminent. But to me, seems good, and explains a few things re flu that I’d otherwise find puzzling:
– 1918 flu occurring at same time as major world war (with trench warfare)
– human flus otherwise normally of low virulence
– wild avian flus mild (maybe even 1961 in S Africa common terns was from farms)
– ready transformation of wild flus in poultry farms, to viruses that are highly pathogenic for poultry (and, now, wild birds)
– inability of wild birds to sustain HPAIs (not just H5N1)
To me interesting that when Wendy mentioned to Paul Ewald re some ducks being able to survive H5N1, he predicted they shed only low amounts, as observed.
2 May 2006 at 8:59 am #3841
Further evidence of evolutionary biology at work in poultry farms comes from UK's H7N3 outbreak. (Not conclusive here, but fits evol biology – as ever with flu.)
Birds on the free range unit, however, suffered only a mild form of the flu and none died from the infection…. the virus was transported from the egg farm to the Banhams chicken farm, where it
killed some 400 chickens and triggered a drop in egg production by other birds.
note also, from intensive farms:
Blood samples from birds on their farm showed that they had been exposed to the H7N3 virus as long ago as four weeks.
– during which, presumably, the virus evolved towards virulence in the "disease factories" Vets track spread of bird flu strain
30 May 2006 at 9:24 am #3842
Article by Wendy Orent, in LA Times, includes:
… the factors that set off a pandemic remain unknown. No one has ever tracked the evolution of a new pandemic. All we have seen — in 1918, 1957 and 1968 — is the aftermath of that evolution.
Still, we are told that all it would take for H5N1 to become a pandemic would be for the virus to mutate so it could spread in a sustained way from person to person. This is known as "mutation to
transmissibility." … The H5N1 virus faces several barriers in jumping to and transmitting among humans. The most important is its ability to replicate in and adapt to human tissues, specifically
the upper respiratory tract (not in deep lung tissue, where it now seems to grow). In the windpipe, the virus would be more likely to spread in a cough or sneeze, infecting other humans. …
[Earl] Brown recognizes what seems to elude most people who worry about pandemic outbreaks: What's necessary to produce a human-adapted virus is humans — a series of person-to-person infections.
Without that chain of transmission, any human adaptation of H5N1 is difficult to imagine. … interact with other viral genes in a human host to improve its ability to infect the host. This is an
adaptive process — and it is true whether the new virus arises directly through mutation or even through recombination with a common flu strain. H5N1 is beautifully, tragically adapted to
chickens and has proved a monstrous predator. It evolved this way by preying on chickens packed into huge commercial chicken farms in Asia. The bird flu virus is still at the starting gate when
it comes to humans. But should any strain of H5N1 manage to survive many sequential transmissions, Darwin's charioteer may drive off. The best transmitters will be favored by selection, as
evolutionary biologist Paul W. Ewald of the University of Louisville contends. The process will continue, human by human, until a fully human-adapted, explosive strain emerges. …
At the beginning, viral adaptation to a host is slow. A disease just beginning to transmit is controllable. Surveillance, flexibility, willingness to impose or undergo quarantines, along with
international cooperation, will be necessary to stop pandemic flu — or any other disease moving from animals to humans — before Darwin's driver gets ahead of us and nothing can be done.
What Darwin has to say about bird flu Can the disease mutate into a widespread threat to humans? Possibly, but it won't happen overnight.
I emailed Wendy to check whether this rather ominous last sentence (and "explosive strain") meant some change in her thinking re not being possible right now to evolve a virulent flu.
Her reply:
No, I haven't changed my position. A pandemic (without WWI etc. conditions) would NOT be a lethal pandemic – just an ordinary one, like 57 or 68. And quarantine would work in the early stages, as
the virus adapts. An explosive strain merely means a highly transmissible strain, not a lethal strain. I am afraid many people may understand this the way you did. It's actually the same argument
I've been making for years – just another piece of it. It would be awful if people think I've changed my position, under pressure maybe. Not at all. I haven't changed a bit – I just wanted to
show why the phrase "mutate to transmissibility" is essentially meaningless, and that the evolution of any pandemic would have to come through natural selection. That's how it happened in the
past; that's how it could happen in the future.
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The Decimal Data Type - VB.NET
Variables of the Decimal type are stored internally as integers in 16 bytes and are scaled by a power of 10. The scaling power determines the number of decimal digits to the right of the floating
point, and it’s an integer value from 0 to 28. When the scaling power is 0, the value is multiplied by 100, or 1, and it’s represented without decimal digits. When the scaling power is 28, the value
is divided by 1028 (which is 1 followed by 28 zeros — an enormous value), and it’s represented with 28 decimal digits.
The largest possible value you can represent with a Decimal value is an integer: 79,228,162, 514,264,337,593,543,950,335. The smallest number you can represent with a Decimal variable is the negative
of the same value. These values use a scaling factor of 0. When the scaling factor is 28, the largest value you can represent with a Decimal variable is quite small, actually. It’s
7.9228162514264337593543950335 (and the smallest value is the same with a minus sign). This is a very small numeric value (not quite 8), but it’s represented with extreme accuracy. The number zero
can’t be represented precisely with a Decimal variable scaled by a factor of 28.
The smallest positive value you can represent with the same scaling factor is 0.00. . .01 (there are 27 zeros between the decimal period and the digit 1) — an extremely small value, but still not
quite zero. The more accuracy you want to achieve with a Decimal variable, the smaller the range of available values you have at your disposal — just as with everything else in life.
When using decimal numbers, the compiler keeps track of the decimal digits (the digits following the decimal point) and treats all values as integers. The value 235.85 is represented as the integer
23585, but the compiler knows that it must scale down the value by 100 when it finishes using it. Scaling down by 100 (that is, 102) corresponds to shifting the decimal point by two places. First,
the compiler multiplies this value by 100 to make it an integer. Then, it divides it by 100 to restore the original value. Let’s say that you want to multiply the following values:
328.558 * 12.4051Code language: VB.NET (vbnet)
First, you must turn them into integers. You must remember that the first number has three decimal digits, and the second number has four decimal digits. The result of the multiplication will have
seven decimal digits. So you can multiply the following integer values:
328558 * 124051Code language: VB.NET (vbnet)
and then treat the last seven digits of the result as decimals. Use the Windows Calculator (in the Scientific view) to calculate the previous product. The result is 40,757,948,458. The actual value
after taking into consideration the decimal digits is 4,075.7948458. This is how the compiler manipulates the Decimal data type. Insert the following lines in a button’s Click event handler and
execute the program:
Dim a As Decimal = 328.558D
Dim b As Decimal = 12.4051D
Dim c As Decimal
c = a * b
Debug.WriteLine(c.ToString)Code language: VB.NET (vbnet)
The D character at the end of the two numeric values specifies that the numbers should be converted into Decimal values. By default, every value with a fractional part is treated as a Double value.
Assigning a Double value to a Decimal variable will produce an error if the Strict option is on, so we must specify explicitly that the two values should be converted to the Decimal type. The D
character at the end of the value is called a type character. Table 2.2 lists all of them.
If you perform the same calculations with Single variables, the result will be truncated (and rounded) to three decimal digits: 4,075.795. Notice that the Decimal data type didn’t introduce any
rounding errors. It’s capable of representing the result with the exact number of decimal digits. This is the real advantage of Decimals, which makes them ideal for financial applications. For
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Predefined C++20 Concepts: Callables
Last Update:
Before you start implementing your custom concepts, it’s good to review some goodies in the Standard Library. There’s a high chance that there’s already a predefined concept for you.
Today let’s have a look at concepts related to callable objects.
Where to find them
You can find most of the predefined concepts in the <concepts> header.
Here’s a good list available at cppreference - Concepts library
What’s more, you can also have a look at section 18 from the C++ Specification: https://eel.is/c++draft/#concepts
Additional concepts can be found in:
Callable concepts
In this category we have six concepts:
• invocable/regular_invocable
• predicate
• relation
• equivalence_relation
• strict_weak_order
They build the following hierarchy:
Read on to see the core concept in the hierarchy: std::invocable:
The std::invocable concept
In short, the std::invocable concept means “can it be called with `std::invoke”.
template< class F, class... Args >
concept invocable =
requires(F&& f, Args&&... args) {
std::invoke(std::forward<F>(f), std::forward<Args>(args)...);
From its definition, we can see that it uses a requires expression to check if a given function object and a list of arguments can be called with std::invoke.
Sidenote: You can read more about std::invoke in my separate article: C++20 Ranges, Projections, std::invoke and if constexpr - C++ Stories or this one: 17 Smaller but Handy C++17 Features - C++
Some examples:
#include <concepts>
#include <functional>
#include <iostream>
template <typename F>
requires std::invocable<F&, int>
void PrintVec(const std::vector<int>& vec, F fn) {
for (auto &elem : vec)
std::cout << fn(elem) << '\n';
int main() {
std::vector ints { 1, 2, 3, 4, 5};
PrintVec(ints, [](int v) { return -v; });
We can also make it shorter with abbreviated function templates:
void f2(C1 auto var); // same as template<C1 T> void f2(T), if C1 is a concept
In our example this translates into:
void PrintVec(const std::vector<int>& vec, std::invocable<int> auto fn) {
for (auto &elem : vec)
std::cout << fn(elem) << '\n';
Here’s the main part:
std::invocable<int> auto fn
Error Messages
Now, let’s try to violate a concept with:
PrintVec(ints, [](int v, int x) { return -v; });
So rather than a single int argument, my lambda requires two parameters. I got the following error on GCC:
<source>:7:6: note: template argument deduction/substitution failed:
<source>:7:6: note: constraints not satisfied
In file included from <source>:1:
/opt/compiler-explorer/gcc-trunk-20210513/include/c++/12.0.0/concepts: In substitution of 'template<class F> requires invocable<F&, int> void PrintVec(const std::vector<int>&, F) [with F = main()::<lambda(int, int)>]':
It’s pretty clear that we don’t have a match in requirements.
But, on the other hand compilers also did well even before concepts:
<source>:16:13: required from here
<source>:9:24: error: no match for call to '(main()::<lambda(int, int)>) (const int&)'
9 | std::cout << fn(elem) << '\n';
| ~~^~~~~~
<source>:9:24: note: candidate: 'int (*)(int, int)' (conversion)
But please note that it’s only for simple functions. If you have long chains of function templates, lots of instantiations, it’s more beneficial to get constraint errors as early as possible.
You can play with code @Compiler Explorer
What’s all about this regularity?
What’s the difference between invocable and regular_invocable?
There’s already an answer on that :)
In short, regularity tells us the following:
An expression is equality preserving if it results in equal outputs given equal inputs.
It looks like it’s purely semantic information for now, and they are syntactically the same. The compiler cannot check it on compile time.
For example:
#include <concepts>
int main() {
auto fn = [i=0](int a) mutable { return a + ++i; };
static_assert(std::invocable<decltype(fn), int>);
static_assert(std::regular_invocable<decltype(fn), int>);
return 0;
See the example @Compiler Explorer
In the above example fn is not regular, because it contains a state that affects the return value. Each time you call fn() then you’ll get a different value:
However, when you compile the code, both of static_assert checks yield the same result.
Writing regular_invocable is a better practice, though, as it conveys more information in the API.
Thanks to Barry Revzin and Ólafur Waage for a Twitter discussion on that :)
After discussing the core concept, we can move to its first derivative:
template<class F, class... Args>
concept predicate =
regular_invocable<F, Args...> &&
boolean-testable<invoke_result_t<F, Args...>>;
In short, this is a callable that returns a value convertible to bool. The boolean-testable check is no a real concept; it’s an exposition-only concept.
Please notice that the predicate uses regular_invocable, so the interface is “stronger” than when using invocable.
An example:
#include <concepts>
#include <functional>
#include <iostream>
void PrintVecIf(const std::vector<int>& vec, std::predicate<int> auto fn) {
for (auto &elem : vec)
if (fn(elem))
std::cout << elem << '\n';
int main() {
std::vector ints { 1, 2, 3, 4, 5};
PrintVecIf(ints, [](int v) { return v % 2 == 0; });
This looks very cool and is so expressive!
Thanks to concepts the function declaration conveys more information about the callable. It’s better than just:
template <typename Fn>
void PrintVecIf(const std::vector<int>& vec, Fn fn);
With std::predicate<int> we can clearly see what the function expects: a callable that takes one int and returns something convertible to bool.
This one is a bit more complicated. Here’s the definition:
template<class R, class T, class U>
concept relation =
predicate<R, T, T> && predicate<R, U, U> &&
predicate<R, T, U> && predicate<R, U, T>;
To understand it better, let’s see some unit tests that we can grab from this repository - libstdc++-v3 test suite:
static_assert( ! std::relation<bool, void, void> );
static_assert( ! std::relation<bool(), void, void> );
static_assert( ! std::relation<bool(), int, int> );
static_assert( std::relation<bool(*)(int, int), short, long> );
static_assert( std::relation<bool(&)(const void*, const void*), char[2], int*> );
Now, we have two additional concepts which are exactly the same as std::relation, but they mean some slightly different categories:
template < class R, class T, class U >
concept equivalence_relation = std::relation<R, T, U>;
Semantically equivalence means a relation that is reflexive, symmetric, and transitive.
And another one:
template < class R, class T, class U >
concept strict_weak_order = std::relation<R, T, U>;
This time, in short, as I found on this old page:
A Strict Weak Ordering is a Binary Predicate that compares two objects, returning true if the first precedes the second.
Along with the language support for Concepts, C++20 also offers a large set of predefined concepts. In most cases, they are formed out of existing type traits, but there are many new named
The exciting part is that you can learn a lot about the overall design and granularity of requirements by exploring those Standard Library concepts.
In this blog post, we reviewed concepts for callables. The main one is invocable, and then we have std::predicate and std::relation.
From my perspective, the two concepts (or three): std::inocable, std::regular_invocable and std::predicate can increase readability and expressiveness in my projects. I’m still looking for some other
examples with std::relation. Please help if you have such use cases.
Back to you
• Have you started using concepts?
• What predefined concepts have you used so far?
Let us know in the comments below the article.
I've prepared a valuable bonus for you!
Learn all major features of recent C++ Standards on my Reference Cards!
Check it out here:
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The Gears of My Childhood - The Daily Papert
The Gears of My Childhood
The Gears of My Childhood
This essay was published as the Foreword to Seymour Papert’s book Mindstorms: Children, Computers, and Powerful Ideas (Basic Books, New York, 1980). (PDF of the chapter here)
Before I was two years old I had developed an intense involvement with automobiles. The names of car parts made up a very substantial portion of my vocabulary: I was particularly proud of knowing
about the parts of the transmission system, the gearbox, and most especially the differential. It was, of course, many years later before I understood how gears work; but once I did, playing with
gears became a favorite pastime. I loved rotating circular objects against one another in gearlike motions and, naturally, my first “erector set” project was a crude gear system.
I became adept at turning wheels in my head and at making chains of cause and effect: “This one turns this way so that must turn that way so…” I found particular pleasure in such systems as the
differential gear, which does not follow a simple linear chain of causality since the motion in the transmission shaft can be distributed in many different ways to the two wheels depending on what
resistance they encounter. I remember quite vividly my excitement at discovering that a system could be lawful and completely comprehensible without being rigidly deterministic.
I believe that working with differentials did more for my mathematical development than anything I was taught in elementary school. Gears, serving as models, carried many otherwise abstract ideas
into my head. I clearly remember two examples from school math. I saw multiplication tables as gears, and my first brush with equations in two variables (e.g., 3x + 4y = 10) immediately evoked the
differential. By the time I had made a mental gear model of the relation between x and y, figuring how many teeth each gear needed, the equation had become a comfortable friend.
Many years later when I read Piaget this incident served me as a model for his notion of assimilation, except I was immediately struck by the fact that his discussion does not do full justice to his
own idea. He talks almost entirely about cognitive aspects of assimilation. But there is also an affective component. Assimilating equations to gears certainly is a powerful way to bring old
knowledge to bear on a new object. But it does more as well. I am sure that such assimilations helped to endow mathematics, for me, with a positive affective tone that can be traced back to my
infantile experiences with cars. I believe Piaget really agrees. As I came to know him personally I understood that his neglect of the affective comes more from a modest sense that little is known
about it than from an arrogant sense of its irrelevance. But let me return to my childhood.
One day I was surprised to discover that some adults–even most adults–did not understand or even care about the magic of the gears. I no longer think much about gears, but I have never turned away
from the questions that started with that discovery: How could what was so simple for me be incomprehensible to other people? My proud father suggested “being clever” as an explanation.
But I was painfully aware that some people who could not understand the differential could easily do things I found much more difficult. Slowly I began to formulate what I still consider the
fundamental fact about learning: Anything is easy if you can assimilate it to your collection of models. If you can’t, anything can be painfully difficult. Here too I was developing a way of thinking
that would be resonant with Piaget’s. The understanding of learning must be genetic. It must refer to the genesis of knowledge.
What an individual can learn, and how he learns it, depends on what models he has available. This raises, recursively, the question of how he learned these models. Thus the “laws of learning” must be
about how intellectual structures grow out of one another and about how, in the process, they acquire both logical and emotional form.
This book is an exercise in an applied genetic epistemology expanded beyond Piaget’s cognitive emphasis to include a concern with the affective. It develops a new perspective for education research
focused on creating the conditions under which intellectual models will take root. For the last two decades this is what I have been trying to do. And in doing so I find myself frequently reminded of
several aspects of my encounter with the differential gear.
First, I remember that no one told me to learn about differential gears. Second, I remember that there was feeling, love, as well as understanding in my relationship with gears. Third, I remember
that my first encounter with them was in my second year. If any “scientific” educational psychologist had tried to “measure” the effects of this encounter, he would probably have failed. It had
profound consequences but, I conjecture, only very many years later. A “preand post-” test at age two would have missed them.
Piaget’s work gave me a new framework for looking at the gears of my childhood. The gear can be used to illustrate many powerful “advanced” mathematical ideas, such as groups or relative motion. But
it does more than this. As well as connecting with the formal knowledge of mathematics, it also connects with the “body knowledge,” the sensorimotor schemata of a child. You can be the gear, you can
understand how it turns by projecting yourself into its place and turning with it. It is this double relationship–both abstract and sensory–that gives the gear the power to carry powerful mathematics
into the mind. In a terminology I shall develop in later chapters, the gear acts here as a transitional object.
A modern-day Montessori might propose, if convinced by my story, to create a gear set for children. Thus, every child might have the experience I had. But to hope for this would be to miss the
essence of the story. I fell in love with the gears. This is something that cannot be reduced to purely “cognitive” terms. Something very personal happened, and one cannot assume that it would be
repeated for other children in exactly the same form.
My thesis could be summarized as: What the gears cannot do the computer might. The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on
a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes. This book is the result of my own attempts over the past decade to turn computers into instruments flexible
enough so that many children can each create for themselves something like what the gears were for me. | {"url":"https://dailypapert.com/the-gears-of-my-childhood/","timestamp":"2024-11-04T20:25:24Z","content_type":"text/html","content_length":"104926","record_id":"<urn:uuid:9627e33e-3a1e-4a35-8b8a-f8a29a2c1859>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00726.warc.gz"} |
Powerdomains and hyperspaces III: the theory of H
Last time, we have seen that the Hoare powerspace construction defined a monad H on Top. I also said that H(X) obeyed the following (in)equational theory:
• (unit) a ∨ 0 = a
• (associativity) (a ∨ b) ∨ c = a ∨ (b ∨ c)
• (commutativity) a ∨ b = b ∨ a
• (idempotence) a ∨ a = a
• (inflationary) a ≤ a ∨ b
This is true, in the following, very weak sense: if you interpret ∨ as binary union of closed sets, 0 as the empty set, and ≤ as inclusion, then those (in)equalities are trivially satisfied. A
topological space with a continuous map ∨ satisfying the above (in)equalities is called a unital inflationary topological semi-lattice.
We shall see a much stronger fact: for each space X, H(X) is the free sober inflationary unital topological semi-lattice above X. This is again due to Schalk [1]. I’ll also explain what the relation
to monads is.
The theory of H
A semi-lattice is a set together with a binary operation ⋁ that is associative, commutative, and idempotent. It is unital if and only if there is an element 0 such that 0 ⋁ a = a ⋁ 0 = a for every a.
(Think of a sup-semi-lattice, where 0 is bottom, and ⋁ is supremum.) It is topological if the underlying set is a topological space, and ⋁ is continuous. In that case, the topological space has a
specialization ordering ≤, and it makes sense to define a topological semi-lattice to be inflationary if and only if a ≤ a ⋁ b for all a, b.
There is a category SUITopSLat (I apologize for the barbaric name; I could not think of any better name) of sober, unital, inflationary topological semi-lattices whose objects are those we just
described, and whose morphisms are continuous maps that send 0 to 0 and preserve the semi-lattice operation ⋁.
There is a forgetful functor U : SUITopSLat → Top, which maps every such topological semi-lattice to the underlying topological space, forgetting about 0, ⋁, and sobriety. In the other direction,
there is a function H that maps every topological space X to its Hoare powerspace. Remember also that there is a continuous map η[X] from X to H(X), which sends every point x to its closure ↓x.
Categorically speaking, η[X] is a morphism in Top from X to UH(X).
To show that H extends to a functor that is left adjoint to U, we only have to show that H(X) is the free sober unital inflationary topological semi-lattice over X (Diagram (5.2), p.175, in the book
). That means the following: for every morphism f: X → UL in Top (i.e., continuous map from X to L, where L is any sober unital inflationary topological semi-lattice), there should be a unique
morphism h from H(X) to L in SUITopSLat such that Uh o η[X] = f —namely, such that h(↓x)=f(x) for every x in X.
If h exists, then we claim that we have no choice. For every finite subset E={x[1], …, x[n]} of X, h(↓E) must be equal to h(↓x[1] ⋃ … ⋃ ↓x[n]) = h(↓x[1]) ⋁ … ⋁ h(↓x[n]) = f(x[1]) ⋁ … ⋁ f(x[n]). Write
the latter as ⋁f(E), at least temporarily. This tells us what the values of h must be on finitary closed subsets of X: h(↓E)=⋁f(E). By continuity, this will also determine h on every element of H(X
), as we now observe.
For every element F of H(X), the finite subsets E of F form a directed family I, ordered by inclusion. When E is included in E’, we can write E’ as the union of E and of some other finite set E”, and
then ⋁f(E‘) = ⋁f(E) ⋁ ⋁f(E”), which is above ⋁f(E) since L is inflationary. It follows that the family of all elements ⋁f(E), when E ranges over the finite subsets of F, is a directed family. Since L
is sober, those elements have a supremum y=sup {⋁f(E) | E finite subset of F} and cl {⋁f(E) | E finite subset of F} = ↓y (Proposition 8.2.34). Because h is monotonic (if it exists), we must have y =
sup {h(↓E) | E finite subset of F} ≤ h(F).
Observe now that F is a limit (in fact, the largest limit) of the monotone net {↓E | E finite subset of F}. Indeed, if F is in ◊U, then F intersects U, say at x, and then any finite subset E of F
that contains x will be in ◊U. Since h is continuous, h(F) must therefore be a limit of the monotone net {⋁f(E) | E finite subset of F}. However, all these limits are in cl {⋁f(E) | E finite subset
of F} = ↓y, so h(F) ≤ y. This shows that h(F) is uniquely determined, and must be equal to the element y defined above.
We have no choice for h. So let us define it as above: h(F) = sup {⋁f(E) | E finite subset of F}, and recall that cl {⋁f(E) | E finite subset of F} = ↓h(F). We use the latter to show that h is
For every open subset V of L that contains h(F), V must intersect cl {⋁f(E) | E finite subset of F}, so V must also intersect {⋁f(E) | E finite subset of F}. Let E={x[1], …, x[n]} be a finite subset
of F such that ⋁f(E) = f(x[1]) ⋁ … ⋁ f(x[n]) belongs to V. Since ⋁ is continuous, there are n open neighborhoods V[1], …, V[n], of f(x[1]), …, f(x[n]) respectively, such that y[1] ⋁ … ⋁ y[n] is in V
for all y[1] in V[1], …, y[n] in V[n]. Then ◊f^-1 (V[1]) ∩ … ∩ ◊f^-1 (V[n]) is an open neighborhood of F in H(X). Moreover, for every F’ in ◊f^-1 (V[1]) ∩ … ∩ ◊f^-1 (V[n]), there must be n points x’
[1], …, x’[n] in F’ such that f(x’[1]), …, f(x’[n]) are in V[1], …, V[n] respectively, hence so that ⋁f(E‘) is in V, for E’={x’[1], …, x’[n]}. This implies that h(F’) is in V, and as V is arbitrary,
that h is continuous at F. Since F is arbitrary, h is continuous.
Verifying that h preserves 0 and ⋁ is much easier, as is the fact that h(↓x)=f(x) for every x in X. This concludes the proof. We sum that up. The result is due to A. Schalk, again.
Theorem. [1, Theorem 6.1] For every topological space X, H(X) is the free sober unital inflationary topological semi-lattice over X.
Monad algebras
The above theorem establishes the existence of an adjunction H ⊣ U, but does it say anything about the monad H?
We need to say a few more things about monads, and their relationship to adjunctions.
There is an automatic way of building monads: every adjunction F ⊣ U gives rise to a monad T=UF. (The latter means U o F.) The unit of the monad is just the unit η[X]: X → UFX of the adjunction. The
extension f^† of f: X → UFY is given by composing Uε[FX] with UF(f), where ε is the counit of the adjunction; alternatively, f^† = U(ran[X, FY] f). (See Section 5.5.2 for a refresher on adjunctions!)
I’ll let you check that the H monad is equal to the monad obtained in this way from the adjunction H ⊣ U. (I hope you’re not troubled by the two functors H. The first one is really UH.)
Conversely, does every monad T stem from an adjunction this way? Yes, and yes.
I mean: yes, in at least two different ways.
The first way is provided by the Kleisli construction, and the second way will require a new notion: (Eilenberg-Moore) T-algebras.
• (Kleisli) There is an adjunction between the Kleisli category C[T] and the original category C. On the one hand, F: C → C[T] maps every object X to itself, and every morphism f: X → Y to η[Y] o f
. On the other hand, U: C[T] → C maps every object X to TX, and every morphism f: X → Y in C[T] (namely, a morphism f: X → TY in C!) to f^†. If you love pushing symbols, it is a fun exercise to
check that F is left adjoint to U and that UF=T.
• (Eilenberg-Moore) We build the category C^T of T-algebras as follows. (Note that T is now a superscript instead of a subscript…)
A T-algebra is, by definition, a pair of an object X of C and of a morphism s: TX → X (the so-called structure map) such that s o η[X] = id[X] and s o Ts = s o μ[X]. Recall that μ[X] = id[TX]^†:
T^2X → TX is the multiplication of the monad T. A morphism of T-algebras, from (X, s) to (Y, t) is just a morphism f from X to Y in C such that t o Tf = f o s.
With that construction, the left adjoint F: C → C^T maps every object X to the algebra (TX, μ[X]), and the right adjoint U: C^T → C maps every T-algebra (X, s) to X. If you love pushing symbols,
it is even funnier to check that F is left adjoint to U, and that UF=T. (If you don’t love pushing symbols, then it’s just boring.)
We shall look at the H monad below. We shall see that the H-algebras are the sober unital inflationary semi-lattices… again! (This is a cunning plan meant to keep you reading.)
To get our hands on the notion of T-algebra, let us look at the powerset monad P on Set.
I claim that the algebras of the powerset monad P on Set are exactly the sup-semi-lattices (with bottom), more precisely, a P-algebra (X, s) is just a set X, together with a map s that sends every
subset of X to its supremum. For which ordering, you might ask? (This is on sets, not topological spaces, so we do not have an underlying specialization preordering.) Well, the only possible one:
x ≤ y if and only if y = s ({x, y}). The algebra equations s o η[X] = id[X] and s o Ts = s o μ[X] require that s ({x}) = x and that, for every family (F[i])[i in I], s (∪[i in I] F[i]) = s ({s (F[i])
| i in I}). If you believe that s is a form of supremum, the latter says that the sup of a union of sets F[i] can also be computed as the sup of the collection of individual suprema s (F[i]), so
that sounds reasonable. Checking that ≤ is an ordering and that s is indeed the supremum operation for that ordering follows from those two equations alone (exercise!).
In general, it is hard to identify what the T-algebras are for a given monad T. For example, the algebras of the ultrafilter monad on Set are exactly the compact Hausdorff spaces (the structure map
s maps every ultrafilter to its unique limit), but this is a pretty hard theorem by Michael Barr—that such algebras are kinds of filter spaces is clear, what is harder is to show that the convergence
structures must stem from a topology.
The algebras of the H monad
The case of the algebras of the H monad is comparatively easy. Similarly to the case of the powerset monad, an H-algebra is a pair (X, s) where X is a topological space and s is a continuous map
from H(X) to X, such that s(↓x)=x, and such that, for every family (F[i])[i in I] of closed subsets of X, s (cl (∪[i in I] F[i])) = s (cl {s (F[i]) | i in I}).
Given s, we can define a binary operation ∨ on X by x ∨ y = s (↓{x, y}). This is automatically continuous, and the above equations (taking finite families) show that ∨ is unital, associative,
commutative, and idempotent. (The unit 0 is the empty set.) For example, associativity is proved as follows. Consider the family (↓{x, y}, ↓{z}). The equations imply that s (↓{x, y, z}) = s (↓{s (↓{
x, y}), s (↓x)}) = (x ∨ y) ∨ z. We obtain a second equation s (↓{x, y, z}) = x ∨ (y ∨ z) by considering the family (↓{x}, ↓{y, z}). Associativity follows.
The ∨ operation is also inflationary: since s is continuous, hence monotonic, s (↓x) ≤ s (↓{x, y}), namely x ≤ x ∨ y.
You may see a difference with the powerset monad here. In the case of P, we needed an infinitary operation s, which worked as a supremum. In the case of H, we only need a binary supremum
operation ∨, and the infinitary suprema will be obtained by continuity.
Finally, the space X must be sober. Indeed, the pair (s, η[X]) defines a retraction of H(X) onto X, by definition of the structure map s. Recall that H(X) is sober (from Part I), and use the fact
that every retract of a sober space is sober. The latter is Exercise 8.2.43 in the book (the proof proceeds by checking the definition, and contains no technical difficulty: try it!).
We have proved half of the following, of which we prove the other half right away. This is again due to A. Schalk.
Theorem. [1, Theorem 6.10] The algebras of the H monad are the sober unital inflationary topological semi-lattices.
We have just proved that all H-algebras are sober unital inflationary topological semi-lattices. Conversely, let (X, ∨, 0) be a sober unital inflationary topological semi-lattice. We use Schalk’s
previous theorem, that H(X) is the free sober unital inflationary topological semi-lattice on X (=U(X, ∨, 0)). The very definition of freeness (see Diagram (5.2), p.175), applied to the identity map
from X to U(X, ∨, 0), implies that there is a unique morphism of sober unital inflationary topological semi-lattices t : H(X) → (X, ∨, 0) such that Ut o η[X] is the identity. We let s = Ut, and
claim this is our structure map. Verifying the algebra equations is done purely categorically: s o η[X] = id is given; for the other equation, s o Hs = s o μ[X], we realize that both sides are
morphisms of sober unital inflationary topological semi-lattices (as compositions of such morphisms), and we now just have to resort to freeness: we show that both sides of the equation are the
unique morphism f such that Uf o η[HX] = s (exercise! use the naturality of η and the defining equation of s on the left-hand side, and one of the monad equations on the right-hand side).
A coincidence?
We have an intriguing coincidence here:
• The algebras of the H monad are the objects of a certain category (sober unital inflationary topological semi-lattices); although we have not checked so, the morphisms are the right ones, too;
• For every space X, H(X) is the free object of the same category.
In other words: take the adjunction H ⊣ U, build the associated monad T = UH, giving rise to an Eilenberg-Moore category C^T (with C = Top here), which in turns gives rise to an adjunction. It turns
out that the adjunction we get in the end is exactly the same as the one we started with (up to equivalence of categories, formally).
When this happens, we say that the adjunction is monadic. This is a desirable property to have. There is a whole theory on that: look for comparison functors, Beck’s monadicity theorem, and also
Duskin’s monadicity theorem (on nLab). If you are seriously into categorical stuff, have a look at the recent book [2] (Section II.3). This would lead me too far, and I have really said a lot
In any case, and somewhat more vaguely, we can sum up the nice situation we are in by the motto:
The theory of H is the theory of (sober) unital inflationary topological semi-lattices.
We recapitulate that theory, for completeness:
• (unit) a ∨ 0 = a
• (associativity) (a ∨ b) ∨ c = a ∨ (b ∨ c)
• (commutativity) a ∨ b = b ∨ a
• (idempotence) a ∨ a = a
• (inflationary) a ≤ a ∨ b
— Jean Goubault-Larrecq (May 28th, 2015)
[1] Andrea Schalk. Algebras for Generalized Power Constructions. PhD Thesis, TU Darmstadt, 1993.
[2] Dirk Hofmann, Gavin J. Seal, Walter Tholen, eds. Monoidal Topology—A Categorical Approach to Order, Metric, and Topology. Encyclopedia of Mathematics and its Applications 153, Cambridge
University, Sep. 2014. | {"url":"https://topology.lmf.cnrs.fr/powerdomains-and-hyperspaces-iii-the-theory-of-h/","timestamp":"2024-11-03T09:36:51Z","content_type":"text/html","content_length":"68667","record_id":"<urn:uuid:30bad9e5-fd62-47f9-a5c6-5c9e44e9e96d>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00357.warc.gz"} |
Accounting Rate Of Return Arr Method
The ARR can be used by businesses to make decisions on their capital investments. It can help a business define if it has enough cash, loans or assets to keep the day to day operations going or to
improve/add facilities to eventually become more profitable. Whether it’s a new project pitched by your team, a real estate investment, a piece of jewelry or an antique artifact, whatever you have
invested in must turn out profitable to you. If the ARR is positive for a certain project it indicates profitability, if it’s less, you can reject a project for it may attract loss on investment. The
initial investment required for this project is 20,00,000. Below is the estimated cost of the project, along with revenue and annual expenses.
Accounting Rate of Return can also help you prioritize your investments. This is a solid tool for evaluating financial performance and it can be applied across multiple industries and businesses that
take on projects with varying degrees of risk. AMC Company has been known for its well-known reputation of earning higher profits, but due to the recent recession, it has been hit, and the gains have
started declining. On investigation, they found out that their machinery is malfunctioning.
Key Topic Revision: Investment Appraisal
This formula specifically helps with capital budget decisions in regards to choosing the right type of investment. ARR is usually used in forecasting calculations so the company can make decisions
that will it will benefit from in the future. The method does not determine the fair rate of return on investment.
• ARR calculation considers the profits generated from the project.
• Therefore, if you’re going to utilize the ARR to evaluate distinct investments, make sure you’re computing it consistently.
• If the investment is a fixed asset, such as property, you’ll need to work out the depreciation expense.
• The Accounting Rate of Return is the overall return on investment for an asset over a certain time period.
• There is no consideration of the increased risk in the variability of forecasts that arises over a long period of time.
• To calculate the ARR, divide the net income from an investment by the total amount invested.
If you’re making long-term investments, it’s important that you have a healthy cash flow to deal with any unforeseen events. Find out how GoCardless can help you with ad hoc payments or recurring
What Is An Accounting Rate Of Return Arr?
This recognizes a loss value of one thousand dollars a year. The average book value over the life expectancy of the oven would be fifteen hundred dollars. Corporate tax on the oven would be
thirty-three percent. According to the bakers projections, the baker expects an average annual turn over of two thousand nine hundred and fifty. According to this, the average net profit would be
slightly over four hundred dollars. The accounting rate of return for this investment would be twenty-six point eight percent. If the baker is satisfied with this accounting rate, he could go ahead
with the purchase of the oven.
This enables the startup to profit from the asset straight away, even if it is still in its first year of operation. Lastly, divide the annual net profit by the asset’s/investment’s original cost.
Because the answer will be in decimals, multiply it by 100 to get the percentage return. After this, remove the accumulated depreciation from your annual revenue amount to obtain the resultant
figures for annual net profit. When calculating the yearly percentage rate of return on a project, the accounting rate of return is a useful financial instrument. The accounting rate of return is an
indicator of the performance or profitability of an investment.
This figure is then divided by two to get the average investment figure. The percentage figure for the average accounting return will tell you if a project is profitable or not. Suppose, if we use
ARR to compare two projects having equal initial investments. Accounting rate of return is a simple and quick way to examine a proposed investment to see if it meets a business’s standard for minimum
required return. Rather than looking at cash flows, as other investment evaluation tools like net present value and internal rate of return do, accounting rate of return examines net income. However,
among its limits are the way it fails to account for the time value of money. The first step in calculating the ARR is to calculate the average annual profit of the investment.
What Is The Difference Between Economic Value Added & Residual Income?
It can be used to evaluate a budget, such as a capital budget. A capital budget is a budget for a large project that lasts more than a year. Rate of Return, as the term is used in our foregoing
discussion, may be calculated by taking income before taxes and depreciation, income before tax and after depreciation.
In order to find out if the above investment will be feasible for the company or not, let us calculate its ARR. Therefore, the accounting rate of return of the renovated store is 11.28%.
Benefits Of Using The Arr Calculator
The external factor is also not considered in this method. It provides a clear view of the project’s profitability and other benefits. Obviously, this is a huge return and a racecar isn’t your
typical investment. This the formula to calculate the accounting rate of return is: great return might have had more to do with your driving abilities than the actual investment, but the principle is
the same. I would still tell you to keep putting money into your racecar with returns like this.
• In this case, the startup will earn a return of 20.71 cents for every dollar it invests.
• Beaver Rental Cars want to incorporate new vehicle models into its business.
• To calculate an ARR, you’ll need to divide the average annual profit of the asset by the amount of the initial investment.
• However, the hurdle rate is dynamic in nature and keeps varying depending upon the risk involved in the project.
• An entity may have several business proposals from which it may have to choose the most profitable.
This method helps the managers to compare the new project with other old projects or cost-reducing projects. This helps the manager in the selection of the best one for the company. The formula is
very simple and there is no need to have any degree to calculate the profit that you will be earning on your investment. Payback Period or Discounted Payback Period – This refers to the time required
to reach the break-even period on any investment.
It aims to ensure that new projects will increase shareholders’ wealth for sustainable growth. In simple terms, it’s the return of investment and the way to whether to accept or not. Besides this, we
also need to have an Average EADT, NCO for calculating the ARR in Excel.
Accounting Rate Of Return Arr Method
This can cause future problems for you and your money can get wasted as well. Knowing how to calculate Accounting Rate of Return is important in capital budgeting as it is used to determine the
appropriateness of a particular investment. When the answer for ARR exceeds a specific rate, which is accepted by the company, then the project will be selected. The measure includes all non-cash
expenses, such as depreciation and amortization, and so does not reveal the return on actual https://intuit-payroll.org/ cash flows experienced by a business. Furthermore, the timing of cash flows is
not taken into account, which can give a false perception of how successful an investment might be. However, it does not take into account cash flow or time value of money, which is why the
accounting rate of return formula is only an indicator rather than a number to live by. The only way to tell how much money your startup makes is to track the entire yearly cash amount of
ABC Inc. is contemplating setting up a solar power plant. It has an existing recycling plant that it can also choose to expand. ABC Inc. wishes to analyze whether the solar power plant project is a
better business proposition.
To calculate the average of EADT, choose a cell for the result, here we have chosen another column cell to calculate an average. Using the spreadsheet it’s easy to track out the easy changes in the
ARR. So, check out the steps to keep on calculating the ARR in Excel. It considers only the rate of return and not the length of project lives. Calculation of IRR involves a more complex algebraic
formula. Hence, the help from calculation tools such as IRR tables and excel formulas are taken. IRR is the rate at which the net present value of the net cashflows (i.e., present value of future
cash inflows less value of cash outflow) of the project is zero.
The calculator will let you know if you should make this investment or not. A return calculator gives you an idea about the investment you are making. If you see that the accounting rate of return
decision rule is not supporting your investment then, you should not opt to invest such an investment.
Accounting Rate Of Return Formula & Calculation Step By Step
The main disadvantage of ARR is that it disregards the time factor in terms of time value of money or risks for long term investments. The ARR is built on evaluation of profits and it can be easily
manipulated with changes in depreciation methods. The ARR can give misleading information when evaluating investments of different size. Cash flows are not considered in this method as cash flows are
an important part of the project than accounting profits. Investing in a project has only one purpose and that is to earn profit. If you are investing your money in any project then, you are likely
to earn profit from this investment. Let’s say that you are investing a handsome amount of money.
The machinery has 10 years of useful life with zero scrap value. The main disadvantage of ARR is actually the advantage of IRR. As it considers the time value of money, it is considered more accurate
than ARR. Its disadvantage being that it is complex to calculate and that it can give erroneous results if there are negative cash flows during the project’s life. Average annual profit is calculated
by subtracting all the expenses incurred that are related to the project from the income generated by the project for a year. You just need to divide the average annual profit with average investment
and your ARR calculation will be right in front of you.
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manipulation, data visualization, data pattern identification, and more.
Our data science program provides you with a foundation in aspects of computer science, statistics, and mathematics—to prepare you for this rapidly expanding field.
Data science graduates are in high demand, which is why our data science program provides you with a foundation in aspects of computer science, statistics, and mathematics—to prepare you for this
rapidly expanding field.
You can accelerate your career with a one-year Master of Data Science, which will prepare you to succeed in a demanding field where you'll apply your knowledge of data mining, data management, data
manipulation, data visualization, data pattern identification, and more.
Our data science program provides you with a foundation in aspects of computer science, statistics, and mathematics—to prepare you for this rapidly expanding field.
Data science graduates are in high demand, which is why our data science program provides you with a foundation in aspects of computer science, statistics, and mathematics—to prepare you for this
rapidly expanding field.
You can accelerate your career with a one-year Master of Data Science, which will prepare you to succeed in a demanding field where you'll apply your knowledge of data mining, data management, data
manipulation, data visualization, data pattern identification, and more.
Our data science program provides you with a foundation in aspects of computer science, statistics, and mathematics—to prepare you for this rapidly expanding field.
Featured Alumni
Nick Smith '21
Fisheries & Aquatic Sciences with a secondary emphasis in Data Science
Nick combines his interest in aquatics and the environment with the skills and tools of data science to study systems and inform interventions to improve the natural world. "These past two
summers I've worked with a professor on campus doing research and I've been able to use the data we've collected to run programs with it to see if there is trends in the data that we don't see
from the raw data. For example, we have been looking at an invasive crawfish species in our local streams and throwing all of the sort of physical appearances of those crawfish into a program,
I've been able to find different trends between them and the native crawfish species"
Featured Alumni
Olivia Kruse '19
Psychology & Data Science
Olivia is employed as a psychology data analyst at Gloo in Boulder doing turnkey analysis and working with clients
A Distinct Experience
Data science is a rapidly expanding discipline providing students with interesting career paths that are in high demand. While most students are employable with an undergraduate degree in data
science, there are many opportunities for advanced study. The data science program provides students a foundation in aspects of computer science, statistics, and mathematics that are important for
analyzing and extracting information from large and complex data sets.
A Distinct Experience
Data science is a rapidly expanding discipline providing students with interesting career paths that are in high demand. While most students are employable with an undergraduate degree in data
science, there are many opportunities for advanced study. The data science program provides students a foundation in aspects of computer science, statistics, and mathematics that are important for
analyzing and extracting information from large and complex data sets.
Learn From Experts
Juniata’s data science program integrates the study of computer science, statistics and mathematics. Some courses are team-taught by professors from several of these areas of expertise, which helps
you identify your specific interests in data science. Data science techniques can be applied to data from any field of study.
Learn From Experts
Juniata’s data science program integrates the study of computer science, statistics and mathematics. Some courses are team-taught by professors from several of these areas of expertise, which helps
you identify your specific interests in data science. Data science techniques can be applied to data from any field of study.
Learn From Experts
Juniata’s data science program integrates the study of computer science, statistics and mathematics. Some courses are team-taught by professors from several of these areas of expertise, which helps
you identify your specific interests in data science. Data science techniques can be applied to data from any field of study.
Learn From Experts
Juniata’s data science program integrates the study of computer science, statistics and mathematics. Some courses are team-taught by professors from several of these areas of expertise, which helps
you identify your specific interests in data science. Data science techniques can be applied to data from any field of study.
Data Science can be applied to any field that has data and that is every field. The data science POE requires you to take 12 credits in a different area (the cognate area) in which you are interested
in applying your data science. Possible cognate areas include business, biology, chemistry, psychology, politics, history, or environmental sciences.
Data Science can be applied to any field that has data and that is every field. The data science POE requires you to take 12 credits in a different area (the cognate area) in which you are interested
in applying your data science. Possible cognate areas include business, biology, chemistry, psychology, politics, history, or environmental sciences.
Data Science can be applied to any field that has data and that is every field. The data science POE requires you to take 12 credits in a different area (the cognate area) in which you are interested
in applying your data science. Possible cognate areas include business, biology, chemistry, psychology, politics, history, or environmental sciences.
Data Science can be applied to any field that has data and that is every field. The data science POE requires you to take 12 credits in a different area (the cognate area) in which you are interested
in applying your data science. Possible cognate areas include business, biology, chemistry, psychology, politics, history, or environmental sciences.
Gain Experience
Students will take the Data Science Consulting class, a class where they will analyze data for a real client. This class or data related research in another field will prepare students to do
internships. Recent internships of data science students include Mutual Benefit Group, Juniata College Advancement, Excela Health and Samsung’s AI lab.
Gain Experience
Students will take the Data Science Consulting class, a class where they will analyze data for a real client. This class or data related research in another field will prepare students to do
internships. Recent internships of data science students include Mutual Benefit Group, Juniata College Advancement, Excela Health and Samsung’s AI lab.
Gain Experience
Students will take the Data Science Consulting class, a class where they will analyze data for a real client. This class or data related research in another field will prepare students to do
internships. Recent internships of data science students include Mutual Benefit Group, Juniata College Advancement, Excela Health and Samsung’s AI lab.
Gain Experience
Students will take the Data Science Consulting class, a class where they will analyze data for a real client. This class or data related research in another field will prepare students to do
internships. Recent internships of data science students include Mutual Benefit Group, Juniata College Advancement, Excela Health and Samsung’s AI lab. | {"url":"https://connect.juniata.edu/academics/data-science/","timestamp":"2024-11-02T17:29:26Z","content_type":"text/html","content_length":"77902","record_id":"<urn:uuid:ccabea9a-ed96-4e67-b81a-d67202b335bf>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00032.warc.gz"} |
Utilization of Axis of Symmetry in General Mathematics - 2021
Utilization of Axis of Symmetry in General Mathematics – Symmetry is profound in our general lives as we often see things that are symmetrical in shape and size. Symmetry is found in nature, in
everyday structures and components, and in many more aspects.
So what exactly is symmetry?
Symmetry is like a reflection in the mirror that we see when we pose in front of it. It is actually denoted as the perfect replica of a shape or line that may look like a reflection. Say, you draw a
horizontal line in the middle section of a butterfly creating into two equal halves. Both the halves would be the same in shape and size and would look symmetrical. This can happen with shapes too.
For example, if we put a line between a circle, then both the halves should form symmetry. Thus in terms of Mathematics, this horizontal line that divides the object into equal and identical halves
is called the axis of symmetry. This term is proficient since no other lines can create a symmetrical reflection of the said object or shapes.
Definition of Line or Axis of Symmetry
Line or Axis of Symmetry is an imaginary line that divides an object or shape into equal halves. These equal halves look like a reflection of each other. There are many notable things present in our
daily life that can be divided into equal and identical halves such as a leaf, an insect, a shape, or a structure. Most basically, an object may have multiple numbers of axes of symmetry or may have
none too.
Different kinds of lines of symmetry
Symmetry is found in our daily routine life and can be seen in shapes, structures, animals, insects, etc. Be it an alphabet, a normal remote control, or a basic shape like a square. Symmetry can be
found in many of them. A line of Symmetry can both be horizontal or vertical in nature. Let us take examples of alphabets.
For example, if we need an axis of Symmetry for the alphabet D or E, the line of Symmetry would be horizontal in nature, since it cuts the Alphabets in equal and identical halves from the middle.
Now, for the alphabets, M and T, if we need to create equal halves, then the line of symmetry should be vertical for producing an exact reflection of the same.
Now for the alphabet X, there could be multiple lines of symmetry which can be vertical as well as horizontal in nature.
Various lines of symmetry
In accordance with a figure, there can be zero or multiple lines of symmetry.
An uneven or opaque object can have zero lines of symmetry for e.g, a trapezium, the alphabet F, and so on.
There are a few objects or shapes that have only one symmetrical axis. For e.g, a butterfly, the alphabet A, etc. have only one vertical line of symmetry.
Some figures that we observe in our daily life can have two lines of symmetry. For e.g, the alphabet I and X can be cut using both horizontal and vertical lines of symmetry for imposing an identical
• Multiple lines of symmetry
There are many objects that are present among us that can utilize multiple lines of symmetry. Let us take an example of a circle. There can be an infinite number of lines of symmetry that can divide
the circle into equal and identical halves.
Thus, the axis of symmetry is a generic or rather an imaginable line that can break an object into identical halves. Axis of symmetry is a mathematical function that is used in algebra, geometry and
deals with physics too. Thus, for more details, do visit Cuemath for your general inquiries and our teachers would be eager to help you with our math classes.
Also Read: Persuasive Writing- Definition and Techniques
Review Utilization of Axis of Symmetry in General Mathematics. | {"url":"https://www.justtechblog.com/axis-of-symmetry-in-general-mathematics/","timestamp":"2024-11-06T20:49:35Z","content_type":"text/html","content_length":"96896","record_id":"<urn:uuid:7fe41b7a-84e1-4e2b-9199-877da739560b>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00032.warc.gz"} |
IEEE 754 floating point special values#
Special values defined in numpy: nan, inf,
NaNs can be used as a poor-man’s mask (if you don’t care what the original value was)
Note: cannot use equality to test NaNs. E.g.:
>>> myarr = np.array([1., 0., np.nan, 3.])
>>> np.nonzero(myarr == np.nan)
(array([], dtype=int64),)
>>> np.nan == np.nan # is always False! Use special numpy functions instead.
>>> myarr[myarr == np.nan] = 0. # doesn't work
>>> myarr
array([ 1., 0., nan, 3.])
>>> myarr[np.isnan(myarr)] = 0. # use this instead find
>>> myarr
array([1., 0., 0., 3.])
Other related special value functions:
isinf(): True if value is inf
isfinite(): True if not nan or inf
nan_to_num(): Map nan to 0, inf to max float, -inf to min float
The following corresponds to the usual functions except that nans are excluded from the results:
>>> x = np.arange(10.)
>>> x[3] = np.nan
>>> x.sum()
>>> np.nansum(x)
How numpy handles numerical exceptions#
The default is to 'warn' for invalid, divide, and overflow and 'ignore' for underflow. But this can be changed, and it can be set individually for different kinds of exceptions. The different
behaviors are:
□ ‘ignore’ : Take no action when the exception occurs.
□ ‘warn’ : Print a RuntimeWarning (via the Python warnings module).
□ ‘raise’ : Raise a FloatingPointError.
□ ‘call’ : Call a function specified using the seterrcall function.
□ ‘print’ : Print a warning directly to stdout.
□ ‘log’ : Record error in a Log object specified by seterrcall.
These behaviors can be set for all kinds of errors or specific ones:
□ all : apply to all numeric exceptions
□ invalid : when NaNs are generated
□ divide : divide by zero (for integers as well!)
□ overflow : floating point overflows
□ underflow : floating point underflows
Note that integer divide-by-zero is handled by the same machinery. These behaviors are set on a per-thread basis.
>>> oldsettings = np.seterr(all='warn')
>>> np.zeros(5,dtype=np.float32)/0.
Traceback (most recent call last):
RuntimeWarning: invalid value encountered in divide
>>> j = np.seterr(under='ignore')
>>> np.array([1.e-100])**10
>>> j = np.seterr(invalid='raise')
>>> np.sqrt(np.array([-1.]))
Traceback (most recent call last):
FloatingPointError: invalid value encountered in sqrt
>>> def errorhandler(errstr, errflag):
... print("saw stupid error!")
>>> np.seterrcall(errorhandler)
>>> j = np.seterr(all='call')
>>> np.zeros(5, dtype=np.int32)/0
saw stupid error!
array([nan, nan, nan, nan, nan])
>>> j = np.seterr(**oldsettings) # restore previous
... # error-handling settings
Interfacing to C#
Only a survey of the choices. Little detail on how each works.
1. Bare metal, wrap your own C-code manually.
□ Plusses:
☆ Efficient
☆ No dependencies on other tools
□ Minuses:
☆ Lots of learning overhead:
○ need to learn basics of Python C API
○ need to learn basics of numpy C API
○ need to learn how to handle reference counting and love it.
☆ Reference counting often difficult to get right.
○ getting it wrong leads to memory leaks, and worse, segfaults
2. Cython
□ Plusses:
☆ avoid learning C API’s
☆ no dealing with reference counting
☆ can code in pseudo python and generate C code
☆ can also interface to existing C code
☆ should shield you from changes to Python C api
☆ has become the de-facto standard within the scientific Python community
☆ fast indexing support for arrays
□ Minuses:
☆ Can write code in non-standard form which may become obsolete
☆ Not as flexible as manual wrapping
3. ctypes
□ Plusses:
☆ part of Python standard library
☆ good for interfacing to existing shareable libraries, particularly Windows DLLs
☆ avoids API/reference counting issues
☆ good numpy support: arrays have all these in their ctypes attribute:
□ Minuses:
☆ can’t use for writing code to be turned into C extensions, only a wrapper tool.
4. SWIG (automatic wrapper generator)
□ Plusses:
☆ around a long time
☆ multiple scripting language support
☆ C++ support
☆ Good for wrapping large (many functions) existing C libraries
□ Minuses:
☆ generates lots of code between Python and the C code
☆ can cause performance problems that are nearly impossible to optimize out
☆ interface files can be hard to write
☆ doesn’t necessarily avoid reference counting issues or needing to know API’s
5. Psyco
□ Plusses:
☆ Turns pure python into efficient machine code through jit-like optimizations
☆ very fast when it optimizes well
□ Minuses:
☆ Only on intel (windows?)
☆ Doesn’t do much for numpy?
Interfacing to Fortran:#
The clear choice to wrap Fortran code is f2py.
Pyfort is an older alternative, but not supported any longer. Fwrap is a newer project that looked promising but isn’t being developed any longer.
Interfacing to C++:#
1. Cython
2. CXX
3. Boost.python
4. SWIG
5. SIP (used mainly in PyQT) | {"url":"https://numpy.org/doc/stable/user/misc.html?highlight=numpy%20nan","timestamp":"2024-11-04T04:10:59Z","content_type":"text/html","content_length":"35580","record_id":"<urn:uuid:51b2cb2e-3831-4a49-921e-d32023498e69>","cc-path":"CC-MAIN-2024-46/segments/1730477027812.67/warc/CC-MAIN-20241104034319-20241104064319-00171.warc.gz"} |
Robust network design with uncertain outsourcing cost
The expansion of a telecommunications network faces two sources of uncertainty, which are the demand for traffic that shall transit through the expanded network and the outsourcing cost that the
network operator will have to pay to handle the traffic that exceeds the capacity of its network. The latter is determined by the future cost of telecommunications services, whose negative
correlation with the total demand is empirically measured in the literature through the price elasticity of demand. Unlike previous robust optimization works on the subject, we consider in this paper
both sources of uncertainty and the correlation between them. The resulting mathematical model is a linear program that exhibits a constraint with quadratic dependency on the uncertainties. To solve
the model, we propose a decomposition approach that avoids considering the constraint for all scenarios. Instead, we use a cutting plane algorithm that generates required scenarios on the fly by
solving linear multiplicative programs. Computational experiments realized on the networks from SNDlib show that our approach is orders of magnitude faster than the classical semidefinite programming
reformulation for such problems. | {"url":"https://optimization-online.org/2014/11/4666/","timestamp":"2024-11-06T09:19:36Z","content_type":"text/html","content_length":"84002","record_id":"<urn:uuid:35413c07-6973-4752-99ec-33ce376606d0>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00282.warc.gz"} |
Compound interest rate calculator
In other words, what the nominal rate of compound interest should be to get the specified accrued amount from the initial amount in a specified period of time.
Compound interest rate calculator
Accrual period[monthly ]
Calculation precision
Digits after the decimal point: 2
Link Save Widget | {"url":"https://planetcalc.com/115/","timestamp":"2024-11-08T04:40:56Z","content_type":"text/html","content_length":"32234","record_id":"<urn:uuid:82225ebf-b167-4e2f-a1df-933f81c91a06>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00557.warc.gz"} |
Binary to Decimal
Free binary to decimal converter - convert binary to decimal online
The binary to decimal converter is a simple online tool that allows you to convert from binary to decimal number system. It is an easy-to-use online tool that allows users to convert binary numbers
to decimal numbers. The converter takes a binary number and converts it to a corresponding decimal number. The process is simple and easy to follow. All you need to do is enter the binary number in
the box provided and click the "Convert" button. The converter then automatically generates the equivalent decimal number.
What is Binary?
To convert a binary number to its decimal equivalent, the place values of each digit must be multiplied by 2^n, where n is the digit's position from the rightmost side. So, for example, if we have
the number 1011 (which is 11 in decimal), we would calculate it like this: 1*2^3 + 0*2^2 + 1*2^1 + 1*2^0 = 8+0 +2+1 = 11.
What is Decimal?
Decimal is the decimal number system, which consists of ten digits: 0,1,2,3,4,5,6,7,8 and 9. This number system is widely used in our daily life and in many scientific applications. Decimal numbers
are sometimes called denary or decanary numbers.
The decimal number system has a long history. It is believed to have originated with the Hindus of India around 3100 BC. The Hindu-Arabic number system we use today was first described by Fibonacci
in 1202 AD. In this system, each consecutive digit represents a multiple of the previous one. For example, the number 12 can be represented as 1 ten and 2 ones, or as 10 twos and 2 ones.
The advantage of the decimal number system is that it is very easy to use and understand. It also allows us to easily perform arithmetic operations such as addition, subtraction, multiplication and
How to Convert Binary to Decimal
Binary to Decimal Converter helps you convert binary numbers to decimal numbers. It is an easy-to-use online tool that allows users to convert from binary number system to decimal number system.
To use the converter, simply enter a binary number in the "Binary number" field and click the "Convert" button. The equivalent decimal number is displayed in the "Decimal number" field.
The converter can handle large binary numbers (up to 63 digits). However, for simplicity, all input and output values are truncated to 32 digits.
So, how does the inverter work?
The converter uses a simple algorithm to perform the conversion.First, it calculates the value of each digit in the binary number and then sums those values. For example, to convert the binary number
"1101" to decimal, we calculate: 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 13 .
And that's it! With this method you can easily convert any binary number to its decimal equivalent.
The binary to decimal converter
Converting a binary number to a decimal number is easy with this online conversion tool. Just enter the binary code and the converter will do the rest! Conversion between these two number systems is
easy with this web-based tool.
How to use the binary to decimal converter
The binary to decimal converter is a tool that allows users to convert binary numbers to decimal numbers. It is an easy-to-use online tool that makes converting from binary number system to decimal
number system quick and painless.
To use the converter, simply enter a binary number in the input field and press the "convert" button. The converter does the rest and spits out the equivalent decimal number. Comfortable!
So why should you convert a binary number to a decimal number? Well, there are a few reasons. Maybe you are working with some binary data and need to convert it for display or storage in a decimal
format.Or maybe you're just curious about how binary numbers work and want to see what the equivalent decimal value is. Whatever the reason, the binary to decimal converter is a handy tool to have in
your arsenal.
The benefits of using the binary to decimal converter
The Binary to Decimal Converter is a free online tool that allows users to quickly and easily convert binary numbers to decimal numbers. The converter is easy to use, just enter the binary you want
to convert and click the "Convert" button. The converter then displays the equivalent decimal number.
The binary to decimal converter is an invaluable tool for anyone working with binary numbers. It is especially useful for students studying math or computer science as it allows them to easily
convert between the two number systems.The converter can also be used by companies or individuals who need to convert between binary and decimal numbers to perform calculations or other operations.
Examples from binary to decimal
Binary to Decimal Converter helps you convert binary numbers to decimal numbers. It is an easy-to-use online tool that allows users to convert from binary number system to decimal number system.
To use the converter, simply enter a binary number in the input field and click "Convert". The converter will output the equivalent decimal number.
Here are some examples of binary to decimal conversions:
Binary Number Decimal Number
The Binary to Decimal Converter is a handy online tool that helps users convert binary numbers to decimal numbers. It is an easy-to-use online tool that allows users to convert from one number system
to another in just a few clicks. Whether you are a student or a professional, this converter can help you save time and energy when working with binary numbers.
David Miller
CEO / Co-Founder
Our mission is to provide 100% free online tools useful for different situations. Whether you need to work with text, images, numbers or web tools, we've got you covered. We are committed to
providing useful and easy-to-use tools to make your life easier. | {"url":"https://toolswad.com/binary-to-decimal","timestamp":"2024-11-14T20:28:38Z","content_type":"text/html","content_length":"83969","record_id":"<urn:uuid:1d0cc9bc-de7c-4b67-b708-8eee36649c3a>","cc-path":"CC-MAIN-2024-46/segments/1730477395538.95/warc/CC-MAIN-20241114194152-20241114224152-00402.warc.gz"} |
JEE Quadratic Equations- Advanced Conceptual Understanding | Brilliant Math & Science Wiki
JEE Quadratic Equations- Advanced Conceptual Understanding
This page will teach you how to master JEE Quadratic Equations up to JEE Advanced level. We highlight the main concepts, provide a list of examples with solutions, and include problems for you to
try. Once you are confident, you can take the quiz to establish your mastery.
A root of the equation \(ax^2+bx+c=0\) is a number (real or complex), say \(\alpha\), which satisfies the equation i.e. \(a\alpha^2+b\alpha+c=0\). The roots of the quadratic equation \(ax^2+bx+c=0\)
with \(a\neq 0\) are given by \(x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}\).
To have mastery over Quadratic Equations of JEE Advanced, the main concepts you should be confident of are polynomial equations reducible to quadratic equations, algebraic interpretation of Rolle's
theorem, intermediate value theorem and analysis of cubic equation with real coefficients.
Polynomial equations reducible to quadratic equations
• An equation of the form \((x-a)(x-b)(x-c)(x-d)=k\)
• An equation of the form \((x-a)(x-b)(x-c)(x-d)=kx^2\), where \(ab=cd\)
• An equation of the form \((x-a)^4+(x-b)^4=k\)
• An equation of the form \(ax^{2n}+bx^n+c=0 \ , a \neq 0 \) and \(n \in \mathbb N\): Substitute \(x^n=y\)
• Reciprocal equations: \(ax^3+bx^2+bx+a=0\) or \(ax^4+bx^3+cx^2+bx+a=0\)
Algebraic interpretation of Rolle's theorem
• Between any two roots of a polynomial equation \(f(x)=0\), there always exists a roots of its derivative \(f'(x)=0\)
• Relation between roots and derivatives
• Some important deductions from Rolle's theorem
Intermediate Value Theorem
• If \(f(x)\) is a polynomial function such that \(f(a) \neq f(b)\), then \(f(x)\) takes every value between \(f(a)\) and \(f(b)\)
• If \(f(a)\) and \(f(b)\) are of opposite signs, then one root of the equation \(f(x)=0\) must lie between \(a\) and \(b\)
Analysis of cubic equation with real coefficients
• Condition for all three real roots of a cubic equation
• Condition for two real roots and one complex root
• Trigonometrical method of solving cubic equation
\[ \begin{array} { l l } A) \, \text{No such value of } \ k \ \text{exists} & \quad \quad \quad \quad \quad & B) \, \frac12 \\ C) \, -\frac12 & & D) \, 1 \\ \end{array} \]
Concepts tested:
Common mistakes:
\[ \begin{array} { l l } A) \, \text{No such value of } \ k \ \text{exists} & \quad \quad \quad \quad \quad & B) \, \frac12 \\ C) \, -\frac12 & & D) \, 1 \\ \end{array} \]
Concepts tested:
Common mistakes:
\[ \begin{array} { l l } A) \, \text{No such value of } \ k \ \text{exists} & \quad \quad \quad \quad \quad & B) \, \frac12 \\ C) \, -\frac12 & & D) \, 1 \\ \end{array} \]
Concepts tested:
Common mistakes:
\[ \begin{array} { l l } A) \, \text{No such value of } \ k \ \text{exists} & \quad \quad \quad \quad \quad & B) \, \frac12 \\ C) \, -\frac12 & & D) \, 1 \\ \end{array} \]
Concepts tested:
Common mistakes:
\[ \begin{array} { l l } A) \, \text{No such value of } \ k \ \text{exists} & \quad \quad \quad \quad \quad & B) \, \frac12 \\ C) \, -\frac12 & & D) \, 1 \\ \end{array} \]
Concepts tested:
Common mistakes:
Once you are confident of Quadratic Equations, move on to JEE Complex Numbers. | {"url":"https://brilliant.org/wiki/jee-quadratic-equations-advanced-conceptual-unders/","timestamp":"2024-11-10T02:58:24Z","content_type":"text/html","content_length":"46950","record_id":"<urn:uuid:c2dd27be-d1fa-4971-94a5-fdabbd3f4371>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00591.warc.gz"} |
Resampling Timeseries with Groupby in Pandas - DNMTechs - Sharing and Storing Technology Knowledge
Resampling Timeseries with Groupby in Pandas
When working with time series data in Python, the Pandas library is a powerful tool that provides various functionalities for data manipulation and analysis. One common task when dealing with time
series data is resampling, which involves changing the frequency of the data points. In this article, we will explore how to resample time series data using the groupby function in Pandas.
Understanding Resampling
Resampling allows us to convert time series data from one frequency to another. This can be useful when we want to aggregate data over a different time period or when we need to fill in missing
values. Pandas provides the resample method, which can be used to perform resampling on a time series DataFrame or Series object.
Resampling can be done in two ways: downsampling and upsampling. Downsampling involves reducing the frequency of the data points, while upsampling involves increasing the frequency. The resample
method in Pandas allows us to specify the desired frequency for resampling.
Using Groupby for Resampling
While the resample method in Pandas is useful for resampling time series data, it may not always provide the flexibility needed for complex resampling operations. In such cases, we can leverage the
groupby function in Pandas to perform resampling.
The groupby function allows us to group the data by a specific column or index level and apply a function to each group. By combining the groupby function with the resample method, we can achieve
more complex resampling operations.
Let’s consider an example where we have a DataFrame with daily stock prices:
import pandas as pd
# Create a DataFrame with daily stock prices
data = {'date': pd.date_range(start='1/1/2022', periods=100),
'symbol': ['AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL', 'AAPL',
'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG', 'GOOG'],
'price': [100, 101, 102, 103, 104, 105, 106, 107, 108, 109,
2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009]}
df = pd.DataFrame(data)
We can use the groupby function to group the data by the ‘symbol’ column and then apply the resample method to each group:
# Group the data by 'symbol' and resample to monthly frequency
df_grouped = df.groupby('symbol').resample('M', on='date').mean()
In the above example, we grouped the data by the ‘symbol’ column and resampled it to a monthly frequency using the resample method with the ‘M’ argument. We also specified the ‘date’ column as the
time column using the ‘on’ parameter.
The resample method allows us to specify various frequency aliases, such as ‘D’ for daily, ‘W’ for weekly, ‘M’ for monthly, ‘Q’ for quarterly, and ‘A’ for annual resampling. We can also use custom
frequencies by specifying the desired number of business days or calendar days.
Performing Aggregations
When using the groupby function for resampling, we can also perform aggregations on the grouped data. This allows us to calculate various statistics or apply custom functions to the resampled data.
For example, let’s say we want to calculate the maximum price for each symbol on a weekly basis:
# Group the data by 'symbol' and resample to weekly frequency, calculating the maximum price
df_grouped = df.groupby('symbol').resample('W', on='date').max()
In the above example, we used the groupby function to group the data by the ‘symbol’ column and resampled it to a weekly frequency using the resample method with the ‘W’ argument. We then applied the
max function to calculate the maximum price for each group.
By combining the groupby function with the resample method, we can perform various aggregations on the resampled data, such as calculating the mean, sum, minimum, or applying custom functions.
In this article, we explored how to resample time series data using the groupby function in Pandas. By leveraging the groupby function, we can achieve more complex resampling operations and perform
aggregations on the resampled data. Resampling time series data is a powerful technique that allows us to change the frequency of the data points and aggregate data over different time periods.
Resampling timeseries data with groupby in Pandas is a powerful technique that allows us to aggregate and manipulate data at different time intervals. It is particularly useful when dealing with
large datasets and when we need to analyze data at different levels of granularity.
Example 1: Resampling and aggregating daily stock prices
import pandas as pd
# Load the stock prices dataset
df = pd.read_csv('stock_prices.csv')
# Convert the 'date' column to datetime
df['date'] = pd.to_datetime(df['date'])
# Set the 'date' column as the index
df.set_index('date', inplace=True)
# Resample the data to monthly frequency and calculate the mean price
monthly_mean = df.resample('M').mean()
# Resample the data to yearly frequency and calculate the maximum price
yearly_max = df.resample('Y').max()
In this example, we have a dataset of daily stock prices. We start by loading the data into a Pandas DataFrame and converting the ‘date’ column to datetime format. We then set the ‘date’ column as
the index, which allows us to easily resample the data.
We use the resample() function to resample the data to different frequencies. In the first case, we resample the data to monthly frequency and calculate the mean price for each month. In the second
case, we resample the data to yearly frequency and calculate the maximum price for each year.
The resulting DataFrames, monthly_mean and yearly_max, contain the aggregated data at the specified frequencies.
Example 2: Resampling and aggregating hourly temperature data
import pandas as pd
# Load the temperature data
df = pd.read_csv('temperature_data.csv')
# Convert the 'timestamp' column to datetime
df['timestamp'] = pd.to_datetime(df['timestamp'])
# Set the 'timestamp' column as the index
df.set_index('timestamp', inplace=True)
# Resample the data to daily frequency and calculate the mean temperature
daily_mean = df.resample('D').mean()
# Resample the data to monthly frequency and calculate the minimum temperature
monthly_min = df.resample('M').min()
In this example, we have a dataset of hourly temperature measurements. We start by loading the data into a Pandas DataFrame and converting the ‘timestamp’ column to datetime format. We then set the
‘timestamp’ column as the index.
We use the resample() function to resample the data to different frequencies. In the first case, we resample the data to daily frequency and calculate the mean temperature for each day. In the second
case, we resample the data to monthly frequency and calculate the minimum temperature for each month.
The resulting DataFrames, daily_mean and monthly_min, contain the aggregated data at the specified frequencies.
Resampling timeseries data with groupby in Pandas is a powerful technique that allows us to aggregate and manipulate data at different time intervals. It provides a convenient way to analyze data at
different levels of granularity, such as daily, monthly, or yearly. By using the resample() function, we can easily resample the data to different frequencies and apply various aggregation functions
to the resampled data.
Overall, resampling timeseries data with groupby in Pandas is a valuable tool for time series analysis and can help us gain insights into the underlying patterns and trends in the data.
Reference links: | {"url":"https://dnmtechs.com/resampling-timeseries-with-groupby-in-pandas/","timestamp":"2024-11-13T09:00:51Z","content_type":"text/html","content_length":"86081","record_id":"<urn:uuid:aa15eb4e-1e6e-4e84-9bdc-1d5474473ac9>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00380.warc.gz"} |
Teacherbot 09 Jan, 13:34:57
Q1. What is the name of the type of question shown in the example? A1. Reasoning question.
Q2. What grade is the question intended for? A2. Year 6.
Q3. What is the value of the number shown in the problem? A3. 150.
Q4. What operation is used in this problem? A4. Multiplication.
Q5. How many part questions are in the answer? A5. 3.
Q6. What is the second part of the question asking? A6. To compare two values using the given information.
Q7. How many steps does the problem feature? A7. 3.
Q8. What is the value of the second digit in the answer? A8. 6.
Q9. How many times is 150 multiplied by the second and third digits? A9. 2 times.
Q10. What number is the highest in the problem? A10. 450.
Q11. What number is the lowest in the problem? A11. 150.
Q12. What is the equivalent for two-thirds? A12. 0.66.
Q13. What is the equivalent for four-tenths? A13. 0.4.
Q14. How many digits does the answer to the problem contain? A14. 3.
Q15. What is the total value when two-thirds and four-tenths are added together? A15. 1.06. | {"url":"https://teacherbot.io/contents/create-15-comprehension-questions-on-year-6-maths-reasoning-questions-with-answers-below","timestamp":"2024-11-07T05:29:06Z","content_type":"text/html","content_length":"33005","record_id":"<urn:uuid:2fb8c98b-ac17-4906-81e9-8ca296c52c33>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00078.warc.gz"} |
NIST Cybersecurity Framework Informative Reference for 800-171 Rev. 1National Institute of Standards and TechnologyCyberESI Consulting Group, IncorporatedCyberESI Consulting Group, Incorporated
2023-09-15T01:36:08-07:00 0.0.1 1.1.0 OSCAL NIST Team oscal@nist.gov National Institute of Standards and Technology Attn: Computer Security Division Information Technology Laboratory 100 Bureau Drive
(Mail Stop 8930) Gaithersburg MD 20899-8930 CyberESI Consulting Group, Incorporated info@cyberesi-cg.com 4109213864 a1c953c4-d026-40e7-bc92-576d137cd1ff 8771d07e-ac1c-4fcf-8644-09cb0b6422a9 | {"url":"https://cyberesi-cg.com/oscal_mapping_1c/OSCAL_Mapping_csf_1_1_0-sp_800_171_1_0_0_230915133608.xml","timestamp":"2024-11-08T12:07:02Z","content_type":"application/xml","content_length":"53880","record_id":"<urn:uuid:ae92a7d2-6ccb-451b-9305-330808165e95>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00031.warc.gz"} |
Dynamic Sharding of Arbitrary Neural Networks | Nesa
Dynamic Sharding of Arbitrary Neural Networks
While the sequential method provides a structured and heuristic-driven approach to partitioning, it operates under the constraints of a linear, predetermined exploration path. This may not fully
capture the dynamism and complexity of modern neural network architectures, where computational and memory demands can vary significantly across different layers and segments of the network. Given an
arbitrary neural network, our objective is to partition the network's computation graph for optimal execution across multiple nodes. This computation graph, $G=(V, E)$, consists of computational unit
operations $V$ and data flow edges $E$, with each operation $v \in V$ outputting a tensor consumed by downstream operations $v$, forming edges $(u,v) \in E$. The graph represents the entirety of the
model's computational workload which ranges from simple arithmetic operations to layer-specific matrix multiplications, each associated with specific computational and memory requirements i.e. the
running time $\text{work}(v)$, the memory footprint of the model parameters $\text{sizeparam}(v)$, and the size of the operation's output $\text{sizeout}(v)$.
Partitioning this graph involves dividing $V$ into $k$ distinct blocks such that each block can be processed on a different node in a swarm under the constraint that the induced quotient graph of $G$
remains acyclic. This division aims to maximize throughput while minimizing inter-node communication subjected to the bandwidth $B$ between nodes, with the I/O cost from node $S$ to node $T$ given
$\text{io}(S,T) = \frac{1}{B} \sum_{v \in N^-(T) \cap S} \text{sizeout}(v),$
where $N^-(T)$ represents the set of nodes whose outputs are consumed by block $T$.
The core challenge lies in efficiently distributing the model's parameters and activations across the available fast memory (e.g., SRAM) of each node. Parameters not fitting in fast memory must be
streamed from slower storage which introduces additional latency. The overflow cost which represents the time to stream parameters exceeding the fast memory limit $M$ is calculated as:
$\text{overflow}(S) = \left(\text{sizeparam}(S) + \text{peak}(S) - M\right) + \frac{\text{peak}(S)}{B},$
where $\text{peak}(S)$ denotes the peak memory requirement for activations within block $S$.
The overall block cost, $f(S)$, combines the costs of receiving input tensors, executing the block's operations (including any overflow cost from streaming parameters), and sending output tensors
$f(S) = \text{io}(V\setminus S,S) + \sum_{v \in S} \text{work}(v) + \text{overflow}(S) + \text{io}(S,V\setminus S).$
The goal of partitioning, defined by the Max-Throughput Partitioning Problem (MTPP), is to minimize the maximum cost across all blocks, optimizing the throughput of the entire pipeline. Formally,
MTPP seeks a partition $P^*$ that minimizes the bottleneck cost:
$P^* = \text{argmin}_{P \in P_k(G)} \left\{ \max_{i\in[k]} f(P_i) \right\},$
where $P_k(G)$ denotes the set of all possible partitions of $G$ into $k$ blocks, and $\text{cost}^*$ is the minimum achievable bottleneck cost across these partitions. | {"url":"https://docs.nesa.ai/nesa/technical-designs/decentralized-inference/dynamic-sharding-of-arbitrary-neural-networks","timestamp":"2024-11-15T04:04:34Z","content_type":"text/html","content_length":"295680","record_id":"<urn:uuid:87e9bed1-fb5e-4c8c-8f01-7fc0b6835036>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00799.warc.gz"} |
Equilateral Triangle Calculator
Equilateral Triangle Calculator
Equilateral Triangle Calculator
What is the Equilateral Triangle Calculator?
The Equilateral Triangle Calculator is a tool designed to help you quickly and accurately find the properties of an equilateral triangle. This type of triangle features three sides of equal length
and equal interior angles. By entering a single side length, you can determine other properties such as the perimeter, height, and radii of the circumcircle and incircle.
Applications of the Equilateral Triangle Calculator
The calculator caters to students, educators, engineers, architects, and anyone interested in geometry. In educational settings, it aids in demonstrating geometric principles. Engineers and
architects may use it for precise calculations during design and construction projects. Its simplicity and accuracy make it a reliable tool for various professional and academic applications where
equilateral triangles are involved.
Benefits of Using this Calculator
This calculator saves time and reduces the risk of manual calculation errors. It allows you to switch between metric and imperial units, ensuring accuracy regardless of the measurement system. The
results include the perimeter, area, height, circumradius, and inradius, providing a comprehensive understanding of the triangle's properties with minimal input.
Understanding the Calculations
To find the properties of an equilateral triangle, you only need the length of one side. The perimeter is calculated by multiplying the side length by three. The height is found by multiplying the
side length by the square root of three divided by two. The area is determined by multiplying the square root of three by a quarter of the square of the side length. The circumradius and inradius of
the triangle are derived from the side length using simple constant multipliers.
Why Use an Equilateral Triangle Calculator?
The calculator helps swiftly convert insights into practical applications, whether for educational demonstrations, project designs, or personal curiosity. It eliminates the complexity of manual
computations, making geometric calculations easier and more accessible to everyone.
1. What measurements can I input into the calculator?
You can input the length of one side of the equilateral triangle. The calculator then determines all other properties based on this single input.
2. Can I switch between metric and imperial units?
Yes, you can switch between metric and imperial units. The calculator is designed to provide accurate results regardless of the measurement system used.
3. How do you calculate the height of an equilateral triangle?
The height is found by multiplying the side length by the square root of three divided by two. This formula is applied automatically by the calculator.
4. What is the formula for finding the perimeter of an equilateral triangle?
The perimeter is calculated by multiplying the length of one side by three. The calculator uses this simple formula to provide the perimeter instantly.
5. How is the area of the triangle calculated?
The area is determined by multiplying the square root of three by a quarter of the square of the side length. This calculation is performed automatically when you enter the side length.
6. What are the circumradius and inradius of an equilateral triangle?
The circumradius is the radius of the circumcircle, which passes through all the vertices of the triangle. The inradius is the radius of the incircle, which is tangent to all the sides of the
triangle. Both of these are calculated using the side length with specific constant multipliers.
7. Why should I use the Equilateral Triangle Calculator?
The calculator helps save time and reduces manual calculation errors. It’s an efficient tool for quickly obtaining precise geometric properties from a single input value.
8. Is this calculator suitable for professional use?
Yes, it’s suitable for professionals like engineers, architects, and educators. It provides accurate and quick results, making it reliable for both academic and professional purposes.
9. Can this calculator be used in educational settings?
Absolutely. The calculator is a great educational tool for demonstrating geometric principles and helping students understand the properties of equilateral triangles.
10. Are there any limitations to using this calculator?
It’s worth noting that this calculator specifically caters to equilateral triangles. For other types of triangles, different calculators or methods will be required. | {"url":"https://www.onlycalculators.com/math/triangle/equilateral-triangle-calculator/","timestamp":"2024-11-08T06:17:56Z","content_type":"text/html","content_length":"238032","record_id":"<urn:uuid:c8b5a081-3fb0-4d5d-a450-8665bac6954e>","cc-path":"CC-MAIN-2024-46/segments/1730477028025.14/warc/CC-MAIN-20241108035242-20241108065242-00184.warc.gz"} |
Kashin Explains His ‘Letter to Leaders’ on ‘Fontanka Office’
Oleg Kashin (L) and Dmitry Medvedev (R)
As we reported in recent weeks, prominent Russian blogger Oleg Kashin has revealed the identities of the men who brutally assaulted him in 2010 for his critical writing, leaving him hospitalized for
months. For years, he investigated the possible perpetrators of the attack, theorizing it could be either related to officials angered at his coverage of environmental protests about a forest to be
cut down in the town of Khimki; the leaders of Nashi, a youth movement founded by the Kremlin that incorporated many nationalists and even violent neo-Nazis which Kashin had criticized; or Pskov
Region then-acting governor Andrei Turchak, who was insulted by Kashin’s frank revelation that Turchak was a crony of President Vladimir Putin which explained his position of power.
On October 6, the Guardian published an English translation of Russian blogger Oleg Kashin’s “Letter to Russian Federation Leaders,” a title that Kashin himself explained was a conscious reference to
the famous “Letter to the Soviet Leaders” written by Alexander Solzhenitsyn in 1973. From his exile in Vermont, Solzhenitsyn had written a scathing critique of Soviet Marxist-Leninist ideology and
heedless industrialization, proposing instead a nationalist small-town pastoralism that was itself criticized in the US.
Yesterday, Kashin gave an interview to Nikolai Nyelyubin and Olga Markina of the St. Petersburg web site Fontanka.ru’s radio show, Fontanka Ofis [Fontanka’s Office] on the reasons for his letter,
which was prompted by the revelation of the identities of his 2010 assailants as in the end related to Governor Turchak, who was elected in 2014 after years of serving as Putin’s interim appointee.
The confessions of one of the suspects jailed, Danila Vesyolov, implicates Turchak as the mastermind of Kashin’s assault, using employees of the security department of a factory owned by Turchak’s
father, Anatoly Turchak. Kashin ended up going abroad for some years, but this year after an operation, he returned with his wife and child to Russia. The Interpreter has provided a full translation;
the comments in brackets are explanations provided by The Interpreter.
Fontanka Office: Oleg, the first question: What is the correct title of your text?
Kashin: “Letter to Leaders of the Russian Federation.”
Fontanka Office: What was the reason for you doing this letter?
Kashin: The explanation is all very simple. On Friday [October 2], on TV Rain, I showed a rather strong video, as it seemed to me, of the confessions of Danila Vesyolov in my case. Vesyolov rather
unperturbedly recounts how in fact it was Pskov Region Governor Andrei Turchak who explained to him which parts of my body have to be broken so that I no longer wrote lampoons. This video seems very
important to me, sensational and so on, but it did not make public opinion catch fire at all. I also understand why. Because for more than a month, I have been battling publicly on this topic. An
audience will get fed up with any topic, even the hottest, after a month. That’s normal, that’s natural. And I’m not interested in that. Because I understand perfectly well that public interest in my
case is my only instrument now which will prevent the perpetrators of the crime from escaping justice. Therefore, I used a trick I had long had up my sleeve. After having written this text, I was
able to get to the level of summing things up a bit. Since really, my case seems very important to me. Not as my personal issue, but as an illustrative story about their morals in general. In the
Kremlin, in law-enforcement agencies and so on.
Fontanka Office: How would you answer the question for those who did not read this text? I think that many of our users did not read it. Although it is not hard to go on Oleg’s site and read it. What
is the letter about, if you could do an excerpt?
Kashin: What is the letter about? It’s about the fact that after a month of my activism in my own case, I am ready to state that the highest officials… I have said repeatedly that Turchak’s fate will
be resolved not by investigative bodies and not in a courtroom. Putin must decide the fate of Turchak. And he intends to resolve it one way or another, since this is his nomenklatura. But after a
month it can be stated that Putin took Turchak’s side, Putin is saving Turchak from possible problems with the investigation.
First, I state this, and second I try to analyze why Putin has made exactly this choice. This seems important to me not only from the perspective of my personal history which should concern only me,
but literally from the perspective of Russia’s history. The title “Letter to Leaders” – that also has to be explained. That is a conscious allusion to the famous letter of Alexander Solzhenitsyn
written years ago. I really do believe that today, in 2015, it is really Solzhenitsyn’s methodology of communicating with the government that deserves both understanding and repetitions. Since there
simply is no other methodology. All the efforts to play by the rules which the Kremlin makes, whether they are elections, rallies in the permitted places or anything else – these are all attempts in
the larger analysis doomed to failure. Therefore we have to take out of our pockets that weapon that we do have. Russia is a logo-centric country. As they say, a word has stopped the sun, a word has
destroyed cities. It is this word that we must use in the same way. I think it is the most appropriate instrument today.
Fontanka Office: There is already a reaction to this letter today. They have read Kashin’s “Open Letter to the Leaders of the Russian Federation” in the Kremlin. “Yes, it was published in the media,”
presidential press secretary Dmitry Peskov said at a briefing on October 5. Peskov replied to a question about the possible reaction to Kashin’s statement: “Based on what has been read, I don’t
particularly count on an answer. For now I can’t say anything on this.” Your reaction to this reaction, Oleg?
Kashin: This is an entirely understandable reaction. If there is nothing to object about, then Putin agrees with what is written there. Furthermore, I imagine how he and Medvedev or Peskov read it
and winked to each other: well, what do you know, this dude gets it totally. Good for him. Peskov’s reaction in fact confirms my conclusions. They’re rather sad, but there is nothing sensational in
them. Everyone understands how all this works anyway.
Fontanka Office: As I understand it, the situation is now such that everything has reached a dead end. What further can be done? This letter is a radical position which did case a public sensation in
a certain sense. But what next, Oleg?
Kashin: Next we have a set of ordinary procedural things in my case. Perhaps you have heard how Vesyolov’s wife — he’s the one who directly beat me… [The reference is to her statement that she has a
copy of an audio recording of Turchak giving the order to beat Kashin].
Fontanka Office: Yes.
Kashin: She is asking for a face-to-face meeting between her husband and Turchak. We have to try to get that face-to-face meeting of course, we have to try to get the interrogation of Turchak and do
some other procedural moves. It would be good even to get Turchak to take a lie-detector test, although understandably, that is more an image story than a procedural story. But at least I wouldn’t
reject that. That is, through attorneys, through interaction with the investigators, we have a rather long-term plan of work. Parallel to this, I will remind you that we have a suit in the European
Court of Human Rights on the inaction of the investigative agencies. Furthermore, when we filed the suit, we had a hypothesis of inaction. Now we have proof of inaction. There is a whole set of
confirming papers of the actions of Investigator Soskov witnessing to the fact that he was consciously rescuing Gorbunov and Turchak. Gorbunov is the manager of the Leninets Factory and Turchak’s
accomplice, according to the perpetrators. And I will recall that they have been charged and Gorbunov is the direct organizer of the attack on me. So in that sense, we will go on working. But this is
painstaking work, and so to say, not sensational. I don’t count on this getting into the front pages of the newspapers. It’s another matter that the earth will burn under these people’s feet even
without newspapers. And in fact I’m glad that the reputation of Andrei Turchak in the last month has somewhat changed. At least, he is already getting a kind of moral punishment. That’s a good thing.
Fontanka Office: In 2010, Anatoly Turchak advised his son Andrei not to get involved, and not to get entangled in public…
Kashin: Stop. That’s a very interesting point. Dad didn’t just advise his son not to get entangled. Dad advised him not to file a suit in court. Here’s a quote: “Prove by deed that he is [the] better
[man].” That is very eloquent, because Turchak, in the larger scheme, if Vesyolov’s testimony is to be believed, Turchak really did prove himself by deed. Furthermore, the very construction…How old
was he then? 35. A 35-year-old adult man, who was offended by somebody on the Internet, calls his dad – a friend of Putin’s – and says, “Dad, what should I do?” That’s an indicator of their morals
and the mixture of gangsterish and childish logic in their actions. That’s why Turchak’s dad’s commentary is so charming, I think. The man really complained to his dad about his offenses on the
Internet. Dad told him then – act – and the man began to act. That’s the story.
Fontanka Office: Oleg, I think this rather casual and entirely assured attitude of the powers that be to your case tells us that they understand perfectly well that generally, any of your disclosures
are not going to cost them potentially anything in terms of risks. Except for some discussion in some narrow circle of people.
Kashin: Yes of course, except public opinion. Yes. Narrow circle or not, hundreds of thousands of people have read my letter.
Fontanka Office: What are hundreds of thousands? We have 140 million in our country.
Kashin: That’s an issue, of course.
Fontanka Office: It is an issue. After all, this enables them to go on not reacting at all to anything you do. And at a certain moment, when a person becomes exhausted, various unpleasant things
happen. And as I understand it, people wrote you in the comments in this vein: “Oleg, be careful.” It’s a question of safety. How do you now approach this, do you have any apprehensions? Because
sooner or later, everyone’s patience ends. And as we know, it ends differently for different people. Do you catch my drift?
Kashin: Of course there are apprehensions. And the very fact that Gorbunov is released so demonstratively and brazenly I believe unquestionably is a directly articulated threat personally to me, to
my security, to everything. Even so, there is a funny aspect to this; at the onset of all this story, when Gorbunov was released, I spoke a bit to my source in the Kremlin and I said, “Here’s the
damn thing, I’m afraid they might kill me.” Not in the Kremlin. I can even say who it is. It’s [Aleksei] Venediktov [editor-in-chief of Ekho Moskvy]. And Venediktov said this to me: “Don’t worry,
they won’t kill you, nothing will happen to you, because [Rostec CEO Sergei] Chemezov has taken responsibility for Gorbunov. And if something happens to you, Chemezov will have some unpleasantness.”
And there’s the Byzantine logic, the logic of the corridors — it chills me to the bone. Because it’s like, okay, they’ll kill me, but what will Chemezov get for that? He will be sentenced or Putin
will shake his finger at him? Or in the most extreme case, Chemezov will be fired. That’s the reassurance if, God forbid, something happens to me. Therefore, I’m not prepared to accept that unlawful
logic which dominates there. I understand perfectly well that yes, they are all ruled by this logic.
Fontanka Office: This media manager you have mentioned [Venediktov], who is he, anyway, in this situation? I don’t really understand why you are talking to him?
Kashin: This media manager I have mentioned is an interesting person in the sense that he clearly, many years ago, and not just once, proved this in deed. Like before the Bolotnaya Square [
demonstrations]. He clearly took upon himself the mission of serving as a middle man between the Kremlin and, roughly speaking, the Moscow creative class. And it even reached the point of being
humorous, when it was people from Ekho, which was a fairly conservative radio station, who were made the organizers of some draft laws or something like that regarding the Internet. They have a web
site, so that means they are the chiefs on the Internet. This is comical. But at least, a fact remains a fact. Therefore, Venediktov is a middle man between Putin and all of us. That is a fact. And
that is a feature of the current Russian apparatchik tradition.
Fontanka Office: So that means this middleman suits you? I am trying to understand the attitude toward the caliber of what he said.
Kashin: In fact I believe what Venediktov is saying. He has conveyed this from over there [the Kremlin]. Here’s a man who has been in the market for many years, and I don’t doubt his abilities as a
conveyor belt.
Fontanka Office: Understood. Oleg, what do you predict? You’re building plans for a future turn of events? Can you tell us what you are expecting, and over what time period? Or do we run up against
the fact that they will totally ignore you? Because as you explained earlier, besides the hundreds of thousands of people who read your letter, there’s nothing else at all. What will come next?
Kashin: It’s a fairly simple answer. I also articulated it in the letter. I am convinced that a quiet resignation awaits Turchak in let’s say 3 to 4 months after I fall silent. After that, the
association disappears whereby if Turchak is removed, that means it’s for Kashin’s case. There will be silence because I think in 3 or 4 months he will be dismissed. That is my political forecast. I
can’t count on anything more regarding Turchak. I see that already, I realize that; moreover I realize this regarding my own fate. A) there is a threat against my security now and it will go on
further; b) this began for me not in the Kashin [assault] case but rather with the Bolotnaya [demonstration]. The ability for me to work in Russian media grows less each time. The fact that this last
month I began a broadcast on TV Rain will sooner or later remain my last refuge. Because it will be more difficult in other places. I sense that.
Fontanka Office: Besides Putin, you addressed your letter to Prime Minister Medvedev. Is there any reaction from him? Because when a person is asked something or he is pointed to in some way, it’s
logical that he reacts. Now Peskov reacted in the name of Putin, one way or another. We haven’t seen [Medvedev’s press secretary Natalya] Timakova. Is that not coincidental? Will we see a reaction,
what do you think?
Kashin: I think it is an accident. Why did Peskov react? Because he was asked. Why did Timakova not react? Because apparently she wasn’t asked. It’s an interesting thing, I’m not exactly complaining
about my colleagues, but it would be a simple matter to have someone call somebody — a journalist could call an official — but you have to spend a long time talking him into it. The journalist.
Because we’ve lost certain habits. I don’t mean to scold my colleagues. For example, if you work in Izvestiya, and [owner] Aram Ashotovich [Gabrelyanov] said that the topic isn’t important. Okay.
That means it isn’t important.
Fontanka Office: Don’t you think that in principle, the topic of Kashin and Turchak is receding in today’s reality, it is gradually melting away, inevitably, with each passing day? Taking into
account that the planes have flown to Syria. Russia has much more global problems and challenges. Everybody gets everything, even the journalist Kashin gets everything. I’m trying to formulate a
certain abstract vision of the situation by some majority of people. Well, how much can you take? Terrorists are advancing on every side here, and he keeps going on about [his case]. Everybody
already got who did it. That’s enough, already.
Kashin: That was exactly my starting point. I am aware myself that it’s impossible to hold the public’s attention for long. So my letter to the leaders was a half-way point. Yes, it’s like that
without a doubt. But my activism on my case is not necessarily calculated to end up in the headlines. My activism will end when the case is investigated not only de facto but de jure. This is not
some fantastically unattainable dream, but what can be achieved by some legal paths in that very complicated legal field which there is in Russia. Here in fact I don’t see a problem. I promise not to
bore your respected audience, mine or anyone’s beyond measure. I realize that I can easily turn into a spammer or that mother-in-law who runs to her neighbors and cries: my son-in-law stole a carload
of firewood. I don’t want to turn into that mother-in-law. But the problem does exist.
Fontanka Office: You have called Turchak’s press service so many times, and you never get a single answer from them, ever?
Kashin: Yes [that’s true]. No, the role of Fontanka in my case, in its reaching its current stage is inestimable in the good sense. If there hadn’t been Fontanka’s publication last summer, the first
publication about Gorbunov, there’d be nothing at all. And now we wouldn’t be discussing either Turchak, or me or my letter or anything at all. I’d be quietly writing about that same Syria. So thanks
to Fontanka, I definitely have no complaints about Fontanka.
Fontanka Office: My colleague asked why Andrei Anatolyevich [Turchak] himself has not said anything coherent? He has not commented on this in any way until now?
Kashin: Regarding Turchak’s responses, from the perspective of calculating some messaging, he regularly gives some interesting replies. When Gorbunov was released, he made a statement about
horse-radish planting. And since the word “plant” [literally “sit” in Russian, the same word used for “jail”] was said, I interpreted that to mean “the hell with you” [as the word “horse radish” is a
euphemism for “f**k you” in Russia], and not about the planting. At some stage he did a photo session in the waters of the Barents Sea in Murmansk Region where the film Leviathan was shot. About the
merging of the government, criminal world and the church.
Fontanka Office: That’s symbolic.
Kashin: Yes. Of course. Thus, he regularly puts out these symbolic responses, and these responses appear rather cynical. Yes? And what kind of direct answer should be given by Turchak? It should be
given, as a minimum, I think, regarding the face-to-face meeting [with Vesyolov], the interrogation [of Turchak], but he can’t make an official statement because an outright lie from the mouth of an
official is not welcome. Usually they try to keep silent or answer with some kind of hints. And he can’t say “It wasn’t me,” of course. Because he knows there is proof to the contrary. | {"url":"https://www.interpretermag.com/kashin-explains-his-letter-to-leaders-on-fontanka-office/","timestamp":"2024-11-11T10:33:32Z","content_type":"text/html","content_length":"37423","record_id":"<urn:uuid:ea352c25-e7e5-4963-b252-0bb39d43f13f>","cc-path":"CC-MAIN-2024-46/segments/1730477028228.41/warc/CC-MAIN-20241111091854-20241111121854-00641.warc.gz"} |
Laue equations - Mono Mole
Laue equations
The Laue equations are formulated in 1914 by Max Theodor Felix Laue, a German physicist. Like the Bragg equation, they serve to explain X-ray diffraction patterns.
Consider a one-dimensional row of equally spaced lattice points of a crystal in the diagram above. If $\alpha&space;_0eq&space;\alpha$, the path difference δ between R[1] and R[2 ]is given by
Since $AC=\frac{a}{h}cos\alpha$ and $BD=\frac{a}{h}cos\alpha&space;_0$,
For constructive interference to occur, the path difference must be an integral multiple of the wavelength of the X-ray radiation. So,
Similarly, for the other two axes of the crystal, we have:
Eq15, eq16 and eq17 are collectively known as the Laue equations. For constructive interference to occur in three dimensions, the three equations must be simultaneously satisfied.
The Laue equations can also be expressed in vector form (see above diagram), where s and s[0 ]are wave vectors of the scattered and incident X-rays respectively; a is the lattice vector along the
a-axis. Again,
Since $AC=\left&space;|&space;\textbf{\textit{a}}\right&space;|cosDAC$ and $\textbf{\textit{a}}\cdot\textbf{\textit{s}}=\left&space;|&space;\textbf{\textit{a}}\right&space;|\left&space;|&space;\
textbf{\textit{s}}\right&space;|cosDAC$, $AC=\textbf{\textit{a}}\cdot&space;\frac{\textbf{\textit{s}}}{\left&space;|&space;\textbf{\textit{s}}&space;\right&space;|}$. Similarly, $BD=\textbf{\textit
{a}}\cdot&space;\frac{\textbf{\textit{s}}_0}{\left&space;|&space;\textbf{\textit{s}}&space;_0\right&space;|}$. So,
Substituting $\left&space;|&space;\textbf{\textit{s}}\right&space;|=\left&space;|&space;\textbf{\textit{s}}_0\right&space;|=\frac{1}{\lambda&space;}$ (see below for explanation) in eq18,
For constructive interference to occur,
Similarly, for the other two axes, we have,
Eq20, eq21 and eq22 are the Laue equations in vector form.
Why is $\left&space;|&space;\textbf{\textit{s}}\right&space;|=\left&space;|&space;\textbf{\textit{s}}_0\right&space;|=\frac{1}{\lambda&space;}$ ?
A wave vector k, like any vector, has a direction and magnitude. Its direction is perpendicular to the wavefront, while its magnitude is defined as the number of waves per unit distance, which is 1/λ
. Therefore, $\left&space;|&space;s&space;\right&space;|=\left&space;|&space;s_0&space;\right&space;|=\frac{1}{\lambda}$.
Wave vectors and have origins in the de Broglie relation, which is p = h/λ = hk where k = 1/λ. Since p is a vector, k must also be a vector, as h is a constant, i.e. p = hk. This implies that k is
also a momentum vector with magnitude of 1/λ. | {"url":"https://monomole.com/laue-equations/","timestamp":"2024-11-03T09:47:40Z","content_type":"text/html","content_length":"104329","record_id":"<urn:uuid:5f4d1ca7-38ef-464c-9bcb-2691d8fa985d>","cc-path":"CC-MAIN-2024-46/segments/1730477027774.6/warc/CC-MAIN-20241103083929-20241103113929-00234.warc.gz"} |
Incentre Angle
Weekly Problem 1 - 2011
Use facts about the angle bisectors of this triangle to work out another internal angle.
The three angle bisectors of triangle $LMN$ meet at a point $O$ as shown.
$\angle LNM$ is $68^{\circ}$. What is the size of $\angle LOM$?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
$\angle OLM = \angle OLN = a^{\circ},$
$\angle OML = \angle OMN = b^{\circ}$ and
$\angle LOM = c^{\circ}$
Angles in a triangle add up to $180^{\circ}$, so from $\triangle LMN$, $$2a^{\circ}+2b^{\circ}+68^{\circ} = 180^{\circ}$$ which gives $$ 2(a^{\circ}+b^{\circ})=112^{\circ}$$ In other words $$a^{\
Also, from $\triangle LOM$, $$a^{\circ}+b^{\circ}+c^{\circ}=180^{\circ}$$ and so
$$ \eqalign{
c^{\circ}&= 180^{\circ} - (a^{\circ}+b^{\circ})\cr &= 180^{\circ}-56^{\circ}\cr &=124^{\circ}}$$ | {"url":"https://nrich.maths.org/problems/incentre-angle","timestamp":"2024-11-13T17:36:30Z","content_type":"text/html","content_length":"38316","record_id":"<urn:uuid:757ef22a-9691-43c7-976d-4dbf2c68da00>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00367.warc.gz"} |
st: Variance of a ratio
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st: Variance of a ratio
From Leonelo Bautista <[email protected]>
To [email protected]
Subject st: Variance of a ratio
Date Fri, 17 Sep 2004 14:32:05 -0500
I have a variable R that represents the risk of disease in each subject. I
regress this variable against predictors of risk:
regress R sex age obese diabetic
In this model obese and diabetic are dichotomous variables. I want to
calculate the proportion of R that is attributable to obesity (P), after
adjustment by sex, age and diabetes. Therefore, I estimated the predicted R
in the whole population and in those without obesity using adjust:
adjust, gen(adj1 seadj1) se
adjust if obese==0, gen(adj2 seadj2) se
Then, I calculate P: gen P=(adj1-adj2)/adj1
However, I need to calculate the variance of P. Since P is a ratio, there
seems to be no analytical way to estimate it. Therefore, I made 10000
simulations of P and got the variance from the simulated values, as follows:
gen Ipop = adj1 + seadj1 * invnorm(uniform())
gen Inull = adj2 + seadj2'* invnorm(uniform())
gen P = (Ipop-Inull)/Ipop
sum P
gen Pmean=r(mean) (Mean of P)
gen Pvar=r(Var) (Var of P)
Is this a reasonable approach?
Leonelo E. Bautista
* For searches and help try:
* http://www.stata.com/support/faqs/res/findit.html
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/ | {"url":"https://www.stata.com/statalist/archive/2004-09/msg00479.html","timestamp":"2024-11-12T16:32:45Z","content_type":"text/html","content_length":"8180","record_id":"<urn:uuid:ef063c6f-b9f7-4f54-bad5-b25a81738bf2>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.63/warc/CC-MAIN-20241112145015-20241112175015-00330.warc.gz"} |
Count All Subarrays With Given Sum for coding interview round
You are given an integer array 'arr' of size 'N' and an integer 'K'.
Your task is to find the total number of subarrays of the given array whose sum of elements is equal to k.
A subarray is defined as a contiguous block of elements in the array.
Input: ‘N’ = 4, ‘arr’ = [3, 1, 2, 4], 'K' = 6
Output: 2
Explanation: The subarrays that sum up to '6' are: [3, 1, 2], and [2, 4].
Input Format
The first input line contains a single integer ‘T’, denoting the number of test cases.
For each Test case:
The first line of each test case input contains two space-separated integers, where the first integer represents the length of the array 'N', and the second integer is the value ‘K’.
The next line of each test contains ‘N’ space-separated integers, which are the elements of the ‘arr’ array.
Output Format:
For every test case, return the count of all subarrays that sum up to the integer 'K'.
You do not need to print anything; it has already been taken care of. Just Implement the given function.
Constraint :
1 <= T <= 10
1 <= N<= 10^3
1 <= arr[i] <= 10^9
1 <= K <= 10^9
Time Limit: 1 sec | {"url":"https://www.naukri.com/code360/problem-details/subarray-sums-i_1467103","timestamp":"2024-11-06T04:19:39Z","content_type":"text/html","content_length":"248242","record_id":"<urn:uuid:a3ae7d55-0cce-4155-a5b5-aec98574d72c>","cc-path":"CC-MAIN-2024-46/segments/1730477027909.44/warc/CC-MAIN-20241106034659-20241106064659-00294.warc.gz"} |
Time 2 Hours
In the following questions each passage consists of six sentences. The first and the sixth sentences are given in the beginning. The middle four sentences in each have been removed and jumbled up.
These are labeled P, Q, R and S. You are required to find out the proper order for the four sentences.
S[1 ] : Many people believe that it is cruel to make use of animals for laboratory studies.
P : They point out that animals too have nervous systems like us and can feel pain.
Q : These people, who have formed the Anti-vivisection Society, have been pleading for a more humane treatment of animals by scientists.
R : Monkeys, rabbits, mice and other mammals are used in large numbers by scientists and many of them are made to suffer diseases artificially produced in them.
S : We can avoid such cruelty to animals if we use alternative methods such as tissue culture, gas chromatography and chemical techniques.
S[6 ]: It is in view of these facts that the Government of India has banned the export of monkeys to America.
The proper sequence should be : | {"url":"https://questionpaper.org/po-mock-test7/","timestamp":"2024-11-04T08:39:34Z","content_type":"text/html","content_length":"845452","record_id":"<urn:uuid:f62ca827-664a-43c1-b611-f58f3f03c4f3>","cc-path":"CC-MAIN-2024-46/segments/1730477027819.53/warc/CC-MAIN-20241104065437-20241104095437-00282.warc.gz"} |
12.1.1 Binary
Binary numbers are the most fundamental numbering system in all computers. A single binary digit (a bit) corresponds to the condition of a single wire. If the voltage on the wire is true the bit
value is 1. If the voltage is off the bit value is 0. If two or more wires are used then each new wire adds another significant digit. Each binary number will have an equivalent digital value. Figure
12.1 Conversion of a Binary Number to a Decimal Number shows how to convert a binary number to a decimal equivalent. Consider the digits, starting at the right. The least significant digit is 1, and
is in the 0th position. To convert this to a decimal equivalent the number base (2) is raised to the position of the digit, and multiplied by the digit. In this case the least significant digit is a
trivial conversion. Consider the most significant digit, with a value of 1 in the 6th position. This is converted by the number base to the exponent 6 and multiplying by the digit value of 1. This
method can also be used for converting the other number system to decimal.
Figure 12.1 Conversion of a Binary Number to a Decimal Number
Decimal numbers can be converted to binary numbers using division, as shown in Figure 12.1 Conversion from Decimal to Binary. This technique begins by dividing the decimal number by the base of the
new number. The fraction after the decimal gives the least significant digit of the new number when it is multiplied by the number base. The whole part of the number is now divided again. This
process continues until the whole number is zero. This method will also work for conversion to other number bases.
Figure 12.1 Conversion from Decimal to Binary
Most scientific calculators will convert between number bases. But, it is important to understand the conversions between number bases. And, when used frequently enough the conversions can be done in
your head.
Binary numbers come in three basic forms - a bit, a byte and a word. A bit is a single binary digit, a byte is eight binary digits, and a word is 16 digits. Words and bytes are shown in Figure 12.1
Bytes and Words. Notice that on both numbers the least significant digit is on the right hand side of the numbers. And, in the word there are two bytes, and the right hand one is the least
significant byte.
Binary numbers can also represent fractions, as shown in Figure 12.1 A Binary Decimal Number. The conversion to and from binary is identical to the previous techniques, except that for values to the
right of the decimal the equivalents are fractions.
Figure 12.1 A Binary Decimal Number
12.1.1.1 - Boolean Operations
In the next chapter you will learn that entire blocks of inputs and outputs can be used as a single binary number (typically a word). Each bit of the number would correspond to an output or input as
shown in Figure 12.1 Motor Outputs Represented with a Binary Number.
Figure 12.1 Motor Outputs Represented with a Binary Number
We can then manipulate the inputs or outputs using Boolean operations. Boolean algebra has been discussed before for variables with single values, but it is the same for multiple bits. Common
operations that use multiple bits in numbers are shown in Figure 12.1 Boolean Operations on Binary Numbers. These operations compare only one bit at a time in the number, except the shift
instructions that move all the bits one place left or right.
12.1.1.2 - Binary Mathematics
Negative numbers are a particular problem with binary numbers. As a result there are three common numbering systems used as shown in Figure 12.1 Binary (Integer) Number Types. Unsigned binary numbers
are common, but they can only be used for positive values. Both signed and 2s compliment numbers allow positive and negative values, but the maximum positive values is reduced by half. 2s compliment
numbers are very popular because the hardware and software to add and subtract is simpler and faster. All three types of numbers will be found in PLCs.
Figure 12.1 Binary (Integer) Number Types
Examples of signed binary numbers are shown in Figure 12.1 Signed Binary Numbers. These numbers use the most significant bit to indicate when a number is negative.
Figure 12.1 Signed Binary Numbers
An example of 2s compliment numbers are shown in Figure 12.1 2s Compliment Numbers. Basically, if the number is positive, it will be a regular binary number. If the number is to be negative, we start
the positive number, compliment it (reverse all the bits), then add 1. Basically when these numbers are negative, then the most significant bit is set. To convert from a negative 2s compliment
number, subtract 1, and then invert the number.
Figure 12.1 2s Compliment Numbers
Using 2s compliments for negative numbers eliminates the redundant zeros of signed binaries, and makes the hardware and software easier to implement. As a result most of the integer operations in a
PLC will do addition and subtraction using 2s compliment numbers. When adding 2s compliment numbers, we don’t need to pay special attention to negative values. And, if we want to subtract one number
from another, we apply the twos compliment to the value to be subtracted, and then apply it to the other value.
Figure 12.1 Adding 2s Compliment Numbers shows the addition of numbers using 2s compliment numbers. The three operations result in zero, positive and negative values. Notice that in all three
operation the top number is positive, while the bottom operation is negative (this is easy to see because the MSB of the numbers is set). All three of the additions are using bytes, this is important
for considering the results of the calculations. In the left and right hand calculations the additions result in a 9th bit - when dealing with 8 bit numbers we call this bit the carry C. If the
calculation started with a positive and negative value, and ended up with a carry bit, there is no problem, and the carry bit should be ignored. If doing the calculation on a calculator you will see
the carry bit, but when using a PLC you must look elsewhere to find it.
Figure 12.1 Adding 2s Compliment Numbers
The integers have limited value ranges, for example a 16 bit word ranges from -32,768 to 32,767 whereas a 32 bit word ranges from -2,147,483,648 to 2,147,483,647. In some cases calculations will give
results outside this range, and the Overflow O bit will be set. (Note: an overflow condition is a major error, and the PLC will probably halt when this happens.) For an addition operation the
Overflow bit will be set when the sign of both numbers is the same, but the sign of the result is opposite. When the signs of the numbers are opposite an overflow cannot occur. This can be seen in
Figure 12.1 Carry and Overflow Bits where the numbers two of the three calculations are outside the range. When this happens the result goes from positive to negative, or the other way.
Figure 12.1 Carry and Overflow Bits
These bits also apply to multiplication and division operations. In addition the PLC will also have bits to indicate when the result of an operation is zero Z and negative N.
12.1.2 Other Base Number Systems
Other number bases are typically converted to and from binary for storage and mathematical operations. Hexadecimal numbers are popular for representing binary values because they are quite compact
compared to binary. (Note: large binary numbers with a long string of 1s and 0s are next to impossible to read.) Octal numbers are also popular for inputs and outputs because they work in counts of
eight; inputs and outputs are in counts of eight.
An example of conversion to, and from, hexadecimal is shown in Figure 12.1 Conversion of a Hexadecimal Number to a Decimal Number and Figure 12.1 Conversion from Decimal to Hexadecimal. Note that
both of these conversions are identical to the methods used for binary numbers, and the same techniques extend to octal numbers also.
Figure 12.1 Conversion of a Hexadecimal Number to a Decimal Number
Figure 12.1 Conversion from Decimal to Hexadecimal
12.1.3 BCD (Binary Coded Decimal)
Binary Coded Decimal (BCD) numbers use four binary bits (a nibble) for each digit. (Note: this is not a base number system, but it only represents decimal digits.) This means that one byte can hold
two digits from 00 to 99, whereas in binary it could hold from 0 to 255. A separate bit must be assigned for negative numbers. This method is very popular when numbers are to be output or input to
the computer. An example of a BCD number is shown in Figure 12.1 A BCD Encoded Number. In the example there are four digits, therefore 16 bits are required. Note that the most significant digit and
bits are both on the left hand side. The BCD number is the binary equivalent of each digit.
Figure 12.1 A BCD Encoded Number
Most PLCs store BCD numbers in words, allowing values between 0000 and 9999. They also provide functions to convert to and from BCD. It is also possible to calculations with BCD numbers, but this is
uncommon, and when necessary most PLCs have functions to do the calculations. But, when doing calculations you should probably avoid BCD and use integer mathematics instead. Try to be aware when your
numbers are BCD values and convert them to integer or binary value before doing any calculations. | {"url":"https://engineeronadisk.com/V2/book_PLC/engineeronadisk-125.html","timestamp":"2024-11-07T12:16:33Z","content_type":"text/html","content_length":"16119","record_id":"<urn:uuid:4f565426-3fd6-4273-b441-f81fae01e40b>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00425.warc.gz"} |
On Kelly and altruism
One-sentence summary: Kelly is not about optimizing a utility function; in general I recommend you either stop pretending you have one of those, or stop talking about Kelly.
There was a twitter thread that triggered some confusion amongst myself and some other people in a group chat I'm in.^
The relevant tweets are these (I've omitted some):
3) Let’s say you were offered a coin flip. 75% it comes up heads, 25% it comes up tails; 1:1 payout. How much would you risk?
4) There are a number of ways to approach this question, but to start: what do you want, in the first place? What’s your utility function?
5) In other words–how cool would it be to make \$10,000? How about \$1,000,000–is that 100 times as good?
For most people the answer is ‘no, it’s more like 10 times as good’. This is because of decreasing marginal utility of money.
8) One reasonable utility function here is U = log(W): approximating your happiness as logarithmic in your wealth. That would mean going from \$10k to \$100k is worth about as much as going from
\$100k to \$1m, which feels…. reasonable?
(this is what the Kelly Criteria assumes)
9) So, if you have \$100k, Kelly would suggest you risk half of it (\$50k). This is a lot! But also 75% odds are good.
10) What about a wackier bet? How about you only win 10% of the time, but if you do you get paid out 10,000x your bet size? (For now, let’s assume you only get to do this bet once.)
11) Kelly suggests you only bet \$10k: you’ll almost certainly lose. And if you kept doing this much more than \$10k at a time, you’d probably blow out.
That this bet is great expected value; you win 1,000x your bet size, way better than the first one! It’s just very risky.
12) In many cases I think \$10k is a reasonable bet. But I, personally, would do more. I’d probably do more like \$50k.
Why? Because ultimately my utility function isn’t really logarithmic. It’s closer to linear.
13) Sure, I wouldn’t care to buy 10,000 new cars if I won the coinflip. But I’m not spending my marginal money on cars anyway. I’m donating it.
And the scale of the world’s problems is…. Huge.
14) 400,000 people die of malaria each year. It costs something like \$5k to save one person from malaria, or \$2b total per year. So if you want to save lives in the developing world, you can
blow \$2b a year just on malaria.
15) And that’s just the start. If you look at the scale of funds spent on diseases, global warming, emerging technological risk, animal welfare, nuclear warfare safety, etc., you get numbers
reaching into the trillions.
16) So at the very least, you should be using that as your baseline: and kelly tells you that when the backdrop is trillions of dollars, there’s essentially no risk aversion on the scale of
thousands or millions.
17) Put another way: if you’re maximizing EV(log(W+\$1,000,000,000,000)) and W is much less than a trillion, this is very similar to just maximizing EV(W).
18) Does this mean you should be willing to accept a significant chance of failing to do much good sometimes?
Yes, it does. And that’s ok. If it was the right play in EV, sometimes you win and sometimes you lose.
19) And more generally, if you look at everyone contributing to the cause as one portfolio–which is certainly true from the perspective of the child dying from malaria–they aren’t worried about
who it was that funded their safety.
22) So given all that, why not bet all \$100k? Why only \$50k?
Because if you bet \$100k and lose, you can never bet again. And to the extent you think you have future ways to provide value that are contingent on having some amount of funding, it can be
important to keep that.
The thing we were trying to figure out was, is his math right? And here's my current understanding of that matter.
On Kelly
The first thing I'd say is, I think the way he talks about Kelly here is confusing. My understanding is:
Under a certain betting framework, if you place bets that each maximize expected log-money, then you get (something good). See Appendix Ⅰ for the definition of the framework, if you want the
technical details.
If you happen have a utility function, and that utility function increases logarithmically with money, then you maximize your expected utility while also getting (something good).
If you happen to have a utility function, and that utility function increases linearly with money - or something else other than logarithmically - then you have to choose between maximizing your
expected utility and getting (something good). And by definition, you'd rather maximize your expected utility. (More likely: that's not your utility function. Even more likely: you don't have a
utility function.)
(I don't think any human has a utility function.^ I think it can be a useful shorthand to talk as though we do, sometimes. I think this is not one of those times. Especially not a utility function
that can be expressed purely in terms of money.)
The (something good) is that, over a long enough time, you'll almost certainly get more money than someone else who was offered the same bets as you and started with the same amount of money but
regularly bet different amounts on them.
This is NOT the same thing as maximizing your average (AKA "expected") amount of money over time. "Almost certainly" hides a small number of outcomes that make a lot of difference to that
calculation. Someone who repeatedly bets their entire bankroll will on average have more money than a Kelly bettor; it's just all concentrated in a single vanishingly unlikely branch where they're
incredibly wealthy, and the rest of the time they have nothing. Someone who repeatedly bets more than Kelly but less than their entire bankroll, will on average have more than the Kelly bettor but
less than the full-bankroll bettor; but still less than the Kelly bettor almost all the time, and very rarely much more.
It still sounds like a very good thing to me! Like, do I want to almost certainly be the richest peson in the room? Do I want to maximize my median payoff, and the 1st percentile and 99th percentile
and in fact every percentile, all at once? Oh, and while I'm at it, maximize my most-likely payoff and minimize "the average time I'll take to reach any given amount of money much more than what I
have now"? Yes please!
(Oh, also, I don't need to choose whether I'm getting that good thing for money or log-money or what. It's the same for any monotonically increasing function of money.)
Separately from that: yeah, I think going from \$10k to \$100k sounds about as good as going from \$100k to \$1m. So if I'm in a situation where it makes sense to pretend I have a utility function,
then it's probably reasonable to pretend my supposed utility function is logarithmic in money.
So that's convenient. I dunno if it's a coincidence or what, but it's useful. If I tried to pretend my utility function was linear in money then I'd be sad about losing that good thing, and then it
would be hard to keep pretending.
To me, Kelly is about getting that good thing. If you have a utility function, just place whatever bet size maximizes expected utility. If instead you want to get that good thing, Kelly tells you how
to do that, under a certain betting framework. And the way to do that is to place bets that each maximize expected log-money.
If you have a utility function and it's proportional to log-money, then you'll happen to get the good thing; but far more important than that, will be the fact that you're maximizing expected
log-money. If you have a utility function and it's different, and you bet accordingly, then a Kelly bettor will almost certainly be richer than you over time; but you're (for now) sitting on a bigger
pile of expected utility, which is what you care about.
Or maybe you want to mix things up a bit. For example, you might care a bit more about your average returns, and a bit less about being the richest person in the room, than a Kelly bettor. Then you
could bet something above the Kelly amount, but less than your full bankroll. You'll almost certainly end up with less than the Kelly bettor, but on average you'll still earn more than them thanks to
unlikely branches.
I'm not sure what to call this good thing. I'm going to go with "rank-optimizing" one's bankroll, focusing on the "be the richest person in the room" part; though I worry that it suggests competing
with other people, where really you're competing with counterfactual versions of yourself. See Appendix Ⅱ for an (admittedly flawed) technical definition of rank-optimization; also, I want to clarify
a few things about it:
• It might be a meaningful concept in situations unlike the betting framework we're currently talking about.
• In some situations, different good things about rank-optimization might not all come together. You might need to choose between them.
• Similarly, in some situations, rank-optimization might not come from maximizing expected log-money. (When it doesn't, might one still have a utility function that's maximized in expectation by
rank-optimizing one's bankroll? I think the answer is roughly "technically yes but basically no", see Appendix Ⅲ.)
So in this lens, the author's argument seems confused. "My utility function is linear in money, so Kelly says" no it doesn't, if you have a utility function or if you're maximizing the expected value
of anything then Kelly can go hang.
…but not everyone thinks about Kelly the same way I do, and I don't necessarily think that's wrong of them. So, what are some non-confused possibilities?
One is that the author has a utility function that's roughly linear in his own wealth. Or, more likely, roughly values money in a way that's roughly linear in his own wealth, such that
rank-optimizing isn't optimizing according to his preferences. And then I think the argument basically goes through. If you want to maximize expected log of "money donated to charity", then yes, that
will look a lot like maximizing expected "money you personally donate to charity", assuming you don't personally donate a significant fraction of it all. (If you want to maximize expected log of
"money donated effectively to charity", that's a smaller pot.) This has nothing to do with Kelly, according to me.
Another is that the author wants to rank-optimize the amount of money donated to charity. In that case I think it doesn't matter that the backdrop is trillions of dollars. If he's acting alone, then
to rank-optimize the total amount donated to charity, he should rank-optimize the amount he personally donates.
But here we come to the "everyone contributing to the cause" argument.
Suppose you have two people who each want to rank-optimize their own bankroll. Alice gets offered a handful of bets, and Kellies them. Bob gets offered a handful of bets, and Kellies them.
And now suppose instead they both want to rank-optimize their total bankroll. So they combine them into one. Whenever Alice gets a bet, she Kellies according to their combined bankrolls. Whenever Bob
gets a bet, he Kellies according to their combined bankrolls. And in the end, their total bankroll will almost certainly be higher than the sum of the individual bankrolls, in the first case.
…Well, maybe. I think the value here doesn't come from sharing their money but from sharing their bets. I've assumed the combined bankroll gets all of the bets from either of the individual ones.
That might not be the case - consider betting on a sports match. Ignoring transaction costs, it doesn't make a difference if one of them Kellies their combined bankroll, or each of them Kellies their
individual bankrolls. "Each of them Kellies their combined bankroll" isn't an option in this framework, so teaming up doesn't help.
But I do think something like this, combined with reasonable assumptions about charity and how bets are found, suggests betting above Kelly. Like, maybe Alice and Bob don't want to literally combine
their bankrolls, but they do trust each other pretty well and are willing to give or lend each other moderate amounts of money, and the two of them encounter different bets. Then I think that to
rank-optimize their individual or combined bankrolls, each of them should probably be betting above Kelly.
Or maybe Alice doesn't encounter bets (or can't act on them or doesn't trust herself to evaluate them or…), but she does encounter Bob and Carol and Dennis and somewhat trusts all of them to be
aligned with her values. Then if she gives each of them some money, and is willing to give them more in future if they lose money, I think that she wants them to make above-Kelly bets. (Just giving
them more money to begin with might be more rank-optimal, but there might be practical reasons not to, like not having it yet.)
Does she want people to bet almost their entire bankrolls? Under strong assumptions, and if the total pool is big enough relative to the bettor… I'm not sure, but I think yes?
This relies on individual donors being small relative to the donor pool. When you're small, maximizing expected log of the pool size (which, in this framework, rank-optimizes the pool size) looks a
lot like maximizing your own expected contributions linearly. When you're big, that's no longer the case.
It doesn't depend on the size of the problem you're trying to solve. That number just isn't an input to any of the relevant calculations, not that I've found. It might be relevant if you're thinking
about diminishing marginal returns, but you don't need to think about those if you're rank-optimizing.
I'm not super confident about this part, so I'm leaving it out of the one-sentence summary. But I do think that rank-optimizing charity donations often means betting above Kelly.
So was the author's math right? Man, I dunno. I'm inclined to say no; he was hand waving in almost the right directions, but I currently think that if he'd tried to formalize his hand waving he'd
have made a key mistake. That being: I think that if you want to rank-optimize, the math says "sure, bet high right now, but slow down when you become a big part of the donor pool". I think maybe he
thought it said "…but slow down when you get close to solving all the world's problems". It's not entirely clear from the tweets though, in part because he was using the word Kelly in a place where I
think it didn't belong. Since I don't want to try comparing this theory to how he actually behaved in practice, I'll leave it there.
In any case I think I understand what's going on better than I used to. Kelly is not about optimizing a utility function.
Appendix Ⅰ: betting framework
Throughout the post I've been assuming a particular "betting framework". What I mean by that is the sequence of bets that's offered and the strategies available to the bettor.
The framework in question is:
• You get offered bets.
• Each bet has a certain probability that you'll win; and a certain amount that it pays out if you win, multiplied by your wager.
• You can wager any amount from zero up to your entire current bankroll.
• If you lose, you lose your entire wager.
• You don't get offered another bet until your first has paid off.
• You keep on receiving bets, and the distribution of bets you receive doesn't change over time.
Wikipedia's treatment relaxes the third and fourth conditions, but I think for my purposes, that complicates things.
Appendix Ⅱ: technical definition
In Kelly's original paper, he defines the growth rate of a strategy \( λ \) as
\[ G(λ) = \lim_{n → ∞} {1 \over n} \log {V_n(λ) \over V_0(λ)} \]
where \( V_n(λ) \) is the bettor's portfolio after \( n \) steps. This is awkward because \( V_n(λ) \) is a random variable, so so is \( G(λ) \). But in the framework we're using, in the space of
strategies "bet some fraction of our bankroll that depends on the parameters of the bet", \( G \) takes on some value with probability \( 1 \). Kelly betting maximizes that value. So we could try to
define rank-optimization as finding the strategy that maximizes the growth rate.
I find this awkward and confusing, so here's a definition that I think will be equivalent for the framework we're using. A strategy \( λ \) is rank-optimal if for all strategies \( μ \),
\[ \lim_{n → ∞} P(V_n(λ) ≥ V_n(μ)) = 1. \]
(And we can also talk about a strategy being "equally rank-optimal" as or "more rank-optimal" than another, in the obvious ways. I'm pretty sure this will be a partial order in general, and I suspect
a total order among strategy spaces we care about.)
I think this has both advantages and disadvantages over the definition based on growth rate. An advantage is that it works with super- or sub-exponential growth. (Subexponential growth like \( V_n =
n \) has a growth rate of \( 0 \), so it's not preferred over \( V_n = 1 \). Superexponential growth like \( V_n = e^{e^n} \) has infinite growth rate which is awkward.)
A disadvantage is it doesn't work well with strategies that are equivalent in the long run but pay off at different times. (If we consider a coin toss game, neither of the strategies "call heads" and
"call tails" will get a long-run advantage, so we can't use rank-optimality to compare them. The limit in the definition will approach \( {1 \over 2 } \).) I think this isn't a problem in the current
betting framework, but I consider it a major flaw. Hopefully there's some neat way to fix it.
What I don't currently expect to see is a betting framework and space of strategies where
• We can calculate a growth rate for each strategy;
• Rank-optimality gives us a total order on strategies;
• There are strategies \( λ, μ \) with \( G(λ) > G(μ) \) but \( μ \) is more rank-optimal than \( λ \).
I wouldn't be totally shocked by that happening, math has been known to throw me some curveballs even in the days when I could call myself a mathematician. But it would surprise me a bit.
Given this definition, it's clear that a rank-optimal strategy maximizes every percentile of return. E.g. suppose \( λ \) is more rank-optimal than \( μ \), but the median of \( V_n(μ) \) is higher
than the median of \( V_n(λ) \). Then we'd have \( P(V_n(μ) > V_n(λ)) ≥ {1 \over 4} \); so this can't hold in the limit.
It's also clear that rank-optimizing for money is the same as rank-optimizing for log-money, or for any monotonically increasing function of money. (Possible caveats around non-strict monotonic
functions and the long-run equivalence thing from above?)
In some situations a rank-optimal strategy might not maximize modal return. I'm not sure if it will always minimize "expected time to reach some payoff much larger than \( V_0 \)".
Appendix Ⅲ: rank-optimization as utility function
A utility function is a function from "states of the world" to real numbers, which represent "how much we value that particular state of the world", that satisfies certain conditions.
When we say our utility function is linear or logarithmic in money, we mean that the only part of the world we care to look at is how much money we have. We maximize our utility in expectation, by
maximizing-in-expectation the amount of money or log-money we have.
Suppose I say "my utility function is such that I maximize it in expectation by rank-optimizing my returns". What would that mean?
I guess it would mean that the part of the world state we're looking at isn't my money. It's my strategy for making money, along with all the other possible strategies I could have used and the
betting framework I'm in. That's weird.
It also means I'm not expecting my utility function to change in future. Like, with money, I have a certain amount of money now, and I can calculate the utility of it; and I have a random variable
for how much money I'll have in future, and I can calculate the utility of those amounts as another random variable. With rank-optimality, I'm not expecting my strategy to be more or less
rank-optimal in future. That's convenient because to maximize expected utility I just have to maximize current utility, but it's also weird.
For that matter, I haven't given a way to quantify rank-optimization. We can say one strategy is "more rank-optimal" than another but not "twice as rank optimal". So maybe I mean my utility function
has a \( 1 \) if I'm entirely rank-optimal and a \( 0 \) if I'm not? But that's weird too. If we can calculate growth rate then we can quantify it like that, I guess.
So in general I don't expect rank-optimizing your returns to maximize your expected utility, for any utility function you're likely to have; or even any utility function you're likely to pretend to
have. Not unless it happens to be the case that the way to rank-optimize your returns is also a way to maximize some more normal utility function like "expected log-money", for reasons that may have
nothing to do with rank-optimization.
Thanks to Justis Mills for comments; and to various members of the LW Europe telegram channel, especially Verglasz, for helping me understand this.
Posted on 24 November 2022
Tagged: rationality; math
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Quantum-Proof Cryptography made easy – with Zenroom
Whether or not the “Post-Quantum Encryptogeddon” is actually coming, it might be good to boost your defenses. Here is how.
Imagine waking up tomorrow, and reading in the news that someone has managed to build a quantum computer with enough qubit to destroy modern public-key cryptography (RSA, ECDH, DSA, ECDSA, …). You
would think that cryptography is dead, and that you and your data are no longer safe.
Let me reassure you: for the time being, you are not in danger. On one hand, quantum computers are still far from being capable of such actions; on the other, many cryptographers all over the globe
are busy developing software resistant to quantum attacks – including us at dyne.org!
All our work on quantum proof safety has been kindly supported by NLNet Foundation and the NGI Assure project.
The National Institute of Science and Technology (NIST) has been leading an effort to define cryptographic standards for new asymmetric encryption algorithms and digital signatures, capable of
withstanding foreseeable attacks made with quantum computers.
Post-Quantum Cryptography | CSRC
Draft FIPS 203, FIPS 204 and FIPS 205, which specify algorithms derived from CRYSTALS-Dilithium, CRYSTALS-KYBER and SPHINCS+, were published August 24, 2023. The public comment period will close
November 22, 2023. PQC Seminars Next Talk: TBD…
Nevertheless, there is still a major real threat: the so-called “capture now, decrypt later” attack. An attacker could steal your encrypted data today, and manage to decrypt it later with the
powerful tools that might be available in the future.
It is best to start using Quantum-Proof Cryptography as soon as possible! And of course, our crypto software “Zenroom” already does this.
Zenroom is a tiny secure execution environment that can be integrated into any platform and application, even on a chip or a web page. It can authenticate, authorize access and execute
human-readable smart contracts for blockchains, databases and much more.
Zenroom’s version 3 is including quantum-proof cryptography from its inception.
Using Zenroom, you can easily create programs that use quantum proof signatures just like any other signature scheme that is already supported and well documented.
Keep reading this article for a step-by-step guide. In the following examples, we are going to use Zenroom’s on-line playground Apiroom.net. Don’t worry: you can easily try it in your browser, no
installation required! Refer to this documentation for a quick introduction to Apiroom.
Now let’s dive into Zenroom’s Quantum-Proof features!
In the cryptographic world, signatures play a fundamental role to ensure the origin and authenticity of a message. The current standardized signature algorithm, that can be used also in Zenroom, is
ECDSA, but this algorithm is not Quantum-Proof! To overcome this issue, the Dilithium2 signature algorithm has been implemented in Zenroom. It is a lattice-based digital signature scheme, whose
security is based on the hardness of finding short vectors in lattices.
How can we use it, you might ask? It’s easier than you think, and you can do it by following the steps below. In a heartbeat, you will have signed your message!
Create a private key
As first step, you have to create your own personal Dilithium private key. To do that, once you have opened the Apiroom.net website, click on the ‘Examples’ button in the top left corner, and scroll
down until you see ‘QP Dilithium generate key’.
The last thing that you need to do is to press ‘Run’ in the top right corner, and you will have generated your Dilithium private key, which will be printed on the right side of your screen in base64
The code is:
Scenario ‘qp’ : Create the dilithium private key
Given I am ‘Alice’
When I create the dilithium key
Then print my ‘keyring’
• In the given phase you declare who you are, so feel free to substitute “Alice” with your name, but make sure to remember it for later.
• In the when phase, you compute the Dilithium private key that is saved in your keyring.
• In the then phase you simply print your keyring.
Generate the public key
The public key can always be created by starting from the secret key, so we can generate it on the fly every time we need it instead of storing it. To generate the dilithium public key click on the
‘Examples’ button, then on ‘QP Dilithium generate public key’ and finally on ‘Run’.
If you want to use the Dilithium private key that you have generated in the previous step, you can simply copy the output of the previous code and paste it in the ‘Keys’ section, substituting what is
present there.
The code is:
Scenario ‘qp’: create the dilithium public key
Given I am ‘Alice’
Given I have my ‘keyring’
When I create the dilithium public key
Then print my ‘dilithium public key’
• In the Given phase, firstly state who you are and secondly upload your Keyring. If you are using your keyring, change “Alice” with the name used in the previous script.
• In the When phase the dilithium public key is computed.
• In the Then phase the dilithium public key is printed.
Sign a message
To sign a message you will need two things: the message to be signed and your secret key. The message can be of any kind, like a simple string, an array or a dictionary. To sign, click on the
‘Examples’ button, then on ‘QP Dilithium create signature’ and finally on ‘Run’.
If you want to use the Dilithium private key that you have generated in the first step then, as before, you can substitute the keyring in the ‘Keys’ section with your keyring. The message that will
be signed is the one present in the ‘Data’ section, so feel free to modify it.
The code is:
Scenario ‘qp’: Alice signs the message
Given I am ‘Alice’
Given I have my ‘keyring’
Given I have a ‘string’ named ‘message’
When I create the dilithium signature of ‘message’
Then print the ‘dilithium signature’
Then print the ‘message’
• In the given phase you state who you are, then upload your keyring and finally upload the message to be signed. If you are using your keyring, change “Alice” with the name used in the first
• In the when phase the dilithium signautre of the message is computed.
• In the then phase the dilithium signature and the message are printed.
Now we can send the dilithium public key (generated in the previous step), the dilithium signature and the message to the receiver, and he or she will be able to verify the authenticity of the
Since the public key can be always created starting from the private key, instead of computing and storing it, you can compute the dilithium public key along with the dilithium signature and send all
the output to the receiver, storing nothing more than the dilithium private key.
The code will be as follows:
Scenario ‘qp’: Alice signs the message
Given I am ‘Alice’
Given I have my ‘keyring’
Given I have a ‘string’ named ‘message’
When I create the dilithium signature of ‘message’
When I create the dilithium public key
Then print the ‘dilithium signature’
Then print the ‘message’
Then print my ‘dilithium public key’
The output of this code contains all that the receiver will need to verify the authenticity of the message.
Verify the signature
The last step is to verify the message’s dilithium signature. You will need three things: the message, the dilithium signature and the signer dilithium public key. To verify a signature click on the
‘Examples’ button, then on ‘QP Dilithium verify signature’ and finally on ‘Run’.
If you have created your dilithium public key, message and dilithium signature and you want to verify it, then you can simply remove everything that is present in the ‘Keys’ and ‘Data’ sections and
then copy and paste the output of the modified signature code in the ‘Data’ section.
The code is:
Scenario ‘qp’ : Bob verifies Alice signature
Given I have a ‘dilithium public key’ from ‘Alice’
Given I have a ‘string’ named ‘message’
Given I have a ‘dilithium signature’
When I verify the ‘message’ has a dilithium signature in ‘dilithium signature’ by ‘Alice’
When I write string ‘Verification of Dilithium signature succeded!’ in ‘verification’
Then print the ‘verification’
• In the Given phase you upload the signer’s dilithum public key, the message and the dilithium signature. If you have changed “Alice” with your name in the previous steps, then do the same here.
• In the When phase Alice’s dilithium signature of the message is verified. If you are using a different name, substitute “Alice” with the name you are using here as well.
• In the Then phase, if the verification succeeded, the string “Verification_of_Dilithium_signature_succeeded!” will be printed.
Key encapsulation mechanism
Key Encapsulation Mechanisms (KEM) are used to secure the exchange of symmetric key using Public-Key Algorithms. In Zenroom there is the possibility to choose between two different types of
Quantum-Proof KEM algorithms: Kyber512 and Streamlined NTRU Prime 761.
Kyber is a lattice-based KEM whose security is based on the hardness of solving the learning-with-errors (LWE) problem over module lattices.
Streamlined NTRU Prime security is based on the NTRU Key Recovery problem. Moreover, the last version of OpenSSH (9.0) uses the hybrid Streamlined NTRU Prime + x25519 key exchange method by default.
The following zencode examples will use Kyber, but if you want to try using Streamlined NTRU Prime then this can be simply done by changing the term kyber with ntrup.
Create the private and public key
This is equivalent to Dilithium. On the Apiroom.net website, click on the ‘Examples’ button in the top left corner, then on ‘QP Kyber generate key’ or ‘QP Kyber generate public key’ to create
respectively the private and the public key.
Private key:
Scenario ‘qp’ : Create the kyber private key
Given I am ‘Alice’
When I create the kyber key
Then print my ‘keyring’
Public key:
Scenario ‘qp’ : Create and publish the kyber public key
Given I am ‘Alice’
Given I have my ‘keyring’
When I create the kyber public key
Then print my ‘kyber public key’
Create the KEM
Now, anyone who has access to your kyber public key can create a shared secret and the corresponding ciphertext for you. To create this pair, simply click on the ‘Examples’ button, then on ‘QP Kyber
create kem’ and finally on ‘Run’.
The code is:
Scenario ‘qp’ : Bob create the kyber kem for Alice
Given I have a ‘kyber public key’ from ‘Alice’
When I create the kyber kem for ‘Alice’
Then print the ‘kyber secret’ from ‘kyber kem’
Then print the ‘kyber ciphertext’ from ‘kyber kem’
• In the given phase you upload Alice’s kyber public key.
• In the when phase the Kyber pair {Shared-Secret, Ciphertext} is computed and saved under the names kyber secret and kyber ciphertext and grouped inside a dictionary named kyber kem.
• In the then phase the kyber secret and the kyber ciphertext are printed.
The kyber secret is the symmetric key that will be use later to exchange information encrypted with some symmetric cipher. Thus you have to keep it secret, and send over the channel only the kyber
ciphertext. Alice will need nothing more to retrieve the kyber secret.
Retrieve the secret
The last step is to retrieve the kyber secret from the kyber ciphertext; in this case, Alice will also receive the kyber secret. We are doing this only to compare it with the secret that was
recreated and show that the two objects match. This will not happen in real life applications. To recreate the kyber secret, click on the ‘Examples’ button, then on ‘QP Kyber recreate secret from
ciphertext’ and finally on ‘Run’.
The code is:
Scenario ‘qp’ : Alice create the kyber secret
Given that I am known as ‘Alice’
Given that I have my ‘keyring’
Given I have a ‘kyber ciphertext’
Given I have a ‘base64’ named ‘kyber secret from Bob’
When I create the kyber secret from ‘kyber ciphertext’
When I verify ‘kyber secret from Bob’ is equal to ‘kyber secret’
When I write string ‘Verification of kyber cyphertext succeded!’ in ‘verification’
Then print ‘verification’
Then print ‘kyber secret’
• In the given phase, declare who you are, upload your keyring, the kyber ciphertext and the kyber secret computed by Bob in the previous step.
• In the when phase the kyber secret is retrieved from the kyber ciphertext and a check is performed to see if it matches the secret computed by Bob.
• In the then phase the kyber secret is printed.
So far we have talked about the security of these cryptographic primitives, but security never comes without a cost. As you have seen before, the first downside is the length of the keys, signatures
and ciphertexts.
Sizes of private and public keys in bytes.
Dilithium2 generates a 2420 bytes signature and, in order to encapsulate a 32 bytes secret Kyber512 and Streamlined NTRU Prime 761, creates a ciphertext of 768 and 1039 bytes respectively.
Now we will investigate the time and memory consumed by each of these Quantum-Proof algorithms, and compare them to ECDSA/ECDH. The results you will see are obtained running the tests that you can
find here for the signature scheme and here for the KEM schemes.
The signature is composed of four main parts: the generation of the private key, the generation of the public key, the signature and the verification. For each of them I have performed 10.000 tests
and took the mean time and mean memory consumed.
Time (µs) and memory (B) consumed by Dilithium2 and ECDSA, computing the private and the public keys.
As you can see, the key generation time and memory are not very different between the two algorithms, even if the Dilithium2 keys are much longer.
The test on signature and verification is done on different message lengths: 100, 500, 1000, 2.500, 5.000, 7.500 and 10.000 bytes. For each length, the test has always been performed 10.000 times.
Time (µs) and memory (B) consumed by Dilithium2 and ECDSA singature and verification.
Also in this case, the time and memory consumed by the two algorithms are really close to each other. In order to have a better view of the time consumed, you can have a look at the following graphs:
So, the only downside of the Dilithium2 signature scheme seems to be the length of the keys and of the signature!
Key Encapsulation Mechansim
The KEM algorithm is composed of four main parts: the generation of the private key, the generation of the public key, the encapsulation/encryption and the decryption. For each of them I have
performed 10.000 tests and took the mean time and mean memory consumed.
Time (µs) and memory (B) consumed by ECDH, Kyber512 and Streamlined NTRU Prime computing the private and public keys.
In the above table, we can see that kyber512 is even faster than ECDH in the computation of private and public keys, while Stremlined NTRU Prime takes a lot more time to compute the private keys, but
it is faster than Kyber512 in the generation of the public key.
Looking at the encapsulation part, ECDH simply encrypts a message so, in order to have a fair comparison, we encrpyted a 32 byte random string. This because the secret exchanged using Kyber512 or
Stremlined NTRU Prime is composed of 32 bytes.
Time (µs) and memory (B) consumed by ECDH, Kyber512 and Streamlined NTRU Prime encapsulation/encryption and decryption.
The results shows that, also in this case, Kyber512 is faster than ECDH, while Stremlined NTRU Prime is a little bit faster than ECDH in the encryption part, while it is slower in the decryption
Thus, also for these algorithms, we find that time consumption and memory usage are not an issue, with the private key generation of Streamlined NTRU Prime schemes being the exception.
Even if the theory behind Quantum-Proof cryptography is really complex and hard to understand: in practice, as you have seen, it is not difficult to use! Moreover, it is as fast as modern
cryptographics and also the memory used is almost the same. So, what are you waiting for? Download Zenroom and start using quantum-proof cryptography to keep your data safe!
Many thanks to the NLnet Foundation for believing in this project and supporting our work on quantum proof safety; as well to the Dyne.org team, especially Alberto Lerda, Denis ‘Jaromil’ Roio and
Andrea D’Intino, for all their precious help and teamwork.
Tune in to the discussion 💬
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RANDOM 2020
Volume 19
(2022) Article 5 pp. 1-3
Guest Editors' Foreword
This collection contains the expanded and fully refereed versions of selected papers presented at the 24th International Conference on Randomization and Computation (RANDOM 2020), and the 23rd
International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX 2020). Due to COVID-related travel restrictions, the conferences were jointly organized in a
virtual setup on August 17--19, 2020.
The proceedings of the meetings was published in the Dagstuhl LIPIcs series. APPROX published 34 contributed papers and RANDOM published 30 contributed papers, selected by the program committees. The
total number of submissions was 67 for each conference.
In consultation with the RANDOM PC, PC chair and guest editor Raghu Meka invited three papers to this Special Issue and the authors of the following two papers accepted the invitation:
• “Iterated Decomposition of Biased Permutations Via New Bounds on the Spectral Gap of Markov chains” by Sarah Miracle, Amanda Streib and Noah Streib
• “Reaching a Consensus on Random Networks: The Power of Few” by Linh Tran and Van Vu.
In consultation with the APPROX PC, PC chair and guest editor Jarosław Byrka invited the following three papers to this Special Issue.
• “Pinning Down the Strong Wilber 1 Bound for Binary Search Trees” by Parinya Chalermsook, Julia Chuzhoy and Thatchaphol Saranurak
• “Maximizing the Correlation: Extending Grothendieck's Inequality to Large Domains” by Dor Katzelnick and Roy Schwartz
• “Parametrized Metrical Task Systems” by Sébastien Bubeck and Yuval Rabani.
These five papers were refereed in accordance with the rigorous standards of Theory of Computing.
We would like to thank the authors for their contributions and the anonymous referees for their hard work that helped improve this issue. We are especially indebted to the referees for their detailed
and high quality reviews.
It was a pleasure to edit this Special Issue for Theory of Computing.
Jarosław Byrka
Guest Editor
for APPROX 2020
Raghu Meka
Guest Editor
for RANDOM 2020
APPROX 2020 Program Committee
Nikhil Bansal, CWI \& TU Eindhoven
Jarosław Byrka , U. Wrocław, PC chair
Andreas Emil Feldmann, Charles U., Prague
Naveen Garg, IIT Delhi
Anupam Gupta, Carnegie Mellon
Pasin Manurangsi, Google Research
Evangelos Markakis, AUEB, Athens
Nicole Megow, U. Bremen
Marcin Mucha, U. Warsaw
Harald Räcke, TU Munich
Laura Sanità, TU Eindhoven & U. Waterloo
Chaitanya Swamy, U. Waterloo
Jakub Tarnawski, Microsoft Research
Anke van Zuylen, William and Mary
David Williamson, Cornell
RANDOM 2020 Program Committee
Nima Anari, Stanford
Eshan Chattopadhyay, Cornell
Gil Cohen, Tel Aviv U.
Parikshit Gopalan, VmWare Research
Prahladh Harsha, Tata Institute of Fundamental Research
Sam Hopkins, UC Berkeley
Valentine Kabanets, Simon Fraser Un.
Gautam Kamath, U. Waterloo
Tali Kaufman, Bar-Ilan U.
Yin-Tat Lee, U. Washington
Sepideh Mahabadi, TTIC Chicago
Raghu Meka, UCLA, PC chair
Jelani Nelson, UC Berkeley
Ryan O'Donnell, Carnegie Mellon
Ilya Razenshteyn, Microsoft Research
Barna Saha, UC Berkeley
Tselil Schramm, Stanford
Madhu Sudan, Harvard
Avishay Tal, UC Berkeley
Eric Vigoda, Georgia Tech
Mary Wootters, Stanford
Brief synopses of papers in the Special Issue
• “Reaching a Consensus on Random Networks: The Power of Few” by Linh Tran and Van Vu.
This paper studies a classical question in population dynamics: Imagine we have $n$ people connected by a graph, and each node starts with a red or blue color. Each subsequent day, every person
revises their color based on some function of the colors of their neighbors. Let us say that a color wins if all people are of that color. How sensitive is the winning color to the initial
configuration? The paper shows, surprisingly, that under the natural `majority rule' (a vertex adopts the color of the majority of its neighbors), if the graph is a random one, then flipping a
constant number of vertices near the decision boundary will change the color with a high probability. That is, if there are $n/2+c$ nodes of one color at the beginning, then that color is very
likely to win. The main point is that the advantage needed to make one color the overwhelming favorite does not depend on$ n$. For instance, if there are $n/2+5$ red nodes initially, red wins
within four days with probability greater than .9. The key difficulty in analyzing the dynamics is that after one step, the colors of the nodes and the random graph are dependent. Hence, it is
difficult to apply concentration inequalities. The authors find a clever way to overcome such dependency issues and obtain a tight analysis of the dynamics.
• “Pinning Down the Strong Wilber 1 Bound for Binary Search Trees” by Parinya Chalermsook, Julia Chuzhoy and Thatchaphol Saranurak
The Dynamic Optimality conjecture of Sleator and Tarjan is relatively easy to state, but remains one of the most intriguing open problems in the area of data structures. Here it is: we want to
maintain a dynamic binary search tree (BST) as some set of elements is accessed via a request sequence. Since the access sequence may have some structure, we are allowed to change the BST in some
local ways (via “rotations”) to reduce the access cost. The Dynamic Optimality conjecture says: for each sequence of accesses, the total cost incurred by the Splay Tree data structure is within a
constant factor of the optimal cost (the cost incurred by the best dynamic BST for that sequence). We can also ask a weaker question: does there exist any algorithm that performs almost optimally
on each access sequence? We do not yet know. In order to get such a universally optimal algorithm, these questions force us to understand the power and inherent trade-offs of basic data
structures like BSTs. What is the optimal cost of a dynamic BST on some sequence? Previous attempts to reason about this optimal cost use one of two bounds proved by Wilbur in 1986. And until
recently it seemed conceivable that either of these bounds was within a constant factor of the optimal cost. This paper shows that the first bound (WB-1) can be a factor of nearly $\Omega(\log \
log n)$ away from the optimal cost on some instances. [Lecomte and Weinstein independently proved the same gap.] Moreover, the paper gives another bound, called the Guillotine bound, which may be
useful in resolving the conjecture. Finally, they ask the algorithmic question: given a sequence, how to compute the optimal cost on it? The final result of this paper is an algorithm that
smoothly translates between an $O(\log \log n)$-approximation in polynomial time, and an exact algorithm in exponential time. We do not know how to compute a constant-approximation in polynomial
time. The Dynamic Optimality conjecture still remains tantalizingly open, but this paper deepens our understanding of this fascinating question.
Keywords: foreword, special issue, APPROX-RANDOM 2020
ACM Classification: G.3, F.2
AMS Classification: 68Q25 | {"url":"https://theoryofcomputing.org/articles/v019a005/","timestamp":"2024-11-07T02:38:53Z","content_type":"text/html","content_length":"13641","record_id":"<urn:uuid:0465c017-4b7e-4311-9101-8753f676e6b3>","cc-path":"CC-MAIN-2024-46/segments/1730477027951.86/warc/CC-MAIN-20241107021136-20241107051136-00340.warc.gz"} |
A Note on General Sliding Window Processes
Let f: R^k→[r] = {1, 2,…,r} be a measurable function, and let {U[i]}[i∈N] be a sequence of i.i.d. random variables. Consider the random process {Z[i]}[i∈N] defined by Z[i] = f(U[i],…,U[i+k-1]). We
show that for all q, there is a positive probability, uniform in f, that Z[1] = Z[2] = … = Z[q]. A continuous counterpart is that if f: R^k → R, and U[i] and Z[i] are as before, then there is a
positive probability, uniform in f, for Z[1],…,Z[q] to be monotone. We prove these theorems, give upper and lower bounds for this probability, and generalize to variables indexed on other lattices.
The proof is based on an application of combinatorial results from Ramsey theory to the realm of continuous probability.
All Science Journal Classification (ASJC) codes
• Statistics and Probability
• Statistics, Probability and Uncertainty
• D-dependent
• De Bruijn
• K-factor
• Ramsey
Dive into the research topics of 'A Note on General Sliding Window Processes'. Together they form a unique fingerprint. | {"url":"https://collaborate.princeton.edu/en/publications/a-note-on-general-sliding-window-processes","timestamp":"2024-11-08T18:18:40Z","content_type":"text/html","content_length":"48226","record_id":"<urn:uuid:1f175018-47a9-4598-b7a5-eee13ffe2c93>","cc-path":"CC-MAIN-2024-46/segments/1730477028070.17/warc/CC-MAIN-20241108164844-20241108194844-00482.warc.gz"} |
How to Split Numbers and Text from String in ExcelHow to Split Numbers and Text from String in Excel
How to Split Numbers and Text from String in Excel
Many times I get mixed data from field and server for analysis. This data is usually dirty, having column mixed with number ans text. While doing data cleaning before analysis, I separate numbers and
text in separate columns. In this article, I’ll tell you how you can do it.
So one our friend on Exceltip.com asked this question in the comments section. “How do I separate numbers coming before a text and in the end of text using excel Formula. For example 125EvenueStreet
and LoveYou3000 etc.”
To extracting text, we use RIGHT, LEFT, MID and other text functions. We just need to know the number of texts to extract. And Here we will do the same first.
Extract Number and Text from a String when Number is in End of String
For above example I have prepared this sheet. In Cell A2, I have the string. In cell B2, I want the text part and in C2 the Number Part.
So we just need to know the position from where number starts. Then we will use Left and other function. So to get position of first number we use below generic formula:
Generic Formula to Get Position of First Number in String:
This will return the position of first number.
For above example write this formula in any cell.
Extract Text Part
It will return 15 as the first number which is found is at 15th position in Text. I will explain it later.
Now, to get Text, from left we just need to get 15-1 character from string. So we will use
LEFT function to extract text.
Formula to Extract Text from Left
Here we just subtracted 1 from what ever number returned by MIN(SEARCH({0,1,2,3,4,5,6,7,8,9},A5&"0123456789")).
Extract Number Part
Now to get numbers we just need to get number characters from 1st number found. So we calculate the total length of string and subtract the position of first number found and add 1 to it. Simple.
Yeah it’s just sound complex, it is simple.
Formula to Extract Numbers from Right
Here we just got total length of string using LEN function and then subtracted the position of first found number and then added 1 to it. This gives us total number of numbers. Learn more here about
extracting text using LEFT and RIGHT functions of Excel.
So the LEFT and RIGHT function part is simple. The Tricky part is MIN and SEARCH Part that gives us the position of first found number. Let’s understand that.
How It Works
We know how LEFT and RIGHT function work. We will explore the main part of this formula that gets the position of first number found and that is: MIN(SEARCH({0,1,2,3,4,5,6,7,8,9},String&"0123456789")
The SEARCH function returns the position of a text in string. SEARCH(‘text’,’string’) function takes two argument, first the text you want to search, second the string in which you want to search.
□ Here in SEARCH, at text position we have an array of numbers from 0 to 9. And at string position we have string which is concatenated with "0123456789" using & operator. Why? I’ll tell you.
□ Each element in the array {0,1,2,3,4,5,6,7,8,9} will be searched in given string and will return its position in array form string at same index in array.
□ If any value is not found, it will cause an error. Hence all formula will result into an error. To avoid this, we concatenated the numbers "0123456789" in text. So that it always finds each
number in string. These numbers are in the end hence will not cause any problem.
□ Now The MIN function returns the smallest value from array returned by SEARCH function. This smallest value will be the first number in string. Now using this NUMBER and LEFT and RIGHT
function, we can split the text and string parts.
Let’s examin our example. In A5 we have the string that has street name and house number. We need to separate them in different cells.
First let’s see how we got our position of first number in string.
□ MIN(SEARCH({0,1,2,3,4,5,6,7,8,9},A5&"0123456789")): this will translate into MIN(SEARCH({0,1,2,3,4,5,6,7,8,9},”Monta270123456789”))
Now, as I explained search will search each number in array {0,1,2,3,4,5,6,7,8,9} in Monta270123456789 and will return its position in an array form. The returned array will be
{8,9,6,11,12,13,14,7,16,17}. How?
0 will be searched in string. It is found at 8 position. Hence our first element is 8. Note that our original text is only 7 characters long. Get it. 0 is not a part of Monta27.
Next 1 will be searched in string and it is also not part of original string, and we get it’s position 9.
Next 2 will be searched. Since it is the part of original string, we get its index as 6.
Similarly each element is found at some position.
□ Now this array is passed to MIN function as MIN({8,9,6,11,12,13,14,7,16,17}). MIN returns the 6 which is position of first number found in original text.
And the story after this is quite simple. We use this number extract text and numbers using LEFT and RIGHT Function.
Extract Number and Text from a String When Number is in Beginning of String
In Above example, Number was in the end of the string. How do we extract number and text when number is in the beginning.
I have prepared a similar table as above. It just has number in the beginning.
Here we will use a different technique. We will count the length of numbers (which is 2 here) and will extract that number of characters from left of String.
So the method is =LEFT (string, count of numbers)
To Count the Number of characters this is the Formula.
Generic Formula to Count Number of Numbers:
☆ SUBSTITUTE function will replace each number found with “” (blank). If a number is found ti substituted and new string will be added to array, other wise original string will be added to
array. In this way, we will have array of 10 strings.
☆ Now LEN function will return length of characters in an array of those strings.
☆ Then, From length of original strings, we will subtract length of each string returned by SUBSTITUTE function. This will again return an array.
☆ Now SUM will add all these numbers. This is the count of numbers in string.
Extract Number Part from String
Now since we know the length of numbers in string, we will substitute this function in LEFT.
Since We have our string an A11 our:
Formula to Extract Numbers from LEFT
Extract Text Part from String
Since we know number of numbers, we can subtract it from total length of string to get number alphabets in string and then use right function to extract that number of characters from right of the
Formula to Extract Text from RIGHT
How it Works
The main part in both formula is SUM(LEN(A11)-LEN(SUBSTITUTE(A11,{"0","1","2","3","4","5","6","7","8","9"},""))) that calculates the first occurance of a number. Only after finding this, we are able
to split text and number using LEFT function. So let’s understand this.
☆ SUBSTITUTE(A11,{"0","1","2","3","4","5","6","7","8","9"},""): This part returns an array of string in A11 after substituting these numbers with nothing/blank (“”). For 27Monta it will
return {"27Monta","27Monta","7Monta","27Monta","27Monta","27Monta","27Monta","2Monta","27Monta","27Monta"}.
☆ LEN(SUBSTITUTE(A11,{"0","1","2","3","4","5","6","7","8","9"},"")): Now the SUBSTITUTE part is wrapped by LEN function. This return length of texts in array returned by SUBSTITUTE
function. In result, we’ll have {7,7,6,7,7,7,7,6,7,7}.
☆ LEN(A11)-LEN(SUBSTITUTE(A11,{"0","1","2","3","4","5","6","7","8","9"},"")): Here we are subtracting each number returned by above part from length of actual string. Length of original
text is 7. Hence we will have {7-7,7-7,7-6,....}. Finally we will have {0,0,1,0,0,0,0,1,0,0}.
☆ SUM(LEN(A11)-LEN(SUBSTITUTE(A11,{"0","1","2","3","4","5","6","7","8","9"},""))): Here we used SUM to sum the array returned by above part of function. This will give 2. Which is number of
numbers in string.
Now using this we can extract the texts and number and split them in different cells. This method will work with both type text, when number is in beginning and when its in end. You just need to
utilize LEFT and RIGHT Function appropriately.
Use SplitNumText function To Split Numbers and Texts from A String
The above to methods are little bit complex and they are not useful when text and numbers are mixed. To split text and numbers use this user defined function.
=SplitNumText(string, op)
String: The String You want to split.
Op: this is boolean. Pass 0 or false to get text part. For number part, pass true or any number greater then 0.
For example, if the string is in A20 then,
Formula for extracting numbers from string is:
Formula for extracting text from string is:
Copy below code in VBA module to make above formula work.
Function SplitNumText(str As String, op As Boolean)
num = ""
txt = ""
For i = 1 To Len(str)
If IsNumeric(Mid(str, i, 1)) Then
num = num & Mid(str, i, 1)
txt = txt & Mid(str, i, 1)
End If
Next i
If op = True Then
SplitNumText = num
SplitNumText = txt
End If
End Function
This code simply checks each character in string, if its a number or not. If it is a number then it is stored in num variable else in txt variable. If user passes true for op then num is returned
else txt is returned.
This is the best way to split number and text from a string in my opinion.
You can download the workbook here if you want.
So yeah guys, these are the ways to split text and numbers in different cells. Let me know if you have any doubts or any better solution in the comments section below. Its always fun to interact with
Click the below link to download the working file:
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Split Numbers and Text from String in Excel
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b2sociality-ergmTerm-ae7e4336: Degree in ergm: Fit, Simulate and Diagnose Exponential-Family Models for Networks
This term adds one network statistic for each node in the second bipartition, equal to the number of ties of that node. For directed networks, see sender and receiver . For unipartite networks, see
sociality .
By default, nodes=-1 means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The
nodes argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels (?nodal_attributes) for details), where both the attribute and the sorted
nodes unique values are the vector of vertex indices (nb1 + 1):n , where nb1 is the size of the first bipartition and n is the total number of nodes in the network. Thus nodes=120 will include only
the statistic for the 120th node in the second biparition, while nodes=I(120) will include only the statistic for the 120th node in the entire network.
form character how to aggregate tie values in a valued ERGM
By default, nodes=-1 means that the statistic for the first node (in the second bipartition) will be omitted, but this argument may be changed to control which statistics are included. The nodes
argument is interpreted using the new UI for level specification (see Specifying Vertex Attributes and Levels (?nodal_attributes) for details), where both the attribute and the sorted unique values
are the vector of vertex indices (nb1 + 1):n , where nb1 is the size of the first bipartition and n is the total number of nodes in the network. Thus nodes=120 will include only the statistic for the
120th node in the second biparition, while nodes=I(120) will include only the statistic for the 120th node in the entire network.
character how to aggregate tie values in a valued ERGM
This term can only be used with undirected bipartite networks.
ergmTerm for index of model terms currently visible to the package.
For more information on customizing the embed code, read Embedding Snippets. | {"url":"https://rdrr.io/cran/ergm/man/b2sociality-ergmTerm-ae7e4336.html","timestamp":"2024-11-04T10:39:06Z","content_type":"text/html","content_length":"36677","record_id":"<urn:uuid:ac8f2545-c0c4-4b6c-85f8-79922dd35fff>","cc-path":"CC-MAIN-2024-46/segments/1730477027821.39/warc/CC-MAIN-20241104100555-20241104130555-00030.warc.gz"} |
multiply-strings | Leetcode
Similar Problems
Similar Problems not available
Multiply Strings - Leetcode Solution
LeetCode: Multiply Strings Leetcode Solution
Difficulty: Medium
Topics: math string simulation
Problem Statement:
Given two non-negative integers num1 and num2 represented as strings, return the product of num1 and num2, also represented as a string.
Example 1:
Input: num1 = "2", num2 = "3" Output: "6"
Example 2:
Input: num1 = "123", num2 = "456" Output: "56088"
The length of both num1 and num2 is < 110. Both num1 and num2 contain only digits 0-9. Both num1 and num2 do not contain any leading zero, except the number 0 itself. You must not use any built-in
BigInteger library or convert the inputs to integer directly.
One approach to solve the problem is to simulate the multiplication process we use in our school. The idea is to multiply each digit of the second number (i.e., num2) with each digit of the first
number (i.e., num1) and add the results at the appropriate positions to get the final product. We can store the result in a list and then convert it to a string.
1. Initialize a list res with length (m+n) and fill it with 0's where m and n are the length of num1 and num2 respectively.
2. Reverse both strings (num1 and num2) to start from the least significant digit.
3. Traverse num1 from right to left and multiply each digit with num2 from right to left. The product will have two digits, and we can keep the least significant digit at the current position and
carry the higher digit to the next position.
4. After completing the first multiplication, we will have m+n-1 digits in the result. If there is a carry at the last position, add it to the next position.
5. Repeat the same process for all digits of num1.
6. Remove the leading zeros from the result, and if the result is empty, return "0".
7. Convert the result list to a string and return it.
Time Complexity: O(m*n), where m and n are the lengths of num1 and num2 respectively, as we need to multiply each digit of num1 with each digit of num2.
Space Complexity: O(m+n), for the result list.
Python Code:
class Solution: def multiply(self, num1: str, num2: str) -> str:
m, n = len(num1), len(num2)
res = [0]*(m+n)
num1 = num1[::-1]
num2 = num2[::-1]
for i in range(m):
carry = 0
for j in range(n):
prod = int(num1[i])*int(num2[j])
pos = i+j
res[pos] += (prod%10 + carry)
carry = prod//10 + res[pos]//10
res[pos] = res[pos]%10
if carry:
res[i+j+1] += carry
while len(res)>1 and res[-1]==0:
return "".join(map(str, res[::-1])) if res else "0"
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Excel Order A List Of Numbers - OrdinalNumbers.com
Excel Formula Ordinal Numbers – There are a myriad of sets that are easily counted using ordinal numbers as a tool. They also can be used to generalize ordinal numbers. 1st One of the most
fundamental concepts of math is the ordinal number. It is a number that identifies the place of an item in … Read more | {"url":"https://www.ordinalnumbers.com/tag/excel-order-a-list-of-numbers/","timestamp":"2024-11-02T10:54:48Z","content_type":"text/html","content_length":"45761","record_id":"<urn:uuid:5101c692-9215-4b58-8737-464497c2f55f>","cc-path":"CC-MAIN-2024-46/segments/1730477027710.33/warc/CC-MAIN-20241102102832-20241102132832-00138.warc.gz"} |
In the Area
An artist’s depiction of two black holes merging.
On its own, a black hole is remarkably easy to describe. The only observable properties a black hole has are its mass, its electric charge (usually zero), and its rotation, or spin. It doesn’t matter
how a black hole forms. In the end, all black holes have the same general structure. Which is odd when you think about it. Throw enough iron and rock together and you get a planet. Throw together
hydrogen and helium, and you can make a star. But you could throw together grass cuttings, bubble gum, and old Harry Potter books, and you would get the same kind of black hole that you’d get if you
just used pure hydrogen.
This strange behavior of black holes is known as the no hair theorem, and it relates to what’s known as the information paradox. In short, since everything in the universe can be described by a
certain amount of information, and objects can’t just disappear, the total amount of information in the universe should be constant. But if you toss a chair into a black hole, it just adds to the
black hole’s mass and spin. All the information about the color of the chair, whether it’s made of wood or steel, and whether it’s tall or short is lost. So where did that information go?
Gr@v — Gravitation @ Aveiro University
A black hole seems to strip information from objects.
One solution to this information paradox could be possible thanks to Stephen Hawking. Back in 1974, he demonstrated that the event horizon of a black hole might not be absolute. Because of quantum
indeterminacy, black holes should emit a tiny amount of light now known as Hawking radiation. Hawking radiation has never been observed, but if it exists the information lost when objects enter a
black hole might be carried out of the black hole via this light. Thus the information isn’t truly lost.
If Hawking radiation is real, that also means that black holes follow the laws of thermodynamics. It’s an idea first proposed by Jacob Bekenstein. If black holes emit light, then they have to have a
thermal temperature. Starting from Bekenstein’s idea, several physicists have shown that there is a set of laws for black holes known as black hole thermodynamics.
Since you’re reading this article, you’re probably familiar with the second law of thermodynamics, which states that the entropy of any system must increase. This is the reason that a cup of hot
coffee cools down over time, slightly heating the room until the coffee and the room are all the same temperature. You never see a cold cup of coffee spontaneously heat up while slightly cooling the
room. Another way to state the second law is that heat flows from a hot object to surrounding cooler objects.
Isi, Maximiliano, et al
Gravitational wave data shows an increase in black hole area.
For black holes, the second law of thermodynamics applies to the area of a black hole’s event horizon. The Hawking temperature of a black hole is related to this area. The larger the black hole, the
lower its Hawking temperature. So the second law of black hole thermodynamics says that for any black hole merger the entropy must increase. That means the surface area of the resulting black hole
must be greater than the surface areas of the two original black holes combined. This is known as Hawking’s Area Theorem.
Of course, all of this is a bunch of mathematical theory. It’s what we expect given our understanding of physics, but proving it is a different matter. Now a study in Physical Review Letters has
given us evidence that it’s true.^1 The team looked at the very first observation of two merging black holes. The event is now known as GW150914 and was a merger of a 29 solar-mass black hole with a
36 solar-mass one. Using a new analysis method on the gravitational waves they produced, the team was able to calculate the event horizon surface areas for the original black holes. When they
compared them to the surface area of the final 62 solar-mass black hole, they found the total area increased.
The results have a confidence level of 97%, which is good but not strong enough to be considered clinching proof. But this method can be applied to other black hole mergers, and it is the first real
evidence that black hole thermodynamics is more than just a theory.
1. Isi, Maximiliano, et al. “Testing the black-hole area law with GW150914.” Physical Review Letters 127.1 (2021): 011103. ↩︎ | {"url":"https://briankoberlein.com/blog/in-the-area/","timestamp":"2024-11-03T23:18:06Z","content_type":"text/html","content_length":"22924","record_id":"<urn:uuid:1a52162f-2c0f-4586-a53e-f20dfb08d271>","cc-path":"CC-MAIN-2024-46/segments/1730477027796.35/warc/CC-MAIN-20241103212031-20241104002031-00150.warc.gz"} |