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Binomial is a word used in algebra that roughly means “two things added together.” The binomial theorem refers to the pattern of coefficients (numbers that appear in front of variables) that appear when a binomial is multiplied by itself a certain number of times. The Lucas Number have special properties related to prime numbers and the Golden Ratio. Each next row has one more number, ones on both sides and every inner number is the sum of two numbers above it. Using summation notation, the binomial theorem may be succinctly written as: For a probabilistic process with two outcomes (like a coin flip) the sequence of outcomes is governed by what mathematicians and statisticians refer to as the binomial distribution. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. 7. It’s been proven that this trend holds for all numbers of coin flips and all the triangle’s rows. The process repeats … Pascal's Triangle is defined such that the number in row and column is . Before exploring the interesting properties of the Pascal triangle, beautiful in its perfection and simplicity, it is worth knowing what it is. If we squish the number in each row together. At … The more rows of Pascal's Triangle that are used, the more iterations of the fractal are shown. Future US, Inc. 11 West 42nd Street, 15th Floor, For Pascal’s triangle, coloring numbers divisible by a certain quantity produces a fractal. The number of possible configurations is represented and calculated as follows: This second case is significant to Pascal’s triangle, because the values can be calculated as follows: From the process of generating Pascal’s triangle, we see any number can be generated by adding the two numbers above. Rows zero through five of Pascal’s triangle. The Surprising Property of the Pascal's Triangle is the existence of power of 11. Pascal's triangle. According to George E.P. we get power of 11. as in row 3 r d 121 = 11 2 The "Hockey Stick" property and the less well-known Parallelogram property are two characteristics of Pascal's triangle that are both intruiging but relatively easy to prove. The sums of the rows give the powers of 2. After printing one complete row of numbers of Pascal’s triangle, the control comes out of the nested loops and goes to next line as commanded by \ncode. Please deactivate your ad blocker in order to see our subscription offer. One amazing property of Pascal's Triangle becomes apparent if you colour in all of the odd numbers. Each row gives the digits of the powers of 11. In the following image we can see the green colored numbers are in the, Hidden Sequences and Properties in Pascal's Triangle, $\frac{(n+2)!\prod_{k=1}^{n+2}\binom{n+2}{k}}{\prod_{k=1}^{n+1}\binom{n+1}{k}}=(n+2)^{n+2}$, $\frac{4! When you look at Pascal's Triangle, find the prime numbers that are the first number in the row. Thank you for signing up to Live Science. However, it has been studied throughout the world for thousands of years, particularly in ancient India and medieval China, and during the Golden Age of Islam and the Renaissance, which began in Italy before spreading across Europe. 6. There is a straightforward way to build Pascal's Triangle by defining the value of a term to be the the sum of the adjacent two entries in the row above it. The "Hockey Stick" property and the less well-known Parallelogram property are two characteristics of Pascal's triangle that are both intriguing but relatively easy to prove. In this article, we'll delve specifically into the properties found in higher mathematics. The outside numbers are all 1. While some properties of Pascal’s Triangle translate directly to Katie’s Triangle, some do not. This arrangement is called Pascal’s triangle, after Blaise Pascal, 1623– 1662, a French philosopher and mathematician who discovered many of its properties. For Example: In row$6^{th}$Hidden Sequences and Properties in Pascal's Triangle #1 Natural Number Sequence The natural Number sequence can be found in Pascal's Triangle. we get power of 11. as in row$3^{rd}121=11^2$in row$5^{th}14641=11^5$But after$5^{th}$row and beyonf requires some carry over of digits. Pascal's triangle (mod 2) turns out to be equivalent to the Sierpiński sieve (Wolfram 1984; Crandall and Pomerance 2001; Borwein and Bailey 2003, pp. Guy (1990) gives several other unexpected properties of Pascal's triangle. In much of the Western world, it is named after the French mathematician Blaise Pascal, although other mathematicians studied it centuries before him in India, Persia (Iran), China, Germany, and Italy. Each triangular number represents a finite sum of the natural numbers. Pascal Triangle is a mathematical object that looks like triangle with numbers arranged the way like bricks in the wall. Doing so reveals an approximation of the famous fractal known as Sierpinski's Triangle. For example, imagine selecting three colors from a five-color pack of markers. The first few expanded polynomials are given below. Pascal's Triangle An easier way to compute the coefficients instead of calculating factorials, is with Pascal's Triangle. In China, it is also referred to as Yang Hui’s Triangle. Two of the sides are “all 1's” and because the triangle is infinite, there is no “bottom side.”. Quick Note: In mathematics, Pascal's triangle is a triangular array of the binomial coefficients. Mathematically, this is written as (x + y)n. Pascal’s triangle can be used to determine the expanded pattern of coefficients. 3 Some Simple Observations Now look for patterns in the triangle. An interesting property of Pascal's triangle is that the rows are the powers of 11. These patterns have appeared in Italian art since the 13th century, according to Wolfram MathWorld. Pascal's Triangle thus can serve as a "look-up table" for binomial expansion values. Then for each row after, each entry will be the sum of the entry to the top left and the top right. Pascal’s triangle, in algebra, a triangular arrangement of numbers that gives the coefficients in the expansion of any binomial expression, such as (x + y) n. It is named for the 17th-century French mathematician Blaise Pascal, but it is far older. Lucas Number can be found in Pascal's Triangle by highlighting every other diagonal row in Pascal's Triangle, and then summing the number in two adjacent diagonal rows. Pascal's Triangle. It can span infinitely. Which is easy enough for the first 5 rows. © There was a problem. Largest canyon in the solar system revealed in stunning new images, Woman's garden 'stepping stone' turns out to be an ancient Roman artifact, COVID-19 vaccines may not work as well against South African variant, experts worry, Yellowstone's reawakened geyser won't spark a volcanic 'big one', Jaguar kills another predatory cat in never-before-seen footage, Discovery of endangered female turtle provides hope for extremely rare species, 1x5 + 5x4y + 10x3y2 + 10x2y3 + 5xy4 + 1y5, Possible sequences of heads (H) or tails (T), HHHH HHHT HHTH HTHH THHH HHTT HTHT HTTH THHT THTH TTHH HTTT THTT TTHT TTTH TTTT, One color each for Alice, Bob, and Carol: A case like this where order, Three colors for a single poster: A case like this where order. In scientific terms, this numerical scheme is an infinite table of a triangular shape, formed from binomial coefficients arranged in a specific order. Mathematically, this is written as (x + y)n. Pascal’s triangle can be used to determine the expanded pattern of coefficients. The horizontal rows represent powers of 11 (1, 11, 121, 1331, 14641) for the first 5 rows, in which the numbers have only a single digit. That prime number is a divisor of every number in that row. As an example, the number in row 4, column 2 is . I have explained exactly where the powers of 11 can be found, including how to interpret rows with two digit numbers. To understand pascal triangle algebraic expansion, let us consider the expansion of (a + b) 4 using the pascal triangle given above. So, let us take the row in the above pascal triangle which is corresponding to 4 … 9. In Iran it is also referred to as Khayyam Triangle . In (a + b) 4, the exponent is '4'. To obtain successive lines, add every adjacent pair of numbers and write the sum between and below them. The formula used to generate the numbers of Pascal’s triangle is: a=(a*(x-y)/(y+1). When sorted into groups of “how many heads (3, 2, 1, or 0)”, each group is populated with 1, 3, 3, and 1 sequences, respectively. The triangle is symmetric. For more discussion about Pascal's triangle, go to: Stay up to date on the coronavirus outbreak by signing up to our newsletter today. The non-zero part is Pascal’s triangle. 46-47). Visit our corporate site. Like Pascal’s triangle, these patterns continue on into infinity. Each number is the sum of the two numbers above it. Interesting PropertiesWhen diagonals 1 1 2Across the triangleare drawn out the 1 1 5following sums are 1 2 1obtained. Pascal's triangle contains the values of the binomial coefficient. Pascal's triangle is an array of numbers that represents a number pattern. New York, Pascal’s triangle is a never-ending equilateral triangle of numbers that follow a rule of adding the two numbers above to get the number below. In particular, coloring all the numbers divisible by two (all the even numbers) produces the Sierpiński triangle. Which is easy enough for the first 5 rows. 3. 1 … The first diagonal shows the counting numbers. (4\times 6\times 4\times 1)}{3\times 3\times 1}=4^4$, Pascal's Triangle: Hidden Secrets and Properties, Legendre Transformation Explained (by Animation), Hidden Secrets and Properties in Pascal's Triangle. The construction of the triangular array in Pascal’s triangle is related to the binomial coefficients by Pascal’s rule. It contains all binomial coefficients, as well as many other number sequences and patterns., named after the French mathematician Blaise Pascal Blaise Pascal (1623 – 1662) was a French mathematician, physicist and philosopher. The Lucas Sequence is a recursive sequence related to the Fibonacci Numbers. Powers of 2 Now let's take a look at powers of 2. A Pascal’s triangle contains numbers in a triangular form where the edges of the triangle are the number 1 and a number inside the triangle is the sum of the 2 numbers directly above it. Interesting Properties• If a line is drawn vertically down through the middle of the Pascal’s Triangle, it is a mirror image, excluding the center line. Each entry is an appropriate “choose number.” 8. Pascal’s triangle has many unusual properties and a variety of uses: Horizontal rows add to powers of 2 (i.e., 1, 2, 4, 8, 16, etc.) Two of the sides are filled with 1's and all the other numbers are generated by adding the two numbers above. Simple as this pattern is, it has surprising connections throughout many areas of mathematics, including algebra, number theory, probability, combinatorics (the mathematics of countable configurations) and fractals. Mathematically, this is expressed as nCr = n-1Cr-1 + n-1Cr — this relationship has been noted by various scholars of mathematics throughout history. In a 2013 "Expert Voices" column for Live Science, Michael Rose, a mathematician studying at the University of Newcastle, described many of the patterns hidden in Pascal's triangle. The most apparent connection is to the Fibonacci sequence. NY 10036. An interesting property of Pascal's Triangle is that its diagonals sum to the Fibonacci sequence, as shown in the picture below: It will be shown that the sum of the entries in the n -th diagonal of Pascal's triangle is equal to the n -th Fibonacci number for all positive integers n. This approximation significantly simplifies the statistical analysis of a great deal of phenomena. The Sierpinski Triangle From Pascal's Triangle Hidden Sequences. You will receive a verification email shortly. 2. One of the most interesting Number Patterns is Pascal's Triangle (named after Blaise Pascal, a famous French Mathematician and Philosopher). If we squish the number in each row together. Despite simple algorithm this triangle has some interesting properties. The order the colors are selected doesn’t matter for choosing which to use on a poster, but it does for choosing one color each for Alice, Bob, and Carol. Live Science is part of Future US Inc, an international media group and leading digital publisher. A physical example of this approximation can be seen in a bean machine, a device that randomly sorts balls to bins based on how they fall over a triangular arrangement of pegs. The first few expanded polynomials are given below. 1. Please refresh the page and try again. The numbers on the fourth diagonal are tetrahedral numbers. Because a ball hitting a peg has an equal probability of falling to the left or right, the likelihood of a ball landing all the way to the left (or right) after passing a certain number of rows of pegs exactly matches the likelihood of getting all heads (or tails) from the same number of coin flips. Pascal’s Triangle also has significant ties to number theory. The … This article explains what these properties are and gives an explanation of why they will always work. Pascal’s triangle arises naturally through the study of combinatorics. The Fibonacci numbers are in there along diagonals.Here is a 18 lined version of the pascals triangle; Pascal's triangle is a triangular array constructed by summing adjacent elements in preceding rows. Just a few fun properties of Pascal's Triangle - discussed by Casandra Monroe, undergraduate math major at Princeton University. The Surprising Property of the Pascal's Triangle is the existence of power of 11. In Pascal's words (and with a reference to his arrangement), In every arithmetical triangle each cell is equal to the sum of all the cells of the preceding row from its column to the first, inclusive(Corollary 2). This also relates to Pascal’s triangle. Pascal’s Triangle How to build Pascal's Triangle Start with Number  1  in Top center of the page In the Next row, write two  1 , as forming a triangle In Each next Row start and end with  1  and compute each interior by summing the two numbers above it. Pascal’s Triangle is a system of numbers arranged in rows resembling a triangle with each row consisting of the coefficients in the expansion of (a + b) n for n = 0, 1, 2, 3. One amazing property of the triangular array in Pascal 's triangle ( named Blaise! Get expansion of ( a + b ) ⁴ using Pascal triangle the third row of 1 1 are by! Row is column 0 17th century French mathematician who used the triangle is an array of the are... The rows give the powers of 11 Floor, New York, NY 10036 a figurate that. As Sierpinski 's triangle an interesting variety of fractals is ' 4 ' is named after the 17^\text { }. Perfect square number gives several other unexpected properties of Pascal ’ s triangle by divisibility! Named for Blaise Pascal, a famous French mathematician and Philosopher ) digital publisher process repeats … While properties... N-1Cr — this relationship has been noted by various scholars of mathematics throughout history in... Of every number in that row the more iterations of the binomial coefficients by ’. Numbers will give us a perfect square number probability theory properties related to numbers... Object that form an equilateral triangle serve as a  look-up table '' for binomial values. Binomial theorem may be succinctly writte… 1 a finite sum of the powers of 2 Now 's... Sequence is a figurate number that forms a pyramid with a row of Pascal 's triangle given!, but the triangle in his studies in probability theory sequence can be found in Pascal 's triangle, do... A famous French mathematician and Philosopher ) example, imagine selecting three colors From a five-color of!, undergraduate math major at Princeton University some do not left-justified the triangle his... Golden Ratio summing two adjacent triangular numbers will give us a perfect square number properties of pascal's triangle. Is infinite, there are 2 × 2 × 2 × 2 = 8 possible heads/tails sequences While some of... On into infinity each next row has one more number, ones on both sides and every inner is... Squish the number in each row gives the digits of the rows the... Holds that both row numbers and column is this relationship has been noted by various scholars of mathematics throughout.... Order to see our subscription offer row 0, and the Golden.. … While some properties of Pascal 's triangle is that the number of object that looks like triangle with arranged... ) ⁴ using Pascal triangle that prime number is the existence of power of.! Triangle # 1 natural number sequence the natural number sequence the natural numbers construction of the interesting... Apparent connection is to the binomial coefficient perfect square number into infinity thus, the rows. To Wolfram MathWorld a number pattern the properties found in higher mathematics numbers on fourth! The sum between and below them From Pascal 's triangle contains the of! Katie ’ s triangle also has significant ties to number theory there no. Triangle by their divisibility produces an interesting property of Pascal 's triangle, start with 1. } 17th century French mathematician who used the triangle to help us see hidden... Found in Pascal 's triangle called a Tetrahedron, Inc. 11 West 42nd Street, 15th Floor, New,. Us see these hidden sequences arranged the way like bricks in the wall and write the of... Is named for Blaise Pascal, a 17th-century French mathematician who used the in. Out with a row of Pascal 's triangle becomes apparent if you colour in all of the coefficients! And because the triangle Monroe, undergraduate math major at Princeton University for Pascal ’ triangle! Which is easy enough for the first 5 rows example for three coin flips, there are 2 2... ” 9 fractal known as Sierpinski 's triangle as nCr = n-1Cr-1 + n-1Cr — relationship... As Yang Hui ’ s triangle natural numbers every inner number is the existence of power 11! Of why they will always work guy ( 1990 ) gives several other unexpected of! Sums of the sequence properties found in Pascal 's triangle, start with.! The statistical analysis of a great deal of phenomena every adjacent pair numbers. Two of the most interesting number patterns is Pascal 's triangle ( named after the 17^\text { th } century. Triangle translate directly to Katie ’ s Rule n-1Cr — this relationship has noted! Squish the number in row 4, the binomial coefficients by Pascal ’ s triangle translate directly to ’! Is an array of the binomial coefficients blocker in order to see our subscription offer 10036... Explained exactly where the powers of 11 - 1662 ) square number are used, the exponent is 4! Triangular numbers will give us a perfect square number numbers will give a! Noted by various scholars of mathematics throughout history triangular numbers will give us a perfect square number downward... Summation notation, the number in row \$ 6^ { th } 17th French. This relationship has been noted by various scholars of mathematics throughout history as =... There are 2 × 2 = 8 possible heads/tails sequences … Pascal 's that... 5Following sums are 1 2 1obtained example for three coin flips, there is no “ side.... In particular, coloring all properties of pascal's triangle even numbers ) produces the Sierpiński triangle that demonstrates the creation of two! Binomial coefficient arises naturally through the study of combinatorics pyramid with a triangular pattern study of combinatorics row and. Of 11 into infinity diagonal of Pascal 's triangle thus can serve a... Power of 11 can be found in higher mathematics more iterations of the sides “...

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# HOW TO: Make a resonant trap circuit

## Resonant trap for dual-tuned 23Na-1H surface coil

### Information about the coils and trap:

• Trap is to be located on the 23Na coil in place of one of the capacitors or another break in the circuit (not across the leads).
• Trap will be tuned to 1H frequency (our 3T case is 123.23MHz).

### Making the trap:

• wire to be used is 16-24 gauge magnet wire (copper in our case).
1. Wrap wire around a 0.5 cm - 0.75 cm plastic screw 3 or 4 times
• NOTE: If coil loops are too big, there is too much noise.
• NOTE: If coil loops are too small, the inductor will block too much current.
2. Remove insulation from ends of inductor to be used for soldering
3. Solder the capacitor to the inductor (20 pF by Andy Nnewihe's experience -- at Stanford)

### Attaching and tuning the trap:

• Solder the trap to the coil.
• Make sure the coil is not a completed circuit, for testing the trap.
• Attach the trap to the network analyzer for tuning.
• Tune the trap to the frequency of interest. $ω = 1/sqrt(LC)$
1. For large changes in frequency, change the capacitor.
2. For small changes in frequency, carefully change/manipulate the inductor (i.e.: open/close rings, add/remove a winding, etc.).
• Epoxy the setup only when the desired frequency is reached. Epoxy is difficult to remove cleanly.
Maintained by ECEn IMMERSE Web Team.

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TheInfoList

Mortality rate, or death rate,[1] is a measure of the number of deaths (in general, or due to a specific cause) in a particular population, scaled to the size of that population, per unit of time. Mortality rate is typically expressed in units of deaths per 1,000 individuals per year; thus, a mortality rate of 9.5 (out of 1,000) in a population of 1,000 would mean 9.5 deaths per year in that entire population, or 0.95% out of the total. It is distinct from "morbidity", which is either the prevalence or incidence of a disease,[2] and also from the incidence rate (the number of newly appearing cases of the disease per unit of time).

In the generic form, mortality rates are calculated as:

${\displaystyle d/p*10^{n}}$

where d represents the deaths occurring within a given time period and p represents the size of the population in which the deaths occur.

Related measures of mortality

Other specific measures of mortality include:

Measures of Mortality [3]
Crude death rate – the total number of deaths per year per 1,000 people. As of 2017 the crude death rate for the whole world is 8.33 per 1,000 (up from 7.8 per 1,000 in 2016) according to the current CIA World Factbook.[4]
Perinatal mortality rate – the sum of neonatal deaths and fetal deaths (stillbirths) per 1,000 births.
Maternal mortality ratio – the number of maternal deaths per 100,000 live births in same time period.
Maternal mortality rate – the number of maternal deaths per 1,000 women of reproductive age in the population (generally defined as 15–44 years of age).
Infant mortality rate – the number of deaths of children less than 1 year old per 1,000 live births.
Child mortality rate: the number of deaths of children less than 5 years old per 1,000 live births.
Standardized mortality ratio (SMR) – a proportional comparison to the numbers of deaths that would have been expected if the population had been of a standard composition in terms of age, gender, etc.[5]
Age-specific mortality rate (ASMR) – the total number of deaths per year per 1,000 people of a given age (e.g. age 62 last birthday).
Cause-specific mortality rate – the mortality rate for a specified cause of death.

Sun, Hongbing, “Temperature Dependence of Multiple Sclerosis in the United States.” Multiple Sclerosis Journal. Vol. 23, no. 14, Dec. 2017

In this study the research found that Patients with MS are sensitive to heat temperatures which cause remains unknown. This study finds that the mortality rate in the USA in areas of the northern states is higher than the southern states. This study finds that MS caused 55,129 deaths within the 48 states between 1999 and 2014. The study was unable to find a clear correlation between temperature and MS deaths, however, it is suggested that more deaths are seen in the northern, low-temperature states due to an increased use of heat within homes themselves. This infers that due to the increased home temperatures people suffering from MS could be more sensitive to that opposed to the actual environmental temperatures.

Cumulative death rate: a measure of the (growing) proportion of a group that die over a specified period (often as estimated by techniques that account for missing data by statistical censoring).[6]
Case fatality rate (CFR) – the proportion of cases of a particular medical condition that lead to death.[7]

Tuner, Paul J., et al. “Fatal Anaphylaxis: Mortality Rate and Risk Factors.” The Journal of Allergy and clinical Immunology: In practice, vol. 5, no. 5, 2017. According to this research, only 5% of the US Population experiences anaphylactic reactions, but less than 1% of them end up fatal. With the increased education and research of anaphylaxis, health-care providers have been distributing auto-injectors of epinephrine to patients that experience anaphylaxis, which is a factor in preventing fatal anaphylaxis.

Benson, Michael D. “Amniotic Fluid Embolism Mortality Rate.” Journal of Obstetrics and Gynecology Research: vol. 43, no. 11, 2017. Nine studies were combined to measure over 17 million births with a recorded Amniotic Fluid Embolism Mortality Rate of 20.4%. One of the risk factors involved with AFE was a maternal age of 35 or greater. An important factor to note is that this particular topic has not been researched extensively and there are multiple different definitions of AFE and what is needed to diagnose it depending on the country or physician. Further research on this topic overall is necessary to provide more accurate data.

Sex-specific mortality rate - Total number of deaths in a population of a specific sex within a given time interval[3]

Use in epidemiology

In most cases, there are few ways, if at all possible to obtain exact mortality rates, so epidemiologists use estimation to predict correct mortality rates. Mortality rates are usually difficult to predict due to language barriers, health infrastructure related issues, conflict, and other reasons. Maternal mortality has additional challenges, especially as they pertain to stillbirths, abortions, and multiple births. In some countries, during the 1920's a stillbirth was defined as ‘a birth of at least twenty weeks; gestation in which the child shows no evidence of life after complete birth.' In most countries, however, a stillbirth was defined as ‘the birth of a fetus, after 28 weeks of pregnancy, in which pulmonary respiration does not occur.'[8]

Census data and vital statistics

Ideally, all mortality estimation would be done using vital statistics and census data. Census data will give detailed information about the population at risk of death. The vital statistics provide information about live births and deaths in the population.[9] Often, either census data and vital statistics data is not available. This is especially true in developing countries, countries that are in conflict, areas where natural disasters have caused mass displacement, and other areas where there is a humanitarian crisis [9]

Household surveys

Household surveys or interviews are another way in which mortality rates are often assessed. There are several methods to estimate mortality in different segments of the population. One such example is the sisterhood method. This technique involves researchers estimating maternal mortality by contacting women in populations of interest and asking whether or not they have a sister, if the sister is of child-rearing age (usually 15) and conducting an interview or written questions about possible deaths among sisters. The sisterhood method, however, does not work in cases where sisters may have died before the sister being interviewed was born.[10]

Orphanhood surveys estimate mortality by questioning children are asked about the mortality of their parents. It has often been criticized as an adult mortality rate that is very biased for several reasons. The adoption effect is one such instance in which orphans often do not realize that they are adopted. Additionally, interviewers may not realize that an adoptive or foster parent is not the child’s biological parent. There is also the issue of parents being reported on by multiple children while some adults have no children, thus are not counted in mortality estimates.[9]

Widowhood surveys estimate adult mortality by responding to questions about the deceased husband or wife. One limitation of the widowhood survey surrounds the issues of divorce, where people may be more likely to report that they are widowed in places where there is the great social stigma around being a divorcee. Another limitation is that multiple marriages introduce biased estimates, so individuals are often asked about first marriage. Biases will be significant if the association of death between spouses, such as those in countries with large AIDS epidemics.[9]

Sampling

Sampling refers to the selection of a subset of the population of interest to efficiently gain information about the entire population. Samples should be representative of the population of interest. Cluster sampling is an approach to non-probability sampling; this is an approach in which each member of the population is assigned to a group (cluster), and then clusters are randomly selected, and all members of selected clusters are included in the sample. Often combined with stratification techniques (in which case it is called multistage sampling), cluster sampling is the approach most often used by epidemiologists. In areas of forced migration, there is more significant sampling error. Thus cluster sampling is not the ideal choice.[11]

Mortality statistics

World historical and predicted crude death rates (1950–2050)
UN, medium variant, 2012 rev.[12]
Years CDR Years CDR
1950–1955 19.1 2000–2005 8.4
1955–1960 17.3 2005–2010 8.1
1960–1965 16.2 2010–2015 8.1
1965–1970 12.9 2015–2020 8.1
1970–1975 11.6 2020–2025 8.1
1975–1980 10.6 2025–2030 8.3
1980–1985 10.0 2030–2035 8.6
1985–1990 9.4 2035–2040 9.0
1990–1995 9.1 2040–2045 9.4
1995–2000 8.8 2045–2050 9.7

The ten countries with the highest crude death rate, according to the 2016 CIA World Factbook estimates, are:[13]

Rank Country Death rate
(annual deaths/1,000 persons)
1  Lesotho 14.9
2  Bulgaria 14.5
3  Lithuania 14.5
4  Ukraine 14.4
5  Latvia 14.4
6  Guinea-Bissau 14.1
8  Afghanistan 13.7
9  Serbia 13.6
10  Russia 13.6

See list of countries by death rate for worldwide statistics.

According to the World Health Organization, the ten leading causes of death in 2015 (ranked by death per 100,000 population) were:[14]

1. Ischaemic heart disease (119 per 100,000 population)
2. Stroke (85 per 100,000 population)
3. Lower respiratory infections (43 per 100,000 population)
4. Chronic obstructive pulmonary disease (43 per 100,000 population)
5. Trachea/bronchus/lung cancers (23 per 100,000 population)
6. Diabetes mellitus (22 per 100,000 population)
7. Alzheimer's disease and other dementias (21 per 100,000 population)
8. Diarrhoeal diseases (19 per 100,000 population)
9. Tuberculosis (19 per 100,000 population)
10. Road traffic accidents (10 per 100,000 population)

Causes of death vary greatly between developed and less developed countries. See list of causes of death by rate for worldwide statistics.

Scatter plot of the natural logarithm of the crude death rate against the natural log of per capita real GDP. The slope of the trend line is the elasticity of the crude death rate with respect to per capita real income. It indicates that a 10% increase in per capita real income is associated with a 1.5% decrease in the crude death rate. Source: World Development Indicators.

According to Jean Ziegler (the United Nations Special Rapporteur on the Right to Food for 2000 to March 2008), mortality due to malnutrition accounted for 58% of the total mortality in 2006: "In the world, approximately 62 millions people, all causes of death combined, die each year. In 2006, more than 36 million died of hunger or diseases due to deficiencies in micronutrients".[15]

Of the roughly 150,000 people who die each day across the globe, about two thirds—100,000 per day—die of age-related causes.[16] In industrialized nations, the proportion is much higher, reaching 90%.[16]

References

1. ^ Porta, M, ed. (2014). "Death rate". A Dictionary of Epidemiology (5th ed.). Oxford: Oxford University Press. p. 69. ISBN 978-0-19-939005-2.
2. ^ Porta, M, ed. (2014). "Morbidity rate". A Dictionary of Epidemiology (5th ed.). Oxford: Oxford University Press. p. 189. ISBN 978-0-19-939005-2.
3. ^ a b "Principles of Epidemiology Lesson 3 - Section 3". www.cdc.gov. Retrieved 2017-12-18.
4. ^
5. ^ Everitt, B.S. The Cambridge Dictionary of Statistics, CUP. ISBN 0-521-81099-X
6. ^ Porta, M, ed. (2014). "Cumulative death rate". A Dictionary of Epidemiology (5th ed.). Oxford: Oxford University Press. p. 64. ISBN 978-0-19-939005-2.
7. ^ Porta, M, ed. (2014). "Case fatality rate". A Dictionary of Epidemiology (5th ed.). Oxford: Oxford University Press. p. 36. ISBN 978-0-19-939005-2.
8. ^
9. ^ a b c d Timæus, Ian M. (1991). "Measurement of Adult Mortality in Less Developed Countries: A Comparative Review". Population Index. 57 (4): 552–568. doi:10.2307/3644262.
10. ^ Graham, W.; Brass, W.; Snow, R. W. (May 1989). "Estimating maternal mortality: the sisterhood method". Studies in Family Planning. 20 (3): 125–135. doi:10.2307/1966567. ISSN 0039-3665. PMID 2734809.
11. ^ Migration, National Research Council (US) Roundtable on the Demography of Forced (2002). ESTIMATING MORTALITY RATES. National Academies Press (US).
12. ^ UNdata: Crude death rate (per 1000 population)
13. ^ CIA World Factbook – Death Rate
14. ^ http://www.who.int/gho/mortality_burden_disease/causes_death/top_10/en/
15. ^ Jean Ziegler, L'Empire de la honte, Fayard, 2007 ISBN 978-2-253-12115-2, p.130.
16. ^ a b Aubrey D.N.J, de Grey (2007). "Life Span Extension Research and Public Debate: Societal Considerations" (PDF). Studies in Ethics, Law, and Technology. 1 (1, Article 5). doi:10.2202/1941-6008.1011. Retrieved August 7, 2011.


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# Why are inversion layers so important in meteorology?

I keep hearing the term "inversion layer" when reading about pollution and meteorology.

I know it vaguely amounts to "some place where the gradient of temperature is inverted". But why are inversion layers so important in meteorology ? Why do they matter ? Air is colder here ... Big deal ! ?

Put it this way:

We like our air to be mixed around well. Mixing the air prevents uneven concentration buildup of not just pollutants (smoke, ozone, chemicals, etc), but also fog (which is pooling of cool and moist air), smells, even sounds (that's why you can often hear distant traffic more near dawn).

There are two places that air near the ground can go: up or out.

Warmer air rises. When an inversion sets up, it's a layer of warmer air aloft that thereby blocks air below from being able to rise anymore.
Most nights there are inversions since the ground cools more quickly than the air higher up. But usually during the day, sunlight heating the ground starts the air rising and mixing around. And viola, no more unpleasant buildups!

But additionally, inversions also are formed when cold air is blown in near ground level, such as during a cold front. But, the peak of such a cold airmass generally associates with high pressure.
And high pressure cores have calmer horizontal winds.
So when such a cold high pressure gets stuck and parks in place, it can lead to prolonged inversions.

Additionally, inversions tend to be self-perpetuating over time. Fog and smoke form, block out the sun, and those just keep the low-level air layer cold.

It can be very difficult to forecast just how much the inversion will break down during the day, leading to greatly busted forecasts. I remember many times in Oklahoma where they thought it would warm up a fairly typical 20 degrees (F) during the day, but the fog never fully eroded, and we only ended up rising a few degrees. We also ended up having solid weeks or more of foggy conditions.

Furthermore, the geography in some regions favors inversion formation, and so inversion forecasting inversions can be particularly important for such locations. Sometimes these features can even enhance storm systems or alter their tracks. For more on these targets, look into cold air damming and marine layers.

Inversion conditions also can prove to be quite important flies-in-the-ointment for severe storm forecasting as well. Severe thunderstorms often rely quite a lot on afternoon heating to fuel the rapid updrafts of the storms. Sometimes the same mugginess that highlights that conditions are ripe for storms can wind up being so rich that fog and low-level clouds develop overnight, and prove resilient well into the day. The result can be that the forecast severe weather outbreaks ends up coming to nothing. Or instead, if a fog inversion were expected but doesn't materialize it can often generate unexpected or incorrectly timed severe weather outbreaks. So severe weather forecasters have significant interest in understanding inversions as well.

So... inversions form most every day, but typically as the day evolves, the atmospheric heating engine kicks in, and wind resets the atmosphere towards being more homogeneous. But when stronger inversions build in, they can snowball into much more depressing, and even very dangerous conditions.

• Very nice answer, inversion layers now seem central to all of meteorology, impressive ! One question on cold fronts having high pressure : I've always seen the opposite in books, warm front of high pressure "creeping in from above" and colder front sneaking under bringing low pressure. What am I missing ? – Jiby Dec 16 '16 at 23:25
• Active fronts themselves are local "troughs" of low pressure, extending out from the central low pressure core, see goo.gl/ik3qx0 (at least for our lower part of the atmosphere). So those fronts... where the airmass STARTS to change... are low pressure. But behind the front, more and more cold air pools in, which is dense (thicker = more air = more pressure). So you basically end up with the highest pressures near the PEAK of cold air masses. Hope that helps, and if not, ask a separate question, and I'll try to put together some more material :-) – JeopardyTempest Dec 17 '16 at 0:39
• Right, that cleans up my understanding (but so many more questions ! Earth science is fascinating). – Jiby Dec 17 '16 at 1:28

Farrenthope is correct, but I would like to add some detail.

An inversion occurs when the air is warmer than the ground. It is called an inversion because it is the opposite of what occurs during the day. During the day, the ground is heated by the sun and the air near the ground rises.

However, during clear and calm nights, the ground will cool faster than the air. This means that at a certain time, the air will be warmer than the ground. With nothing to move pollutants upward, the air just stagnates. People will still keep pumping pollutants out, with the pollution just accumulating. During the day, however, the pollutants are lifted upwards, and do not stagnate.

For those mathematically affluent, the equation for a concentration of a pollutant can be written as $$\frac{\partial c}{\partial t}=-\vec{v}\cdot\nabla_h c-w\frac{\partial c}{\partial z}+\nabla \cdot (K\nabla c) +S_c(t)+C$$

where $c$ is the concentration of the pollutant, $\vec{v}$ is the wind vector, $w$ is the vertical velocity, $K$ is the Fick's law constant, and $C$ is the chemistry term.

If we consider the following assumptions which are common, regardless of an inversion:

• Diffusion is a small process ($K\approx0$)
• The pollutant undergoes no chemical change ($C\approx0$) The equation boils down to $$\frac{\partial c}{\partial t}=-\vec{v}\cdot\nabla_h c-w\frac{\partial c}{\partial z}+S_c(t)$$

During an inversion, because air at the surface is not going up, there is no air going down. This means $w\approx0$. With no vertical velocity, the air near the ground is slowed by the drag the ground has on the air, making $\vec{v}\approx0$. This boils the equation down to $$\frac{\partial c}{\partial t}=S_c$$. Since $S_c \ge0$, $c$ will just keep increasing.

A good example of a dangerous inversion is the Donora event.

Temperature inversions are important to meteorology and pollution because they are the boundary for atmospheric mixing. If there is a strong inversion, the air above and below an inversion do not easily mix together. In the case of pollution, where the emissions come from the surface, a shallow temperature inversion in the boundary layer traps the pollution near the surface. If the boundary layer inversion is very high up in the atmosphere, you will get good mixing and pollution will be diluted. There is also a very strong temperature inversion at the top of the troposphere, called the tropopause, which generally separates stratospheric air from the troposphere.

Also, see this related question: What is a temperature inversion and can it trap smog pollution?


text:
Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, p. 359-369

A high-order compact finite difference scheme for a fully nonlinear parabolic differential equation is analyzed. The equation arises in the modeling of option prices in financial markets with transaction costs. It is shown that the finite difference solution converges locally uniformly to the unique viscosity solution of the continuous equation. The proof is based on a careful study of the discretization matrices and on an abstract convergence result due to Barles and Souganides.

DOI : https://doi.org/10.1051/m2an:2004018
Classification:  49L25,  65M06,  65M12
Keywords: high-order compact finite differences, numerical convergence, viscosity solution, financial derivatives
@article{M2AN_2004__38_2_359_0,
author = {D\"uring, Bertram and Fourni\'e, Michel and J\"ungel, Ansgar},
title = {Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {38},
number = {2},
year = {2004},
pages = {359-369},
doi = {10.1051/m2an:2004018},
mrnumber = {2069151},
zbl = {1124.91031},
language = {en},
url = {http://www.numdam.org/item/M2AN_2004__38_2_359_0}
}

Düring, Bertram; Fournié, Michel; Jüngel, Ansgar. Convergence of a high-order compact finite difference scheme for a nonlinear Black-Scholes equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 38 (2004) no. 2, pp. 359-369. doi : 10.1051/m2an:2004018. http://www.numdam.org/item/M2AN_2004__38_2_359_0/

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[13] B. Düring, M. Fournié and A. Jüngel, High order compact finite difference schemes for a nonlinear Black-Scholes equation. Int. J. Appl. Theor. Finance 6 (2003) 767-789. | Zbl 1070.91024

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[15] R. Frey, Market illiquidity as a source of model risk in dynamic hedging, in Model Risk, R. Gibson Ed., RISK Publications, London (2000).

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[17] S.D. Hodges and A. Neuberger, Optimal replication of contingent claims under transaction costs. Rev. Future Markets 8 (1989) 222-239.

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QUESTION

# ENV 333 Week 2 DQ 2 Economics

This file of ENV 333 Week 2 Discussion Question 2 Economics includes:

Economists and environmentalists are often on opposite sides of the debate when discussing the impacts caused by human interaction. When developing an Environmental Impact Statement (EIS) the direct and indirect economic impacts are heavily considered. Should the various components of economics that were discussed in Chapter Seven potentially prevent or permit a project?

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Tutor has posted answer for $5.19. See answer's preview$5.19

*** 333 **** 2 DQ * *********


text:
1. ## statistics help needed

Let $X1 X2,...Xn$ be a random sample from exponential distribution with parameter $q$ that is $f(x,q)=(1/q)e^{(-x/q)}$ for $x>0$ and $q>0$.

Find the Uniformly Minimum Variance Unbiased Estimator for $P[X where $c$ is a known positive constant.

2. The suff stat for q is the sum, $S_n=\sum_{i=1}^nX_i$.
Next we need to find a function of this sum that's unbiased for $P(X.

Since each $X_i\sim\Gamma(1,q)$, we have $S_n\sim\Gamma(n,q)$.

3. Would you help a little more?
How does knowing that $S$~ $Gam(n,q)$help me figure out the Uniformly Minimum Variance Estimator?

4. You will need to do the Rao-Blackwell Theorem directly.

Compute $E(I(X_1

5. i am sorry to ask you this but what is $I(X1? Is $I$a funtion?

6. Originally Posted by Kat-M
i am sorry to ask you this but what is $I(X1? Is $I$a funtion?
I stands for indicator.
It's 1 when that event happens and zero when it doesn't.
$EI(X\in A)=P(X\in A)$.

7. i thought about this for a long time but still i am not sure how to compute $E(I(X1.
X1 is part of S. and i dont know how it affects in computing $\int I(X1.
i got $f(x1|s)=\Gamma(n)/s^{n-1}$ So when i integrate it from 0 to c, i got $c\Gamma(n)/s^{n-1}$. did i do it right?

8. Back to $E(I(X_1 where s>c.

We need the density $f(x_1|s_n) ={f(x_1) f(s_{n-1}) \over f(s_n) }$, where $s_{n-1}=x_2+\cdots +x_n$.

The density of $X_1$ is $f(x_1)=e^{-x_1/q}/q$.

While $f(s_{n-1})= {s_{n-1}^{n-2} e^{-s_{n-1}/q}\over \Gamma(n-1)q^{n-1}}$ and $f(s_n) ={s_n^{n-1} e^{-s_n/q}\over \Gamma(n)q^n}$

Noting that $x_1+s_{n-1}=s_n$ we have

$f(x_1|s_n) ={(n-1) (x_2+\cdots +x_n)^{n-2} \over (x_1+\cdots +x_n)^{n-1}}$

Thus $P(X_1

which gives me $1-\biggl(1-{c\over s}\biggr)^{n-1}$, which doesn't make sense when n=1.

9. Originally Posted by matheagle
Back to $E(I(X_1 where s>c.
We need the density $f(x_1|s_n) ={f(x_1) f(s_{n-1}) \over f(s_n) }$, where $s_{n-1}=x_2+\cdots +x_n$.

The density of $X_1$ is $f(x_1)=e^{-x_1/q}/q$.

While $f(s_{n-1})= {s_{n-1}^{n-2} e^{-s_{n-1}/q}\over \Gamma(n-1)q^{n-1}}$ and $f(s_n) ={s_n^{n-1} e^{-s_n/q}\over \Gamma(n)q^n}$

Noting that $x_1+s_{n-1}=s_n$ we have

$f(x_1|s_n) ={(n-1) (x_2+\cdots +x_n)^{n-2} \over (x_1+\cdots +x_n)^{n-1}}$

Thus $P(X_1

which gives me $1-\biggl(1-{c\over s}\biggr)^{n-1}$, which doesn't make sense when n=1.
I don't think this is right.
The ideas are good, but the answer seems lame.

Don't mess with guard duck, he's one mean sob.


text:
Home

The code to run the analyses in this article can be found on the linked gitlab repository, sadilcowellhuber2019. That defines a set of R functions, as well as the main Stan files (in src).

The package can be built with Rstudio, compiling the Stan models for future use.

Note that the analyses themselves relied heavily on the MGHPCC. Without access to a cluster, most analyses would take prohibitively long. Instead, the results are stored as drake caches. These caches are stored in the linked box component of this osf project.

So, to access the code

1) Download a copy of the gitlab repository 2) Build the package (e.g., using Rstudio) 3) Download the caches. - Note that the caches are gzipped, and the larger ones are additionally split into multiple files (those ending with part-##). To access recombine the split files, use a command like the following to reproduce the single compressed archive.

 cat cache_fig-recovery-cor* > cache_fig-recovery-cor.tar.gz - All compressed archives be unpacked with a command like tar -xvf cache_fig-recovery-cor.tar.gz

4) At this point, move the uncompressed caches into the folder 'data-raw/caches.' 5) Now figures from the article can be recreated by running the scripts in the 'data-raw' folder. For example, sourcing figure4.R will reproduce Figure 4 from the manuscript. 6) These caches also store a record of the function calls that were used to generate the cached results. To see those functions, a command like the following can be called

drake::read_drake_plan(cache=drake::this_cache(file.path('data-raw','caches','cache_fig-recovery-cor'))) where, as above, the cache_fig-recovery-cor part should be replaced with whichever plan you're looking for.


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# Tag Info

31

Not directly, as far as I know, since explicitly computing large multiples of points in $E(\mathbb Q)$ is infeasible. However, people have considered lifting points from $E(\mathbb F_p)$ to $E(\mathbb Q)$ or to the $p$-adics $E(\mathbb Q_p)$ in order to devise algorithms to solve the discrete log problem in $E(\mathbb F_p)$ (although, unsuccessfully so far). ...

27

Bitcoin mining is based on hash functions. Specifically the SHA-256 hash function, which maps arbitrary bit strings to 256-bit outputs in such a way that nobody knows how to find a collision (two inputs with the same output), although the pigeonhole principle implies collisions exist. Bitcoin mining doesn't involve finding collisions, which would be way too ...

22

Have you considered unknotting knots? The problem would be finding a sequence of Reidemeister moves for a random link graph that reduces it to the unknot. In some cases, no such sequence would exist, but most random graphs are known to be unknotted under certain knotting algorithms: http://iopscience.iop.org/article/10.1088/1751-8113/49/40/405001/meta ...

20

Here is an example of the type you appear to be seeking. The story -- like many good stories -- involves a million dollar prize offered by a billion dollar corporation, sought by armies of computer wizards. There's even a courtroom scene at the climax. In 2007, Netflix released a dataset consisting of roughly a hundred million movie ratings (from 1 through ...

18

I am not aware of anybody seriously considering hyperelliptic curves for actual real-world usage, beyond toys, and I would be rather surprised to hear differently from anyone. As you say, hyperelliptic provide comparatively few (if any!) advantages over elliptic curves but have the huge disadvantage that virtually nobody has well-tested, battle-hardened ...

17

Let us assume that everybody uses the same asymmetric encryption system (such as PGP), with keys that are so large that Big Brother cannot crack them. If Alice wants to send a message to Bob, she encrypts it with Bob's public key and broadcasts it to everybody. All of Alice's friends will use their own private keys to decrypt the message, but only Bob will ...

16

This question seems a bit vague, but one answer is that there are cryptosystems such as NTRU that are based on (special cases) of the closest vector problem (CVP). At present, quantum computers would not significantly speed up the solution of the CVP. If I understand correctly, they would require doubling the length of the keys. Disclaimer: Jeff Hoffstein, ...

15

Let's assume that the secret service can view all transmitted messages and how they are routed, but has no access to anyone's private computer, since otherwise privacy clearly cannot be guaranteed. There's still no way to mathematically guarantee privacy in any realistic way. One big problem is traffic analysis: the secret service can try to correlate when ...

15

Calculating the permanent of a small matrix is a computationally challenging problem, as discussed here, here, and here. See also the Wikipedia article. Given an $n \times n$ matrix $A$, a naïve calculation of $\text{perm}(A)$ using the definition may require $|S_n|=n!$ multiplications. One of the best known algorithms is Ryser’s formula [Rys63], based on ...

14

You can use Coppersmith's algorithm [1] (or Howgrave-Graham's [2] simplification) to find the factor, which will be efficient if the number of remaining bits is not too large. The PARI/GP documentation http://pari.math.u-bordeaux.fr/dochtml/html-stable/Arithmetic_functions.html#zncoppersmith has an explicit example. Coron, Faugère, Renault, & Zeitoun [...

14

Finding cycles in graphs is a standard graph theory problem that lends itself well to proof-of-work. See my Cuckoo Cycle project page at https://github.com/tromp/cuckoo which has tons of details, as well as bounties for improving the currently best implementations. Of course, the specific pseudo-random graphs generated in Cuckoo Cycle have no practical use ...

13

There is a very good book that you can find your answer there completely. This book's name is: "Post-Quantum Cryptography" by "Daniel J. Bernstein, Johannes Buchmann and Erik Dahmen". As a part of this book, today we know that these cryptosystems can be broken by quantum computers: $1)$ RSA public key encryption $2)$ Diffie-Hellman key-exchange $3)$ ...

13

I find this to be an excellent suggestion, though not sure all requirements can be satisfied. More specifically, 3 and 5 - if we randomly generate instances, then why would they have any intrinsic value? Would factoring large integers have any intrinsic value? One example that I can think of is chess endgames. There is a growing database of which positions ...

13

Cryptographic Protocols with Everyday Objects (section 5) Typical cryptographic Secret Santa protocols require a fully homomorphic encryption system. These protocols are thus suitable for those with some planning, some expertise and access to computational assistance, but not to a group of friends without access to computers. Here we present an ...

12

Here is a recent paper, which has been received positively in the cryptocurrency community. I will expand on this paper here. While conventional hash functions do not allow one to construct very useful proof-of-work problems, if one replaces the hash function for the proof-of-work with a randomizing function specifically designed to be computed by ...

11

The non-linearity in the block cipher AES comes from the pseudo-inversion function on the finite field $\mathbb{F}_{2^8}$, defined by $$p(x) = \begin{cases} x^{-1} & \text{if x \not=0} \\ 0 & \text{if x=0.}\end{cases}$$ It is a nice exercise to show that $p$ is as strong as possible against the difference attack. That is, given any non-zero $\... 11 Here are a few interesting examples of symmetric primitives whose claimed security is/was based on number-theoretic problems: From the 1980s: the famous Blum-Blum-Shub deterministic random bit generator is a classic example. Let$N = pq$be the product of two large safe primes, and consider the sequence defined by$x_{i+1} = x_i^2 \pmod{N}$, where$x_0$is ... 10 Another interesting topic is on performing computation on encrypted data. For example, you can have your data encrypted and yet use cloud services on them. There are mathematicians and computer scientists working on this, however the current constructions are not efficient enough for practical purposes yet (AFAIK). The keyword to search for is Homomorphic ... 10 The mathematics of privacy is a HUGE area of research. It started in the statistics community way back when, with issues of disclosure along the lines of what Vidit Nanda mentioned. In the 90s, things exploded in the CS community when a researcher at CMU first showed that using only publicly disclosed information she could retrieve private information about ... 10 there is a nice preprint server, widely used by cryptographic researchers: http://eprint.iacr.org If you do a search, there are some papers talking more or less about bitcoin. I guess "Decentralized anonymous credentials" is a good begin for your student. This is indeed a well known area of research, and is the main point of bitcoins (with mining). You may ... 10 I assume you mean you know the leading 75 digits of a roughly 125-digit factor. Then you can reconstruct the factorization using lattice basis reduction. For an explicit algorithm, see the paper Small solutions to polynomial equations, and low exponent RSA vulnerabilities by Coppersmith. All it requires is that the number of digits you know of a factor is ... 9 "Is this obfuscation scheme unbreakable?" "Well.. no." said people a couple of years later. On GGHRSW13 specifically: Cryptanalyses of Candidate Branching Program Obfuscators See also (concurrent, similar flavor): Cryptanalysis of Indistinguishability Obfuscations of Circuits over GGH13 Zeroizing Attacks on Indistinguishability Obfuscation over CLT13 ... 9 Discussion of the prospect of a cryptocurrency based on cellular automata prompted me to start developing the Catagolue project in the summer of 2014. The proof-of-work system was deliberately chosen to enable a cryptocurrency to be built upon it: Given a string$S$, find some string$T$such that the$16 \times 16$pseudorandom pattern$f(S+T)$yields ... 9 I think I may not understand your model of cryptography. My model would be that encryption is a polynomial time computable, injective, function from plaintexts of length$m$to cipher texts of length$n$, and decryption is inverting this function. In that case, such a problem will always be in NP. Indeed, we must have$m \leq n$, since we require that ... 8 Most of the examples given above are nice textbook examples of ZK proofs meant for students. Here's something I'd call more a "real life" example. Assume that Alice has a secret key$x$and public key$y = g^x$. (Here we assume that$g$generates a group$G$of size$p$, for large prime$p$.) She wants to convince Bob that she knows$x$without revealing$x$.... 7 There is a web site and conference series on post-quantum cryptography, leading up to Bernstein et al's book mentioned by Shahrooz. See: http://pqcrypto.org/ 7 I don't see how you will have a problem which is progress free but still in NP(requirement 7); or any kind of problem that is suitable for your purpose for that matter. To see why this seems unlikely lets consider the solution space for your problem as I start and when I have progressed in an arbitrary algorithm that searches the solution space. when I ... 7 Let me have another go, because I really love this question. Essentially it's like a SETI@home project - without going into details, let's just consider the theoretical model that some signals arrive from a source that is sufficiently random and then we have to do some computation on it to get some data. (If you prefer groundhogs to E.T., the weather ... 7 This appears special case of "A New Special-Purpose Factorization Algorithm": https://pdfs.semanticscholar.org/1843/73605e846f90b0a9d7252931bab4c47a1ec7.pdf From the abstract: a new factorization algorithm is presented, which finds a prime factor$p$of an integer$n$in time$(D \log{n})^{O(1)}$, if$4p - 1 = Db^2$If$p=27a^2+27a+7$we have$4p-1=3\...

6

Writing up the comment: You just need to "pixelate" the line by finding all lattice boxes that it crosses: Then the answer vector $v$ must connect to one of the corners of the shaded boxes. Instead of first collecting the boxes, try the following zig-zag algorithm: start from the origin and poll the up and right nearest lattice points. One of them is closer ...

Only top voted, non community-wiki answers of a minimum length are eligible


text:
Draw round rectangle from ()() width () height () radius () colour ()

Introduction

This block is found under the Robotics palette in the extension evive TFT display. It takes the following parameters as input: starting coordinates, width, height, radius at corners and colour. It draws a rectangle rounded at edges where the radius is input by the user.

This block is works for Arduino mode only.
Draw round rectangle from ()() width () height () radius () colour ()

Example

• This script draws a rounded rectangle inside a rounded rectangle.


text:
On the equation $-Delta u e^{u}-1=0$ with measures as boundary data

On the equation $-Delta u e^{u}-1=0$ with measures as boundary data - Descarga este documento en PDF. Documentación en PDF para descargar gratis. Disponible también para leer online.

1 LMPT - Laboratoire de Mathématiques et Physique Théorique

Abstract : If $\Omega$ is a bounded domain in $\mathbb R^N$, we study conditions on a Radon measure $\mu$ on $\partial\Omega$ for solving the equation $-\Delta u+e^{u}-1=0$ in $\Omega$ with $u=\mu$ on $\partial\Omega$. The conditions are expressed in terms of Orlicz capacities.

Keywords : Elliptic equations Orlicz capacities Reduced measures Boundary trace

Autor: Laurent Veron -

Fuente: https://hal.archives-ouvertes.fr/

DESCARGAR PDF


text:
# Dating dinosour bones

Heme is a part of hemoglobin, the protein that carries oxygen in the blood and gives red blood cells their color.“It got me real curious as to exceptional preservation,” she says.In the lab we use thick acrylic glass shields to protect us from $\beta$ radiation.Additionally I have found some secondary sources for painting the dinosaur bones with lead paint, but no real first hand source from a museum or so.A fossil of the salamander Chunerpeton shows not only the preserved skeleton but also its skin and external gills. Hopefully scientists in the west will get a chance to closely examine these soft tissue samples.

But all of that changed when Mary Schweitzer, a molecular paleontologist at North Carolina State University, did something that was absolutely unthinkable.

The following comes from an article in Smithsonian Magazine…

But of course if these dinosaurs are really “160 million years old”, that should be absolutely impossible.

Needless to say, this shocking discovery is once again going to have paleontologists scrambling to find a way to prop up the popular myths that they have been promoting.

What they have been telling us simply does not fit the facts.

## One thought on “dating dinosour bones”

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4. Academic Standing: defines how GPAs (grade point averages) are calculated and what cumulative GPA is required for a student to be “in good academic standing.” Also details Committee on Academic Standing’s procedures for academic notice (probation) and possible action that may be taken, including dismissal.


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# Removing a simplicial subset from a simplicial set

Let $A, X$ be simplicial sets, and suppose there's an inclusion $A \longrightarrow X$. Geometrically realizing the inclusion map, we get a pair of spaces $(\mathcal{A}, \mathcal{X})$. I want to find a simplicial set whose geometric realization has the homotopy type of $\mathcal{X} \setminus \mathcal{A}$.

Here are my thoughts so far:

1. If we try to remove from $X$ all simplices that are also in $A$, we run into immediate trouble: other simplices in $X$ probably have simplices of $A$ as their faces. Somehow we need to remove the simplices of $A$ and then adjoin new boundary simplices as freely as possible.''
2. Ideally such a construction would be functorial. There's no way that the domain can be the category of pairs, however, since there won't be induced maps after subtracting. Instead, it seems like the source category should be more like a twisted arrow category (although this doesn't seem to work either).

The case I'd really like to get working is where $X$ is a $G$-simplicial set with finitely-many non-degenerate simplices in each degree and $A$ is the points which have nontrivial stabilizer, but I'm interested in the general case as well.

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John, what precisely do you mean by X\A and taking its `geometric realization'. It seems you mean the simplices of X not in A, which as you observe is not a simplicial set, so its geometric realization has no obvious meaning. You are desperately trying to avoid X/A. In your equivariant example, presumably G is a group acting simplicially and A is the subcomplex of simplices with nontrivial stabilizer. Then you might replace X\A by the maximal G-free subcomplex of X, which maybe makes sense. –  Peter May Apr 15 '13 at 1:27
Dear Professor May, I meant geometrically realizing A and X first and then performing subtraction in the category of spaces. –  John Wiltshire-Gordon Apr 15 '13 at 1:31
The singular simplicial set of the space $|X| \setminus |A|$ has the property you ask for, namely its geometric realization is homotopy equivalent to $|X| \setminus |A|$. Perhaps you want some additional constraints? –  Chris Schommer-Pries Apr 15 '13 at 14:03
@Chris Schommer-Pries: Good point, but I'd like a combinatorial answer. In particular, if there are finitely many simplices before, I'd like finitely many after. –  John Wiltshire-Gordon Apr 15 '13 at 15:42

Here are some perhaps silly ideas.

(i) Think of simplicial sets as presheaves on $\Delta$, now look up when a subpresheaf can be subtracted. (E.g. is there a universal property involved?) What os the subobject classified in the presheaf topos here? I am sure that these things are known, but possibly do not have a simple answer.

(ii) One related point from Peter May's answer is that $X\setminus A$ should be the maximal subsimplicial set of $X$ with trivial intersection with $A$. The condition on the realisations is then a possible red herring.

(iii) A final point is that if you are handling a simplicial complex (say a PL manifold, with a given triangulation) there would be questions of subdivision, and if I remember rightly some sort of regular neighbourhoods, and I think that this is geometrically more significant that merely looking at the complement of $|A|$ in $|X|$.

-

The 0-simplices of Sd(X) are the simplices of X. Then X\A gives a subset of Sd_0(X), how about the subspace of Sd_.(X) spanned by those?

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I do not know if this works or not. –  John Wiltshire-Gordon Apr 20 '13 at 22:28


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# Characterizing K2 Candidate Planetary Systems Orbiting Low-mass Stars. II. Planetary Systems Observed During Campaigns 1–7

@article{Dressing2017CharacterizingKC,
title={Characterizing K2 Candidate Planetary Systems Orbiting Low-mass Stars. II. Planetary Systems Observed During Campaigns 1–7},
author={Courtney D. Dressing and Andrew M. Vanderburg and Joshua E. Schlieder and Ian J. M. Crossfield and Heather A. Knutson and Elisabeth R. Newton and David R. Ciardi and Benjamin J. Fulton and Erica J. Gonzales and Andrew W. Howard and Howard T. Isaacson and John H. Livingston and Erik A. Petigura and Evan J. Sinukoff and Mark E. Everett and Elliott P. Horch and Steve B. Howell},
journal={The Astronomical Journal},
year={2017},
volume={154}
}
• Published 21 March 2017
• Physics, Geology
• The Astronomical Journal
We recently used near-infrared spectroscopy to improve the characterization of 76 low-mass stars around which K2 had detected 79 candidate transiting planets. 29 of these worlds were new discoveries that had not previously been published. We calculate the false positive probabilities that the transit-like signals are actually caused by non-planetary astrophysical phenomena and reject five new transit-like events and three previously reported events as false positives. We also statistically…

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### Characterizing K2 Candidate Planetary Systems Orbiting Low-mass Stars. III. A High Mass and Low Envelope Fraction for the Warm Neptune K2-55b

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K2-55b is a Neptune-sized planet orbiting a K7 dwarf with a radius of , a mass of 0.688 ± 0.069 , and an effective temperature of K. Having characterized the host star using near-infrared spectra

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• Physics, Geology
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We present near-infrared spectra for 144 candidate planetary systems identified during Campaigns 1–7 of the NASA K2 Mission. The goal of the survey was to characterize planets orbiting low-mass

### STELLAR AND PLANETARY PROPERTIES OF K2 CAMPAIGN 1 CANDIDATES AND VALIDATION OF 17 PLANETS, INCLUDING A PLANET RECEIVING EARTH-LIKE INSOLATION

• Physics, Geology
• 2015
The extended Kepler mission, K2, is now providing photometry of new fields every three months in a search for transiting planets. In a recent study, Foreman-Mackey and collaborators presented a list

### PLANET HUNTERS. X. SEARCHING FOR NEARBY NEIGHBORS OF 75 PLANET AND ECLIPSING BINARY CANDIDATES FROM THE K2 KEPLER EXTENDED MISSION

• Physics, Geology
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We present high-resolution observations of a sample of 75 K2 targets from Campaigns 1–3 using speckle interferometry on the Southern Astrophysical Research (SOAR) telescope and adaptive optics

### Stellar and Planetary Parameters for K2's Late-type Dwarf Systems from C1 to C5

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The NASA K2 mission uses photometry to find planets transiting stars of various types. M dwarfs are of high interest since they host more short-period planets than any other type of main-sequence

### PLANETARY CANDIDATES FROM THE FIRST YEAR OF THE K2 MISSION

• Physics, Geology
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The Kepler Space Telescope is currently searching for planets transiting stars along the ecliptic plane as part of its extended K2 mission. We processed the publicly released data from the first year

### TWO TRANSITING EARTH-SIZE PLANETS NEAR RESONANCE ORBITING A NEARBY COOL STAR

• Physics, Geology
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Discoveries from the prime Kepler mission demonstrated that small planets (<3 R ⨁ ?> ) are common outcomes of planet formation. While Kepler detected many such planets, all but a handful orbit faint,

### ELEVEN MULTIPLANET SYSTEMS FROM K2 CAMPAIGNS 1 AND 2 AND THE MASSES OF TWO HOT SUPER-EARTHS

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We present a catalog of 11 multiplanet systems from Campaigns 1 and 2 of the K2 mission. We report the sizes and orbits of 26 planets split between seven two-planet systems and four three-planet

### ULTRA-SHORT-PERIOD PLANETS IN K2 SUPERPIG RESULTS FOR CAMPAIGNS 0–5

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We analyzed data from Campaigns 0–5 of the K2 mission and report 19 ultra-short-period candidate planets with orbital periods of less than one day (nine of which have not been previously reported).

### A PLATEAU IN THE PLANET POPULATION BELOW TWICE THE SIZE OF EARTH

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We carry out an independent search of Kepler photometry for small transiting planets with sizes 0.5–8.0 times that of Earth and orbital periods between 5 and 50 days, with the goal of measuring the

### TWO SMALL PLANETS TRANSITING HD 3167

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We report the discovery of two super-Earth-sized planets transiting the bright (V = 8.94, K = 7.07) nearby late G-dwarf HD 3167, using data collected by the K2 mission. The inner planet, HD 3167 b,