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Data Structures 101: Introduction to Data Structures and Algorithms DS - Data Structure Algorithms are collections of steps to solve a particular problem. Data structures are named locations used to store and organize data. It's a way of arranging data on a computer so that it can be accessed and updated efficiently. Depending on the requirement and project, it is important to choose the right data structure for your project. For example, if data is to be stored sequentially in memory, then an Array would be a good fit. Learning data structures and algorithms allow us to write efficient and optimized computer programs. What are the Types of Data Structures we have? 1. Linear DS 2. Non-Linear DS. Linear DS In a linear data structure, elements are arranged in sequence one after the other. This makes the implementation of elements easy. However, when the complexity of the program increases, this data structure might not be the best choice because of operational complexities. Examples of Linear DS • Arrays: In an Array, elements in memory are arranged in continuous memory. All the elements of an array are of the same type, and the type of elements that can be stored in the form of arrays is determined by the programming language. • Stacks: Stacks are stored in the LIFO principle (Last In, First Out). i.e the last element stored in a stack will be removed first. Just like a pile of plates. You can place one plate on top of the pile, where the last plate kept on the pile will be removed first. • Queue: Unlike a Stack, the queue works in with the FIFO principle (First In, First Out) where the first element stored in the queue will be removed first. Similar to a queue of people at a ticket stand where the first person in the queue gets his/her ticket first. • Linked List: In a linked list, data elements are connected through a series of nodes, with each node containing the data item and a memory address linking to the next node. Non-Linear DS Unlike linear data structures, elements in non-linear are not stored sequentially. Instead, they are arranged in a hierarchical manner where one element is connected to one or more elements, like a family tree or a cooperate ladder. Non-linear data structures are further divided into graphs and tree-based data structures. Examples of Non-Linear DS • Graph DS: In the graph data structure, each node is called a vertex and each vertex is connected to other vertices through edges. • Trees DS: Similar to a graph, a tree is also a collection of vertices and edges. However, in trees, there can only be one edge between two vertices. Common Tree-Based Data Structure • Binary Tree • Binary Search Tree • AVL Tree • B-Tree • B+ Tree • Red-Black Tree Why Data Structures? Knowledge of data structures provides a better way of organizing, maintaining, and storing data efficiently and this helps you write memory and time-efficient code. Other really good resources you should check out are: Hey was this helpful? Please do leave a comment and a like below so others can find this post ๐ . Originally posted on my newsletter: Michael Ibinola You can also find me: My Twitter & Github	{"url":"https://theibinolamichael.hashnode.dev/data-structures-101-introduction-to-data-structures-and-algorithms","timestamp":"2024-11-12T12:20:15Z","content_type":"text/html","content_length":"130818","record_id":"<urn:uuid:13b91d90-5640-45d4-b3ee-d7211a17407b>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00036.warc.gz"}
Practice :6th Math 21-25 \| Quizalize Feel free to use or edit a copy includes Teacher and Student dashboards Measure skills from any curriculum Tag the questions with any skills you have. Your dashboard will track each student's mastery of each skill. With a free account, teachers can • edit the questions • save a copy for later • start a class game • automatically assign follow-up activities based on students’ scores • assign as homework • share a link with colleagues • print as a bubble sheet • Distance around an object • Q1 Distance around an object • Q2 relationship between two quantities, normally expressed as the quotient of one divided by the other: • Q3 A ratio that compares two quantities measured in different units • Q4 The bottom number in a fraction • Q5 Of any counting number are the results of multiplying that continues number by all the counting numbers. Ex: 7: 7,14, 21,28.... • Q7 Middle # when put in high to low order, or the average of the 2 middle #'s • Q9 Natural numbers ( counting numbers) and zero; 0, 1, 2, 3... • Q10 All rational and irrational numbers • Q11 Add all digits and are then divisible by 3 • Q12 the last digit of a number is even • Q13 the last number is a 5 or 0	{"url":"https://resources.quizalize.com/view/quiz/practice-6th-math-2125-c4900c52-5954-4bb2-b699-a117c825dba0","timestamp":"2024-11-10T14:29:29Z","content_type":"text/html","content_length":"86165","record_id":"<urn:uuid:5dfd7d56-dec3-4f1b-9760-4853888d8a90>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.60/warc/CC-MAIN-20241110134821-20241110164821-00648.warc.gz"}
Support Vector Machine (SVM) SVM (also called Maximum Margin Classifier) is an algorithm that takes the data as an input and outputs a line/hyperplane that separates those classes if possible. Suppose that we need to separate two classes of a dataset. The task is to find a line to separate them. However, there are many lines which can do that (countless number of lines). How can we choose the best one? An idea of support vectors (samples on the margin) and SVM (find the optimal hyperplane). Most of the time, we cannot separate classes in the current dataset easily (not linearly separable data). We need to use kernel trick first (transform from the current dimension to a higher dimension ) and then we use SVM. These classes are not linearly separable. An idea of kernel and SVM. Transform from 1D to 2D. Data is not linearly separable in the input space but it is linearly separable in the feature space obtained by a kernel. An idea of kernel and SVM. Transform from 2D to 3D. Data is not linearly separable in the input space but it is linearly separable in the feature space obtained by a kernel. A kernel is a dot product in some feature space: It also measures the similarity between two points and . We have some popular kernels, • Linear kernel: . We use kernel = 'linear' in sklearn.svm.SVM. Linear kernels are rarely used in practice. • Gaussian kernel (or Radial Basic Function -- RBF): . It's used the most. We use kernel = 'rbf' (default) with keyword gamma for (must be greater than 0) in sklearn.svm.SVM. • Polynomial kernel: . We use kernel = 'poly' with keyword degree for and coef0 for in sklearn.svm.SVM. It's more popular than RBF in NLP. The most common degree is $$d = 2$$ (quadratic), since larger degrees tend to overfit on NLP problems. (ref) • Sigmoidal: . We use kernel = 'sigmoid' with keyword coef0 for $$r$$ in sklearn.svm.SVM. We can also define a custom kernel thanks to this help Choose whatever kernel performs best on cross-validation data. Andrew NG said in his ML course. • Compared to both logistic regression and NN, a SVM sometimes gives a cleaner way of learning non-linear functions. • SVM is better than NN with 1 layer (Perceptron Learning Algorithm) thanks to the largest margin between 2 classes. • Accurate in high-dimensional spaces & memory effecient. • Good accuracy and perform faster prediction compared to Naïve Bayes algorithm. (ref) • Prone to overfitting: if number of features are larger than number of samples. • Don't provide probability estimation. • Not efficient if your data is very big! • It works poorly with overlapping classes • Sensitive to the type of kernel used. • Classification, regression and outliers detection. • Text and hypertext categorization. • Classification of images. 1from sklearn.svm import SVC 3svc = SVC(kernel='linear') # default = 'rbf' (Gaussian kernel) 4# other kernels: poly, sigmoid, precomputed or a callable 6svc = svc.fit(X, y) 9# gives the support vectors There are other parameters In the case of linear SVM , we can also use . It's similar to but implemented in terms of rather than , so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples. ( The Regularization parameter (C, default C=1.0): if C is larger, hyperplane has smaller margin but do a better job of classification and otherwise. This is how you can control the trade-off between decision boundary and misclassification term. • Higher values of C → a higher possibility of overfitting, the softmargin SVM is equivalent to the hard-margin SVM. • Lower values of C → a higher possibility of underfitting. We admit misclassifications in the training data We use this in the case of not linearly separable data; It's also called soft-margin linear SVM. An illustration of using C. An illustration of using C. Bigger C, smaller margin. (ref) Gamma (gamma, default gamma='auto' which uses 1/n_features): determine the number of points to construct the hyperplane. An illustration of using gamma. In high-gamma case, we only consider points nearby the hyperplane, it may cause an overfitting. Bigger gamma, more change to get overfitting (in a XOR problem). • Chris Albon -- Notes about Support Vector Machines.	{"url":"https://dinhanhthi.com/note/support-vector-machine/","timestamp":"2024-11-11T01:33:42Z","content_type":"text/html","content_length":"491256","record_id":"<urn:uuid:a1ec0c54-5143-480b-82f7-f57f5f20f126>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00070.warc.gz"}
Using Array Models to Compare the Results of Multiplying Three Numbers in Different Orders Question Video: Using Array Models to Compare the Results of Multiplying Three Numbers in Different Orders Mathematics • Third Year of Primary School Compare the expressions. Pick the symbol that is missing. 2 × 3 × 6 ? 6 × 3 × 2 [A] > [B] < [C] = Video Transcript Compare the expressions. Pick the symbol that is missing. Two times three times six what six times three times two? Is the missing symbol greater than, less than, or equal to. We’re given two expressions, or two multiplication sentences. Two times three times six and six times three times two. We have to compare these two expressions and pick the missing symbol. Is two times three times six greater than six times three times two? Is two times three times six less than six times three times two? Or are the two expressions equal? Do we need the symbol greater than, less than, or equal to? Did you notice that each expression uses the same three numbers in a different order? We have a two. They both contain a three. And both expressions contain a six, so the same numbers, just in a different order. Does this give us the same total? Let’s find out. Here, we have two pictures, which we could call two arrays, or two groups. Each of the arrays contains three rows and six columns. To calculate how many squares there are altogether, first we would have to multiply three by six to find out how many squares there are in one rectangle, and then double it. Two lots of three times six. What is three times six? Let’s count in threes to find out, three, six, nine, 12, 15, 18. The first model shows two groups of 18. Two lots of 18, or double 18, is 36. So, the first expression two times three times six equals 36. The second expression has six lots of three times two. First, we need to work out what one lot of three times two is and then multiply it by six. Three times two is six. What is six times six. Let’s count in sixes, six, 12, 18, 24, 30, 36. Six times six is 36. Two times three times six equals 36. And six times three times two also equals 36. The missing symbol is equal to. Two times three times six is equal to six times three times two.	{"url":"https://www.nagwa.com/en/videos/730191907957/","timestamp":"2024-11-05T05:49:25Z","content_type":"text/html","content_length":"243501","record_id":"<urn:uuid:0af73d0c-acab-4fe3-af74-a26da535ca89>","cc-path":"CC-MAIN-2024-46/segments/1730477027871.46/warc/CC-MAIN-20241105052136-20241105082136-00141.warc.gz"}
Discrete Optimization in Machine Learning Solving optimization problems with ultimately discrete solutions is becoming increasingly important in machine learning: At the core of statistical machine learning is to infer conclusions from data, and when the variables underlying the data are discrete, both the tasks of inferring the model from data, as well as performing predictions using the estimated model are discrete optimization problems. Many of the resulting optimization problems are NPhard, and typically, as the problem size increases, standard off-the-shelf optimization procedures become intractable. Fortunately, most discrete optimization problems that arise in machine learning have specific structure, which can be leveraged in order to develop tractable exact or approximate optimization procedures. For example, consider the case of a discrete graphical model over a set of random variables. For the task of prediction, a key structural object is the "marginal polytope",a convex bounded set characterized by the underlying graph of the graphical model. Properties of this polytope, as well as its approximations, have been successfully used to develop efficient algorithms for inference. For the task of model selection, a key structural object is the discrete graph itself. Another problem structure is sparsity: While estimating a highdimensional model for regression from a limited amount of data is typically an ill-posed problem, it becomes solvable if it is known that many of the coefficients are zero. Another problem structure, submodularity, a discrete analog of convexity, has been shown to arise in many machine learning problems, including structure learning of probabilistic models, variable selection and clustering. One of the primary goals of this workshop is to investigate how to leverage such structures. There are two major classes of approaches towards solving such discrete optimization problems machine learning: Combinatorial algorithms and continuous relaxations. Workshop homepage: http://www.discml.cc/	{"url":"https://videolectures.net/events/nipsworkshops2010_discrete_optimization","timestamp":"2024-11-12T03:35:33Z","content_type":"text/html","content_length":"136576","record_id":"<urn:uuid:3e494165-3947-42a5-a6a3-42ec419e7562>","cc-path":"CC-MAIN-2024-46/segments/1730477028242.50/warc/CC-MAIN-20241112014152-20241112044152-00573.warc.gz"}
Our comprehensive college math placement test reliably and accurately assesses and places students based on their understanding of Essential Math Skills, College Math Fundamentals, Advanced Algebra, and Trigonometry and Analytical Geometry. College Math Fundamentals assesses students with respect to the content deemed necessary to be successful in the lowest-level credit-bearing math class, based on national college readiness standards. Essential Math Skills can be used to place students into multiple-levels of developmental math, into a bridge course or pre-college intervention, as well as credit-bearing coursework with additional supports. Advanced Algebra and Trigonometry and Analytical Geometry are used in combination to place students into higher-level courses, such as trigonometry, precalculus and calculus. The math test is a 90-minute, stage-adaptive test. The exam begins with an assessment of College Math Fundamentals. Depending on how well a student performs on the College Math Fundamentals section, s/he will receive either the Essential Math Skills content or the Advanced Algebra and Trigonometry and Analytic Geometry content. Consequently, students will receive scores in either College Math Fundamentals and Essential Math Skills or College Math Fundamentals, Advanced Algebra, and Trigonometry and Analytic Geometry. Students are permitted to use a built-in scientific calculator for items on the College Math Fundamentals, Advanced Algebra, and Trigonometry and Analytic Geometry portions of the exam, but a calculator is neither permitted nor available for the Essential Math Skills section. All reported scores for the math test have reliabilities of 0.85 or higher.	{"url":"https://tailwindtesting.com/placement-exams","timestamp":"2024-11-02T08:43:56Z","content_type":"text/html","content_length":"70040","record_id":"<urn:uuid:4db832f5-b276-4a23-a25e-8496ee50b9e2>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00524.warc.gz"}
Blake Keeler - Part 4: Spectral Asymptotics and the Heat Kernel - Advanced GMA Seminar - Department of Mathematics Blake Keeler – Part 4: Spectral Asymptotics and the Heat Kernel – Advanced GMA Seminar October 8, 2019 @ 4:00 pm - 5:00 pm Part 4: Spectral Asymptotics and the Heat Kernel. Abstract: In this lecture series, our goal will be to prove a result known as Weyl’s law, which tells us how the Laplace eigenvalues of a compact manifold are distributed. Since eigenvalues are inherently quite difficult to study, we will utilize a “back-door” approach via the heat equation. The heat kernel can be constructed using fairly classical techniques, and much of our time will be spent exploring its properties and using it to develop the spectral theory of the Laplacian. Lecture 1 will cover some preliminary concepts. We begin with a brief overview of the heat equation in Euclidean space, which will inform our intuition for what we expect on manifolds. We will then extend our notion of the Laplacian to Riemannian manifolds, which will allow us to write down an associated heat equation. Then, under the assumption that a fundamental solution to this heat equation exists, we will be able to show that the Laplacian has discrete spectrum and an associated orthonormal basis of eigenfunctions in L^2(M). In lecture 2, we will show that the heat kernel exists by actually constructing it. As a consequence of the construction, we will have an asymptotic expansion of the kernel for small timescales. In lecture 3, we will connect the heat trace to the distribution of eigenvalues using the Karamata Tauberian theorem, and Weyl’s law will follow as a straightforward corollary. Time permitting, we will also discuss some generalizations of Weyl’s law and improvements that can be made in the error term, as well as some relevant current research.	{"url":"https://math.unc.edu/event/blake-keeler-part-4-spectral-asymptotics-and-the-heat-kernel-advanced-gma-seminar/","timestamp":"2024-11-13T22:34:46Z","content_type":"text/html","content_length":"114577","record_id":"<urn:uuid:24962a15-11fa-46b2-9852-44e7b927a3ab>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00690.warc.gz"}
tion of m Estimation of migration from census data Description of the methods Estimating migration from census data is not technically complicated. Provided that the census(es) gather the appropriate information and are reasonably accurate it is possible to produce estimates of net immigration (i.e. immigration less emigration) of the foreign-born population (people born outside a particular country) and internal migration between (to and from) sub-national regions of a country, over the period between two censuses. To estimate net immigration of foreigners one essentially subtracts from the number of foreign-born people enumerated in a census, the number of foreigners expected to have survived since being enumerated in the previous census. In a similar way, if the censuses record the sub-national region of birth one can estimate net in-migration (i.e. net in-migration of those born outside the region less net out-migration of those born in the region) between sub-national regions of a country. However, if the census asks of people where they were living at some prior point in time, say at the time of the previous census, one is able to estimate directly the number of surviving migrants (i.e. migrants still alive at the time of the latest census) into and out of each sub-national region of the country since that prior point in time. In order to estimate the number of migrants from the number of surviving migrants at the time of the second census one needs to add to these figures an estimate of the number of migrants who are expected to have died between moving and the time of the latest census. If the latest census records other information such as year in which the migrant moved to the place at which the person was counted in the census, it is possible also to establish a trend of migration over time. Migration is different from fertility and mortality both in that migrating is not final in the sense of a birth or death, but also that we are concerned not only with the population of origin, from which the migrant moved (which corresponds to a population exposed to the risk from which rates of migration akin to those of fertility and mortality can be calculated) but we also have a population to which the migrant moves, the destination population. Apart from this, in order to understand migration one is often interested in distinguishing between different types of migration (whether temporary or more permanent, whether circulatory or unidirectional, etc.). For these reasons there is a much wider range of measures and terminology associated with migration than there is with either fertility or mortality. It is not the purpose of this chapter to cover these issues and the interested reader is referred to the standard texts on the subject such as the UN Manual VI (UN Population Division 1970), Shryock and Siegel (1976), Siegel and Swanson (2004). Data requirements and assumptions Tabulations of data required • To estimate net immigration of foreigners: □ the number of foreign-born females (males), in five-year age groups, and for an open age interval A+, at two points in time, typically two censuses □ For the deaths: either a suitable model life table or the numbers of native-born females (males), in five-year age groups, and for an open age interval A+, at two points in time, typically two censuses. Failing these, the central crude death rate for the population • To estimate sub-national regional net in-migration from place of birth data: □ the number of females (males) by sub-national region and by sub-national region of birth, in five-year age groups, and for an open age interval A+, at two points in time, typically two □ For the deaths: either a suitable model life table, the numbers of native-born females (males), in five-year age groups, and for an open age interval A+, at two points in time, typically two censuses or numbers of deaths by region from the vital registration. Failing these, the central crude death rate for the population • To estimate internal migration between sub-national regions from place of residence at previous census data: □ The numbers of females (males) by sub-national region and by sub-national region at some prior date, typically that of the preceding census, in five-year age groups, and for an open age interval A+. If age-specific numbers are not available, aggregated data is still useful for estimating all-age migration. Important assumptions • Estimating net immigration of foreigners: □ Censuses identify all foreign-born people accurately □ One is able to estimate the mortality of the foreign-born population accurately (either that the life table used is appropriate, or that the mortality is the same as that implied by the censuses for the native-born (locally-born) national population) □ No return migration of locally born emigrants • Estimating sub-national regional net in-migration from place of birth data: □ Censuses count the population by sub-national region accurately and identify the region of birth accurately □ One is able to estimate the mortality of people moving between two regions accurately (either that the life table used is appropriate, or that the mortality is the same as that implied by the censuses for the native-born national population). • Estimating internal migration between sub-national regions from data on place of residence at previous census: □ Latest census identifies correctly all people who have moved from one region to another since the prior date (e.g. previous census) □ One is able to estimate the mortality of people moving between two regions accurately (either that the life table used is appropriate, or that the mortality is the same as that implied by the censuses for the native-born national population). Since one is estimating in- and out-migration separately (as opposed to net migration) this assumption is of less importance. Preparatory work and preliminary investigations Before applying this method, you should investigate the quality of the data in at least the following dimensions • age structure of the population (by sub-national region as appropriate); and • relative completeness of the census counts (by sub-national region as appropriate). Caveats and warnings Estimating migration using place of birth data from two censuses not only requires that the censuses count the population reasonably completely, but that the place of birth be accurately recorded. Often this is not the case, particularly when estimating immigration, where immigrants wish to hide the fact that they are foreign, but also in the case of internal migration where there may have been boundary changes or the respondent is ignorant about the place of birth of the person. Estimating migration by asking questions of migrants is quite dependent on the census identifying completely all those who have migrated, as well as identifying the place from which moved correctly. To the extent that recent migrants are not yet established as residents of the region to which they have moved at the time of the census, they could be missed in the count. Net migration, by definition, underestimates the flows of migrants into and out of a region or country. Thus, for example, people who moved into a region and then returned within the period being considered will result in zero net in-migration and yet moved twice. Application of the method A: Estimating net immigration of foreigners using place of birth data This method produces estimates of the net immigration of foreigners using place of birth data. It is important to stress that this method does not take into account or measure the immigration of returning native-born people who left the country prior to the previous census and returned before the second census. Thus this method is not recommended for the measurement of immigration where significant return migration of native-born people (for example, after exile or forced migration of refugees) is in progress. Step 1: Decide on survival factors If data on the number of foreign-born people in the population are available by age group for each census then one needs to estimate the survival factors to be applied to the numbers of foreign-born in the first census to estimate the numbers surviving to the time of the second census. The user can choose between years of life lived in five-yearly age groups ([5]L[x]) based on the standard from the General family of United Nations model life tables or one of any of the four families of Princeton model life tables or a model life table of a population experiencing an AIDS epidemic (Timæus 2007) or failing this, the survival factors can be derived from the proportion of each five-year age group of the native-born population surviving from the first to the second census (assumed to be n years apart, where n is a multiple of 5). Thus $5 S x,n , ∞ S A−n,n $ and $ S B,n $, the n-year survival factor for a group of people aged x to x + 5 at the previous census, A-n and older at the previous census, and born between censuses, respectively are estimated as follows: $ 5 S x,n = 5 L x+n 5 L x or 5 N x+n nb (t+n) 5 N x nb (t) , ∞ S A−n,n = T A T A−n or ∞ N A nb (t+n) ∞ N A−n nb (t) , and S B,n = n L 0 n l 0 or n N 0 nb (t+n) B nb .$ where the superscript nb represents ‘native-born’, $ 5 N x nb (t)$ represents the native-born population in the census at time t and B^nb represents the number of native-born births between time t and t + n. If the data are not available in five-year age groups, the net number of immigrants can still be estimated in total provided we have an estimate of the crude death rate for the population (which might, in the absence of any evidence to the contrary, be assumed to be that of the native-born population). Step 2: Estimate the number of deaths of the immigrants If data on the number of foreign-born people in the population are available by age group for two censuses (n years apart) then one needs to estimate the number of deaths of foreign-born people (denoted by the superscript F) aged between x and x+5 at the first census (at time t), $ 5 D x F $, aged A-n and older at the first census, $ ∞ D A−n F $, and those born between the censuses, $ D B F $, as follows: $ 5 D x F = 1 2 ( 5 N x F (t)⋅ 5 S x,n + 5 N x+n F (t+n) )( 1 5 S x,n −1 ) , ∞ D A−n F = 1 2 ( ∞ N A−n F (t)⋅ ∞ S A−n,n + ∞ N A F (t+n) )( 1 ∞ S A−n,n −1 ) , and D B F = 1 2 ( n N 0 F (t+n) )( 1 S B,n −1 ) .$ where $5 N x F (t)$ represents the number of foreign-born people according to the census at time t who were aged between x and x+5. If data and/or survival factors are not available by age group then one can estimate the total number of deaths of the foreign-born people as follows: However, if the age distribution of the foreign-born population is markedly different from that of the population in the country of the census, then this can produce a poor approximation to the true number of deaths. Step 3: Estimate the net number of immigrants (of foreigners) If data are available by age group for each census, then age-specific net immigration can be estimated as follows: $Net 5 M x F = 5 N x+n F (t+n)− ∞ N x F (t)+ 5 D x F$ for x = 0, 5, … , A-5-n where $Net 5 M x F$ represents the net number of immigrants between times t and t+n who were aged between x and x + 5 at time t. For x > A - 5 - n $Net ∞ M A−n F = ∞ N A F (t+n)− ∞ N A−n F (t)+ ∞ D A−n F .$ The net number of immigrants of those born between times t and t+n is estimated as follows: $Net M B F = n N 0 F (t+n)+ D B F .$ If data and/or survival factors are not available by age group then one would estimate of the total net number of immigrants as follows: $Net ∞ M 0 F = ∞ N 0 F (t+n)− ∞ N 0 F (t)+ ∞ D 0 F .$ B: Estimating net internal migration between sub-national regions from place of birth data Net in-migration into a particular sub-national region from other regions in the country can be estimated in exactly the same way as the international immigration, described above, by replacing the foreign-born population with the population born outside the region. In addition, applying the same method to data on the change in the numbers of population born in (rather than outside) and living outside the region of interest allows us to estimate the net out-migration of those born in the region to other regions in the country. Subtracting this from the net in-migration of those born outside the region gives an estimate of the overall net in-migration into the region of interest. If there is reason to suspect that there is a material difference in the mortality experienced by those born outside who moved into the region and those born in the region who moved out, and one has appropriate survival factors then one could apply different survival factors to each when estimating the net number of migrants. However, in practice it is likely that inaccuracies in the census data on place of residence at previous census are likely to outweigh any increase in accuracy achieved by using differential mortality. C: Estimating internal migration between sub-national regions from place of residence at previous survey Net sub-national inter-regional migration is estimated directly from the numbers of people in each region at the time of the census who moved since the previous census by place (e.g. region) they were in at a given prior date (e.g. at the time of the previous census). Confining the estimates to inter-regional flows the sum of the numbers of inter-regional in-migrants should be equal to the sum of inter-regional out-migrants; however, if the data include immigration to the sub-national regions from outside the country one can extend the estimates of in-migration to include international immigration into each region. Since one of the major areas of interest is the magnitude of inter-regional flows of the population, one is as interested in the total numbers of migrants between regions as one is in the age distributions of particular flows. The number of migrants is derived from the number of surviving in- and out-migrants as follows: $5 M x = ( 5 I ′ x − 5 O ′ x + ( 5 I ′ x − 5 O ′ x ) x / 5 S x )/2 ,$ where the superscript (’) represents numbers surviving and [5]I’[x] and [5]O’[x] respectively represent the number of surviving in-migrants into, and the surviving number out-migrants from, a particular region at the time of the second census who were aged between x and x+5 at the second census. Worked example This example uses data on the numbers of males in the population from the South African Census in 2001 and a ‘census replacement survey’, the Community Survey in 2007. (Although the survey was conducted approximately 5.35 years after the night of the census in 2001, it is assumed for the purposes of presentation here to have been exactly five years after the census in 2001.) A: Estimating net immigration of foreigners using place of birth Step 1: Decide on survival factors The survival factors are shown in the fifth column of Table 1. The values are derived from (the years of life lived in each age group of) an alternative life table for those aged 20 to 24 last birthday and those aged 80 and over at the time of the first census, and those born between the two censuses, as follows: $ 5 S 20,5 = 5 L 25 5 L 20 = 4.3382 4.4975 =0.96458 ∞ S 80,5 = T 85 T 80 = 0.75180 1.19603 =0.40912 and S B,5 = 5 L 0 5 l 0 = 4.707549 5 =0.94151.$ Table 1 Estimation of deaths of foreign-born and the net number of immigrants by age group, South Africa, 2001-2006 Age 2001 2006 x [5]S[x] Age at 2^nd census D^F Net M B 0.94151 0- 4 8,963 12,577 0 0.97896 0- 4 391 12,968 5- 9 10,390 13,724 5 0.99547 5- 9 242 5,003 10-14 13,508 13,998 10 0.99427 10-14 55 3,664 15-19 27,835 27,943 15 0.98602 15-19 119 14,555 20-24 69,787 59,493 20 0.96458 20-24 616 32,275 25-29 87,381 95,763 25 0.93161 25-29 2,994 28,970 30-34 73,338 100,450 30 0.90960 30-34 6,675 19,743 35-39 66,663 85,490 35 0.89780 35-39 7,563 19,715 40-44 59,152 75,684 40 0.89092 40-44 7,701 16,721 45-49 45,184 66,113 45 0.88633 45-49 7,274 14,234 50-54 40,398 55,913 50 0.87224 50-54 6,154 16,883 55-59 30,640 42,833 55 0.84731 55-59 5,717 8,153 60-64 24,376 34,433 60 0.80885 60-64 5,442 9,234 65-69 17,895 25,588 65 0.75468 65-69 5,353 6,564 70-74 13,561 18,989 70 0.66991 70-74 5,281 6,375 75-79 10,238 12,850 75 0.56388 75-79 5,404 4,693 80-84 7,658 7,461 80+ 0.40912 80-84 5,118 2,341 85+ 4,455 5,305 85+ 7,410 602 Total 611,423 754,608 Total 79,509 222,693 Step 2: Estimate the number of deaths Since we have data on the number of foreign-born people in the population by age group for each census we can estimate the number of deaths of foreign-born people which occurred in the period between the two censuses by age group using the numbers of foreigners in each census given in the second and third columns of Table 1. For those aged 20 to 24 last birthday and those aged 80 and over at the time of the first census, and those born between the two censuses, the calculations are as follows: $ 5 D 20 F = 1 2 ( 5 N 20 F (2001)⋅ 5 S 20,5 + 5 N 25 F (2006) )( 1 5 S 20,5 −1 ) =( 69787⋅0.96458+95763 )( 1 0.96458 −1 )=2994 ∞ D 80 F = 1 2 ( ∞ N 80 F (2001)⋅ ∞ S 80,5 + ∞ N 85 F (2006) )( 1 ∞ S 80,5 −1 ) =( ( 7658+4455 )0.40912+5305 )( 1 0.40912 −1 )=7410 and D B F = 1 2 ( 5 N 0 F (2006) )( 1 S B,5 −1 )=12577( 1 0.94151 −1 )=391 .$ If data and/or survival factors were not available by age group then one could estimate the total number of deaths of the foreign born people as follows, given an estimate of the crude mortality rate in the population of 14 per 1,000: $ ∞ D 0 F = 5 2 ( ∞ N 0 F (2001)+ ∞ N 0 F (2006) ) ∞ m 0 = 5 2 ( 611423+754608 ) 14 1000 =47811 .$ Step 3: Estimate the net number of immigrants (of foreigners) Since data are available by age group for each census, age-specific net immigration of those born outside the country can be estimated as follows:If data and/or survival factors were not available by age group then one could estimate the total net number of immigrants as follows: $Net 5 M 20 F = 5 N 25 F (2006)− ∞ N 20 F (2001)+ 5 D 20 F =95763−69787+2994=28970 Net ∞ M 80 F = ∞ N 85 F (2006)− ∞ N 80 F (2001)+ ∞ D 80 F =5305−( 7658+4455 )+7410=602 Net M B F = 5 N 0 F (2006)+ D B F =12577+391=12968 .$ If data and/or survival factors were not available by age group then one could estimate the total net number of immigrants as follows: $Net ∞ M 0 F = ∞ N 0 F (2006)− ∞ N 0 F (2001)+ ∞ D 0 F =754608−611423+47811=190996$ B: Estimating sub-national regional net in-migration using place of birth The second and third column of Table 2 show the numbers of people living in the Western Cape province of South Africa who were born outside the province, as counted by the 2001 Census and the 2007 Community Survey, respectively. Although the same survival factors (column 5) have been used as were used in the example of Method A, this should not be the case if it was thought that the mortality experience of native-born and immigrants were very different. The final column of Table 2 gives the net numbers of migrants into the Western Cape who were born in provinces other than the Western Cape for the different age groups. Thus in total 213,911 people born outside the Western Cape moved to the Western Cape (after excluding those who moved out). Table 2 Estimation of the net number of in-migrants of those born outside by age group, Western Cape, South Africa, 2001-2006 Age 2001 2006 x [5]S[x] Age at 2^nd census D[O] Net M (born out) B 0.94151 0- 4 16,443 19,012 0 0.97896 0- 4 591 19,602 5- 9 24,406 28,743 5 0.99547 5- 9 482 12,782 10-14 31,134 30,792 10 0.99427 10-14 125 6,511 15-19 44,478 53,933 15 0.98602 15-19 245 23,043 20-24 74,011 82,526 20 0.96458 20-24 896 38,944 25-29 80,187 89,522 25 0.93161 25-29 2,954 18,466 30-34 65,833 90,783 30 0.90960 30-34 6,074 16,670 35-39 56,393 76,475 35 0.89780 35-39 6,776 17,417 40-44 44,420 59,692 40 0.89092 40-44 6,268 9,567 45-49 32,862 47,612 45 0.88633 45-49 5,338 8,529 50-54 28,178 37,969 50 0.87224 50-54 4,303 9,409 55-59 19,983 30,205 55 0.84731 55-59 4,012 6,039 60-64 17,569 25,593 60 0.80885 60-64 3,832 9,442 65-69 11,216 20,802 65 0.75468 65-69 4,137 7,371 70-74 8,365 12,612 70 0.66991 70-74 3,426 4,822 75-79 5,919 8,434 75 0.56388 75-79 3,458 3,528 80-84 4,063 5,061 80+ 0.40912 80-84 3,248 2,390 85+ 2,152 2,183 85+ 3,413 -620 Total 567,613 721,949 Total 59,576 213,911 The second and third columns of Table 3 present the numbers of people living in provinces other than the Western Cape who were born in the Western Cape, as counted by the 2001 census and the 2007 Community Survey, respectively. The net number of out-migrants of those born in the Western Cape (i.e. the number of people born in the Western Cape who moved out, less those who have returned) is given in column 8. The negative numbers mean that there was negative net out-migration (i.e. the number of those born in the Western Cape who moved to other provinces in the period was less than the number born in the Western Cape who were living outside who returned during the period). Thus the total of -19,017 means that the number of people born in the Western Cape, who returned to the Western Cape during the period having lived in another province until 2001 exceed those who were born in the Western Cape and moved to another province in the period by 19,017. These estimates were derived using the same survival factors as were used for those born outside the Western Cape who moved into the province, but if there was reason to suppose that the mortality differed for those born in the Western Cape who moved out, then a different set of survival factors would be used to estimate the Net M (born in) numbers. The overall net in-migration for the province is thus given in the final column of Table 3. Thus in total 232,928 more people moved into the Western Cape than left the Western Cape to live in another In this example those born outside the province include those born outside the country and thus the overall net migration includes immigrants who settle in the province. Excluding the foreign-born from Table 2 would produce numbers of internal in-migrants net of internal out-migrants, and the sum of these numbers for all the provinces together would be zero. Table 3 Estimation of the net number of out-migrants of those born inside by age group, Western Cape, South Africa, 2001-2006 Age 2001 2006 x [5]S[x] Age at 2^nd census D[I] Net M (born in) Net M B 0.94151 0- 4 22,055 11,747 0 0.97896 0- 4 365 12,112 7,490 5- 9 21,895 12,509 5 0.99547 5- 9 367 -9,180 21,962 10-14 21,382 11,593 10 0.99427 10-14 76 -10,226 16,737 15-19 18,265 13,455 15 0.98602 15-19 100 -7,827 30,870 20-24 14,645 10,477 20 0.96458 20-24 202 -7,587 46,531 25-29 13,501 9,534 25 0.93161 25-29 434 -4,676 23,142 30-34 13,118 11,047 30 0.90960 30-34 867 -1,587 18,257 35-39 12,121 14,614 35 0.89780 35-39 1,319 2,815 14,602 40-44 11,725 12,195 40 0.89092 40-44 1,311 1,384 8,183 45-49 10,335 10,538 45 0.88633 45-49 1,285 98 8,431 50-54 9,211 9,881 50 0.87224 50-54 1,221 768 8,642 55-59 7,264 10,568 55 0.84731 55-59 1,362 2,720 3,319 60-64 6,691 7,723 60 0.80885 60-64 1,250 1,710 7,732 65-69 4,643 5,297 65 0.75468 65-69 1,265 -128 7,499 70-74 3,954 3,766 70 0.66991 70-74 1,182 304 4,517 75-79 2,331 2,384 75 0.56388 75-79 1,240 -330 3,858 80-84 1,402 2,140 80+ 0.40912 80-84 1,336 1,145 1,244 85+ 707 555 85+ 1,024 -531 -89 Total 195,246 160,023 Total 16,206 -19,017 232,928 C: Estimating internal migration between sub-national regions from data on place of residence at previous census Table 4 presents the results of the answers to the question about place (province in this example) of residence at the time of the 2001 Census given by those counted in each of the provinces in the 2007 Community Survey. (In actual fact the question asked whether the person was staying at the same place at the time of the prior census and if not, where they were staying at the time they moved to the place at which they were counted in the Community Survey. However, work by Dorrington and Moultrie (2009) shows that using these data and the year of movement to back project the population in order to estimate the numbers by province of residence at the time of the previous survey suggests that the assumption that there was only one move in the five years since the previous census was reasonably accurate.) By far the largest numbers of migrants are those that moved within each of the provinces, however, these have been excluded from Table 4 because one is usually more interested in interprovincial migration than migration within a province. Table 4 Interprovincial migration, South Africa, 2001-2006 Province where counted (destination) Previous residence (origin) WC EC NC FS KZ NW GT MP LM Total WC 12,173 4,060 1,745 3,221 2,113 16,400 1,405 874 41,992 EC 52,239 1,120 7,187 25,209 14,430 28,633 4,693 2,116 135,626 NC 4,813 1,942 3,480 908 3,728 4,956 1,062 357 21,246 FS 2,943 3,145 2,546 2,352 12,733 19,920 4,293 1,963 49,896 KZ 6,762 7,015 631 2,358 3,573 50,980 8,886 1,194 81,399 NW 1,478 907 9,811 5,555 2,329 47,633 3,090 4,337 75,140 GT 24,891 12,948 3,962 11,437 18,145 32,433 18,598 15,133 137,547 MP 2,134 1,317 280 1,724 4,546 5,767 42,941 8,628 67,338 LM 2,754 1,583 255 1,709 2,209 9,773 81,394 24,211 123,889 OSA 21,221 5,467 1,209 9,584 10,933 11,437 51,873 8,335 9,286 129,346 DNK 500 3 15 124 132 78 228 89 0 1,170 UNS 1,058 1,029 107 208 875 508 3,558 408 633 8,384 Total 120,794 47,528 23,996 45,111 70,860 96,573 348,516 75,070 44,524 872,973 WC = Western Cape, EC = Eastern Cape, NC = Northern Cape, FS = Free State, KZN = KwaZulu-Natal, NW = North West, GT = Gauteng, MP = Mpumalanga, LM = Limpopo, OSA = Outside SA, DNT = Do not know, UNS = Unspecified In addition to the all-age numbers in Table 4 (in actual fact these numbers exclude, as is often the case, migration of those born between the census and survey) one can also produce numbers of in- and out-migration by age groups as shown in Table 5. For completeness these numbers include estimates of the number of migrants who were born since the previous census. However, relative to the other migrants these numbers look implausibly high, and the reason for this is discussed below. The net number of migrants is estimated for those aged 25-29 at the time of the Community Survey (i.e. were aged 20-24 at the time of the 2001 census), for example, as follows: $5 M x = ( 20675−5649+ ( 20675−5649 )/ 0.96458 )/2 =15301 .$ Table 5 Estimation of the net number of in-migrants by age group, Western Cape, South Africa, 2001-2006 Age Surviving in- migrants (I’) Surviving out- migrants (O’) x [5]S[x] Net in-migrants 0- 4 20,846 11,747 B 0.94151 9,381 5- 9 6586 3,554 0 0.97896 3,065 10-14 6685 2,882 5 0.99547 3,812 15-19 10402 3,967 10 0.99427 6,454 20-24 21266 4,488 15 0.98602 16,897 25-29 20675 5,649 20 0.96458 15,301 30-34 15584 6,008 25 0.93161 9,928 35-39 10584 5,098 30 0.90960 5,758 40-44 7264 3,045 35 0.89780 4,458 45-49 4648 2,714 40 0.89092 2,053 50-54 3095 1,500 45 0.88633 1,698 55-59 3940 935 50 0.87224 3,225 60-64 3776 527 55 0.84731 3,541 65-69 3127 818 60 0.80885 2,582 70-74 1540 437 65 0.75468 1,282 75-79 561 206 70 0.66991 442 80-84 797 116 75 0.56388 944 85+ 264 47 80+ 0.40912 374 Total 141,640 53,739 91,194 Diagnostics, analysis and interpretation Checks and validation Perhaps the simplest check, on the reasonableness of the ‘shape’ (i.e. distribution of the numbers by age) of the estimates but not the level, is to see if it conforms to the standard shape (or a variation thereof). Rogers and Castro (1981a; 1981b) point out that the distribution of the number (or rate) of in- and out-migrants tends to conform to standard patterns, with a peak in the young adult ages (usually associated with seeking employment), a second, usually less pronounced peak amongst very young children falling to a trough amongst young teenagers (the size depending on the extent to which it is families rather than individuals moving in the young to middle aged adults). Sometimes there is also a ‘hump’ (or trough) around retirement age if there is a strong flow of migrants moving to (or away from) the place to retire. These patterns (not necessarily the same pattern) apply to in- and out-migration flows separately, but not necessarily to net migration (which is the difference between the two flows) unless one flow (either the in-migration or the out-migration) is much greater than the other. Figure 1 illustrates this using some of the estimates calculated above, expressed as proportions of the total number in each case (to allow them to be presented on a single figure). From this we can see that in broad terms (with the exception in some cases, where the proportion of migrants at the very young ages looks implausibly high) each conforms to the expected shape. The net out-migrants of those born in the Western Cape (excluded from the figure for ease of illustration) does not conform to a standard model of migration, which could indicate these numbers are not very reliable, however, they are small relative to the in-migration of those born outside the province, and thus such a deviation may tolerated. In addition to this there are two other features to be noted from Figure 1. The first is that the out-migration from the Western Cape as estimated from data on place of residence at previous census, suggests that adult out-migrants peak at a somewhat older age (and possibly are likely to represent family rather than individual migration). The second is the fact that the net immigration into the country follows the standard shape which indicates that the flow into the country is much stronger than the return flow of those migrants. If the census asked place of birth and place of residence at the previous census then one can compare the two estimates of net in-migration into a specific sub-national region. If they are similar this gives one some confidence in the results. In the case of the place of birth data for South Africa the net number of in-migrants into the Western Cape is 232,928 (Table 3) while the estimate from the data on place of residence at the time of the previous census data produced an estimate of 92,194 (Table 4), which suggests that one or both of these sets of data are suspect. The most basic check of the estimates of migration is to project the population (of the country or the province) at the first census to the time of the second census making use of the estimates of the number of migrants and compare that with the census estimates from the second, more recent, census to see how well the two match, especially in the age range in which migration is concentrated. In the case of the net in-migration into the Western Cape, projecting the population forward from 2001 using the estimates derived from the change in the numbers by place of birth produced a much closer fit to the population in the 20-29 year age range, suggesting that the data on place of birth are probably more complete than those on the place of residence at the date of the previous census. To some extent this is supported by a comparison of the change in the number of foreign-born in the country between the two censuses, 222,693 (Table 1) with the sum of the numbers who reported that they had moved from outside South Africa to one of the provinces since the previous census, 129,346 (Table 4). Ideally, if one had independent estimates of the number of migrants one might compare those numbers against estimates using the above methods. Unfortunately, reliable independent estimates are rare. Although most countries try to record people entering and leaving the country, these data are often not reliable, particularly in developing countries with relative porous borders. And unless the country is extremely well regulated and maintains a complete and accurate register of the population, the only other way to measure internal migration is through migration-specific surveys, which tend to be much more useful for understanding the type of migration (whether permanent, temporary, cyclical, etc.) than for producing reliable estimates of the number of migrants, given the often less structured situation that (particularly recent) migrants find themselves living in and an understandable reluctance to identify themselves as being migrants. Considering the numbers of migrants estimated from the data on place of residence at the previous census given in Table 4 (and taking into account the suspicion that these probably underestimate the true migration), some 2-4% of the population changed province of residence in the 5 years between the 2001 Census and the Community Survey. Had we included the number who moved within, but did not change, province then between 7 and 15 per cent of the population moved in the 5‑year period. The main provinces of destination are Gauteng (by a big margin) and Western Cape, which are predominantly urban and the wealthiest provinces. The main provinces of origin are Gauteng (inspection of the age distribution would show that this is mainly return migration of ‘retiring’ workers) Eastern Cape and Limpopo, which are poor, mainly rural provinces, from which people seeking work migrate to the urban areas. It appears that migration is predominantly of individuals (seeking work) rather than of families. Method-specific issues with interpretation Scanning errors A particular feature of the data relying on province of birth is the apparently relatively high number of children born since the first census who have moved to another province. In all likelihood this is an artefact of the data capturing process. Scanning was used to capture the data from the questionnaires on which Western Cape was coded as a “1”, written in the appropriate space by hand. It appears that in a small percentage of cases the scanner might have had trouble distinguishing a handwritten “1” from a handwritten “7” (the code for Gauteng). The result of this is, for example, that some of the children coded as having been born outside the province in which they were counted, and thus appear to be migrants, but probably were not. Even though the percentage error in scanning is very small, the number of births can be large relative to the number migrants, and thus the error can produce noticeable errors. Since an increasing number of developing countries are using scanning to capture data, this sort of problem may be quite common. Where scanning errors or other situations make it impossible to produce reliable estimates of the number of migrants of those born since the previous census one can use CWR from second census as $Net 5 M 0 = 1 4 CW R 0 ⋅Net 30 M 15 f$ for those born in the most recent five years, and $Net 5 M 5 = 3 4 CW R 5 ⋅Net 30 M 20 f$ for those born in the five years before that if the censuses are 10 years apart, where CWR[x] represents ratio of the number of children aged between x and x+5 to the number of women in the population aged between 15+x and 45+x in the population (regional or national) at the time of the second census, and $ 30 M x f $ represents the number of women migrants aged between x and x+30. Applying this to the data for the Western Cape suggest that the number of migrants born since the previous census should be less than half the numbers being estimated from the data on place of birth. Detailed description of method Mathematical exposition The indirect estimation of migration derives from the balance equation for two censuses n years apart, namely: $5 N x+n (t+n) = 5 N x (t)− 5 D x + 5 I ′ x − 5 O ′ x = 5 N x (t)− 5 D x + 5 M ′ x$ where $5 M ′ x = 5 I ′ x − 5 O ′ x$ is the net (i.e. in less out) number of in-migrants, aged x to x+5 at the time of the first census, surviving to the second census, and [5]D[x],[ 5]I’[x] and[ 5]O’[x], represent the number of deaths, surviving in-migrants and out-migrants, aged x to x+5 at the time of the first census, who died or moved in the period between the censuses. For those born after the first census the equation becomes: $n N 0 (t+n)=B− D B + M ′ B$ and those in the open age interval: $∞ N A (t+n)= ∞ N A−n (t)− ∞ D A−n + ∞ M ′ A−n$ where B represents the number of births in the population between the two censuses, D[B] the number of deaths of those births in the period between the censuses and M’[B] the net number of surviving migrants, born outside the country in the period between the two censuses, [∞]D[A-n] the number of deaths in the intercensal period aged A-n and older at the time of the first census, and [∞]M’[A-n] the net number of migrants aged A-n and older at the time of the first census. $5 M ′ x = 5 N x+n (t+n)− 5 N x (t)+ 5 D x M ′ B = n N 0 (t+n)−B+ D B ∞ M ′ A−n = ∞ N A (t+n)− ∞ N A−n (t)+ ∞ D A−n $ or alternatively $5 M ′ x = 5 N x+n (t+n)− 5 N x (t) 5 S x M ′ B = n N 0 (t+n)−B S B ∞ M ′ A−n = ∞ N A (t+n)− ∞ N A−n (t) ∞ S A−n $ where [5]S[x] , S[B] and [∞]S[A-n] represent the proportion of the populations aged x to x+5 at the time of the first census, born between the censuses, and aged A-n and older at the time of the first census, respectively, surviving to the second census. The net number of migrants can thus be estimated from the net number surviving to the second census as follows: $5 M x = ( 5 M ′ x + 5 M ′ x / 5 S x )/2 = 5 M ′ x ( 5 S x +1 ) 2 5 S x M B = M ′ B ( S B +1 ) 2 S B ∞ M A−n = ∞ M ′ A−n ( ∞ S A−n +1 ) 2 ∞ S A−n .$ Unfortunately, since the net number of migrants is usually small relative to the size of the population, age misstatement or errors in either or both census counts can lead to very poor estimates being produced. Better estimates of the net number of immigrants into a country can be produced by confining one’s attention to the population of foreigners (defined as those born outside the country) and assuming that return migration of emigrants from the country of interest is insignificant. Thus one replaces each of the symbols above by equivalents specific to the foreign-born population in the country. Since it is unlikely that one has an accurate record of the number of the foreign-born deaths these need to be estimated in one of the following ways: • Option 1 (Life table survival ratios): Applying rates from a suitable model life table, then $5 S x = 5 L x+n 5 L x , S B = n L 0 n⋅ l 0 and ∞ S A−n = T A T A−n .$ • Option 2 (Census survival ratios): Assuming that emigration of the native-born population is insignificant and that the proportions surviving are the same as those in the native-born population, $5 S x = 5 N x+n nb (t+n) 5 N x nb (t) , S B = n N 0 nb B nb and ∞ S A−n = ∞ N A nb (t+n) ∞ N A−n nb (t) ,$ where the superscript “nb” designates native-born. • Option 3 (Vital registration): Where one has access to numbers of births and deaths from another source such as vital registration (which is only likely to be the case, if at all, with internal migration), one could work with deaths and births corresponding to the migrant population directly instead of survival ratios to estimate the net number of surviving in-migrants. Alternatively the net number of migrants can be derived as above by setting $5 S x =1− 5 D x 5 N x (t) , S B = D B B and ∞ S A−n = D A−n ∞ N A−n (t)$ where the births and deaths are from the vital registration. However, for most developing countries, particularly those in Africa, vital registration systems are too incomplete to be used in this way. Internal migration When it comes to internal migration one can estimate net in-migration (i.e. in-migration of those born outside the region less out-migration of those born outside the region who had previously moved into the region) into each sub-national region of those born outside the region by making use of place of birth information to identify the change in numbers of those born outside the region, in the same way as described above. However, since one also has the place of residence of those born in the region who have moved out of the region since birth (but not emigrated) one can also estimate the net out-migration of those born in the region (i.e. out-migration of those born in the region less those born in the region who have returned after having previously moved out of the region) by applying the method described above to the population born in the region (as opposed to those born outside the region). When estimating the survival of those born in the various regions the census survival ratios could have an advantage over the life table survival ratios in that any under or over count of the population by region, may well be matched by a similar distortion in the national population and hence in the survival ratios, thus resulting in a more accurate estimate of the number of migrants than would be produced by using life table survival ratios. Apart from place of birth a census can ask of those who moved since the previous census (or some other suitable date) where they were at that census (or some other suitable date) which allows one to measure out-migration and hence (gross) in-migration separately for each sub-national region. If the census asks for the year when the migrant moved (or how long the person has been living in the place where counted in the second census) one can get a sense of the timing of migration, and estimate yearly migration rates. This is a complicated process and is not covered here, but the interested reader is referred to the paper by Dorrington and Moultrie (2009). Working with total numbers only If age-specific numbers are not available or the allocation to age is considered to be unreliable one can still produce estimates by age by estimating the total number of migrants as described below, and then apportioning this total to the age groups using either an age distribution for the same population at a different time (since the age distribution of migration flows tend be consistent over time, or (more likely) an appropriate standard model Rogers and Castro (1981a; 1981b). $Net ∞ M 0 F = ∞ N 0 F (t+n)− ∞ N 0 F (t)+ ∞ D 0 F$ where $ ∞ D 0 F = n 2 ( ∞ N 0 F (t)+ ∞ N 0 F (t+n) ) ∞ m 0$ and [∞]m[0] is an estimate of the crude mortality rate of the population in the country of the census. The primary limitation of using censuses to estimate immigration and net in-migration is the quality of the census, in particular the extent of undercount of the censuses, in general but more significantly one relative to the other. However, even if the census undercount is low, the census might not identify all the migrants. In general recent migrants are often difficult to include in a census because they have yet to settle. More specifically, immigrants may not be keen to identify themselves as immigrants and either avoid being counted or do not admit to being foreign-born. Apart from this, place of birth and/or place of residence at previous census, in the case of internal migrants, might be misreported due to boundary changes or ignorance (or even bias) on the part of the respondent. The third drawback of census data is that it cannot be used to measure emigration from the country of the census. Emigration is particularly difficult to estimate for most countries, but one option is to apply the method for identifying net immigration of the foreigners described above to the censuses of the main countries of destination to which the emigrants move to estimate the change in the numbers of emigrants to those countries. Of course, this is only useful if the censuses of these countries identify the numbers of foreign-born by their countries of birth reasonably accurately. Generally, statistics on immigrants and particularly emigrants that are collected at border posts provide quite poor estimates of the true numbers, unless the borders of the country are quite impenetrable and there are a few well-controlled ports of entry. Even then there may still be many ‘visitors’ who end up living in the country. A final drawback occurs when working with data aggregated over all ages. In these cases one usually has to make use of the crude death rate for the population of the country of the census in order to estimate the number of deaths of the migrant population. However, since the distribution of the migrant population by age can differ from that of the population of the country of the census quite markedly, the estimated number of deaths can be quite inaccurate. Extensions of the method Some censuses ask additional questions which can be of use in interpreting the patterns of migration, if not improving the estimate of the level of migration. Most common of these is probably a question asking about when the migrant moved. These data allow one to estimate annual rates of migration, however, it possible that there could be a tendency for respondents to report moves as occurring more recently than is actually the case (Dorrington and Moultrie 2009). Where a census asks, such as the recent censuses in South Africa, of those who moved since the previous census, where they moved from most recently and when they moved, and not where they were at the time of the previous census, it is possible to back-project the numbers of migrants by applying annual rates of migration between sub-national regions to estimate the number by place at the time of the previous census (Dorrington and Moultrie 2009). However, in the case of South Africa, at least, it appears that the assumption the most migrants moved only once in the past five years, and thus that the place of residence before the most recent move is the same as the place at the time of the previous census, is quite reasonable (Dorrington and Moultrie 2009). Where one has data on both the sub-national region of birth and the place at the time of the previous census, one can cross-tabulate the place of residence data by the place of birth and thus be able to classify recent migrants into primary, secondary and return migrants. Further reading and references For general background to the topic of migration, definition of terms and detail on the analysis and interpretation of the data on internal migration the interested reader is referred to the excellent UN Manual on topic, Manual VI (Shryock and Siegel (1976) or its modern replacement by Siegel and Swanson (2004) also provides an introduction to the topic of migration and cover, in particular, the estimation of international migration. Those interested in the estimation of annual migration rates and the back-projection of migration to estimate the numbers by place of residence at the time of the previous census from data on place of residence before the most recent move and year of move are referred to the paper by Dorrington and Moultrie (2009). Dorrington RE and TA Moultrie. 2009. "Making use of the consistency of patterns to estimate age-specific rates of interprovincial migration in South Africa," Paper presented at Annual conference of the Population Association of America. Detroit, US, 30 April - 2 May. Rogers A and LJ Castro. 1981a. "Age patterns of migration: Cause-specific profiles," in Rogers, A (ed). Advances in Multiregional Demography (RR-81-006). Laxenburg, Austria: International Institute for Applied Systems Analysis, pp. 125-159. https://pure.iiasa.ac.at/id/eprint/1556/1/RR-81-006.pdf Rogers A and LJ Castro. 1981b. Model Migration Schedules (RR-81-030). Laxenburg, Austria: International Institute for Applied Systems Analysis. https://pure.iiasa.ac.at/id/eprint/1543/1/RR-81-030.pdf Shryock HS and JS Siegel. 1976. The Methods and Materials of Demography (Condensed Edition). San Diego: Academic Press. Siegel JS and D Swanson. 2004. The Methods and Materials of Demography. Amsterdam: Elsevier. Timæus IM. 2007. "Impact of HIV on mortality in Southern Africa: Evidence from demographic surveillance", in Caraël M and JR Glynn (eds) HIV, Resurgent Infections and Population Change in Africa. Springer, pp 229–243. doi: https://dx.doi.org/10.1007/978-1-4020-6174-5_12 UN Population Division. 1970. Manual VI: Methods of Measuring Internal Migration. New York: United Nations, Department of Economic and Social Affairs, ST/SOA/Series A/47. https://www.un.org/ Suggested citation Dorrington RE. 2013. Estimation of migration from census data. In Moultrie TA, Dorrington RE, Hill AG, Hill K, Timæus IM and Zaba B (eds). Tools for Demographic Estimation. Paris: International Union for the Scientific Study of Population. https://demographicestimation.iussp.org/content/estimation-migration-census-data. Accessed 2024-11-12.	{"url":"https://demographicestimation.iussp.org/content/estimation-migration-census-data","timestamp":"2024-11-11T23:17:20Z","content_type":"text/html","content_length":"219934","record_id":"<urn:uuid:6705acc2-6a98-42d5-94e5-21c4d60d7547>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00474.warc.gz"}
Statistics in plain English Includes bibliographical references and index. Statistics in Plain English, Second Edition presents brief explanations of a number of statistical concepts and techniques in simple, everyday language. Each self-contained chapter consists of three sections. The first section describes the statistic, including how it is used and what information it provides. The second section reviews how it works, how to calculate the formula, the strengths and weaknesses of the technique, and the conditions needed for its use. The final section provides examples that use and interpret the statistic. A glossary of terms and symbols is also included." "This brief paperback is an ideal supplement for statistics, research methods, or any course that uses statistics, or as a handy reference tool to refresh one's memory about key concepts. The actual research examples are from a variety of fields, including psychology and education and other social and behavioral sciences. There are no comments for this item. Log in to your account to post a comment.	{"url":"https://opac.daiict.ac.in/cgi-bin/koha/opac-detail.pl?biblionumber=31034&shelfbrowse_itemnumber=40808","timestamp":"2024-11-13T21:39:52Z","content_type":"text/html","content_length":"57640","record_id":"<urn:uuid:da4b512e-9025-4481-bd50-3c6e2c515f6a>","cc-path":"CC-MAIN-2024-46/segments/1730477028402.57/warc/CC-MAIN-20241113203454-20241113233454-00717.warc.gz"}
Where can I find professionals for understanding and implementing graph algorithms? Computer Science Assignment and Homework Help By CS Experts Where can I find professionals for understanding and implementing graph algorithms? Hi Nati, I’m new to web application development and while I have seen some tools in web application and databases, I’d like to know what are they is a topic that you can use as a reference for anyone that would like to know more about their own methodologies for designing and implementing general graph algorithms. Thanks Let’s start doing this. I am just starting out going over the basics of graph algorithms, and would like to know if there are tools somewhere in your web page to perform such analysis and look it up. I’d be very grateful if you could take part in any such discussion! Nati, Thanks for your interest in this topic, and understand that you are not going to provide us with free software, but have us know if there are any open source solutions and methodologies that could really benefit from any of your help. If you can give us an answer, I would appreciate it, if you get to discuss the topic again with us, that is something I would appreciate if you may send us a chat. Hi Na, Good Luck! I hope that you are making it down to the computer science assignment help as I’m not sure you understand everything. The thing I would start with is browsing to the topic site of Google’s JPA, which lists about 25 of my own backlinks and they are of interest to anyone who uses their Google Maven / Jenkins infrastructure to “schedule the build or build-time”. Your data will be pretty big, which is something that you could probably do yourself.. I am afraid I would need to pick up around three or four commits since I am up there on that front (but not in the middle of the path) and I see lots of people searching for their own answers that could help me out. Thanks check my blog Tom, thanks for the understanding! I know I’ve had a bit ofWhere can I find professionals for understanding and implementing graph algorithms? Who’s the right website designers for each of these topics? I’ve found a handful of articles written that are worth reading (so if you want not spending time to read only the most important topics etc etc). Here’s an example of the IPC site (one of several high quality options) from Gart (with comment and explanation within each of the comments). If I am not mistaken, this may well be the wrong place to start. There seems to be couple of very good alternative web sites out there that, without further ado, save me from having trouble with a complicated web site I have read the various articles and tutorials about this topic, in some length or for some reasons which I know wrong, yet there is also a discussion of a set of alternative web sites that do make my life easier (and it is mentioned repeatedly several times). Many visitors will be so interested in this topic that they certainly will enjoy it now that other sites offer it again. If you find some worthwhile references for one of this topic in the comments, if you don’t have any on this you can reply (frequently) and/or respond (sometimes) to all of your comments. Hope that makes sense! The goal of my blog post is to provide an introduction my response the graph algorithm for my use case that shall also provide, for instance, more detailed context for using an interactive graph tool to help you understand how each type of graph algorithm works (for each section the graph algorithms are shown in a single graph for display). I am not really interested in understanding more advanced graph algorithms, just general ones involved in a work area. If a related topic are omitted that would then make more sense. I hope that helps helpful hints understand. Are College Online Classes Hard? I also attempted to suggest a website that is well written, well managed and safe. Its just a few links that are not needed because I am sure you can find at least 1 link through each place and I feelWhere can I find professionals for understanding and implementing graph algorithms? What is my top 10 best practices for building graphs? We all know who the most powerful computer vision expert is, so this is my point of this article. If I’m able to prove anything, for example demonstrating the graph generation algorithm techniques, then I’ll be as great as it gets. After that you are off to a great start. See if you can make some recommendations there. It’s my hope, I think, that additional resources opinions will be entertained, useful check entertaining. As I’ve been saying throughout this article, to solve an image problem graph as easy as it gets (obviously), it would be most beneficial to know how graph algorithms work and how much impact/impact those graphs have, and what they do positively or negatively. Anyway, there is another alternative way to solve this problem, though a special, new tool called graph solver to learn more about graph solving just in advance. Graph Solver is a real-time process and will be a part of the development of the open source solutions inside the project. So, in this article, I want to answer the following questions: 1. What is the algorithm for improving the graph solving algorithm? 2. Where can I find those graphs? 3. How can I classify these graphs? Is it possible that Graph Studio can find it? 4. What are my favorite facts about the algorithm? 5. What is the reason for the graph builder to appear in the middle of the proof? 6. How much time do I need to build these graphs? As far as improving the graph making process, is there someone like someone who would actually help you solving this problem? All is for now, can you dig in? Or should I say to try this other way? I am just getting into the work. 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Convert Inches to Feet - Pyron Converter Result: Inch = Feet i.e. in = ft What does Inch mean? What is Inch Unit - All You Need to Know Inch is a unit of Length In this unit converter website, we have converter from Inch (in) to some other Length unit. What does Feet mean? What is Feet Unit - All You Need to Know 1 yard is equal to 3 feet In this unit converter website, we have converter from Feet (ft) to some other Length unit. What does Length mean? Length is one of the most basic and important measurements used in a wide range of applications. It is a fundamental physical property that describes how long an object is. Measuring length accurately is essential in many fields, including engineering, construction, manufacturing, and science. In this article, we will provide a comprehensive guide to length measurements, including the different units of length and how to convert between them. The Standard Unit of Length The standard unit of length in the International System of Units (SI) is the meter (m). It is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second. This definition ensures that the meter is a universal constant that is independent of any physical object. Other Units of Length While the meter is the standard unit of length, there are many other units of length used in different fields and regions. Some of the most common units of length include: Kilometer (km): One thousand meters. Centimeter (cm): One hundredth of a meter. Millimeter (mm): One thousandth of a meter. Micrometer (µm): One millionth of a meter. Nanometer (nm): One billionth of a meter. Inch (in): A unit of length used mainly in the United States, equal to 1/12 of a foot. Foot (ft): A unit of length used mainly in the United States, equal to 12 inches. Yard (yd): A unit of length used mainly in the United States, equal to 3 feet or 36 inches. Mile (mi): A unit of length used mainly in the United States, equal to 5,280 feet. Converting Between Units of Length Converting between units of length is a common task, and it is important to know how to do it accurately. Here are some examples of how to convert between different units of length: To convert meters to centimeters, multiply by 100. To convert meters to millimeters, multiply by 1,000. To convert centimeters to meters, divide by 100. To convert millimeters to meters, divide by 1,000. To convert inches to centimeters, multiply by 2.54. To convert feet to meters, multiply by 0.3048. To convert yards to meters, multiply by 0.9144. To convert miles to kilometers, multiply by 1.609. When converting between units of length, it is important to keep track of the decimal places and round to the appropriate number of significant figures. Applications of Length Measurements Length measurements are used in a wide range of applications, including: Construction: Accurately measuring length is essential in building and construction to ensure that structures are stable and safe. Manufacturing: Length measurements are used in manufacturing to ensure that products are produced to the correct specifications. Science: Length measurements are used in many scientific fields, including physics, chemistry, and biology, to understand the properties and behavior of matter and energy. Navigation: Length measurements are used in navigation to determine the distance between two points, such as in GPS systems and maps. Length is a fundamental physical property that is used in many applications. While the meter is the standard unit of length, there are many other units of length used in different fields and regions. Converting between units of length is important, and accuracy is crucial. Understanding length measurements are essential in many fields, and we hope that this comprehensive guide has been helpful in explaining the basics of length measurements. How to convert Inch to Feet : Detailed Description Inch (in) and Feet (ft) are both units of Length. On this page, we provide a handy tool for converting between in and ft. To perform the conversion from in to ft, follow these two simple steps: Steps to solve Have you ever needed to or wanted to convert Inch to Feet for anything? It's not hard at all: Step 1 • Find out how many Feet are in one Inch. The conversion factor is 0.0833333 ft per in. Step 2 • Let's illustrate with an example. If you want to convert 10 Inch to Feet, follow this formula: 10 in x 0.0833333 ft per in = ft. So, 10 in is equal to ft. • To convert any in measurement to ft, use this formula: in = ft x 0.0833333. The Length in Inch is equal to the Feet multiplied by 0.0833333. With these simple steps, you can easily and accurately convert Length measurements between in and ft using our tool at Pyron Converter. FAQ regarding the conversion between in and ft Question: How many Feet are there in 1 Inch ? Answer: There are 0.0833333 Feet in 1 Inch. To convert from in to ft, multiply your figure by 0.0833333 (or divide by 12.00000480000192). Question: How many Inch are there in 1 ft ? Answer: There are 12.00000480000192 Inch in 1 Feet. To convert from ft to in, multiply your figure by 12.00000480000192 (or divide by 0.0833333). Question: What is 1 in equal to in ft ? Answer: 1 in (Inch) is equal to 0.0833333 in ft (Feet). Question: What is the difference between in and ft ? Answer: 1 in is equal to 0.0833333 in ft. That means that ft is more than a 12.00000480000192 times bigger unit of Length than in. To calculate in from ft, you only need to divide the ft Length value by 0.0833333. Question: What does 5 in mean ? Answer: As one in (Inch) equals 0.0833333 ft, therefore, 5 in means ft of Length. Question: How do you convert the in to ft ? Answer: If we multiply the in value by 0.0833333, we will get the ft amount i.e; 1 in = 0.0833333 ft. Question: How much ft is the in ? Answer: 1 Inch equals 0.0833333 ft i.e; 1 Inch = 0.0833333 ft. Question: Are in and ft the same ? Answer: No. The ft is a bigger unit. The ft unit is 12.00000480000192 times bigger than the in unit. Question: How many in is one ft ? Answer: One ft equals 12.00000480000192 in i.e. 1 ft = 12.00000480000192 in. Question: How do you convert ft to in ? Answer: If we multiply the ft value by 12.00000480000192, we will get the in amount i.e; 1 ft = 12.00000480000192 Inch. Question: What is the ft value of one Inch ? Answer: 1 Inch to ft = 0.0833333.	{"url":"https://pyronconverter.com/unit/length/in-ft","timestamp":"2024-11-05T10:21:04Z","content_type":"text/html","content_length":"130696","record_id":"<urn:uuid:7f388b60-27f4-458a-85fb-094dcf9ddbb9>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00684.warc.gz"}
My 27th birthday........... Exactly 5 weeks until my birthday........Eeeekkkkk!!! Being realistic how much weight do you think I can loose by then??? Having 1600 cals a day, and going to do a min of 4 work outs a week?? Burning from 400 - 600 cals a workout + maybe one yoga class on a sunday morning Whats the most you think I can loose, and a realistic min? Should i drop my cal intake? Push harder? Thanks x • Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. My BMR is 1,413 - What does TDEE mean? Where do I find that? Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. My BMR is 1,413 - What does TDEE mean? Where do I find that? TDEE is your Total Daily Energy Expendature. You can calculate it on this website: www.iifym.com :-) Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. I never heard of this before. Don't know if it's accurate at all. If it is, I can maximum lose 0,8 lbs per week but MFP is projecting I lose more. • So, think of BMR and TDEE as the brackets of how much you can eat every day and lose weight while maintaining good health. BMR is the number of calories your body needs each day to keep your organs, such as your heart and your brain, alive. TDEE is how many calories you actually burn each day, including lifestyle and exercise calories. If you eat fewer calories than your TDEE, you will lose weight. If you eat fewer calories than your BMR, you will lose weight for a while, but a lot of it will come from sources other than body fat, and your metabolism will eventually slow down to stop you from cannibalizing your organs. Plus you won't feel as healthy, and why make yourself miserable when you can lose weight eating more? Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. My BMR is 1,413 - What does TDEE mean? Where do I find that? TDEE is your Total Daily Energy Expendature. You can calculate it on this website: www.iifym.com :-) Thanks for this Just done mine - BMR is 1413 - My TDEE is 2245 - Total 1.664 - So if I dont my maths right, I should be able to lose just over 1lbs and a half.... a week??? Not bad I suppose Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. I never heard of this before. Don't know if it's accurate at all. If it is, I can maximum lose 0,8 lbs per week but MFP is projecting I lose more. That's because MFP sets 1200 calories as the absolute minimum, not BMR. 1200 is the absolute minimum for women on a diet recommended by the US government, just like 2000 is considered "typical" when calculating recommended daily allowances. So, think of BMR and TDEE as the brackets of how much you can eat every day and lose weight while maintaining good health. BMR is the number of calories your body needs each day to keep your organs, such as your heart and your brain, alive. TDEE is how many calories you actually burn each day, including lifestyle and exercise calories. If you eat fewer calories than your TDEE, you will lose weight. If you eat fewer calories than your BMR, you will lose weight for a while, but a lot of it will come from sources other than body fat, and your metabolism will eventually slow down to stop you from cannibalizing your organs. Plus you won't feel as healthy, and why make yourself miserable when you can lose weight eating more? Very interesting information - Thanks for this!!!!!!!!!!!!!!!!!!!!!!!! : ) 1.5lbs a week weight loss is steady, and not to drastic - Im quite slim anyway, and tall, 137lbs, but would def like to shift a few before my birthday.... !! Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. I never heard of this before. Don't know if it's accurate at all. If it is, I can maximum lose 0,8 lbs per week but MFP is projecting I lose more. That's because MFP sets 1200 calories as the absolute minimum, not BMR. 1200 is the absolute minimum for women on a diet recommended by the US government, just like 2000 is considered "typical" when calculating recommended daily allowances. I see. But when I calculated my TDEE for both days when I exercise and days when I don't, it only differs about 100 kcal. How is that possible? MFP recommends to have a deficit of 500/day so then I should eat 1200 on non workout days and only 1300 when I work out. I thought it seemed a bit low? 1300 is still below my BMR that's about 1425. So, think of BMR and TDEE as the brackets of how much you can eat every day and lose weight while maintaining good health. BMR is the number of calories your body needs each day to keep your organs, such as your heart and your brain, alive. TDEE is how many calories you actually burn each day, including lifestyle and exercise calories. If you eat fewer calories than your TDEE, you will lose weight. If you eat fewer calories than your BMR, you will lose weight for a while, but a lot of it will come from sources other than body fat, and your metabolism will eventually slow down to stop you from cannibalizing your organs. Plus you won't feel as healthy, and why make yourself miserable when you can lose weight eating more? Very interesting information - Thanks for this!!!!!!!!!!!!!!!!!!!!!!!! : ) 1.5lbs a week weight loss is steady, and not to drastic - Im quite slim anyway, and tall, 137lbs, but would def like to shift a few before my birthday.... !! I bet you'll be there in no time. Your TDEE is a lot higher than mine. Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. I never heard of this before. Don't know if it's accurate at all. If it is, I can maximum lose 0,8 lbs per week but MFP is projecting I lose more. That's because MFP sets 1200 calories as the absolute minimum, not BMR. 1200 is the absolute minimum for women on a diet recommended by the US government, just like 2000 is considered "typical" when calculating recommended daily allowances. I see. But when I calculated my TDEE for both days when I exercise and days when I don't, it only differs about 100 kcal. How is that possible? MFP recommends to have a deficit of 500/day so then I should eat 1200 on non workout days and only 1300 when I work out. I thought it seemed a bit low? 1300 is still below my BMR that's about 1425. How did you calculate your TDEE? It sounds weird that you would only be burning 100 calories when you work out. If you only have 10-15 lbs left to lose, it could be that you would be better off aiming for less than 1 lb a week. Find BMR. Find TDEE. Subtract BMR from TDEE. Divide by 500. That is the maximum number of pounds you can safely lose each week. I never heard of this before. Don't know if it's accurate at all. If it is, I can maximum lose 0,8 lbs per week but MFP is projecting I lose more. That's because MFP sets 1200 calories as the absolute minimum, not BMR. 1200 is the absolute minimum for women on a diet recommended by the US government, just like 2000 is considered "typical" when calculating recommended daily allowances. I see. But when I calculated my TDEE for both days when I exercise and days when I don't, it only differs about 100 kcal. How is that possible? MFP recommends to have a deficit of 500/day so then I should eat 1200 on non workout days and only 1300 when I work out. I thought it seemed a bit low? 1300 is still below my BMR that's about 1425. How did you calculate your TDEE? It sounds weird that you would only be burning 100 calories when you work out. If you only have 10-15 lbs left to lose, it could be that you would be better off aiming for less than 1 lb a week. Yes, it is weird since I do 50 min intense aerobics which leaves me really sweaty and exhausted. I study from home so non workout days I don't move around a lot but I work out 5 days a week so then I added 50 min of exercise and 20 min of walking to my TDEE, which only gave me an extra 100 kcals burned. It does sound really low. When I add my exercise here on MFP in aerobics general, it gives me 387 kcals burned which is quite a difference.. • In 5 weeks you can probably lose at least 5lbs. If you go all out, even 10 lbs. I don't believe in "safely" losing weight. Your body does not follow a formula. Formula is good to get an estimate. But that's it. Another thing is that most people OVERESTIMATE their calorie consumption. Trust me, you might be surprised how low your BMR may be. Check biolayne.com. He knows what he's talking about. Tons of myths on weight gain and weight loss. • 1.4M Health, Wellness and Goals • 98.8K Social Corner • 3.7K MyFitnessPal Information	{"url":"https://community.myfitnesspal.com/en/discussion/883775/my-27th-birthday","timestamp":"2024-11-12T23:26:24Z","content_type":"text/html","content_length":"293345","record_id":"<urn:uuid:c33329e1-967d-441a-ab9d-a47bdd4b7012>","cc-path":"CC-MAIN-2024-46/segments/1730477028290.49/warc/CC-MAIN-20241112212600-20241113002600-00220.warc.gz"}
Application of block Cayley-Hamilton theorem to generalized inversion In this paper we propose two algorithms for computation of the outer inverse with prescribed range and null space and the Drazin inverse of block matrix. The proposed algorithms are based on the extension of the Leverrier-Faddeev algorithm and the block Cayley-Hamilton theorem. These algorithms are implemented using symbolic and functional possibilities of the packages {\it Mathematica} and using numerical possibilities of {\it Matlab}. Block Cayley Hamilton; generalized inversion; Kronecker product; Leverrier-Faddeev algorithm. S. Barnett Leverrier’s algorithm: a new proof and extensions, SIAM J. Matrix Anal. Appl. 10 (1989), 551–556. A. Ben-Israel, T.N.E. Greville, Generalized inverses: theory and applications, Springer, New York, NY, USA, 2nd edition, 2003. Y. Chen, The generalized Bott–Duffin inverse and its application, Linear Algebra Appl. 134 (1990), 71–91. Y. Chen, Finite Algorithms for the (2)-Generalized Inverse A(2) T,S, Linear and Multilinear Algebra 40 (1995), 61–68. H.P. Decell, An application of the Cayley-Hamilton theorem to generalized matrix inversion, SIAM Review 7 No 4 (1965), 526–528. M.P. Drazin, Pseudo-inverse in associative rings and semigroups, Amer. Math. Monthly 65 (1958), 506–514. D.K. Faddeev and V.N. Faddeeva, Computational Methods of Linear Algebra, Freeman, San Francisko, 1963. T.N.E. Grevile, The Souriau-Frame algorithm and the Drazin pseudoinverse, Linear Algebra Appl. 6 (1973), 205–208. R.E. Hartwig More on the Souriau-Frame algorithm and the Drazin inverse, SIAM J. Appl. Math. 31 No 1 (1976), 42–46. A.J. Getson, F.C. Hsuan, {2}-inverses and their Statistical applications, Lecture Notes in Statistics 47, Springer, New York, NY, USA, 1988. J. Ji, An alternative limit expression of Drazin inverse and its applications, Appl. Math. Comput. 61 (1994), 151–156. T. Kaczorek, New extensions of the Cayley–Hamilton theorem with applicattions, Proceeding of the 19th European Conference on Modelling and Simulation, 2005. T. Kaczorek, An Existence of the Cayley-Hamilton Theorem for Singular 2-D Linear Systems with Non-Square Matrices, Bulletin of the Polish Academy of Sciences. Technical Sciences 43(1) (1995), 39–48. T. Kaczorek, Generalization of the Cayley-Hamilton Theorem for Non-Square Matrices, International Conference of Fundamentals of Electronics and Circuit Theory XVIII- SPETO, Gliwice, 1995, pp. 77–83. T. Kaczorek, An Existence of the Caley-Hamilton Theorem for Non-Square Block Matrices, Bulletin of the Polish Academy of Sciences. Technical Sciences 43(1) (1995), 49–56. T. Kaczorek, An Extension of the Cayley-Hamilton Theorem for a Standard Pair of Block Matrices, Applied Mathematics and Computation Sciences 8(3) (1998), 511–516. T. Kaczorek, Extension of the Cayley-Hamilton theorem to continuoustime linear systems with delays, Int. J. Appl. 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Vitoria, A block–Cayley–Hamilton theorem, Bulletin Mathematique 26(71) (1982), 93–97. G. Wang, L. Qiu, Some New Applications of the Block–Cayley–Hamilton Theorem, J. of Shangai Teachers Univ. (Natural Sciences) 27 (1998), 8–15, In Chinesse. G.Wang, A finite algorithm for computing the weighted Moore-Penrose inverse A†M,N, Appl. Math. Comput. 23 (1987), 277–289. G. Wang, Y. Wei, S. Qiao, Generalized Inverses: Theory and Computations, Science Press, Beijing/New York, 2004. Y. Wei, H. Wu, The representation and approximation for the generalized inverse A(2) T,S, Appl. Math. Comput. 135 (2003), 263–276. Y. Yu, G. Wang, On the generalized inverse A(2) T,S over integral domains, Aust. J. Math. Appl. 4 (2007), 1. Article 16, 1–20. Y. Yu, G. Wang, DFT calculation for the {2}-inverse of a polynomial matrix with prescribed image and kernel, Applied Math. Comput. 215 (2009), 2741–2749. B. Zheng, R. B. Bapat, Generalized inverse A(2) T,S and a rank equation, Appl. Math. Comput. 155 (2004), 407-415. G. Zielke, Report on Test Matrices for Generalized Inverses, Computing 36 (1986), 105–162. • There are currently no refbacks. © University of Niš \| Created on November, 2013 ISSN 0352-9665 (Print) ISSN 2406-047X (Online)	{"url":"https://casopisi.junis.ni.ac.rs/index.php/FUMathInf/article/view/454","timestamp":"2024-11-08T11:34:58Z","content_type":"application/xhtml+xml","content_length":"26255","record_id":"<urn:uuid:6f30bfbe-4195-4a51-a17a-7b3d755b1971>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00841.warc.gz"}
SU-MATH53 FEB212024 A Partial Differential Equation is a Differential Equation which has more than one independent variable: $u(x,y), u(t,x,y), &mldr;$ For instance: $$\pdv{U}{t} = \alpha \pdv[2]{U}{x}$$ Key Intuition • PDEs may have no solutions (unlike Uniqueness and Existance for ODEs) • yet, usually, there are too many solutions—so&mldr; how do you describe all solutions? • usually, there are no explicit formulas See Heat Equation see Wave Equation Transport Equation $$\pdv{u}{t} = \pdv{u}{x}$$ generally any $u = w(x+t)$ should solve this Schrodinger Equation We have some: and its a complex-valued function: $$i \pdv{u}{t} = \pdv[2]{u}{x}$$ which results in a superposition in linear equations Nonlinear Example $$\pdv{u}{t} = \pdv[2]{u}{x} + u(1-u)$$ this is a PDE variant of the logistic equation: this is non-linear Monge-Ampere Equations $$Hess(u) = \mqty(\pdv[2]{u}{x} & \frac{\partial^{2} u}{\partial x \partial y} \\ \frac{\partial^{2} u}{\partial x \partial y} & \pdv[2]{u}{y})$$ If we take its determinant, we obtain: $$\pdv[2]{u}{x} \pdv[2]{u}{y} - \qty(\frac{\partial^{2} u}{\partial x \partial y})^{2}$$ Traveling Wave For two-variable PDEs, it is called a Traveling Wave if solutions to $u$ takes on the form: $$u(t,x) = w(x-ct)$$ for some constant $c$, and where $w(x)$ is a function which depends on only one of the two variables. See also Bell Curves	{"url":"https://www.jemoka.com/posts/kbhsu_math53_feb212024/","timestamp":"2024-11-10T13:03:36Z","content_type":"text/html","content_length":"8368","record_id":"<urn:uuid:cfbabab4-8f32-4f27-be58-d0296893593a>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00208.warc.gz"}
Near-Linear Algorithms for Visibility Graphs over a 1.5-Dimensional Terrain We present several near-linear algorithms for problems involving visibility over a 1.5-dimensional terrain. Concretely, we have a 1.5-dimensional terrain T, i.e., a bounded x-monotone polygonal path in the plane, with n vertices, and a set P of m points that lie on or above T. The visibility graph V G(P, T) is the graph with P as its vertex set and {(p, q) \| p and q are visible to each other} as its edge set. We present algorithms that perform BFS and DFS on V G(P, T), which run in O(n log n + m log^3(m + n)) time. We also consider three optimization problems, in which P is a set of points on T, and we erect a vertical tower of height h at each p ∈ P. In the first problem, called the reverse shortest path problem, we are given two points s, t ∈ P, and an integer k, and wish to find the smallest height h^∗ for which V G(P(h^∗), T) contains a path from s to t of at most k edges, where P(h^∗) is the set of the tips of the towers of height h^∗ erected at the points of P. In the second problem we wish to find the smallest height h^∗ for which V G(P(h^∗), T) contains a cycle, and in the third problem we wish to find the smallest height h^∗ for which V G(P(h^∗), T) is nonempty; we refer to that problem as “Seeing the most without being seen”. We present algorithms for the first two problems that run in O^∗((m + n)^6/5) time, where the O^∗(·) notation hides subpolynomial factors. The third problem can be solved by a faster algorithm, which runs in O((n + m) log^3(m + n)) time. Publication series Name Leibniz International Proceedings in Informatics, LIPIcs Volume 308 ISSN (Print) 1868-8969 Conference 32nd Annual European Symposium on Algorithms, ESA 2024 Country/Territory United Kingdom City London Period 2/09/24 → 4/09/24 • 1.5-dimensional terrain • parametric search • range searching • reverse shortest path • shrink-and-bifurcate • visibility • visibility graph ASJC Scopus subject areas Dive into the research topics of 'Near-Linear Algorithms for Visibility Graphs over a 1.5-Dimensional Terrain'. Together they form a unique fingerprint.	{"url":"https://cris.bgu.ac.il/en/publications/near-linear-algorithms-for-visibility-graphs-over-a-15-dimensiona","timestamp":"2024-11-12T00:25:34Z","content_type":"text/html","content_length":"62610","record_id":"<urn:uuid:42497621-a326-4af7-8bb7-e7afa0415965>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00513.warc.gz"}
Linear Regression When we try to represent relationship between variables, one of them is determining factor and other is explanatory, it is called Linear Regression. The one which is determining factor is called Independent variable while the other is called dependent variable. If there is only one dependent variable it is called Simple Linear Regression. Let us try to explain this by a very simple example, Income of family and expenditure. The expenditure of family is dependent on the income of family. So, here income is the independent variable and the expenditure is dependent variable. Let us explain it through a graph. If there are 5 families and they decide to spend at least 50% of their income and all have same mindset , then this can be called a very simple Linear Regression. In ideal case, things seem like below: Here, the difference between predicted value and real value is 0. Which is the most ideal condition but unlikely to happen. We choose a line on linear regression which has least sum of square of difference between predicted and actual values. Error= Sum of ((y-y')**2) Error should be least for the best slop of line of linear model to be selected. The ideal model as above is called deterministic model. However, deterministic model examples are like conversion models where Celsius is converted into Fahrenheit. Where there is no other factor to be determined and just conversion formula. Let us see below for some values which has some deviation from 50% spending. This variation can happen because of various reasons and mindsets of families. Intercept here is Value of Y axis when x is 0. And slop is determined by y/x. Randomness and unpredictability are the two main components of a regression model. In above case there can be factors which cannot be determined and which brought about change in expenses of families. May be there could have been emergencies, or extravagance or saving streak.	{"url":"https://www.numpyninja.com/post/linear-regression","timestamp":"2024-11-05T04:46:50Z","content_type":"text/html","content_length":"1050526","record_id":"<urn:uuid:966239d1-3b36-4981-9736-d9a2339ca805>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00264.warc.gz"}
How to calculate the cross product of two NumPy arrays? You can calculate the cross product of two NumPy arrays using the cross function from the numpy module. Here's an example: 1 import numpy as np 3 a = np.array([1, 2, 3]) 4 b = np.array([4, 5, 6]) 6 c = np.cross(a, b) 8 print(c) In this example, we first create two NumPy arrays a and b. Then, we use the cross function to calculate their cross product, which is assigned to the variable c. Finally, we print the value of c. Note that the cross function can also be used to calculate the cross product of multiple arrays at once. In this case, the arrays should be passed as separate arguments to the function. For example: 1 import numpy as np 3 a = np.array([1, 2, 3]) 4 b = np.array([4, 5, 6]) 5 c = np.array([7, 8, 9]) 7 d = np.cross(a, b, c) 9 print(d) In this example, we calculate the cross product of three arrays a, b, and c at once, and assign the result to the variable d.	{"url":"https://devhubby.com/thread/how-to-calculate-the-cross-product-of-two-numpy","timestamp":"2024-11-07T13:38:57Z","content_type":"text/html","content_length":"126472","record_id":"<urn:uuid:654f1110-1e48-4a7c-8ec0-b026708626ce>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00131.warc.gz"}
Math Problem Statement A random sample of 140 teams playing in major international team sporting competitions has been selected to study corporate sponsorship and subsequent sporting success. Some of the variables recorded for each team are listed below. Subject ID sex of players number of distinct corporate sponsors the percentage of international games won A simple linear regression is run to answer the research question, ’What is the relation between the percentage of international games won and number of distinct corporate sponsors?’ The results of the analysis are reported below: Estimate Std. Error t value Pr(>\|t\|) (Intercept) 38.2271 2.4433 15.6459 0 numSponsors 0.7093 0.0649 10.9362 0 Address the following questions, assuming as necessary that all test assumptions are verified. What is the null hypothesis? Choose one among the following options: a. The slope of the regression line is zero b. There is a significant relation, linear or non-linear, between the two variables c. The slope of the regression line is significantly different from zero d. There is no relation whatsoever, linear or non-linear, between the two variables e. The slope of the regression line is either positive or negative f. The relation between the two variables is linear Answer 1 Question 3 abcdef From the test statistic as reported above, we can conclude that the estimated value of the slope is: Answer 2 Question 3 10.94 times its standard error1.96 times its standard error1.96 times the population standard deviation10.94 times the population standard deviation From the p-value as reported above, we can conclude that the decision of the test is: Answer 3 Question 3 Accept H0Reject H0Do not accept H0Do not reject H0 What is the conclusion of the test? Answer 4 Question 3 There is evidence of a linear relationship between these two variables.There is no evidence of a linear relationship between these two variables. Ask a new question for Free By Image Drop file here or Click Here to upload Math Problem Analysis Mathematical Concepts Linear Regression Hypothesis Testing Simple Linear Regression: y = β0 + β1x Test Statistic = β1 / SE(β1) p-value calculation for hypothesis testing Null Hypothesis for Regression Slope Interpretation in Regression p-value Significance Testing Suitable Grade Level College level statistics or advanced high school (Grades 11-12)	{"url":"https://math.bot/q/linear-regression-corporate-sponsorship-game-wins-FMOFQdtd","timestamp":"2024-11-05T23:49:48Z","content_type":"text/html","content_length":"91869","record_id":"<urn:uuid:56f5f9ac-4311-416b-93f4-07f65748e528>","cc-path":"CC-MAIN-2024-46/segments/1730477027895.64/warc/CC-MAIN-20241105212423-20241106002423-00747.warc.gz"}
Symbology Settings in WPF Barcode Symbology Settings in WPF Barcode (SfBarcode) 4 May 20214 minutes to read Each Barcode symbol can be associated with optional settings that may affect that specific bar code. The code sample below shows the settings of a code39 Barcode. <sync:Code39Setting BarHeight="45" EnableCheckDigit="False" EncodeStartStopSymbols="True" NarrowBarWidth="1" ShowCheckDigit="False"/> 1D Barcode settings The one dimensional barcodes have some of the settings in common, such as BarHeight which modifies the height of the bars and NarrowBarWidth which modifies the width ratio of the wide and narrow <sync:Code39Setting BarHeight="45" NarrowBarWidth="1"/> The one dimensional barcodes also has the error detection settings. The EnableCheckDigit property enables the redundancy check using a check digit, the decimal equivalent of a binary parity bit. It consists of a single digit computed from the other digits in the message. The check digit can be shown in the barcode or kept hidden by using the ShowCheckDigit property. The EncodeStartStopSymbols property adds Start and Stop symbols to signal a bar code reader that a bar code has been scanned. <sync:Code39Setting EnableCheckDigit="False" EncodeStartStopSymbols="True" ShowCheckDigit="False"/> 2D Barcode Settings The two dimensional barcodes have a common XDimension property which modifies the block size of a two dimensional barcode. DataMatrix Barcode settings The DataMatrix barcode settings has the properties to modify the encoding and size of the DataMatrix barcode. <sync:DataMatrixSetting XDimension="8" Encoding="ASCIINumeric” Size="Size104x104" /> The encoding of the DataMatrix barcode can be modified using the ‘Encoding’ property. The DataMatrixEncoding enumeration has the following four encoding schemes. • ASCII • ASCIINumeric • Auto • Base256 The DataMatrix Barcode settings allow the user to specify the size of the barcode from a set of predefined sizes available in the DataMatrixSize enumeration. Data Matrix size Table Data Matrix Size Description Auto Size is chosen based on the input data Size10x10 Square matrix with 10 rows and 10 columns. Size12x12 Square matrix with 12 rows and 12 columns. Size14x14 Square matrix with 14 rows and 14 columns. Size16x16 Square matrix with 16 rows and 16 columns. Size18x18 Square matrix with 18 rows and 18 columns. Size20x20 Square matrix with 20 rows and 20 columns. Size22x22 Square matrix with 22 rows and 22 columns. Size24x24 Square matrix with 24 rows and 24 columns. Size26x26 Square matrix with 26 rows and 26 columns. Size32x32 Square matrix with 32 rows and 32 columns. Size36x36 Square matrix with 36 rows and 36 columns. Size40x40 Square matrix with 40 rows and 40 columns. Size44x44 Square matrix with 44 rows and 44 columns. Size48x48 Square matrix with 48 rows and 48 columns. Size52x52 Square matrix with 52 rows and 52 columns. Size64x64 Square matrix with 64 rows and 64 columns. Size72x72 Square matrix with 72 rows and 72 columns. Size80x80 Square matrix with 80 rows and 80 columns. Size88x88 Square matrix with 88 rows and 88 columns. Size96x96 Square matrix with 96 rows and 96 columns. Size104x104 Square matrix with 104 rows and 104 columns. Size120x120 Square matrix with 120 rows and 120 columns. Size132x132 Square matrix with 132 rows and 132 columns. Size144x144 Square matrix with 144 rows and 144 columns. Size8x18 Rectangular matrix with 8 rows and 18 columns. Size8x32 Rectangular matrix with 8 rows and 32 columns. Size12x26 Rectangular matrix with 12 rows and 26 columns. Size12x36 Rectangular matrix with 12 rows and 36 columns. Size16x36 Rectangular matrix with 16 rows and 36 columns. Size16x48 Rectangular matrix with 16 rows and 48 columns. QRBarcode settings The QRBarcode settings has properties to modify the version, error correction level and Input mode of the QRBarcode. <sync:QRBarcodeSetting XDimension="8" ErrorCorrectionLevel="High” InputMode="BinaryMode” Version="Auto" /> The QR Barcode uses version from 1 to 40.Version 1 measures 21 modules x 21 modules, Version 2 measures 25 modules x 25 modules and so on increasing in steps of 4 modules per side up to Version 40 which measures 177 modules x 177 modules. Each version has its own capacity. By default the QR Version is Auto, which will automatically set the version according to the input text length. Error correction level The QR Barcode employs error correction to generate a series of error correction codewords which are added to the data code word sequence in order to enable the symbol to withstand damage without loss of data. There are four user–selectable levels of error correction, as shown in the table, offering the capability of recovery from the following amounts of damage. By default the Error correction level is Low. Error Correction Level Table Error Correction Level Recovery Capacity % (approx.) L 7 M 15 Q 25 H 30 Input mode There are three modes for the input as defined in the table. Each mode supports the specific set of Input characters. User may select the most suitable input mode. By default the Input mode is Binary Input Mode Table Input Mode Possible characters Numeric Mode 0,1,2,3,4,5,6,7,8,9 Alphanumeric Mode 0–9, A–Z (upper-case only), space, $, %, *, +, -,., /, : Binary Mode Shift JIS characters	{"url":"https://help.syncfusion.com/wpf/barcode/symbology-settings","timestamp":"2024-11-13T09:04:17Z","content_type":"text/html","content_length":"41103","record_id":"<urn:uuid:89dca496-3e78-4c9e-b36f-5e54dc67b4a9>","cc-path":"CC-MAIN-2024-46/segments/1730477028342.51/warc/CC-MAIN-20241113071746-20241113101746-00272.warc.gz"}
Vol. 32, No. 1, 2006 HOUSTON JOURNAL OF Electronic Edition Vol. 32, No. 1, 2006 Editors: H. Amann (Zürich), G. Auchmuty (Houston), D. Bao (Houston), H. Brezis (Paris), J. Damon (Chapel Hill), K. Davidson (Waterloo), C. Hagopian (Sacramento), R. M. Hardt (Rice), J. Hausen (Houston), J. A. Johnson (Houston), W. B. Johnson (College Station), J. Nagata (Osaka), V. I. Paulsen (Houston), , S.W. Semmes (Rice) Managing Editor: K. Kaiser (Houston) Houston Journal of Mathematics Badawi, Ayman, Department of Mathematics and Statistics, American University of Sharjah, P.O. Box 26666, Sharjah, United Arab Emirates (abadawi@aus.ac.ae), and Lucas, Thomas G., Department of Mathematics and Statistics, University of North Carolina Charlotte, Charlotte, NC 28223, U.S.A. (tglucas@uncc.edu). On Φ-Mori Rings, pp. 1-32. ABSTRACT. A commutative ring R is said to be a φ-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map φ from the total quotient ring T(R) to R localized at Nil(R). An ideal I that properly contains Nil(R) is φ-divisorial if (φ(R): (φ(R):φ(I)))=φ(I). A ring is a φ-Mori ring if it is a φ-ring that satisfies the ascending chain condition on φ-divisorial ideals. Many of the properties and characterizations of Mori domains can be extended to φ-Mori rings, but some cannot. Coykendall, Jim, Department of Mathematics, North Dakota State University, Fargo, ND 58105-5075, U.S.A. (jim.coykendall@ndsu.nodak.edu), Dumitrescu, Tiberiu, Facultatea de Matematica, Universitatea Bucuresti, 14 Academiei Str., Bucharest, RO 010014, Romania (tiberiu@al.math.unibuc.ro), and Zafrullah, Muhammad, Department of Mathematics, Idaho State University, Pocatello, ID 83209, U.S.A. The half-factorial property and domains of the form A+XB[X], pp. 33-46. ABSTRACT. In this note, we use the A+XB[X] and A+XI[X] constructions from a new angle to construct new examples of half factorial domains. Positive results are obtained highlighting the interplay between the notions of GCD domain, GL domain, integrally closed domain and half-factorial domain in A+XB[X] constructions. It is additionally shown that constructions of the form A+XI[X] rarely possess the half-factorial property. F. Fontenele, Departamento de Geometria, Instituto de Matemática, Universidade Federal Fluminense, 24020-140, Niterói, Brazil (fontenele@mat.uff.br), and Sérgio L. Silva, Departamento de Estruturas Matemáticas, Universidade Estadual do Rio de Janeiro, 20550-013, Rio de Janeiro, Brazil (sergiol@ime.uerj.br). On the m-th mean curvature of compact hypersurfaces, pp. 47-57. ABSTRACT. Let M be an n-dimensional compact Riemannian manifold immersed in the (n+1)-dimensional Euclidean space. In a previous paper, the authors proved that if the product of the scalar curvature by the square of some support function is less than or equal to one then the image of M is a geodesic sphere. Also we obtained the analogous result in case the ambient is the (n+1)-dimensional hyperbolic space. In this paper, we obtain the correspondent result for immersions into (n+1)-dimensional Euclidean sphere and generalizations of this type of result for high order mean curvatures. The basic technique is to apply the divergence's theorem in a region containing a subset of interest. This technique allows us to give a new proof of a theorem of Vlachos. Some other results are also Andreev, Fedor, Western Illinois University, Macomb, IL 61455 (F-Andreev@wiu.edu). Direct computation of the monodromy data for P6 corresponding to the quantum cohomology of the projective plane , pp. 59-77. ABSTRACT. A solution to the sixth Painleve equation (P6) corresponding to the quantum cohomology of the projective plane is considered. This is one of the solutions to P6 coming from the Frobenius manifold theory. The resulting generators of the monodromy group are computed. The main difference in the author's approach is its directness, so that no references to the Frobenius manifold theory are needed. The proof presented in the article requires only a) classical results on the asymptotic expansion of some special cases of the hypergeometric function and b) simple, but not obvious rational substitution. The proof also directly demonstrates that the resulting monodromy group is in SL(2,Z). Muzsnay, Zoltán, University of Debrecen, Debrecen, H-4010, PBox 12, Hungary, (muzsnay@math.klte.hu). The Euler-Lagrange PDE and Finsler metrizability, pp. 79-98. ABSTRACT. We investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the Euler-Lagrange partial differential system on the energy function can be reduced to a first order system on this same function. In this way we are able to give effective necessary and sufficient conditions for the local existence of a such Finsler metric in terms of the holonomy algebra generated by horizontal vector-fields. We also consider the Landsberg metrizability problem and prove similar results. This reduction is a significant step in solving the problem whether or not there exists a non-Berwald Landsberg space. Yoshio Tanaka, Tokyo Gakugei University, Tokyo 184-8501, Japan (ytanaka@u-gakugei.ac.jp), and Ying Ge, Suzhou University, Suzhou 215006, P.R.China (geying@pub.sz.jsinfo.net). Around quotient compact images of metric spaces, and symmetric spaces, pp. 99-117. ABSTRACT. We give some new characterizations for certain compact-covering (or sequence-covering) quotient, compact (or ƒÎ-) images of metric spaces in terms of weak bases or symmetric spaces, and consider relations between these compact-covering images and sequence-covering images. Also, we pose some questions around quotient compact images of metric spaces. Ingram, W. T., University of Missouri - Rolla, Rolla, MO 65409-0020 (ingram@umr.edu), and Mahavier, William S., Emory University, Atlanta, GA 30322 (wsm@mathcs.emory.edu). Inverse Limits of Upper Semi-continuous Set Valued Functions, pp. 119-130. ABSTRACT. In this article we define the inverse limit of an inverse sequence (X[1],ƒ[1]), (X[2],ƒ[2]), (X[3],ƒ[3]), ... where each X[i] is a compact Hausdorff space and each ƒ[i] is an upper semi-continuous function from X[i+1] into 2^X[i] . Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse limits. S. Oltra and E.A. Sanchez Perez, Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, Valencia 46071, Spain (soltra@mat.upv.es), (easancpe@mat.upv.es). Order properties and p-metrics on Köthe function spaces, pp. 131-142. ABSTRACT. If L is a Köthe function space, we define and characterize a class of p-pseudo metrics on L using the representation of the dual space by means of integrals. We show that it provides an adequate framework for the study of the relation between the to pology and the order on L. In particular, we obtain in this context new characterizations of the lattice properties of L. We a lso show that these results can be applied in the case of the dual complexity spaces that are used as models for the complexity analysis of algorithms and programs in Theoretical Computer Science. Milutinovic, Uros, University of Maribor, PEF, Koroska 160, 2000 Maribor, Slovenia (uros.milutinovic@uni-mb.si). Approximation of maps into Lipscomb's space by embeddings, pp. 143- 159. ABSTRACT. Let J(t) be Lipscomb's one-dimensional space and let L[n](t) be Lipscomb's n-dimensional universal space of weight t, i.e. the set of all elements of J(t)^n+1 having at least one irrational coordinate. In this paper we prove that if X is a metrizable space and dim X≤n, wX ≤t, then any mapping from X to J(t)^n+1 can be approximated arbitrarily close by an embedding from X to L[n](t). Also, in the separable case an analogous result is obtained, in which the classic triangular Sierpinski curve (homeomorphic to J(3)) is used instead of J(aleph[0]). S. Macias, Instituto de Matematicas, U.N.A.M., Circuito Exterior, Ciudad Universitaria, Mexico, D.F., C.P. 04510 (macias@servidor.unam.mx).. A class of one-dimensional, nonlocally connected continua for which the set function T is continuous, pp. 161-165. ABSTRACT. We present a class of one--dimensional, nonlocally connected continua for which the set function T is continuous. B. Mond, Department of Mathematics, La Trobe University, Bundoora, Vic. 3083, Australia (b.mond@latrobe.edu.au), J. Pevcaric, Faculty of Textile Technology, University of Zagreb, 10000 Zagreb, Croatia, and I. Peric, Faculty of Chemical Engineering & Technology, University of Zagreb, 10000 Zagreb, Croatia, (iperic@pbf.hr). On Reverse Integral Mean Inequalities, pp. 167-181. ABSTRACT. If f s a positive integrable function, then it is well-known that for real numbers p and q, q≤p, the ratio of the p-power integral mean of f by the q-power integral mean is greater than or equal to 1. Different authors have given reverse inequalities for this ratio. Here we present various upper bounds for this ratio for a wider class of weighted power means and functions. These results are extensions of results of Muckenhoupt, Nania and Alzer. Isaac Pesenson, Department of Mathematics, Temple University, Philadelphia, PA 19122 (pesenson@math.temple.edu). Deconvolution of band limited functions on non-compact symmetric spaces, pp. 183-204. ABSTRACT. It is shown that a band limited function on a non-compact symmetric space can be reconstructed in a stable way from some countable sets of values of its convolution with certain distributions of compact support. A reconstruction method in terms of frames is given which is a generalization of the classical result of Duffin-Schaeffer about exponential frames on intervals. The second reconstruction method is given in terms of polyharmonic average splines. Boos, Johann, FernUniversität in Hagen, D-58084 Hagen, Germany (Johann.Boos@FernUni-Hagen.de), and Leiger, Toivo, Puhta Matemaatika Instituut, Tartu Ülikool, EE 50090 Tartu, Eesti (Toivo.Leiger@ut.ee), and Zeltser, Maria, Matemaatika osakond, Tallinna Ülikool, EE 10120 Tallinn, Eesti (mariaz@tln.ee). The intersection of matrix domains including a given sequence space, pp. 205-225. ABSTRACT. On the one hand, Hahn's theorem tells that each convergence domain containing the set of all sequences of 0's and 1's includes all bounded sequences. On the other hand, it is easy to verify that for each unbounded sequence x there exists a convergence domain that includes all bounded sequences but does not contain x. Thus the set of all bounded sequences is the intersection of all convergence domains containing all sequences of 0's and 1's. In this sense the set of all bounded sequences is the `summability hull' of the set of all sequences of 0's and 1's. In the present paper the `summability hull' of arbitrarily given sequence spaces is studied. Anna, Kaminska, Department of Mathematical Sciences, The University of Memphis, Memphis, USA (kaminska@memphis.edu) and Han Ju, Lee, Department of Mathematics, POSTECH, Pohang-shi, Republic of Korea On uniqueness of extension of homogeneous polynomials, pp. 227-252. ABSTRACT. We study the uniqueness of norm-preserving extension of n-homogeneous polynomials in Banach spaces. We show that norm-preserving extensions of n-homogeneous polynomials do not need to be unique for n > 1 in real Banach spaces, and for n> 2 in a large class of complex Banach function spaces. We find further a geometric condition, which in particular yields that a unit ball in X does not possess any complex extreme point, under which for every norm-attaining 2-homogeneous polynomial on a complex symmetric sequence space X there exists a unique norm-preserving extension from X to its bidual. In particular, if M is a Marcinkiewicz sequence space and m is its subspace of order continuous elements, we show that every norm-attaining 2-homogeneous polynomial on m has a unique norm-preserving extension to its bidual M if and only if no element of a unit ball of m is a complex extreme point of its unit ball. We then apply these results to obtain some necessary conditions for the uniqueness of extension of 2-homogeneous polynomials from a complex symmetric space X to its bidual. Englis, Miroslav, MU AV CR, Zitna 25, 11567 Praha 1, Czech Republic (englis@math.cas.cz), Hänninen, Teemu T., Department of Mathematics, University of Helsinki, P.O. Box 4, 00014 Helsinki, Finland (Teemu.Hanninen@helsinki.fi), and Taskinen, Jari, Department of Mathematics, University of Joensuu, P.O. Box 111, 80101 Joensuu, Finland; current address: Dept. of Mathematics, Univ. of Helsinki, P.O.Box 4, 00014 Helsinki, Finland (jari.taskinen@helsinki.fi). Minimal L-infinity-type spaces on strictly pseudoconvex domains on which the Bergman projection is continuous , pp. 253-275. ABSTRACT. We describe the space of functions on a smoothly bounded strictly pseudoconvex domain such that (i) the Bergman projection is continuous on it; (ii) its topology is given by a family of weighted sup-norms, with weights depending only on a given defining function; (iii) it contains all bounded measurable functions; and (iv) it is contained continuously into any other function space satisfying (i)-(iii). This generalizes the results obtained by the third author for the unit disc. We also obtain analogous assertions for the standard weighted Bergman projections, and, under the additional hypothesis that the domain be complete circular, also for the Szegö projection on pluriharmonic functions. Steven M. Seubert, Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403-0221 (sseuber@bgnet.bgsu.edu). Dissipative compressed Toeplitz operators on shift co-invariant subspaces , pp. 277-292. ABSTRACT. Necessary and sufficient conditions for an operator commuting with the compression of the standard unilateral shift on the Hardy space H^2 to a shift co-invariant subspace to be dissipative are given in terms of the coset of symbols of the operator. The lattice of closed invariant subspaces of a dissipative operator commuting with the compression of the shift operator is shown to coincide with the lattices of closed invariant subspaces of the fractional powers of the dissipative operator using semigroup results. Sufficient conditions for the lattice of closed invariant subspaces of a dissipative operator commuting with the compression of the shift operator to coincide with the lattice of closed invariant subspaces of the compression of the shift operator are given whenever the shift co-invariant subspace corresponds to a Blaschke product. Jim Gleason, Department of Mathematics, University of Tennessee, Knoxville, TN, USA 37996-1300 (gleason@math.utk.edu). Current address: Department of Mathematics, The University of Alabama, Tuscaloosa, AL 35487-0350 (jgleason@as.ua.edu). Quasinormality of Toeplitz Tuples with Analytic Symbols, pp. 293-298. ABSTRACT. We study properties of quasinormality for tuples of Toeplitz operators with analytic symbols on the Hardy and Bergman space of the unit ball or the polydisc in C. Also, using examples we show that different notions of quasinormality for commuting tuples of operators correspond to multiplication by the coordinate functions on different domains in C. Kamila Klis, and Marek Ptak, Institute of Mathematics, University of Agriculture, Al. Mickiewicza 24/28, 30-059 Krakow, Poland (rmklis@cyf-kr.edu.pl), (rmptak@cyf-kr.edu.pl). k-Hyperreflexive subspaces, pp. 299-313. ABSTRACT. Changing rank-one operators in a suitable definition of hyperreflexivity to rank k operators we give a definition of k-hyperreflexivity. We give an example of 2-hyperreflexive subspace which second ampliation is not hyperreflexive. There are also given properties and examples of k-hyperreflexivity. It is shown that the space of all Toeplitz operators is 2-hyperreflexive and each k- dimensional subspace is k-hyperreflexive. Bernal-Gonzalez and Calderon-Moreno, M.C., Departamento de Analisis Matematico. Facultad de Matematicas, apdo. 1160. Avenida Reina Mercedes, 41080 Sevilla , Spain (lbernal@us.es), (mccm@us.es) and Luh, W., Fachbereich Mathematik, Universität Trier, D-54286 Trier, Germany (luh@uni-trier.de}. Universal matrix transforms of holomorphic functions , pp. 315-324. ABSTRACT. The phenomenon of overconvergence is related with the convergence of subsequences of the sequence of partial sums of Taylor series at points outside their disk of convergence. During the seventies Chui and Parnes and the third author provided a holomorphic function in the unit disk which is universal with respect to overconvergence. The generic nature of this kind of universality has been recently shown by Nestoridis. In this paper, we connect the overconvergence with the summability theory. We show that there are “many” holomorphic functions in the unit disk such that their sequences of A-transforms have the overconvergence property, A being an infinite matrix. This strengthens Nestoridis' result.	{"url":"https://www.math.uh.edu/~hjm/Vol32-1.html","timestamp":"2024-11-08T09:06:21Z","content_type":"text/html","content_length":"21721","record_id":"<urn:uuid:68b7dc64-deab-4570-a455-b7c2c6390c33>","cc-path":"CC-MAIN-2024-46/segments/1730477028032.87/warc/CC-MAIN-20241108070606-20241108100606-00116.warc.gz"}
Operation of Oscillator Circuit - EEEGUIDE.COM Operation of Oscillator Circuit: The use of positive feedback that results in a feedback amplifier having closed-loop gain \|A[f]\| exceeding unity and satisfies the phase conditions results in operation as an oscillator circuit. An Operation of Oscillator Circuit then provides a constantly varying output signal. If the output signal varies sinusoidally, the circuit is referred to as a sinusoidal oscillator and on the other hand if the output voltage rises quickly to one voltage level and later drops quickly to another voltage level, the circuit is usually referred to as a pulse or square-wave generator. To understand how an Operation of Oscillator Circuit produces an output signal without an external input signal, let us consider the feedback circuit shown in Fig. 21.2 (a), where V[in]Â is the voltage of ac input driving the input terminals bc of an amplifier having voltage gain A. The amplified output voltage is This voltage drives a feedback circuit that is usually a resonant circuit, as we get maximum feedback at one frequency. The feedback voltage returning to point a is given by equation where Î² is the gain of feedback network. If the phase shift through the amplifier and feedback circuit is zero, then AÎ²V[in]Â is in phase with the input signal V[in] that drives the input terminals of the amplifier. Now we connect point ‘a’ to point ‘b’ and simultaneously remove voltage source V[in], then feedback voltage AÎ²V[in]Â drives the input terminals bc of the amplifier, as shown in Fig. 21.2 (b). In case AÎ² is less than unity, AÎ²V[in]Â is less than V[in] and the output signal will die out, as illustrated in Fig. 21.3 (a). On the other hand if AÎ² is greater than unity, the output signal will build up, as illustrated in Fig. 21.3 (b). If AÎ² is equal to unity, AÎ²V[in] equals V[in] and the output signal is a steady sinewave, as illustrated in Fig. 21.3 (c). In this case the circuit supplies its own input signal and produces a sinusoidal output. Certain conditions are required to be fulfilled for sustained oscillations and these conditions are that (i) the loop gain of the circuit must be equal to (or slightly greater than) unity and (ii) the phase shift around the circuit must be zero. These two conditions for sustained oscillations are called Barkhausen criteria. For initiation of oscillations, supply of an input signal is not essential. Only the condition Î²A = 1 must be satisfied for self-sustained oscillations to result. In practice Î²A is made slightly greater than unity, the system starts oscillating by amplifying noise voltage which is always present. Saturation factors in the practical circuits provide an average value of Î²A of 1. The resulting waveforms are never exactly sinusoidal. However, the closer the value of Î²A is to exactly 1, the more nearly sinusoidal is the waveform. Figure 21.4 shows how the noise voltage results in a buildup of a steady-state oscillation condition. Another way of seeing how the feedbackÂ circuit provides Operation of Oscillator Circuit is obtained by noting the denominator in the basic feedback equation, A[f]Â = A/1+Î²A. When Î²A = – 1 or magnitude 1 at a phase angle of 180Â°, the denominator becomes zero and the gain with feedback, A[f] becomes infinite. Thus, an infinitesimal signal (noise voltage) can provide a measurable output voltage, and the circuit acts as an oscillator even without an input signal. By deliberate design the phase shift around the loop is made 0Â° at the resonant frequency. Above and below the resonant frequency, the phase shift is different from 0Â°. Thus, oscillations are obtained at only one frequency, the resonant frequency of the feedback circuit. To understand and apply the Barkhausen criterion, we must consider both the gain and phase shift of AÎ² as a function of frequency. Reactive elements, capacitance in particular, contained in the amplifier and/or feedback causes the gain magnitude and phase shift to vary with the frequency. In general, there will be only one frequency at which the gain magnitude is unity and at which, simultaneously, the total phase shift is equivalent to 0Â° (in phaseâ€”a multiple of 360Â°). The system will oscillate at the frequency that satisfies those conditions. Designing an oscillator amounts to selection of reactive components and their incorporation into circuit in such a way that the conditions will be satisfied at a desired frequency. To show the dependence of the loop gain AÎ² on frequency, we express AÎ²(jÏ‰), a complex phasor that can be expressed in both polar and rectangular form : where \|AÎ²\| is the magnitude of the loop gain, a function of frequency, and Î¸ is the phase shift, also a function of frequency. For satisfaction of Barkhausen criterion, we must have where n is any integer, including 0. In polar and rectangular forms, the Barkhausen criterion is expressed as	{"url":"https://www.eeeguide.com/operation-of-oscillator-circuit/","timestamp":"2024-11-09T00:33:08Z","content_type":"text/html","content_length":"222364","record_id":"<urn:uuid:53db3ffc-86c4-4edf-be81-e286a7f3f6e9>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00417.warc.gz"}
50,362 research outputs found In this work we perform an analysis of the recent AMS-02 antiproton flux and the antiproton-to-proton ratio in the framework of simplified dark matter models. To predict the AMS-02 observables we adopt the propagation and injection parameters determined by the observed fluxes of nuclei. We assume that the dark matter particle is a Dirac fermionic dark matter, with leptophobic pseudoscalar or axialvector mediator that couples only to Standard Model quarks and dark matter particles. We find that the AMS-02 observations are consistent with the dark matter hypothesis within the uncertainties. The antiproton data prefer a dark matter (mediator) mass in the 700 GeV--5 TeV region for the annihilation with pseudoscalar mediator and greater than 700 GeV (200 GeV--1 TeV) for the annihilation with axialvector mediator, respectively, at about 68% confidence level. The AMS-02 data require an effective dark matter annihilation cross section in the region of 1x10^{-25} -- 1x10^ {-24} (1x10^{-25} -- 4x10^{-24}) cm^3/s for the simplified model with pseudoscalar (axialvector) mediator. The constraints from the LHC and Fermi-LAT are also discussed.Comment: 16 pages, 6 figures, 1 table. arXiv admin note: text overlap with arXiv:1509.0221 The decoupling limit in the MSSM Higgs sector is the most likely scenario in light of the Higgs discovery. This scenario is further constrained by MSSM Higgs search bounds and flavor observables. We perform a comprehensive scan of MSSM parameters and update the constraints on the decoupling MSSM Higgs sector in terms of 8 TeV LHC data. We highlight the effect of light SUSY spectrum in the heavy neutral Higgs decay in the decoupling limit. We find that the chargino and neutralino decay mode can reach at most 40% and 20% branching ratio, respectively. In particular, the invisible decay mode BR(H^0(A^0) -> \tilde{\chi}^0_1\tilde{\chi}^0_1) increases with increasing Bino LSP mass and is between 10%-15% (20%) for 30<m_{\tilde{\chi}^0_1}<100 GeV. The leading branching fraction of heavy Higgses decay into sfermions can be as large as 80% for H^0 -> \tilde{t}_1\tilde{t}_1^\ast and 60% for H^0/A^0 -> \tilde{\tau}_1\tilde{\tau}_2^\ast+\tilde{\tau}_1^\ast\tilde{\tau}_2. The branching fractions are less than 10% for H^0 -> h^0h^0 and 1% for A^0 -> h^0Z for m_A>400 GeV. The charged Higgs decays to neutralino plus chargino and sfermions with branching ratio as large as 40% and 60%, respectively. Moreover, the exclusion limit of leading MSSM Higgs search channel, namely gg,b\bar{b} -> H^0, A^0 -> tau^+ tau^-, is extrapolated to 14 TeV LHC with high luminosities. It turns out that the tau tau mode can essentially exclude regime with tan\beta>20 for L=300 fb^{-1} and tan\beta>15 for L=3000 fb^{-1}.Comment: 20 pages, 14 figure We perform an analysis of the simplified dark matter models in the light of cosmic ray observables by AMS-02 and Fermi-LAT. We assume fermion, scalar or vector dark matter particle with a leptophobic spin-0 mediator that couples only to Standard Model quarks and dark matter via scalar and/or pseudo-scalar bilinear. The propagation and injection parameters of cosmic rays are determined by the observed fluxes of nuclei from AMS-02. We find that the AMS-02 observations are consistent with the dark matter framework within the uncertainties. The AMS-02 antiproton data prefer 30 (50) GeV - 5 TeV dark matter mass and require an effective annihilation cross section in the region of 4x10^{-27} (7x10^{-27}) - 4x10^{-24} cm^3/s for the simplified fermion (scalar and vector) dark matter models. The cross sections below 2x10^{-26} cm^3/s can evade the constraint from Fermi-LAT dwarf galaxies for about 100 GeV dark matter mass.Comment: 20 pages, 8 figures, 2 tables. arXiv admin note: text overlap with arXiv:1612.0950 The tau lepton plays important role in distinguishing neutrino mass patterns and determining the chirality nature in heavy scalar mediated neutrino mass models, in the light of the neutrino oscillation experiments and its polarization measurement. We investigate the lepton flavor signatures with tau lepton at LHC upgrades, i.e. HL-LHC, HE-LHC and FCC-hh, through leptonic processes from doubly charged Higgs in the Type II Seesaw. We find that for the channel with one tau lepton in final states, the accessible doubly charged Higgs mass at HL-LHC can reach 655 GeV and 695 GeV for the neutrino mass patterns of normal hierarchy (NH) and inverted hierarchy (IH) respectively, with the luminosity of 3000 fb$^{-1}$. Higher masses, 975-1930 GeV for NH and 1035-2070 GeV for IH, can be achieved at HE-LHC and FCC-hh.Comment: 18 pages, 9 figures, 4 table Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure for finding sparse solutions of underdetermined linear systems. This method has been shown to have strong theoretical guarantee and impressive numerical performance. In this paper, we generalize HTP from compressive sensing to a generic problem setup of sparsity-constrained convex optimization. The proposed algorithm iterates between a standard gradient descent step and a hard thresholding step with or without debiasing. We prove that our method enjoys the strong guarantees analogous to HTP in terms of rate of convergence and parameter estimation accuracy. Numerical evidences show that our method is superior to the state-of-the-art greedy selection methods in sparse logistic regression and sparse precision matrix estimation tasks This paper proposes a formal model selection test for choosing between two competing structural econometric models. The procedure is based on a novel lack-of-fit criterion, namely, the simulated mean squared error of predictions (SMSEP), taking into account the complexity of structural econometric models. It is asymptotically valid for any fixed number of simulations, and allows for any estimator which has a vn asymptotic normality or is superconsistent with a rate at n. The test is bi-directional and applicable to non-nested models which are both possibly misspecified. The asymptotic distribution of the test statistic is derived. The proposed test is general regardless of whether the optimization criteria for estimation of competing models are the same as the SMSEP criterion used for model selection. An empirical application using timber auction data from Oregon is used to illustrate the usefulness and generality of the proposed testing procedure.Lack-of-fit, Model selection tests, Non-nested models, Simulated mean squared error of predictions	{"url":"https://core.ac.uk/search/?q=author%3A(Li%2C%20Tong)","timestamp":"2024-11-10T22:27:08Z","content_type":"text/html","content_length":"103203","record_id":"<urn:uuid:71fdb6df-4764-42fd-bc71-93783bfd436b>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00735.warc.gz"}
Elements of Geometry Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement of the Quadrature of the Circle and the Geometry of Solids Fra bogen Resultater 6-10 af 16 Side 259 ... prism and a parallelepiped , which have the same altitude , are to each other as their bases ; that is , the prism BNM is to the parallelepiped CD as the triangle AEM to the parallelogram LG . For , by the last corollary , the prism ... Side 261 ... prisms are to one another in the ratio compounded of the ratio of their bases , and of the ratio of their altitudes . For every prism is equal to a parallelepiped of the same altitude with it , and of an equal bases . g 2. Cor . 8. 3 ... Side 262 ... , & c . Q. E. D. Cor . In the same manner it may be demonstrated that equal prisms have their bases and altitudes reciprocally pro- portional , and conversely . 1 PROP . XI . THEOR . gunmure / SIMILAR solid 262 ELEMENTS. Side 264 ... prisms are to one another in the tri- plicate ratio , or in the ratio of the cubes , of their homologous sides . For a prism is equal to half of a parallelepiped of the 84. 3. Sup . same base and altitudes . / PROP . XII . THEOR . IF ... Side 266 ... prisms hving all the same altitude may be circumscribed about the pramid ABCD , so that their sum shall exceed ABCD by solid less than Z. Let Z be qual to a prism standing on the same base BCD with the pyrmid , and having for its ... Almindelige termer og sætninger Populære passager Side 121 If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal... Side 42 TO a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Side 63 Therefore, in obtuse-angled triangles, &c. QED PROP. XIII. THEOREM. In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle. Side 3 A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another. Side 183 Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides. Let AC, CF be equiangular parallelograms having the angle BCD equal to the angle ECG ; the ratio of the parallelogram AC to the parallelogram CF is the same with the ratio which is compounded •f the ratios of their sides. Side 3 A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference. Side 291 All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides. Side 160 ... extremities of the base shall have the same ratio which the other sides of the triangle have to one... Side 10 ... shall be greater than the base of the other. Let ABC, DEF be two triangles, which have the two sides AB, AC, equal to the two DE, DF, each to each, viz. Side 14 Therefore, upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extretnity equal to one another. Bibliografiske oplysninger	{"url":"https://books.google.gl/books?q=prism&dq=editions:ISBN0344061817&id=LpdYAAAAMAAJ&hl=da&output=html_text&start=5&focus=searchwithinvolume","timestamp":"2024-11-04T20:39:40Z","content_type":"text/html","content_length":"63743","record_id":"<urn:uuid:3034ab16-f726-49a4-8ad4-831ce7eb359a>","cc-path":"CC-MAIN-2024-46/segments/1730477027861.16/warc/CC-MAIN-20241104194528-20241104224528-00063.warc.gz"}
Printable Multiplication Chart To 144 \| Multiplication Chart Printable Printable Multiplication Chart To 144 Multiplication Table To 144 Multiplication Worksheets Multiplication Printable Multiplication Chart to 144 Printable Multiplication Chart to 144 – A Multiplication Chart is a practical tool for kids to discover how to increase, split, as well as locate the tiniest number. There are lots of usages for a Multiplication Chart. These handy tools assist youngsters understand the process behind multiplication by using tinted courses and filling out the missing out on products. These charts are free to download and publish. What is Multiplication Chart Printable? A multiplication chart can be made use of to aid kids learn their multiplication realities. Multiplication charts come in many kinds, from full web page times tables to single page ones. While private tables serve for presenting chunks of information, a complete web page chart makes it much easier to assess truths that have currently been mastered. The multiplication chart will usually feature a top row and a left column. When you want to find the product of 2 numbers, select the very first number from the left column as well as the 2nd number from the top row. Multiplication charts are valuable discovering tools for both grownups and also kids. Printable Multiplication Chart to 144 are readily available on the Internet and can be printed out and laminated flooring for sturdiness. Why Do We Use a Multiplication Chart? A multiplication chart is a diagram that shows how to increase 2 numbers. It usually consists of a leading row and a left column. Each row has a number standing for the item of both numbers. You pick the first number in the left column, move it down the column, and afterwards choose the 2nd number from the top row. The item will certainly be the square where the numbers meet. Multiplication charts are handy for lots of factors, including aiding children find out just how to separate as well as streamline portions. Multiplication charts can also be practical as workdesk resources since they offer as a consistent tip of the trainee’s development. Multiplication charts are likewise beneficial for assisting students memorize their times tables. They help them learn the numbers by decreasing the number of steps required to finish each operation. One technique for memorizing these tables is to concentrate on a single row or column at once, and then move onto the following one. Ultimately, the whole chart will be committed to memory. Similar to any type of skill, memorizing multiplication tables requires time and also technique. Printable Multiplication Chart to 144 144 Times Table Challenge Times Tables Worksheets Downloadable Multiplication Charts Interactive With Activities Multiplication Chart Missing Numbers PrintableMultiplication Printable Multiplication Chart to 144 If you’re searching for Printable Multiplication Chart to 144, you’ve involved the ideal place. Multiplication charts are offered in various styles, consisting of full size, half dimension, and also a range of adorable designs. Some are vertical, while others feature a straight style. You can additionally locate worksheet printables that include multiplication formulas as well as math truths. Multiplication charts and tables are indispensable tools for kids’s education. These charts are excellent for usage in homeschool math binders or as class posters. A Printable Multiplication Chart to 144 is an useful tool to strengthen mathematics facts and also can assist a kid discover multiplication swiftly. It’s likewise a great tool for miss counting and also learning the times tables. Related For Printable Multiplication Chart to 144	{"url":"https://multiplicationchart-printable.com/printable-multiplication-chart-to-144/","timestamp":"2024-11-13T02:48:26Z","content_type":"text/html","content_length":"41949","record_id":"<urn:uuid:abedecfb-be31-4a27-8d5c-6e375df8a0eb>","cc-path":"CC-MAIN-2024-46/segments/1730477028303.91/warc/CC-MAIN-20241113004258-20241113034258-00390.warc.gz"}
T.J. Gaffney Here is my extended resume and some projects that I've worked on. Email me any questions, at gaffney.tj@gmail.com. Personal Projects Snakes on a Projective Plane (2010) Presentations, Blogs, and Writing Linear Algebra for Those Who Know Linear Algebra (2021-) Probability is in the Eye of the Beholder… Probably (2022) Half Derivatives: An Operator Theory Prospective (2020) Higher-Dimensional Pascal Simplices	{"url":"http://gaffneytj.com/?filter=Math","timestamp":"2024-11-05T09:56:25Z","content_type":"text/html","content_length":"15990","record_id":"<urn:uuid:defe1d40-43d9-4fdf-bafe-1d92f671f150>","cc-path":"CC-MAIN-2024-46/segments/1730477027878.78/warc/CC-MAIN-20241105083140-20241105113140-00249.warc.gz"}
Lesson 12 Practice With Proportional Relationships Lesson Narrative This optional lesson gives students an additional opportunity to practice finding unknown values in proportional relationships using contextual examples. The problems preview using the Pythagorean Theorem, which is a key idea in a subsequent lesson. They also preview finding all unknown values in right triangles, which is a key idea in a subsequent unit. Students have a chance to reason abstractly and quantitatively as they think about whether their answers make sense in context (MP2). Learning Goals Teacher Facing • Calculate unknown values in proportional relationships. • Determine scale factors to describe similar figures (using words and other representations). Student Facing • Let’s find unknown values in proportional relationships. Student Facing • I can find scale factors and use them to solve problems. Print Formatted Materials Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials. Student Task Statements pdf docx Cumulative Practice Problem Set pdf docx Cool Down Log In Teacher Guide Log In Teacher Presentation Materials pdf docx Blackline Masters zip Additional Resources Google Slides Log In PowerPoint Slides Log In	{"url":"https://im-beta.kendallhunt.com/HS/teachers/2/3/12/preparation.html","timestamp":"2024-11-09T20:49:28Z","content_type":"text/html","content_length":"82795","record_id":"<urn:uuid:2fa7f7de-43e2-4eb8-94cf-85540e86cc32>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00140.warc.gz"}
Squares and Square Root Worksheet (printable, online, answers, examples) There are seven sets of exponents worksheets: Examples, solutions, videos, and worksheets to help Grade 6 and Grade 7 students learn how to find squares and square roots. How to evaluate squares and square roots? Squares and square roots are two closely related concepts in mathematics. A square is a number that is multiplied by itself, and a square root is a number that, when multiplied by itself, equals the original number. For example, 4 is a square because it is equal to 2 multiplied by itself (2 × 2 = 4). The square root of 4 is 2, because 2 × 2 = 4. We can denote the square of a number using exponents. For example, 3 × 3 = 3^2 = 9. The square root is denoted by the symbol “√”. For example, the square root of 9 is written as √9. It’s important to note that the square root can have both positive and negative values. For example, the square root of 9 is both 3 and -3, because 3 × 3 = 9 and -3 × -3 = 9. The square root that is positive is called the principal square root. However, in most cases, when we refer to the square root, we are referring to the principal square root, which is the positive value. Perfect squares are numbers that can be expressed as the square of an integer. It is obtained by multiplying an integer by itself. For example, 16 is a perfect square because it can be expressed as 4 × 4 = 16. This also means that that the square roots of perfect squares are integers. Other examples of squares and square roots: Have a look at this video if you need to review how to evaluate perfect squares and square roots. Click on the following worksheet to get a printable pdf document. Scroll down the page for more Squares and Square Root Worksheets. More Squares and Square Root Worksheets (Answers on the second page.) Squares and Square Root Worksheet Squares & Cubes (whole number, fraction & decimal bases) Cubes & cube roots Squares with bases 0 to 10 Squares with bases 2 to 20 Squares with bases -10 to 0 Squares with bases -20 to 0 Cubes with bases 0 to 10 Cubes with bases 2 to 20 Cubes with bases -10 to 0 Cubes with bases -20 to 0 Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.	{"url":"https://www.onlinemathlearning.com/squares-square-root-worksheet.html","timestamp":"2024-11-14T17:56:54Z","content_type":"text/html","content_length":"41053","record_id":"<urn:uuid:516597a2-d3e0-4e29-b4f5-4dba4f2b68b1>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00873.warc.gz"}
In order to avoid $log(x) = -\infty$ for $x=0$ in log-transformations there's often a constant added to the variable before taking the $log$. This is not always a pleasable strategy. The function LogSt handles this problem based on the following ideas: • The modification should only affect the values for "small" arguments. • What "small" is should be determined in connection with the non-zero values of the original variable, since it should behave well (be equivariant) with respect to a change in the "unit of • The function must remain monotone, and it should remain (weakly) convex. These criteria are implemented here as follows: The shape is determined by a threshold $c$ at which - coming from above - the log function switches to a linear function with the same slope at this This is obtained by $$g(x) = \left\{\begin{array}{ll} log_{10}(x) &\textup{for }x \ge c\\ log_{10}(c) - \frac{c - x}{c \cdot log(10)} &\textup{for } x < c \end{array}\right. $$ Small values are determined by the threshold $c$. If not given by the argument threshold, it is determined by the quartiles $q_1$ and $q_3$ of the non-zero data as those smaller than $c = \ frac{q_1^{1+r}}{q_3^r}$ where $r$ can be set by the argument mult. The rationale is, that, for lognormal data, this constant identifies 2 percent of the data as small. Beyond this limit, the transformation continues linear with the derivative of the log curve at this point. Another idea for choosing the threshold $c$ was: median(x) / (median(x)/quantile(x, 0.25))^2.9) The function chooses $log_{10}$ rather than natural logs by default because they can be backtransformed relatively easily in mind. A generalized log (see: Rocke 2003) can be calculated in order to stabilize the variance as: function (x, a) { return(log((x + sqrt(x^2 + a^2)) / 2))	{"url":"https://www.rdocumentation.org/packages/DescTools/versions/0.99.57/topics/LogSt","timestamp":"2024-11-10T19:26:25Z","content_type":"text/html","content_length":"103721","record_id":"<urn:uuid:7dec37d5-0e7e-4a30-af07-e641456cdb43>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00786.warc.gz"}
Rapidly Exploring Dense Trees 5.5 Rapidly Exploring Dense Trees This section introduces an incremental sampling and searching approach that yields good performance in practice without any parameter tuning.^5.14The idea is to incrementally construct a search tree that gradually improves the resolution but does not need to explicitly set any resolution parameters. In the limit, the tree densely covers the space. Thus, it has properties similar to space filling curves [842], but instead of one long path, there are shorter paths that are organized into a tree. A dense sequence of samples is used as a guide in the incremental construction of the tree. If this sequence is random, the resulting tree is called a rapidly exploring random tree (RRT). In general, this family of trees, whether the sequence is random or deterministic, will be referred to as rapidly exploring dense trees (RDTs) to indicate that a dense covering of the space is obtained. This method was originally developed for motion planning under differential constraints [608,611]; that case is covered in Section 14.4.3. Subsections Steven M LaValle 2020-08-14	{"url":"https://lavalle.pl/planning/node230.html","timestamp":"2024-11-09T19:06:16Z","content_type":"text/html","content_length":"6284","record_id":"<urn:uuid:c3451dd1-5d99-4357-82d2-4e8bed990dc1>","cc-path":"CC-MAIN-2024-46/segments/1730477028142.18/warc/CC-MAIN-20241109182954-20241109212954-00288.warc.gz"}
Irradiance Map GI This page gives an overview of the Irradiance map process. Starting with V-Ray 5, the Irradiance Map GI method is deprecated in V-Ray for 3ds Max, Maya, Cinema 4D, Nuke. Irradiance is a function defined for any point in the 3D space, representing the light arriving at a point and all the directions from which the light arrives. The irradiance map GI method creates a map of this lighting. In general, irradiance is different at every point and can represent a large amount of information. However, there are two useful restrictions that can be made when using irradiance for rendering. The first is the restriction of looking only at surface irradiance, which is the irradiance arriving at points that lie on the surface of objects in the scene. This is a natural restriction since we are usually interested in the illumination of objects in the scene, and objects are usually defined by their surfaces. The second restriction is that for diffuse surface irradiance (the total amount of light arriving at a given surface point) we can disregard the direction from which the light comes. In more simple terms, one can think of the diffuse surface irradiance as being the visible color of a surface, if we assume that its material is purely white and diffuse. In V-Ray, the term irradiance map refers to a method of efficiently computing the diffuse surface irradiance for objects in the scene. Since not all parts of the scene have the same detail in indirect illumination, it makes sense to compute GI more accurately in the important parts (e.g. where objects are close to each other, or in places with sharp GI shadows), and less accurately in large, uniformly lit areas. The irradiance map is therefore built adaptively. This is done by rendering the image several times (each rendering is called a pass) with the rendering resolution being doubled with each pass. The idea is to start with a low resolution (say a quarter of the resolution of the final image) and work up to the final image resolution. The irradiance map is in fact a collection of points in 3D space (a point cloud) along with the computed indirect illumination at those points. When an object is hit during a GI pass, V-Ray looks into the irradiance map to see if there are any points similar in position and orientation to the current one. From those already computed points, V-Ray can extract various information (i.e. if there are any objects close by, how fast the indirect illumination is varying etc). Based on that information, V-Ray decides if the indirect illumination for the current point can be adequately interpolated from the points already in the irradiance map, or not. If not, the indirect illumination for the current point is computed, and that point is stored in the irradiance map. During the actual rendering, V-Ray uses a sophisticated interpolation method to derive an approximation of the irradiance for all surfaces in the scene. The diagram above shows the way the Irradiance map is generated. The Irradiance map method can only be selected as the Engine for Primary bounces; it is not available for Secondary bounces. Since the method is view-dependent, the first rays (the black lines in the diagram) are traced from the camera into the scene in order to determine the placement of the irradiance samples. Once this is done, GI rays (red) are traced from the samples into the scene in order to determine the illumination coming from the environment. The number of traced rays is determined by the Subdivs parameter. The irradiance map only traces one bounce of light. All additional bounces (blue) are traced by the secondary engine. The irradiance map is created on several passes - each pass adding more samples where this is needed. During rendering, for each rendered point, V-Ray takes several samples from the already complete irradiance map and interpolates between them in order to create a smooth GI solution. The number of samples taken is determined by the Interp. samples parameter.	{"url":"https://docs.chaos.com/display/THEORY/Irradiance+Map+GI","timestamp":"2024-11-03T19:41:14Z","content_type":"text/html","content_length":"114804","record_id":"<urn:uuid:9b7ef03a-4b7d-40c3-8b0a-06db9cefc9cc>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00406.warc.gz"}
PROsetta 0.4.1 • Now requires TestDesign (>= 1.5.1). • Response probabilities are now computed faster using cpp functions. • Deprecated guiPROsetta() is removed. Use PROsetta() instead. • Updated documentation. • Made minor updates to the Shiny app in PROsetta(). • Removed ncat column in anchor parameters. This is now inferred from the number of parameters. • Added cpp routine for EAP computation after Lord-Wingersky recursion. This improves the speed of runRSSS(). • getRSSS() now nudges the user if the prior mean input looks like a T-score, which should be entered in the theta metric. • Updated CITATION to use bibentry() to meet CRAN requirements. PROsetta 0.3.5 • runRSSS() output now includes linear approximation betas when the CPLA method is used. • runLinking() output now includes the latent mean and variance when the FIXEDPAR method is used. • runCalibration(), runLinking(), runEquateObserved(), getCompleteData() gains verbose argument for printing status messages. Status messages that were used to be printed in previous versions are now suppressed by default. PROsetta 0.3.4 • Removed unused columns (min_score, reverse, scores) in example datasets for clarity. The package functions do not use these columns. • loadData() now warns if there is a variable that may need reverse coding. This is triggered by a negative correlation value. PROsetta 0.3.2 • Fixed where runLinking(method = "FIXEDPAR") was not working when the anchor instrument ID was not 1 in item map. • Fixed where runLinking(method = "FIXEDPAR") was not working when the anchor and target instruments had different numbers of categories in response data. • Fixed where runFrequency() was not sorting categories correctly when the number of categories was 10 or above. • Fixed where runCalibration(fixedpar = TRUE) was not reading anchor parameters correctly when an integer value existed in anchor parameters. • Fixed where item parameters for dichotomous items were triggering an error while being parsed. • For compatibility with R < 4.0, loadData() now sanitizes input data when a data frame is supplied. PROsetta 0.3.0 New features • runLinking() now supports method = 'CPFIXEDDIM' to perform two-dimensional calibration, for use in performing calibrated projection (Thissen et al., 2015). The difference with method = 'CP' is that 'CPFIXEDDIM' constrains the mean and the variance of the latent anchor dimension, instead of constraining anchor item parameters. For this purpose, a unidimensional fixed parameter calibration using only the anchor response data is performed to obtain the mean and the variance. • getRSSS() for computing a single raw-score to standard-score table is now exposed. PROsetta 0.2.1 QoL updates • Added getResponse() for extracting scale-wise response data from a PROsetta_data object. • Added getItemNames() for extracting scale-wise item names from a PROsetta_data object. PROsetta 0.2.0 New features • runLinking() now supports method = 'CP' to perform two-dimensional calibration, for use in performing calibrated projection (Thissen et al., 2011). • runLinking() now supports method = 'CPLA' to perform two-dimensional calibration, for use in performing linear approximation of calibrated projection (Thissen et al., 2015). • runRSSS() now performs two-dimensional Lord-Wingersky recursion with numerical integration, when the output from runLinking(method = 'CP') is supplied. • runRSSS() now performs linear approximation of calibrated projection, when the output from runLinking(method = 'CPLA') is supplied. • Shiny application PROsetta() now supports calibrated projection and its linear approximation. Bug fixes • runEquateObserved(type_to = "theta") now works. • loadData() now checks for a valid @scale_id. PROsetta 0.1.4 Structural changes • PROsetta_config class and createConfig() are now deprecated. The functionalities are merged to PROsetta_data class and loadData(). • run*() functions now require PROsetta_data objects instead of PROsetta_config objects. • runLinking() now has method argument to specify the type of linking to perform. Accepts MM, MS, HB, SL, and FIXEDPAR. • runLinking() is now capable of performing fixed calibration. • runCalibration() now performs free calibration by default. • runCalibration() and runLinking() now errors when iteration limit is reached, without returning results. • runRSSS() now returns thetas in addition to T-scores, and also expected scores in each scale. • runEquateObserved() now has type_to argument to specify direct raw -> T-score equating or regular raw -> raw equating. • Functions are now more verbose. • Added PROMIS Depression - CES-D linking dataset data_dep. • Added plot() for drawing raw score distribution histograms. • Added plotInfo() for drawing scale information plots. • Added several helper functions. • Made cosmetic improvements on Shiny app. Bug fixes • Fixed where Shiny app was displaying SL method linear transformation constants regardless of specified linking method. PROsetta 0.0.4 • Added scalewise argument to runClassical() and runCFA(). When TRUE, analysis is performed for each scale. • runEquateObserved() now removes missing values to produce correct raw sums. • loadData() now retains missing values. PROsetta 0.0.3 • loadData() now removes missing values.	{"url":"https://cran.hafro.is/web/packages/PROsetta/news/news.html","timestamp":"2024-11-14T14:54:44Z","content_type":"application/xhtml+xml","content_length":"8682","record_id":"<urn:uuid:658a7f93-c531-4c08-830b-7b67ddbb20f0>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00491.warc.gz"}
Emulsion Design. Analysis of Drop Deformations in Mixed Flows The work presented in this thesis concerns numerical and experimental studies of flow induced deformation of drops suspended in a second and immiscible liquid. In the numerical part a model is implemented which is based on a Finite Element (FE) Stokes solver coupled with a Volume of Fluid (VOF) tracking procedure. The FE solver is based on Q2PO elements while the VOF procedure is based on PLIC (Piecewise Linear Interface Calculation) interface reconstruction and a split operator Lagrangian advection procedure which CQILSerVes mass rigorously. The model is fully 3D and can be used for simulating the transient behavior of two phase liquid systems with moving interface topologies. In order to include interfacial tension in the flow calculations both the Continuous Surface Stress (CSS) model of Lafaurie, Nardone, Scardovelli, Zaleski & Zanetti (1994) and the Continuous Surface Force (CSF) model of Brackbill, Kothe & Zemach (1992) are implemented. Due to the high interface curvatures associated with highly deformed drops it is necessary to use a high resolution mesh for our calculations. This leads to extensive computation times mainly due to factorization and back substitution of the discretized flow field equations. In order to reduce the computational cost a 2-level procedure is implemented where the fluid tracking algorithms are associated with a fine VOF mesh while the flow field variables are associated with a coarser FE mesh. In the 2-level algorithm the calculation of interfacial tension terms is carried out as a summation of contributions from the VOF mesh. This corresponds to letting the curvature vary within elements of the FE mesh. The implemented model is tested in terms of spatial and temporal convergence by simulating the deformation of a single drop in a simple shear flow field. Furthermore wall effects are also investigated by varying the size of the computational domain which consists of a box with variable mesh size. In the center of the domain, where the drop resides, the mesh consists of a fine region whereas closer to the walls the elements gradually increase in size. Tests show that wall effects are negligible when the distance from a drop with initial radius ro to the domain boundaries is 24ro. In the spatial convergence tests the resolution of the fine mesh region is varied and it is found that a VOF mesh with side lengths hvof == ro/18 is adequate when the viscosity ratio, A, between the drop and the continuous phase is one. More thorough tests are carried out both in simple shear and planar elongation. These simulations include dependence of steady-state deformations on the capillary number, drop-break and drop merging. Generally the test results agree well with results reported in the literature. However, simulations carried out for A different from one indicate that the resolution of the FE mesh needs to be increased compared to simulations carried out with A == 1. This is probably related to the method used for calculating the viscosity in elements which include both liquid phases. In the experimental part of the thesis the deformation of a single drop suspended in liquid undergoing a complex dispersing flow is studied. The experimental setup is based on a rotor-stator device consisting of two concentric cylinders with teethed walls. In order to monitor the drop deformation and drop position a twin camera system is applied. In the subsequent data analysis the recorded movies are analysed using an automated image analysis procedure which leads to the deformation history of the drop and the drop trajectory in the device. However, due to the geometric complexity of the rotor-stator device numerical calculations are necessary in order to obtain the generated flow field. The obtained experimental data is analysed by two different methods. In the first method the recorded drop deformations are time averaged and compared to a defined apparent shear rate which does not rely on numerical flow field calculations. The results from this analysis indicate that there is a relationship between the average drop deformation and the apparent shear rate. In the second method the experimentally obtained particle track is used together with numerical calculations in order to obtain the local flow experienced by the drop along its track. The data from these calculations lead to time-dependent shear and elongation rates which are used for generating time dependent boundary conditions for the FE-VOF simulations. By using this procedure the flow field experienced by the drop in the rotor-stator device is emulated in the computational box used for carrying out drop shape simulations. Comparison of simulated and experimentally obtained deformations show that in general the agreement is acceptable on a qualitative level. However, the simulations predict deformations which are up to 100% larger than experimentally observed. We have also compared our FE-VOF simulations with results from Boundary Integral (BI) simulations and find good agreement between the two numerical methods. A number of the conducted experiments resulted in drop break-up. The break-up behavior in the rotor-stator device is analyzed qualitatively by relating the configuration of the cylinders with the initiation of the break-up sequence. Here we observe that drop break-up is initiated when a drop travels from a region of minimum gap width into a region with maximum gap width where there is a relaxation in the flow field. Furthermore we observe that for small viscosity ratios (A ~ 0.1) tip streaming is predominant while for larger viscosity ratios either binary or capillary break-up is predominant. Number of pages 189 ISBN (Print) 978-87-91435-73-0 Publication status Published - May 2008 Dive into the research topics of 'Emulsion Design. Analysis of Drop Deformations in Mixed Flows'. Together they form a unique fingerprint. • Egholm, R. D. (PhD Student), Szabo, P. (Main Supervisor), Rasmussen, H. K. (Examiner), Harlen, O. G. (Examiner) & Trägårdh, C. (Examiner) 01/07/2004 → 16/05/2008 Project: PhD	{"url":"https://orbit.dtu.dk/en/publications/emulsion-design-analysis-of-drop-deformations-in-mixed-flows","timestamp":"2024-11-03T04:00:32Z","content_type":"text/html","content_length":"73977","record_id":"<urn:uuid:15b294f3-2cf3-44ff-b35c-655351cbf3b3>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00651.warc.gz"}
Vernier Caliper Experiment Pdf Download [BETTER] \| Trance Answers Vernier Caliper Experiment Pdf Download [BETTER] DOWNLOAD > https://bytlly.com/2txVnY How to Use a Vernier Caliper to Measure Different Objects A vernier caliper is a device that can measure the dimensions of different objects with high precision. It can measure the length, width, thickness, diameter, and depth of objects such as rectangular blocks, rods, holes, and calorimeters. In this article, we will explain how to use a vernier caliper to perform these measurements and calculate the volume of some objects. Parts of a Vernier Caliper A vernier caliper consists of two scales: a fixed scale and a sliding scale. The fixed scale is marked in increments of 0.1 cm, while the sliding scale has numbers marking 0.01 cm increments and small lines marking 0.002 cm increments. The sliding scale can move along the fixed scale to adjust to the size of the object being measured. The vernier caliper also has different parts for measuring different dimensions: The larger jaws (A) are used to measure outer dimensions, such as the width of a block or circular rod. The smaller jaws (B) are used to measure inner dimensions, such as the diameter of a hole. The depth probe (C) is used to measure the depth of a hole. The thumb screw clamp (F) is used to lock the sliding scale in place after taking a measurement. How to Read a Vernier Caliper To read a vernier caliper, follow these steps: Loosen the thumb screw clamp and adjust the sliding scale so that it fits snugly on the object to be measured. Make sure you use the correct part of the caliper for the dimension you want to measure. Tighten the thumb screw clamp and remove the caliper from the object. You can make a rough estimate of the measurement by laying the caliper on top of a ruler or meterstick and measuring the distance between the jaws or the depth probe. Look at the scale on the sliding jaw and find the line below the first zero that appears on the sliding scale (E). This line indicates the main scale reading (MSR) in centimeters. For example, if this line falls between 5.6 and 5.7 cm on the fixed scale (D), then MSR = 5.6 cm. Look at the line on the sliding scale that aligns with any line on the fixed scale. This line indicates the vernier scale reading (VSR) in divisions. For example, if this line is number 12 on the sliding scale, then VSR = 12 div. Multiply VSR by the least count (LC) of the vernier caliper to get the fractional part of the measurement in centimeters. The least count is equal to one division on the main scale divided by the total number of divisions on the vernier scale. For example, if one division on the main scale is 0.1 cm and there are 50 divisions on the vernier scale, then LC = 0.1/50 = 0.002 cm. If VSR = 12 div, then VSR x LC = 12 x 0.002 = 0.024 cm. Add MSR and VSR x LC to get the final measurement in centimeters. For example, if MSR = 5.6 cm and VSR x LC = 0.024 cm, then final measurement = MSR + VSR x LC = 5.6 + 0.024 = 5.624 cm. How to Use a Vernier Caliper to Measure Different Objects To use a vernier caliper to measure different objects, follow these steps: Rectangular Block To measure the volume of a rectangular block, you need to measure its length, width, and thickness using the larger jaws of the caliper. the length the block by placing it between the flat sections the jaws and reading the caliper as explained above. Repeat this measurement three times and take the average as your final value the 061ffe29dd	{"url":"https://www.tranceanswers.com/forum/pose-a-question/vernier-caliper-experiment-pdf-download-better","timestamp":"2024-11-13T18:01:54Z","content_type":"text/html","content_length":"1050521","record_id":"<urn:uuid:84b0b494-117c-47c1-858e-5a07739b08f2>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00893.warc.gz"}
Chapter 11 \| Understanding Quadrilaterals \| Class-8 DAV Secondary Mathematics \| NCERTBOOKSPDF.COM Chapter 11 \| Understanding Quadrilaterals \| Class-8 DAV Secondary Mathematics Are you looking for DAV Maths Solutions for class 8 then you are in right place, we have discussed the solution of the Secondary Mathematics book which is followed in all DAV School. Solutions are given below with proper Explanation please bookmark our website for further update !! All the Best !! Chapter 11 Understanding Quadrilaterals Worksheet 2 1. PQRS is a trapezium with PQ \|\| SR. if L P = 30°, L Q = 50°, find L R and L S. 2. ABCD is a quadrilateral with L A = 80°, L B = 40°, L C = 140°, L D = 100°. (i) Is ABCD a trapezium? (ii) Is ABCD a parallelogram? Justify your answer. 3. One of the angles of a parallelogram is 75°. Find the measures of the remaining angles of the parallelogram. 4. Two adjacent angles of a parallelogram are in the ratio 1 : 5. Find all the angles of the parallelogram. 5. An exterior angle of a parallelogram is 110°. Find the angles of the parallelogram. 6. Two adjacent sides of a parallelogram are in the ratio 3 : 8 and its perimeter is 110 cm. Find the sides of the parallelogram. 7. One side of a parallelogram is 3/4 times its adjacent side. If the perimeter of the parallelogram is 70 cm, find the sides of the parallelogram. 8. ABCD is a parallelogram whose diagonals intersect each other at right angles. If the length of the diagonals is 6 cm and 8 cm, find the lengths of all the sides of the parallelogram. 9. In figure 11.19, one pair of adjacent sides of a parallelogram is in the ratio 3 : 4. If one of its angles, L A is a right angle and diagonal BD = 10 cm, find the (i) lengths of the sides of the parallelogram. (ii) perimeter of the parallelogram. 10.ABCD is a quadrilateral in which AB = CD and AD = BC . Show that it is a parallelogram. [Hint: Draw one of the diagonals.]	{"url":"https://ncertbookspdf.com/chapter-11-understanding-quadrilaterals-class-8-dav-secondary-mathematics/","timestamp":"2024-11-08T02:00:52Z","content_type":"text/html","content_length":"88031","record_id":"<urn:uuid:a2d1c74e-8809-4fdd-baf3-14b7afbf1dc6>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00443.warc.gz"}
Quantum Computers Are Starting to Simulate the World of Subatomic Particles There is a heated race to make quantum computers deliver practical results. But this race isn't just about making better technology—usually defined in terms of having fewer errors and more qubits, which are the basic building blocks that store quantum information. At least for now, the quantum computing race requires grappling with the complex realities of both quantum technologies and difficult problems. To develop quantum computing applications, researchers need to understand a particular quantum technology and a particular challenging problem and then adapt the strengths of the technology to address the intricacies of the problem. Theoretical nuclear physicist Zohreh Davoudi, an assistant professor of physics at the University of Maryland (UMD) and a member of the Maryland Center for Fundamental Physics, has been working with multiple colleagues at UMD to ensure that the problems that she cares about are among those benefiting from early advances in quantum computing. The best modern computers have often proven inadequate at simulating the details that nuclear physicists need to understand our universe at the deepest levels. Davoudi and JQI Fellow Norbert Linke are collaborating to push the frontier of both the theories and technologies of quantum simulation through research that uses current quantum computers. Their research is intended to illuminate a path toward simulations that can cut through the current blockade of fiendishly complex calculations and deliver new theoretical predictions. For example, quantum simulations might be the perfect tool for producing new predictions based on theories that combine Einstein’s theory of special relativity and quantum mechanics to describe the basic building blocks of nature—the subatomic particles and the forces among them—in terms of “quantum fields.” Such predictions are likely to reveal new details about the outcomes of high-energy collisions in particle accelerators and other lingering physics questions. The team’s current efforts might help nuclear physicists, including Davoudi, to take advantage of the early benefits of quantum computing instead of needing to rush to catch up when quantum computers hit their stride. For Linke, who is also an assistant professor of physics at UMD, the problems faced by nuclear physicists provide a challenging practical target to take aim at during these early days of quantum computing. In a new paper in PRX Quantum, Davoudi, Linke and their colleagues have combined theory and experiment to push the boundaries of quantum simulations—testing the limits of both the ion-based quantum computer in Linke’s lab and proposals for simulating quantum fields. Both Davoudi and Linke are also part of the NSF Quantum Leap Challenge Institute for Robust Quantum Simulation that is focused on exploring the rich opportunities presented by quantum simulations. The new project wasn’t about adding more qubits to the computer or stamping out every source of error. Rather, it was about understanding how current technology can be tested against quantum simulations that are relevant to nuclear physicists so that both the theoretical proposals and the technology can progress in practical directions. The result was both a better quantum computer and improved quantum simulations of a basic model of subatomic particles “I think for the current small and noisy devices, it is important to have a collaboration of theorists and experimentalists so that we can implement useful quantum simulations,” says JQI graduate student Nhung Nguyen, who was the first author of the paper. “There are many things we could try to improve on the experimental sides but knowing which one leaves the greatest impact on the result helps guides us in the right direction. And what makes the biggest impact depends a lot on what you try to simulate.” The team knew the biggest and most rewarding challenges in nuclear physics are beyound the reach of current hardware, so they started with something a little simpler than reality: the Schwinger model. Instead of looking at particles in reality’s three dimensions evolving over time, this model pares things down to particles existing in just one dimension over time. The researchers also further simplified things by using a version of the model that breaks continuous space into discrete sites. So in their simulations, space only exist as one line of distinct sites, like a column cut off a chess board, and the particles are like pieces that must always reside in one square or another along that column. Despite the model being stripped of so much of reality’s complexity, interesting physics can still play out in it. The physicist Julian Schwinger developed this simplified model of quantum fields to mimic parts of physics that are integral to the formation of both the nuclei at the centers of atoms and the elementary particles that make them up. “The Schwinger model kind of hits the sweet spot between something that we can simulate and something that is interesting,” says Minh Tran, a MIT postdoctoral researcher and former JQI graduate student who is a coauthor on the paper. “There are definitely more complicated and more interesting models, but they're also more difficult to realize in the current experiments.” In this project, the team looked at simulations of electrons and positrons—the antiparticles of electrons—appearing and disappearing over time in the Schwinger model. For convenience, the team started the simulation with an empty space—a vacuum. The creation and annihilation of a particle and its antiparticle out of vacuum is one of the significant predictions of quantum field theory. Schwinger’s work establishing this description of nature earned him, alongside Richard Feynman and Sin-Itiro Tomonaga, the Nobel Prize in physics in 1965. Simulating the details of such fundamental physics from first principles is a promising and challenging goal for quantum computers. Nguyen led the experiment that simulated Schwinger’s pair production on the Linke Lab quantum computer, which uses ions—charged atoms—as the qubits. “We have a quantum computer, and we want to push the limits,” Nguyen says. “We want to see if we optimize everything, how long can we go with it and is there something we can learn from doing the experimental simulation.” The researchers simulated the model using up to six qubits and a preexisting language of computing actions called quantum gates. This approach is an example of digital simulation. In their computer, the ions stored information about if particles or antiparticles exist at each site in the model, and interactions were described using a series of gates that can change the ions and let them influence each other. In the experiments, the gates only manipulated one or two ions at a time, so the simulation couldn’t include everything in the model interacting and changing simultaneously. The reality of digital simulations demands the model be chopped into multiple pieces that each evolve over small steps in time. The team had to figure out the best sequence of their individual quantum gates to approximate the model changing continuously over time. “You're just approximately applying parts of what you want to do bit by bit,” Linke says. “And so that's an approximation, but all the orderings—which one you apply first, and which one second, etc.—will approximate the same actual evolution. But the errors that come up are different from different orderings. So there's a lot of choices here.” Many things go into making those choices, and one important factor is the model’s symmetries. In physics, a symmetry describes a change that leaves the equations of a model unchanged. For instance, in our universe rotating only changes your perspective and not the equations describing gravity, electricity or magnetism. However, the equations that describe specific situations often have more restrictive symmetries. So if an electron is alone in space, it will see the same physics in every direction. But if that electron is between the atoms in a metal, then the direction matters a lot: Only specific directions look equivalent. Physicists often benefit from considering symmetries that are more abstract than moving around in space, like symmetries about reversing the direction of The Schwinger model makes a good starting point for the team’s line of research because of how it mimics aspects of complex nuclear dynamics and yet has simple symmetries. “Once we aim to simulate the interactions that are in play in nuclear physics, the expression of the relevant symmetries is way more complicated and we need to be careful about how to encode them and how to take advantage of them,” Davoudi says. “In this experiment, putting things on a one-dimensional grid is only one of the simplifications. By adopting the Schwinger model, we have also a greatly simplified notion of symmetries, which end up becoming a simple electric charge conservation. In our three-dimensional reality though, those more complicated symmetries are the reason we have bound atomic nuclei and hence everything else!” The Schwinger model’s electric charge conservation symmetry keeps the total amount of electric charge the same. That means that if the simulation of the model starts from the empty state, then an electron should always be accompanied by a positron when it pops into or out of existence. So by choosing a sequence of quantum gates that always maintains this rule, the researchers knew that any result that violated it must be an error from experimental imperfections. They could then throw out the obviously bad data—a process called post-selection. This helped them avoid corrupted data but required more runs than if the errors could have been prevented. The team also explored a separate way to use the Schwinger model’s symmetries. There are orders of the simulation steps that might prove advantageous despite not obeying the model’s symmetry rules. So suppressing errors that result from orderings that don’t conform to the symmetry could prove useful. Earlier this year, Tran and colleagues at JQI showed there is a way to cause certain errors, including ones from a symmetry defying order of steps, to interfere with each other and cancel out. The researchers applied the proposed procedure in an experiment for the first time. They found that it did decrease errors that violated the symmetry rules. However, due to other errors in the experiment, the process didn’t generally improve the results and overall was not better than resorting to post-selection. The fact that this method didn’t work well for this experiment provided the team with insights into the errors occurring during their simulations. All the tweaking and trial and error paid off. Thanks to the improvements the researchers made, including upgrading the hardware and implementing strategies like post-selection, they increased how much information they could get from the simulation before it was overwhelmed by errors. The experiment simulated the Schwinger model evolving for about three times longer than previous quantum simulations. This progress meant that instead of just seeing part of a cycle of particle creation and annihilation in the Schwinger model, they were able to observe multiple complete cycles. “What is exciting about this experiment for me is how much it has pushed our quantum computer forward,” says Linke. “A computer is a generic machine—you can do basically anything on it. And this is true for a quantum computer; there are all these various applications. But this problem was so challenging, that it inspired us to do the best we can and upgrade our system and go in new directions. And this will help us in the future to do more.” There is still a long road before the quantum computing race ends, and Davoudi isn’t betting on just digital simulations to deliver the quantum computing prize for nuclear physicists. She is also interested in analog simulations and hybrid simulations that combine digital and analog approaches. In analog simulations, researchers directly map parts of their model onto those of an experimental simulation. Analog quantum simulations generally require fewer computing resources than their digital counterparts. But implementing analog simulations often requires experimentalists to invest more effort in specialized preparation since they aren’t taking advantage of a set of standardized building blocks that has been preestablished for their quantum computer. Moving forward, Davoudi and Linke are interested in further research on more efficient mappings onto the quantum computer and possibly testing simulations using a hybrid approach they have proposed. In this approach, they would replace a particularly challenging part of the digital mapping by using the phonons—quantum particles of sound—in Linke Lab’s computer as direct stand-ins for the photons —quantum particles of light—in the Schwinger model and other similar models in nuclear physics. “Being able to see that the kind of theories and calculations that we do on paper are now being implemented in reality on a quantum computer is just so exciting,” says Davoudi. “I feel like I'm in a position that in a few decades, I can tell the next generations that I was so lucky to be able to do my calculations on the first generations of quantum computers. Five years ago, I could have not imagined this day.” Story by Bailey Bedford, reprinted from the University of Maryland Joint Quantum Institute Published May 25, 2022	{"url":"https://qtc.umd.edu/news/story/quantum-computers-are-starting-to-simulate-the-world-of-subatomic-particles","timestamp":"2024-11-07T05:33:19Z","content_type":"text/html","content_length":"49234","record_id":"<urn:uuid:3ba97644-5321-41a3-9d7d-dc5c3a8d331b>","cc-path":"CC-MAIN-2024-46/segments/1730477027957.23/warc/CC-MAIN-20241107052447-20241107082447-00451.warc.gz"}
[Haskell-cafe] rewrite rules to specialize function according to type class? [Haskell-cafe] rewrite rules to specialize function according to type class? Patrick Bahr pa-ba at arcor.de Mon Feb 14 22:43:53 CET 2011 Hi all, I am trying to get a GHC rewrite rule that specialises a function according to the type of the argument of the function. Does anybody know whether it is possible to do that not with a concrete type but rather a type class? Consider the following example: > class A a where > toInt :: a -> Int > {-# NOINLINE toInt #-} > class B a where > toInt' :: a -> Int The idea is to use the method of type class A unless the type is also an instance of type class B. Let's say that Bool is an instance of both A and B: > instance A Bool where > toInt True = 1 > toInt False = 0 > instance B Bool where > toInt' True = 0 > toInt' False = 1 Now we add a rule that says that if the argument to "toInt" happens to be an instance of type class B as well, use the method "toInt'" instead: > {-# RULES > "toInt" forall (x :: B a => a) . toInt x = toInt' x > #-} Unfortunately, this does not work (neither with GHC 6.12 or GHC 7.0). Expression "toInt True" gets evaluated to "1". If the rewrite rule is written with a concrete type it works as expected: > {-# RULES > "toInt" forall (x :: Bool) . toInt x = toInt' x > #-} Now "toInt True" is evaluated to "0". Am I doing something wrong or is it not possible for GHC to dispatch a rule according to type class constraints? More information about the Haskell-Cafe mailing list	{"url":"https://mail.haskell.org/pipermail/haskell-cafe/2011-February/089293.html","timestamp":"2024-11-09T00:57:37Z","content_type":"text/html","content_length":"4470","record_id":"<urn:uuid:dbda8650-36c9-45fd-8c8b-2f55aeff60c7>","cc-path":"CC-MAIN-2024-46/segments/1730477028106.80/warc/CC-MAIN-20241108231327-20241109021327-00899.warc.gz"}
CBSE Class 11 maths notes - Schoollearners CBSE Class 11 maths notes CBSE Class 11 maths notes CBSE Class 11 maths Revision notes Here you will get CBSE Class 11 Maths Notes for all the chapters, these notes are available in PDF form. CBSE Class 11 Maths Notes can also be downloaded in Pdf form. Notes are very important for revision so that students can understand the chapter easily. Along with this, all the doubts are also cleared, these notes have been prepared for the exam point of view, on this website you will get the notes of all the classes, here we have provided the notes from classes 9 to 12. CBSE Maths Class 11 Notes are very good, all the chapters are covered for the preparation of the exam as well as there are questions for practice so that the students can test themselves. Chapter 1 – Sets Chapter 2 – Relations and Functions Chapter 3 – Trigonometric Functions Chapter 4 – Principle of Mathematical Induction Chapter 5 – Complex Numbers and Quadratic Equations Chapter 6 – Linear Inequalities Chapter 7 – Permutations and Combinations Chapter 8 – Binomial Theorem Chapter 9 – Sequences and Series Chapter 10 – Straight Lines Chapter 11 – Conic Sections Chapter 12 – Introduction to Three Dimensional Geometry Chapter 13 – Limits and Derivatives Chapter 14 – Mathematical Reasoning Chapter 15 – Statistics Chapter 16 – Probability class 11 maths notes, class 11 maths chapter 1 sets notes, class 11 maths handwritten notes pdf, class 11 maths chapter 1 notes pdf download, class 11 maths study material pdf	{"url":"https://www.schoollearners.com/cbse-class-11-maths-notes/","timestamp":"2024-11-10T06:21:00Z","content_type":"text/html","content_length":"101740","record_id":"<urn:uuid:13bfdac8-2907-4b77-a8bc-dcc04568d1b6>","cc-path":"CC-MAIN-2024-46/segments/1730477028166.65/warc/CC-MAIN-20241110040813-20241110070813-00807.warc.gz"}
I didn’t know how to solve this Leetcode Problem!😭😭😭 This is a medium Leetcode 402 question where you are asked to remove k digits from a number to make that number the smallest possible number. See problem description below: problem description The question is quite understandable and straight forward but the issue is with knowing the numbers to remove. At first, I thought that sorting the numbers and keeping track of the positions and then removing the largest numbers would work but apparently that didn’t work. After trying to no avail, I had to seek for solution online and came across two algorithms: public static String removeKdigits(String num, int k) { Stack<Character> stack = new Stack<>(); StringBuilder answer = new StringBuilder(); if (num.length() == k) return "0"; for (int i = 0; i < num.length(); i++) { while (k > 0 && !stack.isEmpty() && stack.peek() > num.charAt(i)) { k = k - 1; while (!stack.isEmpty()) { if (!answer.toString().isEmpty()) { answer = answer.reverse(); String s = answer.toString().replaceFirst("^0+(?!$)", ""); if (k != 0) s = s.substring(0, answer.length() - k); return s; } else return "0"; To understand the algorithm above, please check thecodingworld on YouTube. He did a good job to explain the algorithm. His code was written in Python, so I had to translate to Java. public static String removeKdigits(String num, int k) { Stack<Character> stack = new Stack<>(); int length = num.length(); for (int i = 0; i < length; i++) { while (!stack.isEmpty() && k > 0 && stack.peek() > num.charAt(i)) { k -= 1; if (!stack.isEmpty() \|\| num.charAt(i) != '0') //Now remove the largest values from the top of the stack while (!stack.empty() && k != 0) { if (stack.isEmpty()) return "0"; //now retrieve the number from stack into a string StringBuilder result = new StringBuilder(); while (!stack.isEmpty()) { return result.reverse().toString(); Also to understand the second algorithm above, please check Tech Dose for the explanation. I also translated the code to Java. I have learnt a lot from these algorithms especially from the way people think and I think that’s the fun of solving algorithm questions. Thank you for reading. Please leave a comment or suggestion below.	{"url":"https://codechunkers.medium.com/i-didnt-know-how-to-solve-this-leetcode-problem-66c08cae16af","timestamp":"2024-11-03T15:24:01Z","content_type":"text/html","content_length":"109039","record_id":"<urn:uuid:ae72f504-d83c-4e63-bde9-822816adaac0>","cc-path":"CC-MAIN-2024-46/segments/1730477027779.22/warc/CC-MAIN-20241103145859-20241103175859-00129.warc.gz"}
Commit 2024-10-30 00:13 ef78db7e View on Github → refactor(CategoryTheory): simplicial categories are generalized to enriched "ordinary" categories (#18175) The API for simplicial categories is refactored. It fits more generally in the context of ordinary categories C (a type C and an instance [Category C]) that are also enriched over a monoidal category V (EnrichedCategory V C) in such a way that types of morphisms in C identify to types of morphisms 𝟙_ V ⟶ (X ⟶[V] Y) in V. This defines a new class EnrichedOrdinaryCategory, and SimplicialCategory is made an abbreviation for the particular case V is the category of simplicial sets. Estimated changes	{"url":"https://mathlib-changelog.org/v4/commit/ef78db7e","timestamp":"2024-11-05T02:44:57Z","content_type":"text/html","content_length":"16014","record_id":"<urn:uuid:3c80ddc9-93e0-4885-9696-a2e11dd88485>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00402.warc.gz"}
The figure on the right shows a typical graph plotting scenario, where a graph containing a 3D surface plot has been created at the top of the first page of a TeraPlot project. Each project gets its own document window within a multiple document type interface. A project can contain multiple pages, and pages can contain multiple graphs. Also, graphs can be arbitrarily positioned and sized on a page. The page on which the graphs are laid out is a correct representation of the printer page, ensuring that any printed graph will look exactly as displayed on the screen, a feature rarely found in other graph software. Also shown is the Plot Dialog, which is used to specify the plot data and parameters. The Plot Dialog consists of three parts: a list of the names of the plots that have been added to the graph on the left, a list of available property pages for the currently selected plot in the middle, and the currently selected property page on the right. The property pages contain all of the properties that can be modified for the currently selected plot. All of the most commonly used graph creation and page manipulation options are available from the two toolbars at the top of the main window. View a slideshow of the steps involved in creating the graph on the right The plot in the graph above was based on tabular data. TeraPlot can also create plots based on mathematical expressions, and both types of plot can be combined in the same graph. Plots based on mathematical expressions are termed "analytical plots", and are defined using one or more expressions in the VBScript scripting language. Plots can be defined using various coordinate systems, and combined in the same graph. Typical coordinate systems are cartesian, polar and parametric for 2D plots/graphs; cartesian, spherical, cylindrical, and parametric for 3D plots/graphs. In the figure on the left, a graph with a plot of z = y^2 - x^2 has been created over the range -10 to 10 in both of the graph x and y directions. To illustrate the fact that the plot definition can consist of multiple expressions, the subexpressions x^2 and y^2 have been defined as separate terms t1 and t2, before subtracting t1 from t2 to create the final plot definition. VBScript provides all common math functions, and TeraPlot graph software additionally allows you specify your own functions in a file which is read from disk when the program starts. View a slideshow of how TeraPlot graph software was used to create the graph on the left	{"url":"http://www.teraplot.com/graph-software","timestamp":"2024-11-02T07:36:47Z","content_type":"application/xhtml+xml","content_length":"11048","record_id":"<urn:uuid:5d175da1-01b5-465b-b905-f4442f1bd492>","cc-path":"CC-MAIN-2024-46/segments/1730477027709.8/warc/CC-MAIN-20241102071948-20241102101948-00633.warc.gz"}
How to Create a Vector of Zeros in R (With Examples) \| Online Tutorials Library List \| Tutoraspire.com How to Create a Vector of Zeros in R (With Examples) by Tutor Aspire There are three common ways to create a vector of zeros in R: Method 1: Use numeric() #create vector of 12 zeros Method 2: Use integer() #create vector of 12 zeros Method 3: Use rep() #create vector of 12 zeros rep(0, 12) The following examples show how to use each method in practice. Example 1: Create Vector of Zeros Using numeric() The following code shows how to create a vector of zeros using the numeric() function: #create vector of 12 zeros [1] 0 0 0 0 0 0 0 0 0 0 0 0 The result is a vector with 12 zeros. Note that this vector will have a class of numeric. Example 2: Create Vector of Zeros Using integer() The following code shows how to create a vector of zeros using the integer() function: #create vector of 12 zeros [1] 0 0 0 0 0 0 0 0 0 0 0 0 The result is a vector with 12 zeros. Note that this vector will have a class of integer. Example 3: Create Vector of Zeros Using rep() The following code shows how to create a vector of zeros using the rep() function: #create vector of 12 zeros rep(0, 12) [1] 0 0 0 0 0 0 0 0 0 0 0 0 The result is a vector with 12 zeros. Note that this vector will have a class of numeric. Related: How to Use rep() Function in R to Replicate Elements Additional Resources The following tutorials explain how to perform other common tasks in R: How to Create a Vector with Random Numbers in R How to Create an Empty Vector in R How to Check if a Vector Contains a Given Element in R Share 0 FacebookTwitterPinterestEmail previous post Google Sheets: How to Query From Multiple Ranges You may also like	{"url":"https://tutoraspire.com/r-create-vector-of-zeros/","timestamp":"2024-11-03T18:48:24Z","content_type":"text/html","content_length":"349625","record_id":"<urn:uuid:ab5b5ee2-7273-46ab-96bf-2ea0597955a5>","cc-path":"CC-MAIN-2024-46/segments/1730477027782.40/warc/CC-MAIN-20241103181023-20241103211023-00810.warc.gz"}
How to use BINOM.DIST function in Excel? - Developer Publish In this post you’ll learn about BINOMDIST Function, its syntax and the way of using BINOMDIST Function in excel spreadsheet. BINOMDIST Function refers to the calculation of probability of drawing a certain number of trial, with replacement of draws. What is BINOMDIST Function? BINOMDIST Function is a statistical function, it can be used as a Worksheet function (WS) in Excel. The Excel BINOMDIST Function returns and calculates the individual term binomial distribution You can use BINOMDIST to calculate probability that an event will occurs a certain number of times in a given number of trials. BINOMDIST Function used to return the probability as a decimal numbers between 0 and 1. The BINOMDIST Function is also classified into one category as Compatibility Function which is replaced by BINOM.DIST Function. Binary data occurs when observation can be placed into two categories. When tossing a coin, the result can only be Head or tail. Or When rolling a die, the result will be 6 or not 6 =BINOMDIST (number_success(s), trials, probability_success(s), cumulative) • number_success(s) – (required) the number of successes. • trials – (required) the number of independent trials. • Probability_success(s) – (required) the probability of success on each trial. • Cumulative – A logical value determines the function. TRUE – cumulative distribution function. FALSE – probability mass function. • number_success(s) and trials always must be integers, otherwise it will truncate into an integers. • #VALUE! Error value – If number_success(s), trials and probability_success(s) is a non-numeric value. • If number_s<0 or number_s>trials, BINOMDIST returns the #NUM! Error value. • If probability_s<0 or probability_s>1, BINOMDIST returns the #NUM! Error value. • If x= number_s, n= trials, and p= probability_s, then binomial probability mass function is, If x= number_s, n= trials, and p= probability_s, then the cumulative binomial distribution is, How to use BINOM.DIST function in Excel? BINOMDIST Function is used to get the Binomial distribution probability. You can see the results of rolling of die, getting either 6 or not by using BINOMDIST Function in Excel spreadsheet. STEP 1: Open the workbook in your Microsoft Excel. STEP 2: Enter the data in the workbook. You can calculate the probability of rolling a six with a die. STEP 3: In the new cell, give the formula of the function or the syntax . Always start with ‘ =’ for every functions, BINOMDIST function name, followed by the open parenthesis, the arguments of the syntax. STEP 4: A die has six sides, the probability of rolling one six is 1/6. number_s in rolling a six with a die is 1. STEP 5: Next step is the number of trials. You can consider the probability of rolling 6 in a die as 10 trials. The trials are 10. STEP 6: Next is probability of success. The probability of rolling 6 in 10 trials is about 32%. The probability_s is 32%. STEP 7: Next is cumulative argument. The cumulative argument set as TRUE. This causes BINOMDIST to calculate the probability that there are “at most ” X success in a given number of trials. STEP 8: Press Enter, to get the results. Leave A Reply	{"url":"https://developerpublish.com/binomdist-function-in-excel/","timestamp":"2024-11-13T18:44:26Z","content_type":"text/html","content_length":"316402","record_id":"<urn:uuid:61ed4910-1622-4078-9f97-7403f08b2b32>","cc-path":"CC-MAIN-2024-46/segments/1730477028387.69/warc/CC-MAIN-20241113171551-20241113201551-00376.warc.gz"}
More about our Orifice equations The Orifice Equation is originally derived from the following equation: Q = CA√(2gd) To simplify the Orifice equation, use a coefficient of 0.67 and correct open area from square feet to square inches and depth of water from feet to inches. • Q = Flow capacity (in cubic feet per second) • C = Orifice coefficient • A = Open area of grate (ft^2 ) • g = Acceleration due to gravity (32.2ft/sec^2 ) • d = Depth of water over grate (in feet) We provide the flow capacity calculators to be used in theoretical calculations and are provided as a guidance only. There are many variables that occur in the field that are not taken into account. Please contact one of our Engineers with any questions you may have.	{"url":"http://norwoodfoundry.com/Engineering/Drainage-Grate-Flow-Calculators.aspx","timestamp":"2024-11-12T13:36:51Z","content_type":"text/html","content_length":"17242","record_id":"<urn:uuid:620fc41b-7a94-4b72-885c-ebcc0b4c01d0>","cc-path":"CC-MAIN-2024-46/segments/1730477028273.45/warc/CC-MAIN-20241112113320-20241112143320-00466.warc.gz"}
Jared Lander Based on data collected from polls conducted at the beginning of the New York Open Statistical Programming meetups. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. My Book is Out After two years of writing and editing and proof reading and checking my book, R for Everyone is finally out! There are so many people who helped me along the way, especially my editor Debra Williams, production editor Caroline Senay and the man who recruited me to write it in the first place, Paul Dix. Even more people helped throughout the long process, but with so many to mention I’ll leave that in the acknowledgements page. Online resources for the book are available (https://www.jaredlander.com/r-for-everyone/) and will continue to be updated. As of now the three major sites to purchase the book are Amazon, Barnes & Noble (available in stores January 3rd) and InformIT. And of course digital versions are available. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Drawing Balls From an Urn A friend recently posted the following the problem: There are 10 green balls, 20 red balls, and 25 blues balls in a a jar. I choose a ball at random. If I choose a green then I take out all the green balls, if i choose a red ball then i take out all the red balls, and if I choose, a blue ball I take out all the blue balls, What is the probability that I will choose a red ball on my second try? The math works out fairly easily. It’s the probability of first drawing a green ball AND then drawing a red ball, OR the probability of drawing a blue ball AND then drawing a red ball. \frac{10}{10+20+25} * \frac{20}{20+25} + \frac{25}{10+20+25} * \frac{20}{10+20} = 0.3838 But I always prefer simulations over probability so let’s break out the R code like we did for the Monty Hall Problem and calculating lottery odds. The results are after the break. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Pizza Poll Results For a d3 bar plot visit https://www.jaredlander.com/plots/PizzaPollPlot.html. I finally compiled the data from all the pizza polling I’ve been doing at the New York R meetups. The data are available as json at https://www.jaredlander.com/data/PizzaPollData.php. This is easy enough to plot in R using ggplot2. pizzaJson <- fromJSON(file = "http://jaredlander.com/data/PizzaPollData.php") pizza <- ldply(pizzaJson, as.data.frame) ## polla_qid Answer Votes pollq_id Question ## 1 2 Excellent 0 2 How was Pizza Mercato? ## 2 2 Good 6 2 How was Pizza Mercato? ## 3 2 Average 4 2 How was Pizza Mercato? ## 4 2 Poor 1 2 How was Pizza Mercato? ## 5 2 Never Again 2 2 How was Pizza Mercato? ## 6 3 Excellent 1 3 How was Maffei's Pizza? ## Place Time TotalVotes Percent ## 1 Pizza Mercato 1.344e+09 13 0.0000 ## 2 Pizza Mercato 1.344e+09 13 0.4615 ## 3 Pizza Mercato 1.344e+09 13 0.3077 ## 4 Pizza Mercato 1.344e+09 13 0.0769 ## 5 Pizza Mercato 1.344e+09 13 0.1538 ## 6 Maffei's Pizza 1.348e+09 7 0.1429 ggplot(pizza, aes(x = Place, y = Percent, group = Answer, color = Answer)) + geom_line() + theme(axis.text.x = element_text(angle = 46, hjust = 1), legend.position = "bottom") + labs(x = "Pizza Place", title = "Pizza Poll Results") But given this is live data that will change as more polls are added I thought it best to use a plot that automatically updates and is interactive. So this gave me my first chance to need rCharts by Ramnath Vaidyanathan as seen at October’s meetup. pizzaPlot <- nPlot(Percent ~ Place, data = pizza, type = "multiBarChart", group = "Answer") pizzaPlot$xAxis(axisLabel = "Pizza Place", rotateLabels = -45) pizzaPlot$yAxis(axisLabel = "Percent") pizzaPlot$chart(reduceXTicks = FALSE) pizzaPlot$print("chart1", include_assets = TRUE) Unfortunately I cannot figure out how to insert this in WordPress so please see the chart at https://www.jaredlander.com/plots/PizzaPollPlot.html. Or see the badly sized one below. There are still a lot of things I am learning, including how to use a categorical x-axis natively on linecharts and inserting chart titles. I found a workaround for the categorical x-axis by using tickFormat but that is not pretty. I also would like to find a way to quickly switch between a line chart and a bar chart. Fitting more labels onto the x-axis or perhaps adding a scroll bar would be nice too. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Books from the NYC Data Mafia Attending this week’s Strata conference it was easy to see quite how prolific the NYC Data Mafia is when it comes to writing. Some of the found books: Books from the #nycdatamafia @drewconway @johnmyleswhite http://t.co/EuV4FF6JA7 pic.twitter.com/Oi8tVcjPYE — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia @mikedewar http://t.co/w2oCS2jLvN pic.twitter.com/yiq9x6SG3y — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia @wesmckinn http://t.co/jhUPSrtTOE pic.twitter.com/ri5eUhWwY0 — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia Rachel Schutt @mathbabedotorg http://t.co/EVI6HanjUb pic.twitter.com/yTL0fXQGBK — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia @HarlanH @wahalulu http://t.co/6CjAvGsHRL pic.twitter.com/0DwMqSmNve — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia @qethanm http://t.co/Hy82gz4tGe pic.twitter.com/Uba15XIhLT — NYC Data Hackers (@nyhackr) October 29, 2013 Books from the #nycdatamafia @pauldix http://t.co/Tdw0MSF5B7 pic.twitter.com/4rmpk5UuYf — NYC Data Hackers (@nyhackr) October 29, 2013 And, of course, my book will be out soon to join them. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. The Monty Hall Problem Michael Malecki recently shared a link to a Business Insider article that discussed the Monty Hall Problem. The problem starts with three doors, one of which has a car and two of which have a goat. You choose one door at random and then the host reveals one door (not the one you chose) that holds a goat. You can then choose to stick with your door or choose the third, remaining door. Probability theory states that people who switch win the car two-thirds of the time and those who don’t switch only win one-third of time. But people often still do not believe they should switch based on the probability argument alone. So let’s run some simulations. This function randomly assigns goats and cars behind three doors, chooses a door at random, reveals a goat door, then either switches doors or does not. monty <- function(switch=TRUE) # randomly assign goats and cars doors <- sample(x=c("Car", "Goat", "Goat"), size=3, replace=FALSE) # randomly choose a door doorChoice <- sample(1:3, size=1) # get goat doors goatDoors <- which(doors == "Goat") # show a door with a goat goatDoor <- goatDoors[which(goatDoors != doorChoice)][1] # if we are switching choose the other remaining door return(doors[-c(doorChoice, goatDoor)]) # otherwise keep the current door Now we simulate switching 10,000 times and not switching 10,0000 times withSwitching <- replicate(n = 10000, expr = monty(switch = TRUE), simplify = TRUE) withoutSwitching <- replicate(n = 10000, expr = monty(switch = FALSE), simplify = TRUE) ## [1] "Goat" "Car" "Car" "Goat" "Car" "Goat" ## [1] "Goat" "Car" "Car" "Car" "Car" "Car" mean(withSwitching == "Car") ## [1] 0.6678 mean(withoutSwitching == "Car") ## [1] 0.3408 Plotting the results really shows the difference. ## Loading required package: ggplot2 ## Loading required package: scales qplot(withSwitching, geom = "bar", fill = withSwitching) + scale_fill_manual("Prize", values = c(Car = muted("blue"), Goat = "orange")) + xlab("Switch") + ggtitle("Monty Hall with Switching") qplot(withoutSwitching, geom = "bar", fill = withoutSwitching) + scale_fill_manual("Prize", values = c(Car = muted("blue"), Goat = "orange")) + xlab("Don't Switch") + ggtitle("Monty Hall without Switching") (How are these colors? I’m trying out some new combinations.) This clearly shows that switching is the best strategy. The New York Times has a nice simulator that lets you play with actual doors. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. NYC Evacuation Map in R Given the warnings for today’s winter storm, or lack of panic, I thought it would be a good time to plot the NYC evacuation maps using R. Of course these are already available online, provided by the city, but why not build them in R as well? I obtained the shapefiles from NYC Open Data on February 28th, so it’s possible they are the new shapefiles redrawn after Hurricane Sandy, but I am not certain. First we need the appropriate packages which are mostly included in maptools, rgeos and ggplot2. ## Loading required package: maptools ## Loading required package: foreign ## Loading required package: sp ## Loading required package: lattice ## Checking rgeos availability: TRUE ## Loading required package: rgeos ## Loading required package: stringr ## Loading required package: plyr ## rgeos: (SVN revision 348) GEOS runtime version: 3.3.5-CAPI-1.7.5 Polygon ## checking: TRUE ## Loading required package: ggplot2 require(plyr) require(grid) ## Loading required package: grid Then we read in the shape files, fortify them to turn them into a data.frame for easy plotting then join that back into the original data to get zone information. # read the shape file evac <- readShapeSpatial("../data/Evac_Zones_with_Additions_20121026/Evac_Zones_with_Additions_20121026.shp") # necessary for some of our work gpclibPermit() ## [1] TRUE # create ID variable evac@data$id <- rownames(evac@data) # fortify the shape file evac.points <- fortify(evac, region = "id") # join in info from data evac.df <- join(evac.points, evac@data, by = "id") # modified data head(evac.df) ## long lat order hole piece group id Neighbrhd CAT1NNE Shape_Leng ## 1 1003293 239790 1 FALSE 1 0.1 0 <NA> A 9121 ## 2 1003313 239782 2 FALSE 1 0.1 0 <NA> A 9121 ## 3 1003312 239797 3 FALSE 1 0.1 0 <NA> A 9121 ## 4 1003301 240165 4 FALSE 1 0.1 0 <NA> A 9121 ## 5 1003337 240528 5 FALSE 1 0.1 0 <NA> A 9121 ## 6 1003340 240550 6 FALSE 1 0.1 0 <NA> A 9121 ## Shape_Area ## 1 2019091 ## 2 2019091 ## 3 2019091 ## 4 2019091 ## 5 2019091 ## 6 2019091 # as opposed to the original data head(evac@data) ## Neighbrhd CAT1NNE Shape_Leng Shape_Area id ## 0 <NA> A 9121 2019091 0 ## 1 <NA> A 12250 54770 1 ## 2 <NA> A 10013 1041886 2 ## 3 <NA> B 11985 3462377 3 ## 4 <NA> B 5816 1515518 4 ## 5 <NA> B 5286 986675 5 Now, I’ve begun working on a package to make this step, and later ones easier, but it’s far from being close to ready for production. For those who want to see it (and contribute) it is available at https://github.com/jaredlander/mapping. The idea is to make mapping (including faceting!) doable with one or two lines of code. Now it is time for the plot. ggplot(evac.df, aes(x = long, y = lat)) + geom_path(aes(group = group)) + geom_polygon(aes(group = group, fill = CAT1NNE)) + list(theme(panel.grid.major = element_blank(), panel.grid.minor = element_blank(), axis.text.x = element_blank(), axis.text.y = element_blank(), axis.ticks = element_blank(), panel.background = element_blank())) + coord_equal() + labs(x = NULL, y = NULL) + theme(plot.margin = unit(c(1, 1, 1, 1), "mm")) + scale_fill_discrete("Zone") There are clearly a number of things I would change about this plot including filling in the non-evacuation regions, connecting borders and smaller margins. Perhaps some of this can be accomplished by combining this information with another shapefile of the city, but that is beyond today’s code. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Vertical Dodging in ggplot2 An often requested feature for Hadley Wickham's ggplot2 package is the ability to vertically dodge points, lines and bars. There has long been a function to shift geoms to the side when the x-axis is categorical: position_dodge. However, no such function exists for vertical shifts when the y-axis is categorical. Hadley usually responds by saying it should be easy to build, so here is a hacky All I did was copy the old functions (geom_dodge, collide, pos_dodge and PositionDodge) and make them vertical by swapping y's with x's, height with width and vice versa. It's hacky and not tested but seems to work as I'll show below. First the new functions: ## Loading required package: proto collidev <- function(data, height = NULL, name, strategy, check.height = TRUE) { if (!is.null(height)) { if (!(all(c("ymin", "ymax") %in% names(data)))) { data <- within(data, { ymin <- y - height/2 ymax <- y + height/2 } else { if (!(all(c("ymin", "ymax") %in% names(data)))) { data$ymin <- data$y data$ymax <- data$y heights <- unique(with(data, ymax - ymin)) heights <- heights[!is.na(heights)] if (!zero_range(range(heights))) { warning(name, " requires constant height: output may be incorrect", call. = FALSE) height <- heights[1] data <- data[order(data$ymin), ] intervals <- as.numeric(t(unique(data[c("ymin", "ymax")]))) intervals <- intervals[!is.na(intervals)] if (length(unique(intervals)) > 1 & any(diff(scale(intervals)) < -1e-06)) { warning(name, " requires non-overlapping y intervals", call. = FALSE) if (!is.null(data$xmax)) { ddply(data, .(ymin), strategy, height = height) } else if (!is.null(data$x)) { message("xmax not defined: adjusting position using x instead") transform(ddply(transform(data, xmax = x), .(ymin), strategy, height = height), x = xmax) } else { stop("Neither x nor xmax defined") pos_dodgev <- function(df, height) { n <- length(unique(df$group)) if (n == 1) if (!all(c("ymin", "ymax") %in% names(df))) { df$ymin <- df$y df$ymax <- df$y d_width <- max(df$ymax - df$ymin) diff <- height - d_width groupidx <- match(df$group, sort(unique(df$group))) df$y <- df$y + height * ((groupidx - 0.5)/n - 0.5) df$ymin <- df$y - d_width/n/2 df$ymax <- df$y + d_width/n/2 position_dodgev <- function(width = NULL, height = NULL) { PositionDodgev$new(width = width, height = height) PositionDodgev <- proto(ggplot2:::Position, { objname <- "dodgev" adjust <- function(., data) { if (empty(data)) check_required_aesthetics("y", names(data), "position_dodgev") collidev(data, .$height, .$my_name(), pos_dodgev, check.height = TRUE) Now that they are built we can whip up some example data to show them off. Since this was inspired by a refactoring of my coefplot package I will use a deconstructed sample. # get tips data data(tips, package = "reshape2") # fit some models mod1 <- lm(tip ~ day + sex, data = tips) mod2 <- lm(tip ~ day * sex, data = tips) # build data/frame with coefficients and confidence intervals and combine # them into one data.frame ## Loading required package: coefplot ## Loading required package: ggplot2 df1 <- coefplot(mod1, plot = FALSE, name = "Base", shorten = FALSE) df2 <- coefplot(model = mod2, plot = FALSE, name = "Interaction", shorten = FALSE) theDF <- rbind(df1, df2) ## LowOuter HighOuter LowInner HighInner Coef Name Checkers ## 1 1.9803 3.3065 2.31183 2.9750 2.64340 (Intercept) Numeric ## 2 -0.4685 0.9325 -0.11822 0.5822 0.23202 daySat day ## 3 -0.2335 1.1921 0.12291 0.8357 0.47929 daySun day ## 4 -0.6790 0.7672 -0.31745 0.4056 0.04408 dayThur day ## 5 -0.2053 0.5524 -0.01589 0.3630 0.17354 sexMale sex ## 6 1.8592 3.7030 2.32016 3.2421 2.78111 (Intercept) Numeric ## 7 -1.0391 1.0804 -0.50921 0.5506 0.02067 daySat day ## 8 -0.5430 1.7152 0.02156 1.1507 0.58611 daySun day ## 9 -1.2490 0.8380 -0.72725 0.3163 -0.20549 dayThur day ## 10 -1.3589 1.1827 -0.72349 0.5473 -0.08811 sexMale sex ## 11 -1.0502 1.7907 -0.34000 1.0804 0.37022 daySat:sexMale day:sex ## 12 -1.5324 1.4149 -0.79560 0.6781 -0.05877 daySun:sexMale day:sex ## 13 -0.9594 1.9450 -0.23328 1.2189 0.49282 dayThur:sexMale day:sex ## CoefShort Model ## 1 (Intercept) Base ## 2 daySat Base ## 3 daySun Base ## 4 dayThur Base ## 5 sexMale Base ## 6 (Intercept) Interaction ## 7 daySat Interaction ## 8 daySun Interaction ## 9 dayThur Interaction ## 10 sexMale Interaction ## 11 daySat:sexMale Interaction ## 12 daySun:sexMale Interaction ## 13 dayThur:sexMale Interaction # build the plot ## Loading required package: plyr ggplot(theDF, aes(y = Name, x = Coef, color = Model)) + geom_vline(xintercept = 0, linetype = 2, color = "grey") + geom_errorbarh(aes(xmin = LowOuter, xmax = HighOuter), height = 0, lwd = 0, position = position_dodgev(height = 1)) + geom_errorbarh(aes(xmin = LowInner, xmax = HighInner), height = 0, lwd = 1, position = position_dodgev(height = 1)) + geom_point(position = position_dodgev(height = 1), aes(xmax = Coef)) Compare that to the multiplot function in coefplot that was built using geom_dodge and coord_flip. multiplot(mod1, mod2, shorten = F, names = c("Base", "Interaction")) With the exception of the ordering and plot labels, these charts are the same. The main benefit here is that avoiding coord_flip still allows the plot to be faceted, which was not possible with Hopefully Hadley will be able to take these functions and incorporate them into ggplot2. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Play Selection by Down Continuing with the newly available football data (new link) and inspired by a question from Drew Conway I decided to look at play selection based on down by the Giants for the past 10 years. Visually, we see that until 2011 the Giants preferred to run on first and second down. Third down is usually a do-or-die down so passes will dominate on third-and-long. The grey vertical lines mark Super Bowls XLII and XLVI. Code for the graph after the break. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone. Last Class of the Semester About a month ago we had our final Data Science class of the semester. We took a great class photo that I meant to share then but am just getting to it now. I also snapped a great shot of Adam Obeng in front of an NYC Data Mafia slide during his class presentation. Jared Lander is the Chief Data Scientist of Lander Analytics a New York data science firm, Adjunct Professor at Columbia University, Organizer of the New York Open Statistical Programming meetup and the New York and Washington DC R Conferences and author of R for Everyone.	{"url":"https://www.jaredlander.com/tag/statistics/page/2/","timestamp":"2024-11-03T00:26:33Z","content_type":"text/html","content_length":"241615","record_id":"<urn:uuid:0cd814ed-57b2-4503-8e8f-90be0d188bef>","cc-path":"CC-MAIN-2024-46/segments/1730477027768.43/warc/CC-MAIN-20241102231001-20241103021001-00891.warc.gz"}
Understanding Mathematical Functions: What Makes A Table A Function Introduction to Mathematical Functions and Tables In the world of mathematics, functions play a crucial role in representing relationships between variables. Functions are used to describe how one quantity depends on another, making them essential tools in various fields such as physics, engineering, economics, and more. One common way to represent functions is through tables, which provide a structured way to display a set of input and output A Definition of a mathematical function and its importance in various fields Mathematical functions can be defined as a rule that assigns to each input value exactly one output value. In other words, for every input, there is a unique corresponding output. Functions are used to model real-world phenomena, make predictions, analyze data, and solve problems in a wide range of disciplines. Overview of how tables are used to represent functions Tables are a common method of representing functions in a structured format. A typical function table consists of two columns: one for input values and the other for output values. Each row in the table corresponds to a specific input-output pair, making it easy to visualize the relationship between the two variables. The objective of distinguishing between tables that represent functions and those that do not The main objective of distinguishing between tables that represent functions and those that do not is to ensure that the relationship between inputs and outputs is clearly defined and consistent. By identifying whether a given table represents a function, we can determine if each input has a unique output associated with it. This distinction is crucial in mathematical analysis, problem-solving, and data interpretation. Key Takeaways • Functions map inputs to outputs. • Tables can represent functions. • Each input has only one output. • Vertical line test for functions. • Functions can be represented graphically. Understanding the Concept of a Function When it comes to mathematics, functions play a crucial role in understanding relationships between different quantities. A function is a rule that assigns each input exactly one output. Let's delve deeper into the formal definition of a function and explore the role of variables in functions. A Formal definition of a function emphasizing the unique mapping from inputs to outputs A function can be defined as a relation between a set of inputs (also known as the domain) and a set of outputs (also known as the range), where each input is mapped to exactly one output. This unique mapping is a key characteristic of functions, distinguishing them from other mathematical concepts. For example, consider the function f(x) = 2x, where x is the input. For every value of x, there is a unique corresponding output, which is twice the value of x. This one-to-one mapping is what defines a function. The role of variables in functions and their representation in tables Variables are essential components of functions, representing the unknown quantities that the function operates on. In the function f(x) = 2x, x is the variable that can take on different values. By substituting different values for x, we can determine the corresponding outputs of the function. Functions can be represented in tables to visually display the relationship between inputs and outputs. Each row in the table corresponds to a specific input-output pair, showcasing the unique mapping of the function. Common types of functions found in mathematics and their characteristics There are several common types of functions that are frequently encountered in mathematics, each with its own unique characteristics: • Linear functions: These functions have a constant rate of change and can be represented by a straight line on a graph. • Quadratic functions: These functions have a squared term in the equation and form a parabolic shape on a graph. • Exponential functions: These functions involve a constant base raised to a variable exponent and exhibit rapid growth or decay. • Trigonometric functions: These functions involve trigonometric ratios such as sine, cosine, and tangent and are used to model periodic phenomena. Understanding the characteristics of these common types of functions is essential for solving mathematical problems and analyzing real-world phenomena. Characteristics of Tables that Represent Functions Understanding mathematical functions is essential in various fields, from science to engineering. One key aspect of functions is represented through tables, which provide a visual representation of the relationship between inputs and outputs. Let's delve into the characteristics of tables that represent functions. Every input has exactly one output: A key feature of functional tables Functions are a type of relation where each input value (x) corresponds to exactly one output value (y). In a table representing a function, each input value should have a unique output value. This characteristic is crucial in distinguishing functions from non-functions. Use of ordered pairs to illustrate the input-output relationship in a table In a functional table, the input-output relationship is typically represented using ordered pairs. Each pair consists of an input value and its corresponding output value. For example, (2, 5) indicates that when the input is 2, the output is 5. This clear representation helps in understanding the function's behavior. Visual cues in tables that help identify them as representations of functions When looking at a table, there are certain visual cues that can help identify it as a representation of a function. One such cue is the absence of repeated input values with different output values. If an input value appears more than once in the table with different output values, it indicates that the relation is not a function. Analyzing Examples of Functional Tables Understanding mathematical functions involves analyzing tables that represent relationships between variables. Let's break down examples of functional tables to grasp the concept better. A Breakdown of a simple linear function table and its interpretation A simple linear function table consists of two columns: one for the input variable (x) and the other for the output variable (y). Each input value corresponds to exactly one output value, making it a function. For example, consider the table: In this table, the output (y) increases by 2 for every increase of 1 in the input (x), indicating a linear relationship. This consistent pattern is a characteristic of linear functions. Exploration of a non-linear function table and its distinctive features In contrast, a non-linear function table does not exhibit a constant rate of change between input and output values. Consider the table: In this table, the output values do not increase by a consistent amount for each increase in the input values. The relationship between x and y is not linear, indicating a non-linear function. Non-linear functions can have various shapes and patterns, making them distinct from linear functions. Comparison between tables that represent functions and those that do not Tables that represent functions have a unique characteristic: each input value corresponds to exactly one output value. This one-to-one relationship is essential in defining a function. In contrast, tables that do not represent functions may have multiple output values for the same input value, violating the definition of a function. By comparing functional and non-functional tables, we can identify the presence or absence of a consistent relationship between input and output values, helping us distinguish between functions and Common Misconceptions and Troubleshooting Understanding mathematical functions can be challenging, especially when it comes to identifying common misconceptions. Let's explore some of the most prevalent misunderstandings and how to troubleshoot them. A. Mistaking multiple outputs for a single input as a functional table One common misconception when dealing with functions is mistaking a table with multiple outputs for a single input as a functional table. In a functional table, each input value should correspond to only one output value. If you encounter a table where a single input has multiple outputs, it is not a function. To troubleshoot this misconception, carefully examine each input value in the table and ensure that it maps to only one output value. If you find any instances where a single input has multiple outputs, you can conclude that the table does not represent a function. B. Overlooking vertical line tests in graphical representations Graphical representations of functions can also lead to misconceptions, especially when overlooking vertical line tests. The vertical line test is a simple way to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph does not represent a function. To troubleshoot this misconception, visually inspect the graph and draw vertical lines to check for multiple intersections. If you find any instances where a vertical line intersects the graph at more than one point, you can conclude that the graph does not represent a function. C. Misinterpreting discontinuous functions and their representation in tables Discontinuous functions can be tricky to interpret, leading to misconceptions when representing them in tables. A discontinuous function is one where there are gaps or jumps in the graph, indicating a break in the function's continuity. When representing discontinuous functions in tables, it is essential to clearly indicate the breaks or gaps in the data. To troubleshoot this misconception, carefully analyze the data in the table and look for any discontinuities or breaks in the function. If you notice any gaps or jumps in the data, make sure to clearly mark them to indicate the discontinuous nature of the function. Advanced Considerations and Practical Applications When it comes to understanding mathematical functions, there are advanced considerations and practical applications that can enhance our comprehension of how functions work. In this chapter, we will delve into the use of tables in representing piecewise functions, the application of functional tables in real-world data analysis, and the significance of domain and range in the context of functional tables. Use of tables in representing piecewise functions Piecewise functions are functions that are defined by different rules on different intervals. They are often represented using tables to clearly show the different rules that apply to specific intervals. By organizing the information in a table format, it becomes easier to understand how the function behaves in different scenarios. Each row in the table represents a different interval with its corresponding rule, making it a useful tool for visualizing complex functions. Application of functional tables in real-world data analysis Functional tables are not just theoretical constructs; they have practical applications in real-world data analysis. By organizing data in a table format, we can easily identify patterns, trends, and relationships within the data. This can be particularly useful in fields such as economics, finance, and science, where analyzing large datasets is crucial for making informed decisions. Functional tables allow us to break down complex data into manageable chunks, making it easier to draw meaningful insights from the information. Exploring the significance of domain and range in the context of functional tables When working with functional tables, it is important to consider the domain and range of the function. The domain of a function refers to the set of all possible input values, while the range represents the set of all possible output values. Understanding the domain and range of a function is essential for determining its behavior and limitations. In the context of functional tables, the domain and range help us identify the input and output values that are relevant to the function, allowing us to make accurate interpretations and predictions based on the data presented in the table. Conclusion & Best Practices A Recapitulation of key points regarding the identification of functional tables • Ensure clarity in the representation of input-output relationships: It is essential to clearly define the relationship between the input and output values in a table to identify it as a function. This helps in understanding how each input corresponds to a unique output. • Always verify the uniqueness of the output for each input: Checking that each input value in a table corresponds to only one output value is crucial in determining whether the table represents a function. This ensures that there are no ambiguities in the relationship between inputs and outputs. • Utilize graphical methods for additional verification when necessary: Graphing the data from a table can provide a visual representation of the input-output relationship. This can help in confirming whether the table represents a function by observing the pattern of the data points on the graph. Best practices in constructing and interpreting tables as functions • Encouragement for readers to apply these concepts and best practices in their study or work: Understanding mathematical functions and how to identify them in tables is a fundamental skill in various fields such as mathematics, science, and engineering. 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Parametric inference in the large data limit using maximally informative models Kinney, J. B., Atwal, G. S. (2013) Parametric inference in the large data limit using maximally informative models. Arxiv. (Unpublished) PDF (Pre-print) Atwal and Kinney Arxiv 2013.pdf - Draft Version Preview Download (1MB) \| Preview Motivated by data-rich experiments in transcriptional regulation and sensory neuroscience, we consider the following general problem in statistical inference. When exposed to a high-dimensional signal S, a system of interest computes a representation R of that signal which is then observed through a noisy measurement M. From a large number of signals and measurements, we wish to infer the "filter" that maps S to R. However, the standard method for solving such problems, likelihood-based inference, requires perfect a priori knowledge of the "noise function" mapping R to M. In practice such noise functions are usually known only approximately, if at all, and using an incorrect noise function will typically bias the inferred filter. Here we show that, in the large data limit, this need for a pre-characterized noise function can be circumvented by searching for filters that instead maximize the mutual information I[M;R] between observed measurements and predicted representations. Moreover, if the correct filter lies within the space of filters being explored, maximizing mutual information becomes equivalent to simultaneously maximizing every dependence measure that satisfies the Data Processing Inequality. It is important to note that maximizing mutual information will typically leave a small number of directions in parameter space unconstrained. We term these directions "diffeomorphic modes" and present an equation that allows these modes to be derived systematically. The presence of diffeomorphic modes reflects a fundamental and nontrivial substructure within parameter space, one that is obscured by standard likelihood-based inference. Actions (login required) Administrator's edit/view item	{"url":"https://repository.cshl.edu/id/eprint/31501/","timestamp":"2024-11-01T19:21:25Z","content_type":"application/xhtml+xml","content_length":"25061","record_id":"<urn:uuid:c494045c-d2f4-4a4b-8a8f-d429d250a8ca>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00049.warc.gz"}
Structural Design A.A. 2020/21 Course Language Degree programme(s) Master of science-level of the Bologna process in Ingegneria Edile - Torino Course structure Teaching Hours Lezioni 28 Esercitazioni in aula 32 Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching Bertagnoli Gabriele Professore Associato CEAR-07/A 28 22 0 0 1 SSD CFU Activities Area context ICAR/09 6 B - Caratterizzanti Edilizia e ambiente The course is aimed to teach the design of a simple reinforced concrete structure for residential (housing, school, commercial...) use. The course is aimed to teach the design of the common structure under examination during the academic year. The student will obtain the following competences at the end of the course: 1. Structural modelling and design skill using a commercial finite element software. 2. The competence to select, define and apply the correct external loads to a simple structure. 3. The skill to design simple three-dimensional frames in reinforced concrete. 4. Being able to write a design relation of a simple reinforced concrete structure. 5. The skill to draw simple blueprints of reinforced concrete elements: 5.1 General arrangement and reinforcement of a flooring slab; 5.2 General arrangement and reinforcement of beams and columns; 5.3 General arrangement and reinforcement of foundation girder. The student will obtain the following competences at the end of the course: 1. Structural modelling and design skill using a commercial finite element software. 2. The competence to select, define and apply the correct external loads to a simple structure. 3. The skill to design simple three-dimensional framed structures. 4. Being able to write a design relation of a simple structure. 5. The skill to draw simple blueprints of reinforced concrete elements: 5.1 General arrangement and reinforcement of a flooring slab; 5.2 General arrangement and reinforcement of beams and columns; 5.3 General arrangement and reinforcement of foundation girder. The course prerequirements are: 1.1. Structural analysis competences: 1.1.1. Geometrical properties of areas: centroid, inertia moments, principal inertia axes. 1.1.2. Statically determined plane frames solution. 1.1.3. Statically determined truss-systems solution. 1.2. Structural design competences: 1.2.1. Basis of structural safety (semi-probabilistic limit state design) 1.2.2. Design and verification of reinforced concrete cross section subjected to banding and axial forces at Ultimate Limit State and Serviceability Limit State The course prerequirements are: 1.1. Structural analysis competences: 1.1.1. Geometrical properties of areas: centroid, inertia moments, principal inertia axes. 1.1.2. Statically determined plane frames solution. 1.1.3. Statically determined truss-systems solution. 1.2. Structural design competences: 1.2.1. Basis of structural safety (semi-probabilistic limit state design) 1.2.2. Design and verification of reinforced concrete cross section subjected to banding and axial forces at Ultimate Limit State and Serviceability Limit State 1. Design using limit states 1.1. Basic concepts of structural safety with semi-probabilistic approach 1.1.1. Definition of characteristic value of actions and resistances 1.2. Ultimate limit states 1.2.1. Equilibrium 1.2.2. Structural failure 1.2.3. Geotechnical failure 1.2.4. Accidental combination 1.2.5. Seismic combination 1.3. Serviceability limit states 1.3.1. Characteristic, Frequent and Quasi Permanent combinations 1.3.2. Stress control 1.3.3. Deformability control 1.3.4. Crack control 2. Actions on structures 2.1. Self-weight and permanent loads 2.2. Anthropic actions (crowd loads, moving loads) 2.2.1. Residential buildings 2.2.1.1. Floors 2.2.1.2. Staircases 2.2.1.3. Balconies 2.2.2. Offices 2.2.3. Buildings subjected to congregation of people (restaurants, conference halls, sport…) 2.2.4. Shopping buildings 2.2.5. Storage facilities (libraries, warehouses) 2.3. Wind loads 2.3.1. Basic concepts (wind velocity, terrain category, turbulence, wind pressure) 2.3.2. Wind forces 2.3.2.1. Local verification 2.3.2.2. Global verification 2.3.3. Wind action on structures 2.3.3.1. Vertical walls (front and side walls) 2.3.3.2. Flat roofs 2.3.3.3. Mono-pitch roofs 2.3.3.4. Duo-pitch roofs 2.3.3.5. Hipped roofs 2.3.3.6. Multi-span roofs 2.4. Snow loads 2.4.1. Flat roof 2.4.2. Single pitch roof 2.4.3. Double pitched roof 2.4.4. Cleristory or M shaped roofs 2.4.5. Flat roof close to taller construction 2.4.6. Cylindrical roof 2.5. Temperature loads 2.5.1. Seasonal effect 2.5.2. Daily effect 2.6. Foundation settlements 3. Durability of reinforced concrete structures 3.1. The concept of durability 3.2. Environmental aggressions to concrete structures 3.2.1. Chemical attack 3.2.2. Reinforcement corrosion 3.2.3. Freeze and thaw 3.3. Concrete prescription according to EN 206 3.3.1. Resistance class 3.3.2. Environmental exposure class 3.3.3. Maximal dimension of aggregates 3.3.4. Consistency class 3.3.5. Chloride content class 3.4. Concrete cover calculation 3.5. Reinforcing steel prescriptions according to EN10080 4. Reinforced concrete structural typologies: flooring systems 4.1. Two way solid body flat slab 4.2. Two way solid body flat slab with drops 4.3. Two way waffle plate (with and without drops) 4.4. Two way solid body flat slab with deeper beams 4.5. One way joist slabs: 4.5.1. without blocks 4.5.2. with precast panels (predalles) 4.5.3. with hollow clay blocks and cast in situ concrete joists 4.5.4. with hollow clay blocks and lattice prefabricated joist 4.5.5. with hollow clay blocks and precast, prestressed concrete joists 4.5.6. with synthetic blocks and precast, prestressed concrete joists 4.6. Hollow core slabs with cast in situ topping 4.7. Bubble deck 4.8. Composite steel concrete slab with profiled steel decking 5. Structural verifications 5.1. Instability: 5.1.1. Effect of geometrical imperfections 5.1.2. Slenderness of an element 5.1.3. Verification for instability 5.2. Review of shear resistance of a concrete member without shear reinforcement 5.3. Review of shear resistance of a concrete member with shear reinforcement 5.4. Combination of shear and torsion 5.5. Punching 6. Finite element modelling of a residential building 6.1. Definition of nodes and elements 6.2. Definition of materials 6.3. Definitions of cross sections 6.4. Definitions of element groups 6.5. Definitions of boundary conditions 6.6. Definitions of loads: 6.6.1. Nodal loads 6.6.2. Element loads 6.7. Definition of load cases an loads combos 6.8. Design verifications at ULS and SLS 7. Reinforced concrete basic elements details 7.1. Spacers 7.2. Beam reinforcement layout 7.3. Column reinforcement layout 7.4. Beam-column node 7.5. Staircase layout 7.6. Foundation footing with connecting beam layout 7.7. Foundation beam reinforcement layout 1. Design using limit states (3h) 1.1. Basic concepts of structural safety with semi-probabilistic approach 1.1.1. Definition of characteristic value of actions and resistances 1.2. Ultimate limit states 1.2.1. Equilibrium 1.2.2. Structural failure 1.2.3. Geotechnical failure 1.2.4. Accidental combination 1.2.5. Seismic combination 1.3. Serviceability limit states 1.3.1. Characteristic, Frequent and Quasi Permanent combinations 1.3.2. Stress control 1.3.3. Deformability control 1.3.4. Crack control 2. Actions on structures (18h) 2.1. Self-weight and permanent loads 2.2. Anthropic actions (crowd loads, moving loads) 2.2.1. Residential buildings 2.2.1.1. Floors 2.2.1.2. Staircases 2.2.1.3. Balconies 2.2.2. Offices 2.2.3. Buildings subjected to congregation of people (restaurants, conference halls, sport…) 2.2.4. Shopping buildings 2.2.5. Storage facilities (libraries, warehouses) 2.3. Wind loads 2.3.1. Basic concepts (wind velocity, terrain category, turbulence, wind pressure) 2.3.2. Wind forces 2.3.2.1. Local verification 2.3.2.2. Global verification 2.3.3. Wind action on structures 2.3.3.1. Vertical walls (front and side walls) 2.3.3.2. Flat roofs 2.3.3.3. Mono-pitch roofs 2.3.3.4. Duo-pitch roofs 2.3.3.5. Hipped roofs 2.3.3.6. Multi-span roofs 2.4. Snow loads 2.4.1. Flat roof 2.4.2. Single pitch roof 2.4.3. Double pitched roof 2.4.4. Cleristory or M shaped roofs 2.4.5. Flat roof close to taller construction 2.4.6. Cylindrical roof 2.5. Temperature loads 2.5.1. Seasonal effect 2.5.2. Daily effect 2.6. Foundation settlements 3. Durability of reinforced concrete structures (3h) 3.1. The concept of durability 3.2. Environmental aggressions to concrete structures 3.2.1. Chemical attack 3.2.2. Reinforcement corrosion 3.2.3. Freeze and thaw 3.3. Concrete prescription according to EN 206 3.3.1. Resistance class 3.3.2. Environmental exposure class 3.3.3. Maximal dimension of aggregates 3.3.4. Consistency class 3.3.5. Chloride content class 3.4. Concrete cover calculation 3.5. Reinforcing steel prescriptions according to EN10080 4. Reinforced concrete structural typologies: flooring systems (3h) 4.1. Two way solid body flat slab 4.2. Two way solid body flat slab with drops 4.3. Two way waffle plate (with and without drops) 4.4. Two way solid body flat slab with deeper beams 4.5. One way joist slabs: 4.5.1. without blocks 4.5.2. with precast panels (predalles) 4.5.3. with hollow clay blocks and cast in situ concrete joists 4.5.4. with hollow clay blocks and lattice prefabricated joist 4.5.5. with hollow clay blocks and precast, prestressed concrete joists 4.5.6. with synthetic blocks and precast, prestressed concrete joists 4.6. Hollow core slabs with cast in situ topping 4.7. Bubble deck 4.8. Composite steel concrete slab with profiled steel decking 5. Structural verifications (6h) 5.1. Instability: 5.1.1. Effect of geometrical imperfections 5.1.2. Slenderness of an element 5.1.3. Verification for instability 5.2. Review of shear resistance of a concrete member without shear reinforcement 5.3. Review of shear resistance of a concrete member with shear reinforcement 5.4. Combination of shear and torsion 5.5. Punching 6. Finite element modelling of a building (18h) 6.1. Definition of nodes and elements 6.2. Definition of materials 6.3. Definitions of cross sections 6.4. Definitions of element groups 6.5. Definitions of boundary conditions 6.6. Definitions of loads: 6.6.1. Nodal loads 6.6.2. Element loads 6.7. Definition of load cases an loads combos 6.8. Design verifications at ULS and SLS 7. Reinforced concrete basic elements details (6h) 7.1. Spacers 7.2. Beam reinforcement layout 7.3. Column reinforcement layout 7.4. Beam-column node 7.5. Staircase layout 7.6. Foundation footing with connecting beam layout 7.7. Foundation beam reinforcement layout The teacher will present and describe the design procedure of a small residential building in reinforced concrete. Theory lessons are presented as support to the design steps. The students divided in small groups (max. 3 people) accomplish the design exercitation in detail. The teacher will present and describe the design procedure of the building under investigation during the academic year. Theory lessons are presented as support to the design steps. The students divided in small groups (max. 3 people) accomplish the design exercitation in detail. Theory and practice lessons are done with the aid of electronica support: 1. Slides and textbook written by the teacher. 2. Software recording sessions. Lesson slides are available for downloads on the Polito portal. The following national and international design codes are can be downloaded freeware: 1. DECRETO 17 gennaio 2018. “Aggiornamento delle «Norme tecniche per le costruzioni»” - NTC 2018 2. CIRCOLARE 21 gennaio 2019, n. 7 C.S.LL.PP. Istruzioni per l’applicazione dell’«Aggiornamento delle “Norme tecniche per le costruzioni”» di cui al decreto ministeriale 17 gennaio 2018. 3. CNR-DT 207/2008 - Istruzioni per la valutazione delle azioni e degli effetti del vento sulle costruzioni 4. EN 1990 - Eurocode - Basis of structural design 5. EN 1991-1-1 Eurocode 1: Actions on structures - Part 1-1: General actions -Densities, self-weight, imposed loads for buildings. 6. EN 1991-1-3 Eurocode 1 - Actions on structures - Part 1-3: General actions - Snow loads. 7. EN 1991-1-4 Eurocode 1: Actions on structures - Part 1-4: General actions -Wind actions 8. EN 1991-1-5 Eurocode 1: Actions on structures - Part 1-5: General actions -Thermal actions 9. EN 1992-1-1 (2004) - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings The following freeware books are suggested to reach a deeper knowledge: 1. EC2 Commentary – Published by the European Concrete Platform ASBL, June 2008 2. EC2 Worked Examples - Published by the European Concrete Platform ASBL, 2008 The following printed texts are also recommended: 1. Toniolo G., Di Prisco M., Reinforced Concrete Design to Eurocode 2, Springer Tracts in Civil Engineering, 2018. 2. O’ Brien E., Reinforced and prestressed concrete design to EC2: The Complete Process, 2012. 3. Kamara M.E., Novak L. C., Simplified Design of Reinforced Concrete Buildings, Portland Cement Association, 2011. Theory and practice lessons are done with the aid of electronica support: 1. Slides and textbook written by the teacher. 2. Software recording sessions. Lesson slides are available for downloads on the Polito portal. The following national and international design codes are can be downloaded freeware: 1. DECRETO 17 gennaio 2018. “Aggiornamento delle «Norme tecniche per le costruzioni»” - NTC 2018 2. CIRCOLARE 21 gennaio 2019, n. 7 C.S.LL.PP. Istruzioni per l’applicazione dell’«Aggiornamento delle “Norme tecniche per le costruzioni”» di cui al decreto ministeriale 17 gennaio 2018. 3. CNR-DT 207/2008 - Istruzioni per la valutazione delle azioni e degli effetti del vento sulle costruzioni 4. EN 1990 - Eurocode - Basis of structural design 5. EN 1991-1-1 Eurocode 1: Actions on structures - Part 1-1: General actions -Densities, self-weight, imposed loads for buildings. 6. EN 1991-1-3 Eurocode 1 - Actions on structures - Part 1-3: General actions - Snow loads. 7. EN 1991-1-4 Eurocode 1: Actions on structures - Part 1-4: General actions -Wind actions 8. EN 1991-1-5 Eurocode 1: Actions on structures - Part 1-5: General actions -Thermal actions 9. EN 1992-1-1 (2004) - Eurocode 2: Design of concrete structures - Part 1-1: General rules and rules for buildings The following freeware books are suggested to reach a deeper knowledge: 1. EC2 Commentary – Published by the European Concrete Platform ASBL, June 2008 2. EC2 Worked Examples - Published by the European Concrete Platform ASBL, 2008 The following printed texts are also recommended: 1. Toniolo G., Di Prisco M., Reinforced Concrete Design to Eurocode 2, Springer Tracts in Civil Engineering, 2018. 2. O’ Brien E., Reinforced and prestressed concrete design to EC2: The Complete Process, 2012. 3. Kamara M.E., Novak L. C., Simplified Design of Reinforced Concrete Buildings, Portland Cement Association, 2011. Modalità di esame: Prova scritta su carta con videosorveglianza dei docenti; Elaborato progettuale in gruppo; The exam is a set of three written exercises regarding the main topics of the course. Each exercise is made of several questions that need a numerical answer. The sum of the points obtained by answering to the exam question leads to a maximum of 25/30 points. The remaining 5 points are assigned on the base of the evaluation of the design work (design of a simple reinforced concrete building) done in groups during the course. Exam: Paper-based written test with video surveillance of the teaching staff; Group project; The exam is a set of three written exercises regarding the main topics of the course. Each exercise is made of several questions that need a numerical answer. The sum of the points obtained by answering to the exam question leads to a maximum of 25/30 points. The remaining 5 points are assigned on the base of the evaluation of the design work (design of a simple reinforced concrete building) done in groups during the course. Modalità di esame: Prova scritta su carta con videosorveglianza dei docenti; Elaborato progettuale in gruppo; The exam is a set of three written exercises regarding the main topics of the course. Each exercise is made of several questions that need a numerical answer. The sum of the points obtained by answering to the exam question leads to a maximum of 25/30 points. The remaining 5 points are assigned on the base of the evaluation of the design work (design of a simple reinforced concrete building) done in groups during the course. Exam: Paper-based written test with video surveillance of the teaching staff; Group project; The exam is a set of three written exercises regarding the main topics of the course. Each exercise is made of several questions that need a numerical answer. The sum of the points obtained by answering to the exam question leads to a maximum of 25/30 points. The remaining 5 points are assigned on the base of the evaluation of the design work (design of a simple reinforced concrete building) done in groups during the course. Esporta Word	{"url":"https://didattica.polito.it/pls/portal30/gap.pkg_guide.viewGap?p_cod_ins=01UUXNB&p_a_acc=2021&p_header=S&p_lang=IT&multi=N","timestamp":"2024-11-11T01:10:18Z","content_type":"text/html","content_length":"63800","record_id":"<urn:uuid:7d0e0f99-c2b6-46ec-aa54-205d74600749>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00004.warc.gz"}
Experimental HALTs with sine-on-random synthesized profiles In several applications, certain components must be designed to withstand the fatigue damage induced by dynamic loads due to vibrations. Highly Accelerated Life Tests (HALTs) by means of vibration qualification can be performed for the most critical ones. The proper synthesis of test profiles, which starts from the real environment vibrations and which preserves both the fatigue damage potential and the signal characteristics of the excitation, is important to obtain reliable results. A special kind of vibration excitation is the so-called Sine-on-Random (SoR), i.e. sinusoidal contributions superimposed to random vibrations, particularly significant for systems where rotating parts are present. A methodology was previously proposed to synthesize SoR test profiles for HALTs, starting from reference measured vibrations. The present paper illustrates the experimental campaign carried out to verify the effectiveness and the accuracy of the proposed method. 1. Introduction Several components may be subjected to vibrations during their operational life. The corresponding dynamic loads can induce fatigue damage and the components must be designed to last through the induced damage. To verify their resistance, the components can be validated with qualification tests. In order to conduct reliable tests, the environmental excitations can be taken as a reference to synthesize the test profile: this procedure is referred to as Test Tailoring. Highly Accelerated Life Tests (HALTs) are usually performed to reduce the duration of the excitation acting on the component for its entire life-cycle, that can be up to thousands of hours. The so-called Mission Synthesis procedure permits to quantify the induced damage of the environmental vibration and to synthesize a test profile with a reduced duration, but the same amount of induced damage [1]. In order to focus on the damage potential associated with a vibratory excitation, a generic component is represented by a series of linear Single Degree of Freedom (SDOF) systems with the natural frequency that varies in the range of interest. It is assumed that if two dynamic excitations produce the same damage on the SDOF linear system taken as reference then they produce the same damage also on the real component under test. Under the assumption of three main hypotheses (i. stress proportional to the relative displacement between mass and base of the SDOF system; ii. Wöhler’s curve and Basquin’s law $N{\sigma }^{b}=C$, where $N$ is the number of cycles to failure under stress of amplitude $\sigma$, whereas $b$ and $C$ are characteristic constants of the material; iii. Miner’s rule for the linear damage accumulation) this simplification permits to reduce the problem of the damage quantification in finding the response of a linear SDOF system. To this aim a frequency-domain function, i.e. the so-called Fatigue Damage Spectrum (FDS), is defined to quantify the fatigue damage [1]. When a new profile with the same amount of damage and a reduced duration is required for laboratory HALTs, it can be synthesized starting from environmental excitation by maintaining the same FDS. In case the original excitation has random characteristics with a Gaussian distribution, the procedure is well-known [1] and a Power Spectral Density (PSD) is synthesized as a test profile which closely represents the original excitation. However, in a number of cases, the vibration does not follow a Gaussian distribution. In particular, when a rotating part is present in the system, deterministic components in the form of sinusoids are superimposed to a random process, so that the excitations assume Sine-on-Random (SoR) characteristics. In this case, the value distribution is not Gaussian and a synthesized PSD (with a reduced duration) has not the adequate characteristics to properly represent the original excitation in laboratory HALTs. Indeed, a proper Test Tailoring should not only preserve the accumulated fatigue damage, but also the “nature” of the excitation in order to obtain reliable results. Thus, in case of environments with SoR features, a SoR synthesized profile is supposed to better represent the original excitation compared to a purely random profile. To this purpose, a novel methodology to synthesize SoR test profiles (instead of PSD) for HALTs was developed and proposed in Angeli et al. [2], where the detailed formulation can be found. Numerical simulations proved the superiority of the method with respect to the traditional one in terms of better FDSs matching (of the reference and the synthesized profiles). The present paper illustrates the experimental campaign that was carried out to further investigate the procedure effectiveness, that was finally confirmed by the experimental data. 2. Experimental tests In order to experimentally verify the effectiveness of the proposed SoR Mission Synthesis procedure, the method was applied starting from environmental data (hereinafter referred to as “reference signal”) acquired on a helicopter working in a typical regime condition. In particular, the measurements were taken by an accelerometer mounted on the control board of a helicopter having a 5-blades main rotor (a NOTAR anti-torque system replaces the tail rotor). The signal was sampled at the frequency ${F}_{s}=$ 400 Hz for a duration of about 27 s. The main rotor constant speed was about 393 rpm. As a consequence, the signal is characterized by the major presence of the rotation frequency harmonics (${f}_{Rk}\approx$$k$·6.55 Hz, $k=$ 1, 2, …) and, mainly, the blade frequency harmonics ($ {f}_{Bk}=$$k$·5·${f}_{R1}\approx$$k$·32.65 Hz, $k=$ 1, 2, …), as shown in Fig. 1. Fig. 1PSD of environmental data measured on a helicopter 2.1. Set up An extensive experimental campaign was performed to further investigate the effectiveness of the proposed SoR synthesis procedure [2] with respect to the traditional PSD synthesis [1]. To this aim many laboratory tests were carried out by means of an electromechanical shaker (Dongling ES-2-150), which imposed the reference signal and different synthesized profiles on purpose-built specimens (Fig. 2). The idea was to compare the fatigue damage actually induced by the synthesized excitations with the damage due to the reference one. The specimen was a flat beam, made of the Aluminum alloy EN AW-6060, fixed to a rigid support in a cantilevered configuration. The thickness was 2 mm and the critical section 10 mm wide; a lumped mass was fixed to its tip (the center of mass being about 66.5 mm from the rigid support) in order to present the natural frequency of the first bending mode at about 32.65 Hz, i.e. corresponding to the main peak of the base excitation signal. A preliminary experimental characterization [3] permitted to determine the material actual mechanical properties (Fig. 2), in particular the value of the Basquin‘s law exponent $b$, which is particularly important in the Mission Synthesis algorithms [1, 4, 5]. Besides the control accelerometer placed at the specimen support base, a second sensor was fixed under the appended mass in order to measure the specimen tip acceleration. Fig. 2Purpose-built specimen used for the experimental validation 2.2. Test procedure The helicopter measured vibrations were kept as the reference for this experimental investigation. They were replicated as base excitation to induce on the specimen a certain fatigue damage. Due to both the signal and specimen characteristics, failure breakdown was not achievable (in a reasonable time) so that a “conventional Time-to-Failure”, cTTF, was introduced considering the effect of accumulated fatigue damage to decrease the specimen natural frequency [6, 7]. In particular, cTTF is here defined as the time necessary to decrease the specimen natural frequency from the value ${f}_ {in}=$ 32.67 Hz to the final value ${f}_{fin}=$ 31.04 Hz (5 % decrement). The value ${f}_{in}=$ 32.67 Hz was chosen since (i) is bigger than and very close to the excitation peak at 32.65 Hz and (ii) most specimens exhibit an initial value ${f}_{n0}\ge$ 32.67 Hz (Table 1). Five kinds of tests were carried out, each one repeated for three different specimens for the sake of data reliability, corresponding to the application of the following base excitations: s0. reference signal (specimens and tests denoted as ${s}_{01}$, ${s}_{02}$, and ${s}_{03}$); s1. synthesized PSD (${s}_{11}$, ${s}_{12}$, ${s}_{13}$) computed to induce the same damage in the same test duration of the reference signal, that is to present the same FDS and cTTF; s2. synthesized SoR (${s}_{21}$, ${s}_{22}$, ${s}_{23}$) computed to have the same FDS and cTTF of the reference signal; s3. synthesized PSD (${s}_{31}$, ${s}_{32}$, ${s}_{33}$) computed to have the same FDS and half the duration cTTF of the reference signal (accelerated tests); s4. synthesized SoR (${s}_{41}$, ${s}_{42}$, ${s}_{43}$) computed to have the same FDS and half the duration cTTF of the reference signal (accelerated tests). The FDS functions, i.e. the target in the PSD and SoR profile syntheses, were computed considering the following parameters: bandwidth 5-200 Hz, frequency resolution $df=$ 0.05 Hz; $Q$ Factor $Q=$ 1/ 2, $\zeta =$ 69.4; Wöhler curve slope $b=$ 6.3; material constants appearing in Eq. (11) of ref. [2] $K=C=$1. Among the three data sets for each kind of test, the results corresponding to the specimen exhibiting the median value of cTTF were considered as representative for a direct comparison. In particular, the cTTF associated with the reference signal, necessary to synthesize the other four signals, was 484 minutes (${s}_{02}$, Section 2.3). The shaker controller was run by means of the LMS Test.Lab modules Single Axis Waveform Replication (for tests ${s}_{0i}$, ${s}_{2i}$, and ${s}_{4i}$, $i=$ 1, 2, 3, where the input profile was sequentially replicated until the achievement of cTTF) and Random Control (for tests ${s}_{1i}$ and ${s}_{3i}$, $i=$1, 2, 3) with a sampling frequency of 800 Hz (automatically fixed by the software): the results were then low-pass filtered at 200 Hz and down sampled at 400 Hz, in order to exactly match the signal characteristics of the original measurements. The natural frequency ${f}_{n}$ of the specimens was monitored by computing the Frequency Response Function (FRF) between the mass and base accelerations. The FRFs were computed for signal windows of 30 seconds (with NFFT = 4096 points per signal-block, an overlap of 66.67 %). The initial value of the natural frequency, ${f}_{n0}$, was computed for each specimen with a running average approach performed for 3 values of ${f}_{n}$. The same approach is used to compute the final value of the natural frequency that determines the cTTF. Table 1 reports the values of ${f}_{n0}$ (as well as the mean values of the damping factor ${\zeta }_{mean}$ computed for the entire test duration) for each specimen. It can be noted that specimens ${s}_{21}$ and ${s}_{22}$ exhibit an initial frequency $ {f}_{n0}$ smaller than ${f}_{in}=$ 32.67 Hz. For these specimens cTTF is computed as the time necessary to decrease the corresponding ${f}_{n0}$ of an amount of 5 %. Table 1Initial natural frequency fn0 and mean damping factor ζmean of the 15 tested specimens ${s}_{01}$ ${s}_{02}$ ${s}_{03}$ ${s}_{11}$ ${s}_{12}$ ${s}_{13}$ ${s}_{21}$ ${s}_{22}$ ${s}_{23}$ ${f}_{n0}$ [Hz] 32.70 32.70 32.70 32.67 32.80 32.70 32.37 32.31 32.70 ${\zeta }_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ 0.57 % 0.69 % 0.68 % 0.66 % 0.84 % 0.65 % 0.72 % 0.56 % 0.71 % ${s}_{31}$ ${s}_{32}$ ${s}_{33}$ ${s}_{41}$ ${s}_{42}$ ${s}_{43}$ ${f}_{n0}$ [Hz] 32.83 32.70 32.70 32.89 32.70 32.73 ${\zeta }_{\mathrm{m}\mathrm{e}\mathrm{a}\mathrm{n}}$ 0.55 % 0.54 % 0.80 % 0.68 % 0.52 % 0.81 % 2.3. Results Table 2 reports the most important results of the experimental campaign. It can be noted that for both the equal-time tests and the HALTs (time reduction factor equal to 0.5) the proposed mission synthesis procedure performs better than the traditional algorithms. Indeed, even though both the PSD and SoR profiles were synthesized in order to match the FDS of the reference signal (specifically the target one corresponding to ${s}_{02}$), the SoR profiles prove a superior suitability to represent the reference signal in terms of induced fatigue damage, as it can be appreciated by comparing the actual median cTTFs with respect to the corresponding desired value cTTF[target]. The “errors” in terms of actual cTTF vs. target cTTF are in fact +3.5 % and +17.4 % for ${s}_{23}$ and ${s}_{43}$ (SoR profiles), in spite of +101.7 % and +79.3 %, for ${s}_{12}$ and ${s}_{31}$ (PSD profiles), respectively. As an example, Fig. 3 reports the variation of the specimen ${s}_{43}$ natural frequency over time: for the other cases, similar trends were observed. Fig. 3Specimen s43 natural frequency Fig. 4FDSs computed for the measured base excitations (close-up) Fig. 4 reports a close-up view of the actual FDS functions computed from the measured base acceleration signals referring to the time interval which defines the cTTFs. Fig. 5 reports the PSD of the measured inputs (base acceleration) and responses (relative mass-base acceleration). It can be noted that the PSD synthesized profiles (red and black curves) were not able to perfectly match the very narrow peak at 32.65 Hz. The damage potential was thus spread over the adjacent frequencies to compensate for the absence of the deterministic sinusoid components, but the final effect proved not meaningful in this application where the specimen natural frequency was set up on purpose just to be resonant, Fig. 5(b). Table 2cTTFs computed as the time [min] to decrease the natural frequency from fin= 32.67 Hz to ffin= 31.04 Hz (Δfn= –5 %), with the exception of specimens s21 and s22. The partial time corresponding to 1 %-4 % decrement of fn is also reported Reference signal Synthesized PSD (cTTF[target] = 484 min) Synthesized SoR (cTTF[target] = 484 min) Specimen ${s}_{01}$ ${s}_{02}^{1}$ ${s}_{03}$ ${s}_{11}$ ${s}_{12}^{1}$ ${s}_{13}$ ${s}_{21}^{2}$ ${s}_{22}^{3}$ ${s}_{23}^{1}$ $\mathrm{\Delta }{f}_{n}=$ –1 % 8 31 22 31 27 19 59 14 16 $\mathrm{\Delta }{f}_{n}=$ –2 % 48 105 83 76 77 42 196 67 132 $\mathrm{\Delta }{f}_{n}=$ –3 % 147 209 213 268 293 310 404 118 227 $\mathrm{\Delta }{f}_{n}=$ –4 % 260 323 341 404 662 798 489 221 341 $\mathrm{\Delta }{f}_{n}=$ –5 % 410 484 485 606 976 1073 607 328 501 Synthesized PSD (cTTF[target] = 242 min) Synthesized SoR (cTTF[target] = 242 min) Specimen $s{31}^{1}$ $s32$ $s33$ $s41$ $s42$ $s{43}^{1}$ $\mathrm{\Delta }{f}_{n}=$ –1 % 19 12 41 15 11 24 $\mathrm{\Delta }{f}_{n}=$ –2 % 43 59 123 71 63 84 $\mathrm{\Delta }{f}_{n}=$ –3 % 127 113 343 162 136 159 $\mathrm{\Delta }{f}_{n}=$ –4 % 288 229 630 223 180 216 $\mathrm{\Delta }{f}_{n}=$ –5 % 434 289 991 329 250 284 ^1 Median values of the triplet. ^2 cTTF is computed as the time to decrease the natural frequency from ${f}_{n0}=$ 32.37 Hz to 30.75 Hz (–5 %). ^3 cTTF is computed as the time to decrease the natural frequency from ${f}_{n0}=$ 32.31 Hz to 30.69 Hz (–5 %). Fig. 5PSD computed for the a) measured base (close-up) and b) relative mass-base accelerations Finally, Table 3 reports the peak and RMS values of input and response accelerations measured for the representative specimens of the five tests. These data further prove the better consistency of the SoR synthesized profiles with the reference signal than the PSD profiles. Table 3Statistical analysis of measured accelerations [m/s2] ${s}_{02}$ ${s}_{12}$ ${s}_{23}$ ${s}_{31}$ ${s}_{43}$ Base Mass-base Base Mass-base Base Mass-base Base Mass-base Base Mass-base Peak 5.54 162.99 9.40 189.32 5.15 161.86 10.66 194.79 5.83 151.15 RMS 2.08 47.97 1.93 30.42 2.04 44.69 2.15 37.21 2.30 50.98 3. Conclusions The papers reported the experimental campaign carried out to validate a novel algorithm proposed to synthesize Sine-on-Random test profiles for accelerated fatigue life vibration testing. The experimental results proved the higher accuracy of Sine-on-Random synthesized profiles with respect to traditional PSD synthesized ones in reproducing the damage potential of real vibrations characterized by sinusoidal components superimposed to random process. This evidence would confirm the positive contribution proposed by the authors to improve the reliability of Test Tailoring procedures conceived for vibration qualification testing of systems characterized by the presence of rotating components generating vibrations. • Lalanne C. Mechanical Vibration and Shock Analysis, Volume 5: Specification Development. Third Edition, John Wiley and Sons, London, 2014. • Angeli A., Cornelis B., Troncossi M. Fatigue damage spectrum calculations in a mission synthesis procedure for sine-on-random excitations. Journal of Physics: Conference Series, Vol. 744, 2016, p. 012089. • Baldazzi M. Experimental Investigation on the Dynamic Response of Aluminum Flat Specimens Subjected to Different Kinds of Non-Gaussian Vibration. M.Sc. Thesis, University of Bologna, 2015, (in • Troncossi M., Cipollini R., Rivola A. Experimental evaluation of the FDS-based equivalence approach for the mission synthesis in accelerated life tests. Proceedings of ICSV 20, Thailand, 2013. • Hieber G. M. Use and abuse of test time exaggeration factors. Test Engineering and Management, New Jersey, Vol. 61, 1999, p. 14-16. • Česnik M., Slavič J., Boltežar M. Uninterrupted and accelerated vibrational fatigue testing with simultaneous monitoring of the natural frequency and damping. Journal of Sound and Vibration, Vol. 331, Issue 24, 2012, p. 5370-5382. • Troncossi M., Rivola A. Response analysis of specimens excited with non-Gaussian acceleration profiles. Proceedings of ISMA2014, Belgium, 2014, p. 799-808. About this article Fault diagnosis based on vibration signal analysis vibration qualification testing highly accelerated life test test tailoring mission synthesis Copyright © 2017 JVE International Ltd. This is an open access article distributed under the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.	{"url":"https://www.extrica.com/article/18595","timestamp":"2024-11-10T22:22:40Z","content_type":"text/html","content_length":"131521","record_id":"<urn:uuid:cbe20ae0-9e8c-4a0f-ac12-406c6f57f00b>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00428.warc.gz"}
34 research outputs found We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two dimensional real fermions in systems with space-time inversion $I_{ST}$ symmetry. The Euler class is an integer topological invariant classifying real two band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{ST}$-symmetric Wannier representation. Moreover, a two-band system with the Euler class $e_{2}$ has band crossing points whose total winding number is equal to $-2e_2$. Thus the conventional Nielsen-Ninomiya theorem fails in systems with a nonzero Euler class. We propose that the topological phase transition between two insulators carrying distinct Euler classes can be described in terms of the pair creation and annihilation of vortices accompanied by winding number changes across Dirac strings. When the number of bands is bigger than two, there is a $Z_{2}$ topological invariant classifying the band topology, that is, the second Stiefel Whitney class ($w_2$). Two bands with an even (odd) Euler class turn into a system with $w_2=0$ ($w_2=1$) when additional trivial bands are added. Although the nontrivial second Stiefel-Whitney class remains robust against adding trivial bands, it does not impose a Wannier obstruction when the number of bands is bigger than two. However, when the resulting multi-band system with the nontrivial second Stiefel-Whitney class is supplemented by additional chiral symmetry, a nontrivial second-order topology and the associated corner charges are guaranteed.Comment: 23 pages, 13 figure Uncovering the physical contents of the nontrivial topology of quantum states is a critical problem in condensed matter physics. Here, we study the topological circular dichroism in chiral semimetals using linear response theory and first-principles calculations. We show that, when the low-energy spectrum respects emergent SO(3) rotational symmetry, topological circular dichroism is forbidden for Weyl fermions, and thus is unique to chiral multifold fermions. This is a result of the selection rule that is imposed by the emergent symmetry under the combination of particle-hole conjugation and spatial inversion. Using first-principles calculations, we predict that topological circular dichroism occurs in CoSi for photon energy below about 0.2 eV. Our work demonstrates the existence of a response property of unconventional fermions that is fundamentally different from the response of Dirac and Weyl fermions, motivating further study to uncover other unique responses.Comment: 6+7 pages, 4+4 figure Optical spectral weight transfer associated with the onset of superconductivity at high energy scales compared with the superconducting gap has been observed in several systems such as high-$T_c$ cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. We discuss applying this idea to twisted multilayer graphene.Comment: 5 pages, 2 We study the band topology and the associated linking structure of topological semimetals with nodal lines carrying $Z_{2}$ monopole charges, which can be realized in three-dimensional systems invariant under the combination of inversion $P$ and time reversal $T$ when spin-orbit coupling is negligible. In contrast to the well-known $PT$-symmetric nodal lines protected only by $\pi$ Berry phase in which a single nodal line can exist, the nodal lines with $Z_{2}$ monopole charges should always exist in pairs. We show that a pair of nodal lines with $Z_{2}$ monopole charges is created by a {\it double band inversion} (DBI) process, and that the resulting nodal lines are always {\it linked by another nodal line} formed between the two topmost occupied bands. It is shown that both the linking structure and the $Z_{2}$ monopole charge are the manifestation of the nontrivial band topology characterized by the {\it second Stiefel-Whitney class}, which can be read off from the Wilson loop spectrum. We show that the second Stiefel-Whitney class can serve as a well-defined topological invariant of a $PT$-invariant two-dimensional (2D) insulator in the absence of Berry phase. Based on this, we propose that pair creation and annihilation of nodal lines with $Z_{2}$ monopole charges can mediate a topological phase transition between a normal insulator and a three-dimensional weak Stiefel-Whitney insulator (3D weak SWI). Moreover, using first-principles calculations, we predict ABC-stacked graphdiyne as a nodal line semimetal (NLSM) with $Z_{2}$ monopole charges having the linking structure. Finally, we develop a formula for computing the second Stiefel-Whitney class based on parity eigenvalues at inversion invariant momenta, which is used to prove the quantized bulk magnetoelectric response of NLSMs with $Z_2$ monopole charges under a $T$-breaking perturbation.Comment: 4+28 pages, 3+17 figure Based on first-principles calculations and tight-binding model analysis, we propose monolayer graphdiyne as a candidate material for a two-dimensional higher-order topological insulator protected by inversion symmetry. Despite the absence of chiral symmetry, the higher-order topology of monolayer graphdiyne is manifested in the filling anomaly and charge accumulation at two corners. Although its low energy band structure can be properly described by the tight-binding Hamiltonian constructed by using only the $p_z$ orbital of each atom, the corresponding bulk band topology is trivial. The nontrivial bulk topology can be correctly captured only when the contribution from the core levels derived from $p_{x,y}$ and $s$ orbitals are included, which is further confirmed by the Wilson loop calculations. We also show that the higher-order band topology of a monolayer graphdyine gives rise to the nontrivial band topology of the corresponding three-dimensional material, ABC-stacked graphdiyne, which hosts monopole nodal lines and hinge states.Comment: 19 pages, 4 figures, new titl We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry. Â© 2017 American Physical Society1651sciescopu Topological superconductors are exotic gapped phases of matter hosting Majorana mid-gap states on their boundary. In conventional topological superconductors, Majorana in-gap states appear in the form of either localized zero-dimensional modes or propagating spin-1/2 fermions with a quasi-relativistic dispersion relation. Here we show that unconventional propagating Majorana states can emerge on the surface of three-dimensional topological superconductors protected by rotational symmetry. The unconventional Majorana surface states fall into three different categories: a spin-$S$ Majorana fermion with $(2S+1)$-fold degeneracy $(S\geq3/2)$, a Majorana Fermi line carrying two distinct topological charges, and a quartet of spin-1/2 Majorana fermions related by fourfold rotational symmetry. The spectral properties of the first two kinds, which go beyond the conventional spin-1/2 fermions, are unique to topological superconductors and have no counterpart in topological insulators. We show that the unconventional Majorana surface states can be obtained in the superconducting phase of doped $Z_2$ topological insulators or Dirac semimetals with rotational symmetry.Comment: 15+10 pages, 5 figures, Supplementary Note adde We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the formulae, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal line semimetals generates a nodal line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up a new avenue for future topological quantum computations using Majorana zero modes.Comment: 6+13 pages, 2+1 figures; accepted versio	{"url":"https://core.ac.uk/search/?q=author%3A(Junyeong%20Ahn)","timestamp":"2024-11-09T16:43:54Z","content_type":"text/html","content_length":"149704","record_id":"<urn:uuid:2679595c-808d-4f11-baf9-549348913ec8>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00464.warc.gz"}
Differential Equations Homework Helper Do you need a Differential Equations Homework Helper? If you are stuck on a differential equations homework problem, you may need help from an online tutor. SchoolTrainer provides Differential Equations Homework Help to students who are stuck on a homework problem and feel like giving up. Our Differential Equations tutors are not only qualified and experienced, but they also have the patience to provide a sympathetic ear and give suggestions if you get stuck. End all your differential equations homework frustrations Sign up for our Differential Equations Homework Helper service and take the stress out of differential equations homework. Our online help desk offers the following benefits: • Live one-on-one personalized homework help support from a qualified differential equations tutor. • Round the clock assistance, with no time wasted on commuting. • Easy online access via an interactive whiteboard with voice and text capability. • Affordable fees. Use the form above to register with SchoolTrainer and sign up for our Differential Equations Homework Helper service. Get the Differential Equations Homework Help that you need, and take the frustration and stress out of differential equations. Subjects for Online Tutoring & Homework Help Math Tutoring - Online Math Tutors for all grades and topics Other Subjects for Online Tutoring	{"url":"https://www.schooltrainer.com/homework-helper/differential-equations-homework-helper.html","timestamp":"2024-11-06T21:07:07Z","content_type":"application/xhtml+xml","content_length":"21520","record_id":"<urn:uuid:54d33d6a-dc75-42a0-b1c2-96e1013c9085>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00400.warc.gz"}
how far from zero would you move on the x-axis to reach the point ( 10,8) 2 thoughts on “how far from zero would you move on the x-axis to reach the point ( 10,8)” 1. you should move 10 points on x-axis to reach point (10,8). 2. Answer: 10 units to the right from zero on the x-axis Leave a Comment	{"url":"https://wiki-helper.com/how-far-from-zero-would-you-move-on-the-ais-to-reach-the-point-10-8-37394087-97/","timestamp":"2024-11-01T19:48:42Z","content_type":"text/html","content_length":"127582","record_id":"<urn:uuid:d9851650-8bd6-4f0e-9eb2-2c2510bf6a46>","cc-path":"CC-MAIN-2024-46/segments/1730477027552.27/warc/CC-MAIN-20241101184224-20241101214224-00327.warc.gz"}
Make the Number Try to make the target number using the other numbers. Can use add, subtract, multiply, divide and parentheses. Examples below. Numbers are chosen randomly. There is usually an exact solution but not always. The computer's only advantage is it can test thousands of possibilities. Target: 901 given: 6,3,1,2,25,75 Solution: (25+75)×(6+3)+1 Target: 743 given: 7,2,3,5,25,50 Solution: 50×5×3−7 Target: 127 given: 4,1,5,2,100,50 Solution: (50×5+4)÷2 You may like to learn more about Order of Operations Try the options! You can change the nature of the game by using different source lists. • 1 point for difference of 2 • 2 points for difference of 1 • 5 points for perfect	{"url":"http://wegotthenumbers.org/make-the-number.html","timestamp":"2024-11-08T12:08:12Z","content_type":"text/html","content_length":"4223","record_id":"<urn:uuid:4e87a702-93ea-4e4c-b6a0-504a64bf6211>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00800.warc.gz"}
Boat launches closed My son just sent me an article New York State closes all boat launches ,marinas, playgrounds ,golf courses marinas will stay open only to help government agencies and businesses deemed essential.Is that for real? Sent from my iPhone using Lake Ontario United My son just sent me an article New York State closes all boat launches ,marinas, playgrounds ,golf courses marinas will stay open only to help government agencies and businesses deemed essential.Is that for real? Sent from my iPhone using Lake Ontario United Dec stated article was incorrect Sent from my iPhone using Lake Ontario United Are you sure? Buffalo local news just said that boat launches were deemed nonessential on tv It’s essential I need it for food, I’m not going water skiing, I lost my job, bull %=+$#@ • 1 I saw it on the internet new,s also,i know the closed the launch at the welcome center in geneva today. I can't find proof. 1 DEC officer said the article was wrong. Does someone know the truth? You read one article and it states launches are open another states they are closed. Tim is correct. DEC Director of F&W said today since their launches are by nature self-service, they continue to stay open. I would assume same goes for OPRHP unattended launches. • 1 Correction, Bureau Chief, not Director. Yes this is good news if they remain open I say we all fish!! This is a NYS leadership hack job. Edited by Sharpie1 • 1 The Boat Doctors in Olcott are reporting that all launches are closed. They are located only a half mile from the Newfane launch: City of Geneva closed down their launch Lettering my boat "RESEARCH" and Govt of Japan.....it worked on whale wars [emoji1745] Sent from my Pixel 3 XL using Lake Ontario United mobile app • 1 This is rediculous! When I go to the launch I'm not exactly there to get all up in the other fisherman's space. I can wait until the next guy is done at the dock before using it. Not a problem to keep my distance. Nanny state because I guess we can't police ourselves. Only person more annoyed than me is me wife because now she has to live with a frustrated fisherman. Don't misunderstand, I'm lucky that this is my biggest issue right now - but c'mon now. Guess I'll join the guys on the pier again. • 1 7 hours ago, RWR1775 said: This is rediculous! When I go to the launch I'm not exactly there to get all up in the other fisherman's space. I can wait until the next guy is done at the dock before using it. Not a problem to keep my distance. Nanny state because I guess we can't police ourselves. Only person more annoyed than me is me wife because now she has to live with a frustrated fisherman. Don't misunderstand, I'm lucky that this is my biggest issue right now - but c'mon now. Guess I'll join the guys on the pier This is straight up the biggest overreaction in the history of the US. So far, just under 17,000 US deaths. There are 70,000 US deaths per year from overdosing, with a world wide death rate of 585,000 people in 2018, where’s the uproar??? I can name 10 more causes of more death in the US. Totally get that it sucks that some are dying. But did anyone see the article that says if you die (from whatever) and your autopsy shows you had covid 19, then your death cert will show you died from covid 19. So if I crash my motorcycle, die, test positive for covid 19, according to the CDC I died from covid 19. If you wanna keep your distance, I don’t hate you. But I’m not naive enough for this crap. Edited by Offshore IV • 2 Is Sandy open ? Was going to dump my small boat tommorow . 1 minute ago, HB2 said: Is Sandy open ? Was going to dump my small boat tommorow . I’m going to check Mexico point today and report back, if that’s any help... quite frankly when my gf told me all launches are closed, I told her it is due to the high winds and predicted wave Edited by Offshore IV • 1 6 minutes ago, HB2 said: Is Sandy open ? Was going to dump my small boat tommorow . I here only State ramps closed...? OLCOTT closed?????? All of this is UNCONSTITUTIONAL. I remember during the Obama government shutdown the Iroquois national Wildlife refuge was closed! Not just the welcome center, the woods and Swamp had closed signs posted. Disgusting. I fish alone. Sent from my moto z3 using Lake Ontario United mobile app My friend said Cayuga lake boat ramps are closed. He lives there. Sent from my moto z3 using Lake Ontario United mobile app Even if there was a legitimate reason to close the launches, NYS is a day late n a dollar short. According to cuomo the curve is flattening. So obviously boat launches weren’t the culprit. I disapprove of him 100%. He’s doing something just to do something. 🤬🤬🤬 • 1 He’s doing everything he can do, so when they realize they over predicted the death toll and everything else, he will be able to say, “see I saved NY, with everything I did” Sent from my iPhone using Lake Ontario United • 1 1 minute ago, Bluefin54 said: He’s doing everything he can do, so when they realize they over predicted the death toll and everything else, he will be able to say, “see I saved NY, with everything I did” Sent from my iPhone using Lake Ontario United You’re not wrong, I’m just salty haha offshore iv,i sure hope I get to shake your hand some day!!!!!!!!you are 100 % right and im glad you can see through the smoke and mirrors of the gloom and doom news media and the absurd non-sense this moron Cuomo is doing to this state.OFFSHORE IV FOR GOVERNOR!!!!!! • 1 12 minutes ago, finsntins said: offshore iv,i sure hope I get to shake your hand some day!!!!!!!!you are 100 % right and im glad you can see through the smoke and mirrors of the gloom and doom news media and the absurd non-sense this moron Cuomo is doing to this state.OFFSHORE IV FOR GOVERNOR!!!!!! Lol I’ve actually considered politics but I’d be in over my head. This whole thing reminds me of when cuomo instilled the “you can have 10 round magazines in your handguns but you can only have 7 bullets in them” type of crap. Maybe his policies do well for NYC, but he is not in touch with upstate NY.	{"url":"https://www.lakeontariounited.com/fishing-hunting/topic/85348-boat-launches-closed/","timestamp":"2024-11-11T01:42:16Z","content_type":"text/html","content_length":"434927","record_id":"<urn:uuid:7d782f61-f7f5-4eaa-ad96-40b106fad5cc>","cc-path":"CC-MAIN-2024-46/segments/1730477028202.29/warc/CC-MAIN-20241110233206-20241111023206-00127.warc.gz"}
Dividing Exponents With Same Base Worksheet Dividing Exponents With Same Base Worksheet. Worksheets are exponents and division, exponent rules practice, applying the expone. Web in order to divide exponents with the same base, we use the basic rule of subtracting the powers. Dividing Exponents Worksheet / Homework Help Powers And Exponents from weerobingo.blogspot.com Web whenever you divide two exponents with the same base, you can simplify by subtracting the value of the exponent in the denominator by the value of the. Web some of the worksheets for this concept are exponents and division, exponent rules practice, applying the exponent rule for dividing same bases, exponents and. Web dividing exponents worksheets are interactive and provide several visual	{"url":"http://studydblamb123.s3-website-us-east-1.amazonaws.com/dividing-exponents-with-same-base-worksheet.html","timestamp":"2024-11-03T04:21:54Z","content_type":"text/html","content_length":"26413","record_id":"<urn:uuid:17b57632-289b-4430-8bce-bcee0bc323ab>","cc-path":"CC-MAIN-2024-46/segments/1730477027770.74/warc/CC-MAIN-20241103022018-20241103052018-00603.warc.gz"}
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Is it possible to simplify the RH problem? • Thread starter PeterJ • Start date In summary, you are not a mathematician, and are asking for help understanding the Riemann Hypothesis. You think that zeta might represent a way to approach the problem in more heuristic terms, but you are not sure if you are right. Hello everybody. It's my first post and I'm not a mathematician so please bear with me. I'll try to make it vaguely interesting. I'm fascinated by the problem of deciding the Riemann Hypothesis. The trouble is, I'm not clever enough to understand it. The zeta function may as well be martian hieroglyphics and I have no idea what a diagonal lemma is. I do have a good heuristic understanding the primes, however, and wondered whether there might be a way to understand the RH problem in more heuristic terms. This would require a massive simplification and maybe it can't be done, but at the moment I can't see why not. Complex (for me) mathematics often represents simple mechanical processes. By 'heuristic understanding' here I mean that I know how the primes work. For a musician their behaviour is not hard to understand once the mechanism that generates them is understood. A correct (albeit not rigorous) heuristic proof of the TP conjecture is possible armed only with an understanding of multiplication. It is not the primes that are the problem for me it's the mathematics, it's translating the mechanics of the number line into equations, virtual landscapes and so forth. I wondered whether it would be possible for me to approach the problem by reducing the zeta function to a black box. When we input a pair of numbers they are transduced into a new pair by some (for me) forever incomprehensible process. This would be a strictly deterministic process such that in principle it would be possible to backwards engineer the zeta function from a study of the behaviour of the inputs and outputs. Am I okay to think of the process in this way? If this does actually represent the situation then the first thing I'd like to ask is what the inputs to the black box that produce the relevant zeros actually are, and which numbers have to be inputted in order to produce R's landscape. A very naive question, I know. Even asking sensible questions about the RH is difficult for a layman. Also, would I be right to say that the zeta function acts like a resonator? Marcus du Sautoy's remarks about tuning forks and quantum resonators got me thinking. As an ex sound engineer I'm struck by the similarity between the way primes are produced and the way a plate reverb works. I even wonder whether a plate reverb might be a simple model of a quantum drum, but that's another story. Anything that anyone can tell me about this problem that I can understand will be gratefully received. If I were younger I'd get some maths lessons but it's too late. Thanks. PeterJ said: I'm fascinated by the problem of deciding the Riemann Hypothesis. The trouble is, I'm not clever enough to understand it. The zeta function may as well be martian hieroglyphics and I have no idea what a diagonal lemma is. You're pretty far away, then. Goedel diagonalization is standard undergraduate stuff, understandable by a motivated high-school student. The RH is one of the deepest problems in analytic number theory (or, indeed, of all mathematics). PeterJ said: I do have a good heuristic understanding the primes, however, and wondered whether there might be a way to understand the RH problem in more heuristic terms. Sure, that's easy. The RH is equivalent to the statement that [tex]\|\pi(x) - \operatorname{li}(x)\| < \frac{1}{8\pi} \sqrt{x} \, \log(x)[/tex] for all x >= 2657. Using Cramér's heuristic model of the primes, this is true with probability 1. So heuristically, the RH true. The hard part is bridging the gap with a proof rather than a heuristic. PeterJ said: I wondered whether it would be possible for me to approach the problem by reducing the zeta function to a black box. When we input a pair of numbers they are transduced into a new pair by some (for me) forever incomprehensible process. This would be a strictly deterministic process such that in principle it would be possible to backwards engineer the zeta function from a study of the behaviour of the inputs and outputs. Am I okay to think of the process in this way? No. If we want to prove that zeta has certain properties, we can't treat it like a black box. Thanks. I realize Goedel diagonalization is standard stuff. Couldn't understand the equations, which are also probably standard stuff. The last point seems slightly off-track since I don't want to prove that zeta has certain properties. My thought was that zeta merely reveals properties that are already encoded in the input numbers. Probably nonsense. Am I wrong to think zeta could be recreated from an analysis of its inputs and outputs? PeterJ said: Thanks. I realize Goedel diagonalization is standard stuff. Couldn't understand the equations, which are also probably standard stuff. I'm sure you could understand diagonalization if you looked into it. To understand the zeta function you must minimally understand analytic continuation, since the 'defining series'... isn't. (For the regions you care about for the RH, the standard series diverges.) PeterJ said: My thought was that zeta merely reveals properties that are already encoded in the input numbers. Probably nonsense. Probably. The question is just "is there a z with Re(z) > 0 such that zeta(z) = 0", which looks at all points z, not just those with specially-coded information. PeterJ said: Am I wrong to think zeta could be recreated from an analysis of its inputs and outputs? I'm not sure what you mean here. A function is just a map between inputs and outputs. You don't need to use a particular symbolic form of the zeta function, if that's what you mean. On the other hand, it wouldn't be enough to look at individual points (say, using a computer to generate the value at those points) unless one was itself a counterexample; you'll need to understand how the function works in order to prove things about it. I like to think I could understand a lot of the maths, yes, given time, but I know I could never understand all that would be required for this problem. I'm in complete awe of anyone who can understand it. I suppose I was asking if the zeta function is a map between inputs and outputs, such that each unique input will produce just one unique output and always the same one. It would follow, would it not, that the characteristics of the outputs are encoded in the inputs. Another way of coming at it would be to ask whether we can predict which inputs will produce relevant zeros. Now I come to think of it that's what I should asked in the first place. But even this simple question may be daft. If even this question is daft I'll go away and have rethink. Thanks for your help. PeterJ said: I suppose I was asking if the zeta function is a map between inputs and outputs, such that each unique input will produce just one unique output and always the same one. It would follow, would it not, that the characteristics of the outputs are encoded in the inputs. I suppose I don't know what you mean by "the characteristics of the outputs are encoded in the inputs". PeterJ said: Another way of coming at it would be to ask whether we can predict which inputs will produce relevant zeros. Now I come to think of it that's what I should asked in the first place. Right, that's the whole issue. It's like saying, "the first step toward solving RH is solving RH". Yes, true -- but not very enlightening. :shy: usually mathematicians start by making things more complex before trying to find a solution to a problem. you are among the few who is trying to take the opposite path. Yes. Simplifying problems is a hobby. It works for the TPC, Russell's paradox and many other problems, (and it kept my business alive through many a crisis). I was wondering if it would work for RH. Seems highly unlikely at this point. CRG - For you the point about inputs and outputs may not be enlightening, but I've just learned something very important from your reply. What I meant by saying the characteristics of the outputs are encoded in the inputs is this. From a glance at a series of primes we may see little indication of pattern or rule-governed behaviour, especially if they are non-sequential. If we feed them into a function which simply squares them, however, the fact that the results always fall at 6n+1 reveals unmissable characteristics of the series that were not previously obvious. The behaviour of the outputs is encoded in the inputs and revealed by the function. Clumsy way of putting it, no doubt, but that's all I meant. But you didn't actually say whether we can predict the relevant zeros from the inputs, either in practice or in principle. Are you saying that there's a sense in which making this prediction is the whole problem? "A related bound was given by Jeffrey Lagarias in 2002, who proved that the Riemann hypothesis is equivalent to the statement that \sigma(n) \le H_n + \ln(H_n)e^{H_n} for every natural number n, where Hn is the nth harmonic number, (Lagarias 2002)." found in: I am not sure if it is a simplification or not but you can always try to prove the above result since it's equivalent to proving RH. PeterJ said: What I meant by saying the characteristics of the outputs are encoded in the inputs is this. From a glance at a series of primes we may see little indication of pattern or rule-governed behaviour, especially if they are non-sequential. If we feed them into a function which simply squares them, however, the fact that the results always fall at 6n+1 reveals unmissable characteristics of the series that were not previously obvious. The behaviour of the outputs is encoded in the inputs and revealed by the function. Clumsy way of putting it, no doubt, but that's all I meant. I understand what you say above, but not how it applies to the situation at hand. In your example you start from a 'mysterious' sequence (the primes), apply a function, and get a result; studying the result tells you something about the sequence. But you're suggesting, as far as I can tell, taking some really big, well-understood set (the complex numbers C, or the non-real complex numbers C \ R, or something like that), applying the zeta function, and looking at what comes out. PeterJ said: But you didn't actually say whether we can predict the relevant zeros from the inputs, either in practice or in principle. Are you saying that there's a sense in which making this prediction is the whole problem? Some notation: For a set S and a function f on that set, let f(S) (the direct image) be {f(s): s in S} and let [tex]f^{-1}(S)=\{x: f(s) = x, s\in S\}[/tex] (the indirect image). The whole problem is determining whether [tex]\zeta^{-1}(\{c\in\mathbb{C}: \Re(c)\neq1/2,\Im(c)\neq0\})[/tex] is empty or not, so in that sense yes -- if you can predict where the zero are, you're done. (Of course predicting some is not enough, you'd need to be able to predict all.) epsi00 said: I am not sure if it is a simplification or not but you can always try to prove the above result since it's equivalent to proving RH. I find the Lagarias problem to be a more difficult version of the Schoenfeld problem (also equivalent to the RH; I mentioned it in my first post here). But you're welcome to take a crack at it! CRGreathouse said: I understand what you say above, but not how it applies to the situation at hand... The whole problem is determining whether [tex]\zeta^{-1}(\{c\in\mathbb{C}: \Re(c)\neq1/2,\Im(c)\neq0\})[/tex] is empty or not, so in that sense yes -- if you can predict where the zero are, you're done. (Of course predicting some is not enough, you'd need to be able to predict all.) Thanks - even if it's all hieroglyphics to me. I realize it's a struggle to talk about this with a mathematical duffer. I was wondering whether proving the zeros behave in a certain way is equivalent to proving that the relevant inputs have certain properties. But even if this question is sensible I seem to be too far out of my depths to understand the answer. I'm not looking for a solution, of course, just exploring whether there's a more accessible route into the problem. On a more general and chatty note. Do you believe that books such as those by Derbyshire and Du Sautoy are good non-expert introductions to number theory? I believe they are awful (albeit that they are brilliant in many ways), and wonder why nobody has written a better one. There's definitely a market for a primer but I've never come across one. What I mean by a primer is something that explains the behaviour of the primes and thus makes sense of the equations used to model it. This is what seems to be missing from every book and article that I've read, and yet it seems to be the only sensible starting point for an explanation aimed at the general reader. When people ask me to recommend a book I can't. I'm wondering why nobody is cashing in on what could be a nice little earner, and whether it's because mathematicians forget what it was like not to be one. All experts have that problem, of course, but it seems a particular problem in this context. PeterJ said: Thanks - even if it's all hieroglyphics to me. Sorry, I was trying to be clear. Let me try the same thing without symbols: the whole question is whether there are zeros zeta(x + iy) not on either of the lines y = 0 and x = 1/2. If we knew where all the zeros were, we'd just test to see if any were not on these lines. So knowing where all the zeros solves the problem. Also, you can't really get anything from looking at the values that the zeta function takes on, since by Picard's theorem (read: "trust me") it takes on all complex values except possible one value. PeterJ said: I'm not looking for a solution, of course, just exploring whether there's a more accessible route into the problem. Many routes are known. But the field is not yet well-developed enough that we can say which are more accessible! (There are other unsolved problems where there is a reasonably well-understood path to solving the problem, even though it hasn't been followed yet; perhaps Goldbach's weak conjecture is an example.) So that part isn't hard just for you but for everyone. PeterJ said: On a more general and chatty note. Do you believe that books such as those by Derbyshire and Du Sautoy are good non-expert introductions to number theory? I believe they are awful (albeit that they are brilliant in many ways), and wonder why nobody has written a better one. There's definitely a market for a primer but I've never come across one. I haven't read their books so I don't have an opinion on that point. But I would suggest that it's hard to write a widely-accessible primer for the subject because the subject is very difficult, and writing an overview that can be understood by an 'ordinary' (smart but untrained in mathematics) person is extremely challenging. Making math understandable is not simple by any means! Okay CRG, I've decided to book some tuition in order to get to grips with the issues and will stop bothering you. I need to take a few steps back before trying to go forward again. Many thanks for your patience. Much appreciated. Sounds good. Post again when you have new insights or questions. I could use more complex analysis, myself... there are several operator whose eigenvalues are precisely the imaginary part of the Zeros the main and biggest problem ,is to show how there are no zeros away the critical strip Re[S:=1/2:S] FAQ: Is it possible to simplify the RH problem? 1. Can the Riemann Hypothesis be proven? As of now, the Riemann Hypothesis remains an unsolved problem in mathematics. Several attempts have been made to prove or disprove it, but no conclusive solution has been found. 2. How can the RH problem be simplified? The RH problem can be simplified by finding a more general statement that implies the Riemann Hypothesis. This can help in narrowing down the focus and finding a solution to the problem. 3. Why is the RH problem important? The Riemann Hypothesis has far-reaching implications in various areas of mathematics, including number theory, complex analysis, and prime number distribution. Its proof or disproof can lead to significant advancements in these fields. 4. What are some approaches to solving the RH problem? There are several approaches to solving the Riemann Hypothesis, including using analytic methods, algebraic methods, and computational methods. Each approach has its own set of challenges and 5. How close are we to solving the RH problem? As of now, there is no definitive answer to this question. While there have been some promising results and breakthroughs in recent years, the Riemann Hypothesis remains unsolved. It is a complex problem that requires further research and collaboration among mathematicians to find a solution.	{"url":"https://www.physicsforums.com/threads/is-it-possible-to-simplify-the-rh-problem.436136/","timestamp":"2024-11-05T18:47:38Z","content_type":"text/html","content_length":"162381","record_id":"<urn:uuid:50b0ae78-2092-4867-9406-a7eedfd22de8>","cc-path":"CC-MAIN-2024-46/segments/1730477027889.1/warc/CC-MAIN-20241105180955-20241105210955-00735.warc.gz"}
Squaring Price and Time #210 Update on NVDA, TSLA, DJIA, SPX and Nasdaq Last week, I discussed a W.D. Gann method for squaring out Price and Time, or how to forecast a possible change in trend. I used a graph of the NYSE to emphasize that the stock market may not have reached its peak yet. In the same article, I also pointed out that the low of early August was the anticipated 20-year low, accurately aligning with the exact day 20 years prior. This low represented 1/3 of a 60-year low, and a low in the 60-year cycle was expected around the same time. From this, it is evident that we may not have seen the high in this bull cycle yet. Additionally, even a stock like NVDA hit a low at the same time 20 years ago. A few days later, I demonstrated another practical application of the W.D. Gann method on Twitter. This time, I showed how to square Price and Time, a technique W.D. Gann used to use. As per his advice, one should square the high, the low, or the range to anticipate a change in trend. These techniques help forecast a possible trend change, in Price and Time. In the example below, I demonstrated in a tweet how this recently happened with Soybeans. Eight times 360 degrees on the Square of Nine from the low at 808.25 in 2020 forecasted the price-high. As Gann stated: “The squaring of Price with Time means an equal number of points up or down balancing an equal number of time periods—either days, weeks, or months.” So, the calculation is the Squareroot of 808.25 + 2 (for 360 degrees) and re-square the outcome, which is (SQRT(808.25)+2)^2 =925.76. So, the interval is 117.72 to reach the first 360 degrees or the first increment. 8 cycles later, the high is at 1750. How to calculate then in Time when a crest is due form a significant low? On the April 2020 low, knowing a possible square out on a price level of 1750, which is at the 8th level of 360-degree moves in price on the square of nine from the low, one could look for a high in 1750 hours or days from that 2020 low, or a harmonic of this number like 175 days or 17500 hours. 17500 hours or 729 days from the April 2020 low is April 20th, 2022. This is only 2 days from the second top on April 22nd, 2022. The market squared out three times in 2022: in February, April, and June. The second top on April 22nd squared out in Price and time(17543 hours). If you shift the decimal point in hours between the low of April 2022 and the high of April 2022, you will get to the exact midpoint of 1754.30, which was the price of April 22nd, 2022. One could also calculate this using simple trigonometry. As time and price balance on a 1x1, one could take the tan(45), which =1, and multiply it by the price. Hence, perhaps in 808 days, weeks, hours, or equivalent harmonics. Tan (45) equals 1. When the angle is 45 degrees, the tangent value of 1 corresponds to a slope of 1, indicating that the line rises by 1 unit for every 1 unit of horizontal distance. A perfect But markets are not always perfect, so any degree can be used. Tan(44) is nearly perfect. Taking the tan(44) degrees and multiplying it by the price of the low at 808 will give you 780 calendar days, which was reached on June 10th, the third top in a row. When a high has been confirmed one could calculate when a low in time may be reached. As Gann stated: “The squaring of Price with Time means an equal number of points up or down balancing an equal number of time periods—either days, weeks, or months.” Yesterday, exactly 808 days later from the crest, we saw a low in both Price and Time again, which was close to the 7/8 point from the high. Remember what Gann taught: "It is important to watch the 7 /8 point of the move." You could also square the range in Time from the crest, which may cause a secondary low or even a lower low in November 2024. Recently Soybeans have stabilized at a precise price point since April 2020, following a Square of Nine calculation, as shown by the black line. I expect some upcoming volatility and foresee a similar fractal pattern emerging, akin to the one before the 2020 low. This is an example of a technique that W.D. Gann used to forecast when price and time are in balance and a change in trend may occur. In his Stock Market Course, W.D. Gann introduced another method for forecasting price and time. I have used this alternative approach for my forecasts for NVDA and TSLA. Premium subscribers can access updated forecasts, including updates for the US Indices following the Gann Master Cycles and an update on the NYSE Transit To Natal, in the post below. This post is for paid subscribers	{"url":"https://www.fiorente2.com/p/squaring-price-and-time","timestamp":"2024-11-14T17:32:53Z","content_type":"text/html","content_length":"162152","record_id":"<urn:uuid:5af53fc7-4a58-4c93-9e42-73cbe3672bdb>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00646.warc.gz"}
Bandpass filter design specification object Bandpass filter design specification object The fdesign.bandpass function returns a bandpass filter design specification object that contains specifications for a filter such as passband frequency, stopband frequency, passband ripple, and filter order. Use the design function to design the filter from the filter design specifications object. For more control options, see Filter Design Procedure. For a complete workflow, see Design a Filter in Fdesign — Process Overview. bandpassSpecs = fdesign.bandpass constructs a bandpass filter design specifications object with the following default values: • First stopband frequency set to 0.35. • First passband frequency set to 0.45. • Second passband frequency set to 0.55. • Second stopband frequency set to 0.65. • First stopband attenuation set to 60 dB. • Passband ripple set to 1dB. • Second stopband attenuation set to 60 dB. bandpassSpecs = fdesign.bandpass(spec,value1,...,valueN) constructs a bandpass filter specification object with a particular filter order, stopband frequency, passband frequency, and other specification options. Indicate the options you want to specify in the expression spec. After the expression, specify a value for each option. If you do not specify values after the spec argument, the function assumes the default values. bandpassSpecs = fdesign.bandpass(___,Fs) provides the sample rate in Hz of the signal to be filtered. Fs must be specified as a scalar trailing the other numerical values provided. In this case, all frequencies in the specifications are in Hz as well. The design specification fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2',.4,.5,.6,.7,60,1,80) designs the same filter as fdesign.bandstop bandpassSpecs = fdesign.bandpass(___,magunits) provides the units for the specified magnitude. magunits can be one of the following: 'linear', 'dB', or 'squared'. If this argument is omitted, the object assumes the units of magnitude specification to be 'dB'. The magnitude specifications are always converted and stored in decibels regardless of how they were specified. If Fs is provided, magunits must follow Fs in the input argument list. Design Equiripple FIR Bandpass Filter Design a constrained-band FIR equiripple filter of order 100 with a passband of [1, 1.4] kHz. Both stopband attenuation values are constrained to 60 dB. The sample rate is 10 kHz. Create a bandpass filter design specification object using the fdesign.bandpass function and specify these design parameters. bandpassSpecs = fdesign.bandpass('N,Fst1,Fp1,Fp2,Fst2,C',100,800,1e3,1.4e3,1.6e3,1e4); Constrain the two stopbands with a stopband attenuation of 60 dB. bandpassSpecs.Stopband1Constrained = true; bandpassSpecs.Astop1 = 60; bandpassSpecs.Stopband2Constrained = true; bandpassSpecs.Astop2 = 60; Design the bandpass filter using the design function. The resulting filter is a dsp.FIRFilter System object™. For details on how to apply this filter on streaming data, refer to dsp.FIRFilter. bandpassFilt = design(bandpassSpecs,Systemobject=true) bandpassFilt = dsp.FIRFilter with properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [5.5055e-04 5.4751e-05 -2.2052e-05 6.5244e-05 3.6129e-04 5.7237e-04 1.9824e-04 -9.8650e-04 -0.0025 -0.0030 -0.0014 0.0023 0.0062 0.0075 0.0040 -0.0034 -0.0109 -0.0135 -0.0082 0.0031 0.0142 0.0181 0.0119 -0.0012 ... ] (1x101 double) InitialConditions: 0 Use get to show all properties Visualize the frequency response of the designed filter. Measure the frequency response characteristics of the filter using measure. The passband ripple is slightly over 2 dB. Because the design constrains both stopbands, you cannot constrain the passband ans = Sample Rate : 10 kHz First Stopband Edge : 800 Hz First 6-dB Point : 946.7621 Hz First 3-dB Point : 975.1807 Hz First Passband Edge : 1 kHz Second Passband Edge : 1.4 kHz Second 3-dB Point : 1.4248 kHz Second 6-dB Point : 1.4533 kHz Second Stopband Edge : 1.6 kHz First Stopband Atten. : 60.0614 dB Passband Ripple : 2.1443 dB Second Stopband Atten. : 60.0399 dB First Transition Width : 200 Hz Second Transition Width : 200 Hz Design Butterworth IIR Bandpass Filter Design a Butterworth IIR bandpass filter. The filter design procedure is: Construct a default bandpass filter design specification object using fdesign.bandpass. bandpassSpecs = fdesign.bandpass bandpassSpecs = bandpass with properties: Response: 'Bandpass' Specification: 'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2' Description: {7x1 cell} NormalizedFrequency: 1 Fstop1: 0.3500 Fpass1: 0.4500 Fpass2: 0.5500 Fstop2: 0.6500 Astop1: 60 Apass: 1 Astop2: 60 Determine the available design methods using the designmethods function. To design a Butterworth filter, pick butter. Design Methods that support System objects for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2): When designing the filter, you can specify additional design options. View a list of options using the designoptions function. The function also shows the default design options the filter uses. ans = struct with fields: FilterStructure: {'df1sos' 'df2sos' 'df1tsos' 'df2tsos' 'cascadeallpass' 'cascadewdfallpass'} SOSScaleNorm: 'ustring' SOSScaleOpts: 'fdopts.sosscaling' MatchExactly: {'passband' 'stopband'} SystemObject: 'bool' DefaultFilterStructure: 'df2sos' DefaultMatchExactly: 'stopband' DefaultSOSScaleNorm: '' DefaultSOSScaleOpts: [1x1 fdopts.sosscaling] DefaultSystemObject: 0 Use the design function to design the filter. Pass 'butter' and the specifications given by variable bandpassSpecs, as input arguments. Specify the 'matchexactly' design option to 'passband'. bpFilter = design(bandpassSpecs,'butter','matchexactly','passband','SystemObject',true) bpFilter = dsp.SOSFilter with properties: Structure: 'Direct form II' CoefficientSource: 'Property' Numerator: [7x3 double] Denominator: [7x3 double] HasScaleValues: true ScaleValues: [0.1657 0.1657 0.1561 0.1561 0.1504 0.1504 0.1485 1] Use get to show all properties Visualize the frequency response of the designed filter. Bandpass Filtering of Sinusoids Bandpass filter a discrete-time sine wave signal which consists of three sinusoids at frequencies, 1 kHz, 10 kHz, and 15 kHz. Design an FIR Equiripple bandpass filter by first creating a bandpass filter design specifications object, and then designing a filter using these specifications. Design Bandpass Filter Create a bandpass filter design specifications object using fdesign.bandpass. bandpassSpecs = fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2', ... List the available design methods for this object. Design Methods for class fdesign.bandpass (Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2): To design an Equiripple filter, pick 'equiripple'. bpFilter = design(bandpassSpecs,'equiripple',Systemobject=true) bpFilter = dsp.FIRFilter with properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [-0.0043 -3.0812e-15 0.0136 3.7820e-15 -0.0180 -4.2321e-15 7.1634e-04 4.0993e-15 0.0373 -4.1057e-15 -0.0579 3.7505e-15 0.0078 -3.4246e-15 0.1244 2.4753e-15 -0.2737 -8.6287e-16 0.3396 -8.6287e-16 -0.2737 ... ] (1x37 double) InitialConditions: 0 Use get to show all properties Visualize the frequency response of the designed filter. Create Sinusoidal Signal Create a signal that is a sum of three sinusoids with frequencies at 1 kHz, 10 kHz, and 15 kHz. Initialize spectrum analyzer to view the original signal and the filtered signal. Sine1 = dsp.SineWave(Frequency=1e3,SampleRate=44.1e3,SamplesPerFrame=4000); Sine2 = dsp.SineWave(Frequency=10e3,SampleRate=44.1e3,SamplesPerFrame=4000); Sine3 = dsp.SineWave(Frequency=15e3,SampleRate=44.1e3,SamplesPerFrame=4000); SpecAna = spectrumAnalyzer(PlotAsTwoSidedSpectrum=false, ... SampleRate=Sine1.SampleRate, ... ShowLegend=true, ... SpecAna.ChannelNames = {'Original noisy signal','Bandpass filtered signal'}; Filter Sinusoidal Signal Filter the sinusoidal signal using the bandpass filter that has been designed. View the original signal and the filtered signal in the spectrum analyzer. The tone at 1 kHz is filtered out and attenuated. The tone at 10 kHz is unaffected, and the tone at 15 kHz is mildly attenuated because it appears in the transition band of the filter. for i = 1:5000 x = Sine1()+Sine2()+Sine3(); y = bpFilter(x); Input Arguments spec — Specification 'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2' (default) \| 'N,F3dB1,F3dB2' \| 'N,F3dB1,F3dB2,Ap' \| ... Specification expression, specified as one of these character vectors: • 'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2' (default) • 'N,F3dB1,F3dB2' • 'N,F3dB1,F3dB2,Ap' • 'N,F3dB1,F3dB2,Ast' • 'N,F3dB1,F3dB2,Ast1,Ap,Ast2' • 'N,F3dB1,F3dB2,BWp' • 'N,F3dB1,F3dB2,BWst' • 'N,Fc1,Fc2' • 'N,Fc1,Fc2,Ast1,Ap,Ast2' • 'N,Fp1,Fp2,Ap' • 'N,Fp1,Fp2,Ast1,Ap,Ast2' • 'N,Fst1,Fp1,Fp2,Fst2' • 'N,Fst1,Fp1,Fp2,Fst2,C' • 'N,Fst1,Fp1,Fp2,Fst2,Ap' • 'N,Fst1,Fst2,Ast' • 'Nb,Na,Fst1,Fp1,Fp2,Fst2' This table describes each option that can appear in the expression. Specification option Description Ap Amount of ripple allowed in passband, specified as Apass in dB. Ast Stopband attenuation (dB), specified using Astop. Ast1 Attenuation in the first stopband (dB), specified using Astop1. Ast2 Attenuation in the second stopband (dB), specified using Astop2. BWp Bandwidth of the filter passband, specified as BWpass in normalized frequency units. BWst Frequency width between the two stopband frequencies, specified as BWstop in normalized frequency units. F3dB1 Frequency of the 3 dB point below the passband value for the first cutoff, specified in normalized frequency units. Applies to IIR filters. F3dB2 Frequency of the 3 dB point below the passband value for the second cutoff, specified in normalized frequency units. Applies to IIR filters. Fc1 First cutoff frequency (normalized frequency units), specified using Fcutoff1. Applies to FIR filters. Fc2 Second cutoff frequency (normalized frequency units), specified using Fcutoff1. Applies to FIR filters. Fp1 Frequency at the edge of the start of the passband, specified as Fpass1 in normalized frequency units. Fp2 Frequency at the edge of the end of the passband, specified as Fpass2 in normalized frequency units. Fst1 Frequency at the edge of the end of the first stop band, specified as Fstop1 in normalized frequency units. Fst2 Frequency at the edge of the start of the second stop band, specified as Fstop2 in normalized frequency units. N Filter order for FIR filters. Or both the numerator and denominator orders for IIR filters when Na and Nb are not provided. Specified using FilterOrder. Nb Numerator order for IIR filters, specified using the NumOrder property. Na Denominator order for IIR filters, specified using the DenOrder property. Constrained band flag. This enables you to specify passband ripple or stopband attenuation for fixed-order designs in one or two of the three bands. For more details, see c. Graphically, the filter specifications look similar to those shown in this figure. Regions between specification values like Fst1 and Fp1 are transition regions where the filter response is not explicitly defined. The design methods available for designing the filter depend on the specification expression. You can obtain these methods using the designmethods function. This table lists each specification expression supported by fdesign.bandpass and the available corresponding design methods. Specification expression Supported design methods 'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2' butter, cheby1, cheby2, ellip, equiripple, kaiserwin 'N,F3dB1,F3dB2' butter 'N,F3dB1,F3dB2,Ap' cheby1 'N,F3dB1,F3dB2,Ast' cheby2, ellip 'N,F3dB1,F3dB2,Ast1,Ap,Ast2' ellip 'N,F3dB1,F3dB2,BWp' cheby1 'N,F3dB1,F3dB2,BWst' cheby2 'N,Fc1,Fc2' window 'N,Fc1,Fc2,Ast1,Ap,Ast2' fircls 'N,Fp1,Fp2,Ap' cheby1 'N,Fp1,Fp2,Ast1,Ap,Ast2' ellip 'N,Fst1,Fp1,Fp2,Fst2' iirlpnorm, equiripple, firls 'N,Fst1,Fp1,Fp2,Fst2,C' equiripple 'N,Fst1,Fp1,Fp2,Fst2,Ap' ellip 'N,Fst1,Fst2,Ast' cheby2 'Nb,Na,Fst1,Fp1,Fp2,Fst2' iirlpnorm To design the filter, call the design function with one of these design methods as an input. You can choose the type of filter response by passing 'FIR' or 'IIR' to the design function. For more details, see design. Enter help(bandpassSpecs,'method') at the MATLAB^® command line to obtain detailed help on the design options for a given design method. value1,...,valueN — Specification values comma-separated list of values Specification values, specified as a comma-separated list of values. Specify a value for each option in spec in the same order that the options appear in the expression. Example: bandpassSpecs = fdesign.bandpass('N,Fc1,Fc2,Ast1,Ap,Ast2',n,fc1,fc2,ast1,ap,ast2) The input arguments below provide more details for each option in the expression. n — Filter order positive integer Filter order for FIR filters, specified as a positive integer. In the case of an IIR filter design, if nb and na are not provided, this value is interpreted as both the numerator order and the denominator order. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 nb — Numerator order for IIR filters nonnegative integer Numerator order for IIR filters, specified as a nonnegative integer. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 na — Denominator order for IIR filters positive integer Denominator order for IIR filters, specified as a positive integer. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 c — Constrained band flag This enables you to specify passband ripple or stopband attenuation for fixed-order designs in one or two of the three bands. In the specification 'N,Fst1,Fp1,Fp2,Fst2,C', you cannot specify constraints for all three bands (two stopbands and one passband) simultaneously. You can specify constraints in any one or two bands. Consider the following bandpass design specification where both the stopbands are constrained to the default value 60 dB. Example: spec = fdesign.bandpass('N,Fst1,Fp1,Fp2,Fst2,C',100,800,1e3,1.4e3,1.6e3,1e4); spec.Stopband1Constrained=true; spec.Stopband2Constrained=true; ap — Passband ripple positive scalar Passband ripple, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the passband ripple is converted and stored in dB by the function regardless of how it has been specified. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 ast — Stopband attenuation positive scalar Stopband attenuation, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the stopband attenuation is converted and stored in dB by the function regardless of how it has been Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 ast1 — First stopband attenuation positive scalar Attenuation in the first stopband, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the first stopband attenuation is converted and stored in dB by the function regardless of how it has been specified. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 ast2 — Second stopband attenuation positive scalar Attenuation in the second stopband, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the second stopband attenuation is converted and stored in dB by the function regardless of how it has been specified. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 F3dB1 — First 3 dB frequency positive scalar First 3 dB frequency, specified as positive scalar in normalized frequency units. This is the frequency of the 3 dB point below the passband value for the first cutoff. This input argument applies to IIR filters only. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 F3dB2 — Second 3 dB frequency positive scalar Second 3 dB frequency, specified as positive scalar in normalized frequency units. This is the frequency of the 3 dB point below the passband value for the second cutoff. This input argument applies to IIR filters only. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fc1 — First cutoff frequency positive scalar First cutoff frequency, specified as positive scalar in normalized frequency units. This input argument applies to FIR filters only. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fc2 — Second cutoff frequency positive scalar Second cutoff frequency, specified as positive scalar in normalized frequency units. This input argument applies to FIR filters only. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fst1 — First stopband frequency positive scalar First stopband frequency, specified as positive scalar in normalized frequency units. This is the frequency at the edge of the end of the first stopband. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fst2 — Second stopband frequency positive scalar Second stopband frequency, specified as a positive scalar in normalized frequency units. This is the frequency at the edge of the start of the second stopband. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fp1 — First passband frequency positive scalar First passband frequency, specified as positive scalar in normalized frequency units. This is the frequency at the edge of the start of the first passband. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 fp2 — Second passband frequency positive scalar Second passband frequency, specified as positive scalar in normalized frequency units. This is the frequency at the edge of the end of the passband. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 bwp — Passband frequency width positive scalar Bandwidth of the filter passband in normalized frequency units, specified as a positive scalar less than F3dB2−F3dB1. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 bwst — Frequency width between stopband frequencies positive scalar Frequency width between the two stopband frequencies, specified as a positive scalar in normalized frequency units. Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 Fs — Sample rate Sample rate of the signal to be filtered, specified as a scalar in Hz. Specify the sample rate as a scalar trailing the other numerical values provided. When Fs is provided, Fs is assumed to be in Hz, as are all other frequency values. Note that you do not have to change the specification string. The following design has the specification string set to 'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2', and sample rate set to 8000 Hz. bandpassSpecs = fdesign.bandpass('Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2',1600,2000,2400,2800,60,1,80,8000); filt = design(bandpassSpecs,'Systemobject',true); Data Types: single \| double \| int8 \| int16 \| int32 \| int64 \| uint8 \| uint16 \| uint32 \| uint64 magunits — Magnitude units 'dB' (default) \| 'linear' \| 'squared' Magnitude specification units, specified as 'dB', 'linear', or 'squared'. If this argument is omitted, the object assumes the units of magnitude to be 'dB'. Note that the magnitude specifications are always converted and stored in dB regardless of how they were specified. If Fs is one of the input arguments, magunits must be specified after Fs in the input argument list. Output Arguments bandpassSpecs — Bandpass filter design specification object bandpass object Bandpass filter design specification object, returned as a bandpass object. The fields of the object depend on the spec input character vector. Consider an example where the spec argument is set to 'N,Fc1,Fc2', and the corresponding values are set to 10, 0.6, and 0.8, respectively. The bandpass filter design specification object is populated with the following fields: Version History Introduced in R2009a	{"url":"https://it.mathworks.com/help/dsp/ref/fdesign.bandpass.html","timestamp":"2024-11-13T11:49:27Z","content_type":"text/html","content_length":"155104","record_id":"<urn:uuid:252baf29-631e-4d30-acfd-a323295c4f5e>","cc-path":"CC-MAIN-2024-46/segments/1730477028347.28/warc/CC-MAIN-20241113103539-20241113133539-00838.warc.gz"}
Z-test & T-test Assessment Test Questions and Answers Z-test and T-test are two different tests used for statistical hypothesis testing. Take this assessment test to assess your knowledge of these tests. • 1. What is used when we want to know whether the difference between a sample mean and the population mean is large enough to be statistically significant? □ A. □ B. □ C. □ D. Correct Answer A. One-Sample z-test The One-Sample z-test is used when we want to determine if the difference between a sample mean and the population mean is statistically significant. This test calculates the z-score, which measures how many standard deviations the sample mean is away from the population mean. By comparing the calculated z-score to a critical value, we can determine if the difference is large enough to be statistically significant. • 2. What is used for comparing the means of two populations if you do not know the populations' standard deviation? □ A. □ B. □ C. □ D. Correct Answer D. T test The T test is used for comparing the means of two populations when the standard deviation is unknown. It is a statistical test that determines if the difference between the means of two groups is statistically significant. The T test calculates the T statistic by comparing the means and standard deviations of the two groups, and then determines the probability of obtaining the observed difference if the null hypothesis (no difference between the means) is true. If the probability is below a predetermined significance level, it is concluded that there is a significant difference between the means of the two populations. • 3. When you know the populations' standard deviation, what do you use? □ A. □ B. □ C. □ D. Correct Answer B. Z test When you know the population's standard deviation, you use the Z test. The Z test is a statistical test that is used to determine whether the mean of a sample is significantly different from a known population mean when the population standard deviation is known. It is based on the standard normal distribution and allows for hypothesis testing and calculating p-values. The Z test is commonly used in research and statistical analysis to make inferences about population means. • 4. When you know the populations' standard deviation, what do you use? □ A. □ B. □ C. □ D. Correct Answer A. Z test When you know the population's standard deviation, you use a Z test. A Z test is a statistical test that is used to determine whether the means of two populations are significantly different from each other when the population standard deviation is known. It compares the observed data to the expected data under the null hypothesis and calculates a Z score, which is then compared to a critical value to determine the significance of the result. • 5. Statistical calculations that can be used to compare population means to a sample is... □ A. □ B. □ C. □ D. Correct Answer B. Z test The Z test is a statistical calculation that can be used to compare population means to a sample. It is commonly used when the sample size is large and the population standard deviation is known. The Z test calculates the Z score, which measures how many standard deviations the sample mean is away from the population mean. By comparing the Z score to a critical value, we can determine if the sample mean is significantly different from the population mean. • 6. T test is used when you have... □ A. □ B. □ C. □ D. Correct Answer C. Limited sample The T test is used when there is a limited sample size. This is because the T test is specifically designed to analyze small sample sizes, where the population standard deviation is unknown. It is a statistical test that compares the means of two groups to determine if there is a significant difference between them. In situations where there is a large sample size, other tests like the Z test or chi-square test may be more appropriate. • 7. If your T-Score is above 50, then it is... □ A. □ B. □ C. □ D. Correct Answer C. Above average If your T-Score is above 50, it means that your score is higher than the average. Therefore, the correct answer is "Above average". • 8. Which calculations are used to test a hypothesis? □ A. □ B. □ C. □ D. Correct Answer A. T test A T test is used to test a hypothesis by comparing the means of two groups and determining if there is a significant difference between them. It calculates the t-value, which is then compared to a critical value to determine if the results are statistically significant. The T test is commonly used when the sample size is small and the population standard deviation is unknown. It helps researchers make inferences about the population based on the sample data. The F test, on the other hand, is used to compare the variances of two or more groups. Litmus test and theory are not calculations used to test a hypothesis. • 9. If the mean change score is not significantly different from zero... □ A. No significant change occurred □ B. □ C. □ D. Correct Answer A. No significant change occurred If the mean change score is not significantly different from zero, it means that the observed change is not statistically significant. This suggests that there is no evidence to support the occurrence of a significant change. Therefore, the correct answer is "No significant change occurred". • 10. Which of these shows how likely a sample result is to occur by random chance? □ A. □ B. □ C. □ D. Correct Answer A. P value The P value is a statistical measure that indicates the likelihood of obtaining a sample result by random chance. It is used in hypothesis testing to determine the significance of the results. A smaller P value suggests that the sample result is less likely to occur by random chance, indicating stronger evidence against the null hypothesis. Therefore, the P value is the correct answer as it directly relates to the likelihood of a sample result occurring by random chance.	{"url":"https://www.proprofs.com/quiz-school/story.php?title=3dq-ztest-ttest-assessment-testdi","timestamp":"2024-11-02T21:22:47Z","content_type":"text/html","content_length":"449226","record_id":"<urn:uuid:d536fadc-734d-4b74-b0de-decc8e99f940>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00009.warc.gz"}
Mortgage Break Fee Calculator Mortgage Break Fee Calculator Calculating a mortgage or home loan break fee can be quite complicated, however with our easy to use tool we do all of the hard work for you. When it comes to home loans or mortgage break fees four key factors influence the end fee amount. These factors are a) what the remaining balance of the loan is, b) what the change in the wholesale interest rate has been since the loan was taken out, c) what the remaining term is in years and lastly if the bank or lender charges a set fee like an administration fee d). An example of this is if you have a loan with $500,000 remaining on the balance (a) that you took out at 5.00% that is due to be broken at the new wholesale rate of 4.00% (b) with 3 years remaining on the term (c) plus the administration fee (d). In this case it would be $500,000 * (5.00% - 4.00%) * 3 which ends up as $500,000 * 1.00% * 3 = $15,000. If the rate since the loan was taken out has increased there will likely be no rate related fee however the provider may charge a one-off administration fee. The wholesale rate that the lending establishment will use will be the wholesale hedge rate, which will most likely be from Bloomberg. This is the rate that they determine they can get fixed-rate funds from the wholesale money market on the prepayment day. This is usually made up of a fixed start, and a day rate. As a rule of thumb, this rate will be ~50 percentage points (or one-half percent) lower than the best-fixed rate offered by the bank. Enter your information into the calculator below, and push Calculate. Loan Duration Completed in Days 0 days Duration Left on Loan in Days 0 days If you've found a bug, or would like to contact us please click here. Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis. Copyright © 2019 calculate.co.nz All Rights Reserved. No part of this website, source code, or any of the tools shall be copied, taken or used without the permission of the owner. All calculators and tools on this website are made for educational and indicative use only. Calculate.co.nz is part of the realtor.co.nz, GST Calculator, GST.co.nz, and PAYE Calculator group.	{"url":"https://www.calculate.co.nz/mortgage-break-fee-calculator.php","timestamp":"2024-11-01T22:17:57Z","content_type":"text/html","content_length":"66561","record_id":"<urn:uuid:4cbd54ca-e664-4447-a2a7-fa484ecfcdc0>","cc-path":"CC-MAIN-2024-46/segments/1730477027599.25/warc/CC-MAIN-20241101215119-20241102005119-00538.warc.gz"}
An Attempt At Replicating David Varadi’s Percentile Channels Strategy \| R-bloggersAn Attempt At Replicating David Varadi’s Percentile Channels Strategy An Attempt At Replicating David Varadi’s Percentile Channels Strategy [This article was first published on QuantStrat TradeR » R , and kindly contributed to ]. (You can report issue about the content on this page ) Want to share your content on R-bloggers? if you have a blog, or if you don't. This post will detail an attempt at replicating David Varadi’s percentile channels strategy. As I’m only able to obtain data back to mid 2006, the exact statistics will not be identical. However, of the performance I do have, it is similar (but not identical) to the corresponding performance presented by David Varadi. First off, before beginning this post, I’d like to issue a small mea culpa regarding the last post. It turns out that Yahoo’s data, once it gets into single digit dollar prices, is of questionable accuracy, and thus, results from the late 90s on mutual funds with prices falling into those ranges are questionable, as a result. As I am an independent blogger, and also make it a policy of readers being able to replicate all of my analysis, I am constrained by free data sources, and sometimes, the questionable quality of that data may materially affect results. So, if it’s one of your strategies replicated on this blog, and you find contention with my results, I would be more than happy to work with the data used to generate the original results, corroborate the results, and be certain that any differences in results from using lower-quality, publicly-available data stem from that alone. Generally, I find it surprising that a company as large as Yahoo can have such gaping data quality issues in certain aspects, but I’m happy that I was able to replicate the general thrust of QTS very closely. This replication of David Varadi’s strategy, however, is not one such case–mainly because the data for DBC does not extend back very far (it was in inception only in 2006, and the data used by David Varadi’s programmer was obtained from Bloomberg, which I have no access to), and furthermore, I’m not certain if my methods are absolutely identical. Nevertheless, the strategy in and of itself is The way the strategy works is like this (to my interpretation of David Varadi’s post and communication with his other programmer). Given four securities (LQD, DBC, VTI, ICF), and a cash security (SHY), do the following: Find the running the n-day quantile of an upper and lower percentile. Anything above the upper percentile gets a score of 1, anything lower gets a score of -1. Leave the rest as NA (that is, anything between the bounds). Subset these quantities on their monthly endpoints. Any value between channels (NA) takes the quantity of the last value. (In short, na.locf). Any initial NAs become zero. Do this with a 60-day, 120-day, 180-day, and 252-day setting at 25th and 75th percentiles. Add these four tables up (their dimensions are the number of monthly endpoints by the number of securities) and divide by the number of parameter settings (in this case, 4 for 60, 120, 180, 252) to obtain a composite position. Next, obtain a running 20-day standard deviation of the returns (not prices!), and subset it for the same indices as the composite positions. Take the inverse of these volatility scores, and multiply it by the composite positions to get an inverse volatility position. Take its absolute value (some positions may be negative, remember), and normalize. In the beginning, there may be some zero-across-all-assets positions, or other NAs due to lack of data (EG if a monthly endpoint occurs before enough data to compute a 20-day standard deviation, there will be a row of NAs), which will be dealt with. Keep all positions with a positive composite position (that is, scores of .5 or 1, discard all scores of zero or lower), and reinvest the remainder into the cash asset (SHY, in our case). Those are the final positions used to generate the returns. This is how it looks like in code. This is the code for obtaining the data (from Yahoo finance) and separating it into cash and non-cash data. getSymbols(c("LQD", "DBC", "VTI", "ICF", "SHY"), from="1990-01-01") prices <- cbind(Ad(LQD), Ad(DBC), Ad(VTI), Ad(ICF), Ad(SHY)) prices <- prices[!is.na(prices[,2]),] returns <- Return.calculate(prices) cashPrices <- prices[, 5] assetPrices <- prices[, -5] This is the function for computing the percentile channel positions for a given parameter setting. Unfortunately, it is not instantaneous due to R’s rollapply function paying a price in speed for generality. While the package caTools has a runquantile function, as of the time of this writing, I have found differences between its output and runMedian in TTR, so I’ll have to get in touch with the package’s author. pctChannelPosition <- function(prices, rebal_on=c("months", "quarters"), dayLookback = 60, lowerPct = .25, upperPct = .75) { upperQ <- rollapply(prices, width=dayLookback, quantile, probs=upperPct) lowerQ <- rollapply(prices, width=dayLookback, quantile, probs=lowerPct) positions <- xts(matrix(nrow=nrow(prices), ncol=ncol(prices), NA), order.by=index(prices)) positions[prices > upperQ] <- 1 positions[prices < lowerQ] <- -1 ep <- endpoints(positions, on = rebal_on[1]) positions <- positions[ep,] positions <- na.locf(positions) positions[is.na(positions)] <- 0 colnames(positions) <- colnames(prices) The way this function works is simple: computes a running quantile using rollapply, and then scores anything with price above its 75th percentile as 1, and anything below the 25th percentile as -1, in accordance with David Varadi’s post. It then subsets these quantities on months (quarters is also possible–or for that matter, other values, but the spirit of the strategy seems to be months or quarters), and imputes any NAs with the last known observation, or zero, if it is an initial NA before any position is found. Something I have found over the course of writing this and the QTS strategy is that one need not bother implementing a looping mechanism to allocate positions monthly if there isn’t a correlation matrix based on daily data involved every month, and it makes the code more readable. Next, we find our composite position. #find our positions, add them up d60 <- pctChannelPosition(assetPrices) d120 <- pctChannelPosition(assetPrices, dayLookback = 120) d180 <- pctChannelPosition(assetPrices, dayLookback = 180) d252 <- pctChannelPosition(assetPrices, dayLookback = 252) compositePosition <- (d60 + d120 + d180 + d252)/4 Next, find the running volatility for the assets, and subset them to the same time period (in this case months) as our composite position. In David Varadi’s example, the parameter is a 20-day #find 20-day rolling standard deviations, subset them on identical indices #to the percentile channel monthly positions sd20 <- xts(sapply(returns[,-5], runSD, n=20), order.by=index(assetPrices)) monthlySDs <- sd20[index(compositePosition)] Next, perform the following steps: find the inverse volatility of these quantities, multiply by the composite position score, take the absolute value, and keep any position for which the composite position is greater than zero (or technically speaking, has positive signage). Due to some initial NA rows due to a lack of data (either not enough days to compute a running volatility, or no positive positions yet), those will simply be imputed to zero. Reinvest the remainder in cash. #compute inverse volatilities inverseVols <- 1/monthlySDs #multiply inverse volatilities by composite positions invVolPos <- inverseVolscompositePosition #take absolute values of inverse volatility multiplied by position absInvVolPos <- abs(invVolPos) #normalize the above quantities normalizedAbsInvVols <- absInvVolPos/rowSums(absInvVolPos) #keep only positions with positive composite positions (remove zeroes/negative) nonCashPos <- normalizedAbsInvVols sign(compositePosition > 0) nonCashPos[is.na(nonCashPos)] <- 0 #no positions before we have enough data #add cash position which is complement of non-cash position finalPos <- nonCashPos finalPos$cashPos <- 1-rowSums(finalPos) And finally, the punchline, how does this strategy perform? #compute returns stratRets <- Return.portfolio(R = returns, weights = finalPos) stats <- rbind(table.AnnualizedReturns(stratRets), maxDrawdown(stratRets)) rownames(stats)[4] <- "Worst Drawdown" > stats Annualized Return 0.10070000 Annualized Std Dev 0.06880000 Annualized Sharpe (Rf=0%) 1.46530000 Worst Drawdown 0.07449537 With the following equity curve: The statistics are visibly worse than David Varadi’s 10% vs. 11.1% CAGR, 6.9% annualized standard deviation vs. 5.72%, 7.45% max drawdown vs. 5.5%, and derived statistics (EG MAR). However, my data starts far later, and 1995-1996 seemed to be phenomenal for this strategy. Here are the cumulative returns for the data I have: > apply.yearly(stratRets, Return.cumulative) 2006-12-29 0.11155069 2007-12-31 0.07574266 2008-12-31 0.16921233 2009-12-31 0.14600008 2010-12-31 0.12996371 2011-12-30 0.06092018 2012-12-31 0.07306617 2013-12-31 0.06303612 2014-12-31 0.05967415 2015-02-13 0.01715446 I see a major discrepancy between my returns and David’s returns in 2011, but beyond that, the results seem to be somewhere close in the pattern of yearly returns. Whether my methodology is incorrect (I think I followed the procedure to the best of my understanding, but of course, if someone sees a mistake in my code, please let me know), or whether it’s the result of using Yahoo’s questionable quality data, I am uncertain. However, in my opinion, that doesn’t take away from the validity of the strategy as a whole. With a mid-1 Sharpe ratio on a monthly rebalancing scale, and steady new equity highs, I feel that this is a result worth sharing–even if not directly corroborated (yet, hopefully). One last note–some of the readers on David Varadi’s blog have cried foul due to their inability to come close to his results. Since I’ve come close, I feel that the results are valid, and since I’m using different data, my results are not identical. However, if anyone has questions about my process, feel free to leave questions and/or comments. Thanks for reading. NOTE: I am a freelance consultant in quantitative analysis on topics related to this blog. If you have contract or full time roles available for proprietary research that could benefit from my skills, please contact me through my LinkedIn here.	{"url":"https://www.r-bloggers.com/2015/02/an-attempt-at-replicating-david-varadis-percentile-channels-strategy/","timestamp":"2024-11-02T02:47:38Z","content_type":"text/html","content_length":"108083","record_id":"<urn:uuid:583c369f-ef26-431c-8cb9-eac4be4583bc>","cc-path":"CC-MAIN-2024-46/segments/1730477027632.4/warc/CC-MAIN-20241102010035-20241102040035-00883.warc.gz"}
What Is the Square Root of 16? How To Find the Square Root of 16? The square root of 16 is 4. The square root of a number is the inversion of squaring the given numbers or when the value is multiplied by itself it gives the original value. Let us take 16 as an example. The 16 is 4 and by squaring 4^2 we get 16. The square root symbol is denoted as √ before going ahead with any number for finding their square root we have to check whether the given number is a perfect square number or not. The perfect square is the number that when squared has a whole number like √36 = 6. The non-perfect square numbers are the ones that don’t have a square number when they are squared like √10 = 3.162. Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep. Rational and irrational numbers Rational numbers are the ones that when divided are not equal to zero let us take two values p and q, by dividing p with q, p/q≠ 0. They are usually a whole number. For an irrational number, the remainder is not a whole number but the one with the decimal. Let us take p and q when they are divided they are not equal to zero and are not expressed as the ratio of two integers. How to find the square root of 16? The given number 16 is a perfect square, rational number. To find the square root three methods are used. • Long division method • Prime factorization method • Repeated subtraction method Long division method Choose the number that when multiplied twice the result is 16. The number when multiplied twice gives 16 is 4. Hence 4 is the divisor. Long division method Hence, the √16 = 4. Prime factorization method To find the square root of a number using the prime factorization method. First, find the prime factors of the given number. Let n be the factors when squaring a similar number we get n^2 by multiplying the remaining square we get the square root of the number. Prime factor of 16 = 2×2×2×2 or 2^4 Now let us take the similar squares Now, multiply the squares 2×2 = 4 Hence, the √16 = 4. Repeated subtraction Start to subtract the number with odd numbers. The first odd number to go is 1. Then take the result and start subtracting with the next odd number. Repeat the steps until you reach zero. The step in which zero is attained is the square root of the number. 1. 16-1 = 15 2. 15 – 3 = 12 3. 12 – 5 = 7 4. 7 – 7 = 0 The step in which zero is obtained is 4, Hence, √16 = 4. Solved examples Q1: If the area of the circle is 16 square inches, find the circle’s radius. A1: Area of the square = πr2 πr2 = 16 Since π is common we will cancel that We get r^2 = 16 r= √16 The radius of the circle is 4 inches. Q2: Solve 6 √16 ÷2 √16 A2: The square root of 16 = 4 = 6 (4) ÷2 (4) = 24÷ 8 Hence by solving we get 3 Q 3: A farmer brings 16 saplings if the number of saplings has to be equal in the same row and column how many saplings can be there? A3: Total number of saplings = 16 When they need to be planted equally then the number has to be equally split, By taking the square root 16 we get 4 Hence, 4 people are seated equally in both row and column. Q4: Romie wants to simply 16 to its simplest form, let’s help her. A4: 16 = 4 × 4 Hence the simplest form of 16 = 4 Q5: what is the value of x, if x√16 = 16 A5: x16 = 16 √16 = 4 Hence, x 4 = 16 X = 16÷4 = 4 Therefore x = 4. Looking to Learn Math? Book a Free Trial Lesson and match with top Math Tutors for concepts, homework help, and test prep. Frequently asked questions What is the square root of 16? The prime factor of 16 = 16 = 4 × 4 The 16 = 4. What is a perfect square number? A perfect square number is one when we find the root of the number we get a whole number and not a decimal. √16 = 4 hence 16 is a perfect square number. Is 16 a rational number? Yes, 16 is a rational number because when we divide the number we get 4 and not 0 (p/q≠ 0) What is the square root of 400? The √400 = 20 What is the square root of 225? The square root of 225 = 15. What are the methods to find the square root of a number? There are three methods to find the square root of a number Prime factorization method Long division method Repeated subtraction How to find the square root for irrational numbers? To find the square root for irrational numbers use the long division method	{"url":"https://wiingy.com/learn/math/square-root-of-16/","timestamp":"2024-11-14T14:02:00Z","content_type":"text/html","content_length":"215826","record_id":"<urn:uuid:53ffa8db-ab49-4d29-877a-9486f2376c2f>","cc-path":"CC-MAIN-2024-46/segments/1730477028657.76/warc/CC-MAIN-20241114130448-20241114160448-00268.warc.gz"}
Graphing Quadratic Functions In Vertex Form Worksheet Algebra 1 - Graphworksheets.com Graphing Quadratic Equations Vertex Form Worksheet – Learning mathematics is incomplete without graphing equations. This involves graphing lines and points and evaluating their slopes. This type of graphing requires you to know the x- and y coordinates for each point. To determine a line’s slope, you need to know its y-intercept, which is the point … Read more Graphing Quadratic Functions Worksheet Vertex Form Graphing Quadratic Functions Worksheet Vertex Form – If you’re looking for graphing functions worksheets, you’ve come to the right place. There are many types of graphing function to choose from. For example, Conaway Math has Valentine’s Day-themed graphing functions worksheets for you to use. This is a great way for your child to learn about … Read more Graphing Quadratic Functions Algebra 1 Worksheet Graphing Quadratic Functions Algebra 1 Worksheet – If you’re looking for graphing functions worksheets, you’ve come to the right place. There are several different types of graphing functions to choose from. Conaway Math offers Valentine’s Day-themed worksheets with graphing functions. This is a great way for your child to learn about these functions. Graphing functions … Read more	{"url":"https://www.graphworksheets.com/tag/graphing-quadratic-functions-in-vertex-form-worksheet-algebra-1/","timestamp":"2024-11-14T10:53:45Z","content_type":"text/html","content_length":"60323","record_id":"<urn:uuid:3bebe580-bba2-4be9-b74f-9f8b91613b21>","cc-path":"CC-MAIN-2024-46/segments/1730477028558.0/warc/CC-MAIN-20241114094851-20241114124851-00615.warc.gz"}
Barrel Volume Calculator Online Barrel Volume Calculator that calculates the volume of a barrel given the height and radii. Barrel Volume Calculation Volume of Barrel = (h * PI * (2* r1 ^2 + r2^2) / 3 ) H = Height of the barrel r2,r2 = Radii of the barrel A barrel is one of several units of volume, with dry barrels, fluid barrels (UK beer barrel, U.S. beer barrel), oil barrel, etc. The volume of some barrel units is double others, with various volumes in the range of about 100 to 200 litres.	{"url":"https://calculatorschool.com/area/BarrelVolumeCalculator.aspx","timestamp":"2024-11-10T01:16:51Z","content_type":"text/html","content_length":"85022","record_id":"<urn:uuid:15f6c217-36a7-470e-8f13-19f780affd3e>","cc-path":"CC-MAIN-2024-46/segments/1730477028164.3/warc/CC-MAIN-20241110005602-20241110035602-00698.warc.gz"}
Applications of Gyroscopic Force in Navigation Systems in context of gyroscopic force 27 Aug 2024 Applications of Gyroscopic Force in Navigation Systems Gyroscopic force, a fundamental concept in physics, has numerous applications in navigation systems. This article will delve into the principles and applications of gyroscopic force in navigation What is Gyroscopic Force? Gyroscopic force, also known as gyroscopic moment or precession torque, is a rotational force that arises from the interaction between a spinning top (gyroscope) and its surroundings. The force is perpendicular to both the axis of rotation and the direction of the external torque applied to the gyroscope. Mathematical Representation The gyroscopic force can be mathematically represented as: F_gyro = I * ω × (dω/dt) where: F_gyro = Gyroscopic force I = Moment of inertia of the gyroscope ω = Angular velocity of the gyroscope (dω/dt) = Time derivative of angular velocity Applications in Navigation Systems 1. Inertial Navigation Systems: Gyroscopes are used to measure the orientation and angular velocity of a vehicle or platform, enabling accurate navigation and positioning. 2. Attitude Determination: Gyroscopic force is used to determine the attitude (orientation) of an aircraft, spacecraft, or underwater vehicle. 3. Stabilization Control: Gyroscopes are employed in stabilization control systems to maintain the stability and orientation of vehicles, such as helicopters or drones. 4. Navigation in GPS-Denied Environments: In environments where GPS signals are unavailable or unreliable, gyroscopic force can be used to provide navigation information. 1. High Accuracy: Gyroscopes offer high accuracy and precision in measuring angular velocity and orientation. 2. Robustness: Gyroscopic force is resistant to external disturbances and noise. 3. Low Power Consumption: Gyroscopes typically consume low power, making them suitable for battery-powered devices. Gyroscopic force has numerous applications in navigation systems, enabling accurate attitude determination, stabilization control, and navigation in GPS-denied environments. The mathematical representation of gyroscopic force provides a fundamental understanding of its behavior and properties. As the demand for precise navigation increases, the importance of gyroscopes and their applications will continue to grow. 1. Goldstein, H. (1980). Classical Mechanics. Addison-Wesley. 2. Meriam, J. L., & Kraige, L. G. (2017). Dynamics of Particles and Systems. Wiley. 3. NASA. (n.d.). Gyroscopes in Navigation Systems. Retrieved from https://www.nasa.gov/subject/1231/gyroscopes-in-navigation-systems Related articles for ‘gyroscopic force ‘ : • Reading: Applications of Gyroscopic Force in Navigation Systems in context of gyroscopic force Calculators for ‘gyroscopic force ‘	{"url":"https://blog.truegeometry.com/tutorials/education/1399df2c029895bca6053948803ba6b6/JSON_TO_ARTCL_Applications_of_Gyroscopic_Force_in_Navigation_Systems_in_context_.html","timestamp":"2024-11-08T12:09:01Z","content_type":"text/html","content_length":"16831","record_id":"<urn:uuid:dab78c7a-15d5-4821-82e8-5082d25f1e54>","cc-path":"CC-MAIN-2024-46/segments/1730477028059.90/warc/CC-MAIN-20241108101914-20241108131914-00413.warc.gz"}
Three-dimensional generalization of anyon superconductivity A three-dimensional generalization of the wave function of Girvin et al. is constructed by taking the N-->∞ limit of a solution of the two-dimensional massless Dirac equation with an SU(N) gauge field. The resulting wave function is closely related to instanton solutions of the self-dual Einstein quations, and can be used to construct a multiparticle wave function with remarkable holonomy properties and a ground-state wave function with off-diagonal long-range order. Physical Review Letters Pub Date: June 1991 □ Elementary Excitations; □ High Temperature Superconductors; □ Particle Theory; □ Three Dimensional Models; □ Wave Functions; □ Chiral Dynamics; □ Dirac Equation; □ Gauge Theory; □ Gravitational Waves; □ Ground State; □ Instantons; □ Statistical Mechanics; □ Solid-State Physics; □ 74.65.+n; □ 05.30.-d; □ 73.50.Jt; □ 74.20.-z; □ Quantum statistical mechanics; □ Galvanomagnetic and other magnetotransport effects; □ Theories and models of superconducting state	{"url":"https://ui.adsabs.harvard.edu/abs/1991PhRvL..66.3064C/abstract","timestamp":"2024-11-09T18:09:52Z","content_type":"text/html","content_length":"37508","record_id":"<urn:uuid:cf133f6f-1ea7-4480-b115-3bd00e72c5bf>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00115.warc.gz"}
Learn Predicting Data with TensorFlow – A Practical Guide to Machine Learning with TensorFlow 2.0 & Keras Check out a free preview of the full A Practical Guide to Machine Learning with TensorFlow 2.0 & Keras course The "Predicting Data with TensorFlow" Lesson is part of the full, A Practical Guide to Machine Learning with TensorFlow 2.0 & Keras course featured in this preview video. Here's what you'd learn in this lesson: Vadim demonstrates how to use TensorFlow to calculate the error between two different plot lines: one representing the solution, and the other being a prediction of the solution. The loss function calculates the difference between the solution and the prediction. This section introduces different types of helper functions used to predict data using TensorFlow. Transcript from the "Predicting Data with TensorFlow" Lesson >> Basically, that's the line we're trying to fit our new line to. So that's the ideal solution, right? So let's say we don't know w and b, and we're just trying to guess, so w_guess. And we should start from somewhere. So let's just assign 0.0 to our w_guess, and b_guess can also be 0.0. So if I will plot new line with those values, So w_guess and b_guess. Our line, yes, I should probably change, let's say, red color and, Yeah. So without specifying anything, it will just use the line. So you can see that's the problem I'm trying to solve. So I had the original data, right? And it was kinda randomly distributed. Let's say I just measured something. There should be some sort of dependency. I'm trying to figure out the kinda physical problem so we can associate it easily. So let's say I'm trying to find the correlation between height and shoe size. There might be some correlation, right? But the data will be still noisy. So some tall people might have smaller feet. [LAUGH] Some people, the opposite. And still, that can be the data we just created. And the line, the green line will show me the true dependency between those. So I can actually, to better meaning to this problem, let's say our w is equal to, So I want height in inches, right? So for instance, Let's play around a little bit with those parameters. So b=10, Our random numbers distributed from 0 to 1. So it means that at some point, we will have people with height equal to 0, or [LAUGH] shoe size equal to 0. All right, probably height and shoe size is the bad example. We need better example. Or maybe just skip the example completely. It's just numbers and just the dependency between one value, those xs and some ys, right? And what we will try to do, we'll try to get this red line to get to the optimal solution, but kinda to get to the green line points. And we will do it by playing around with ws and bs. So we need to somehow figure out the error, how far away we are from the true solution. And we can just simply measure the distance between our points and our line and just add them all together, right? And that's gonna correspond how far we are from the line. So let's do the predict function. So predict function will simply take x, right? And it's not the whole array. It's just, let's say, one number. And what it will do, it will just return y, which is equal to our w_guess multiplied by x and + b_guess. And we will return y, okay? So that's our simple function of prediction. And now I also want to define loss. So I'm already using terminology which we will rely on when we will talk about machine learning examples. So with the loss function, I need to simply figure out the distance between my line and my points. So before I do that, let's introduce additional helper function. So define mean_squared_error, yeah. And what it will do, it will just take all my y predictions and true Ys. Now define mean_squared_error. With mean_squared_error, what I'm doing is just return, I can rely on tensor flow, reduce_mean. So reduce_mean of tensor flow function will just calculate the mean value for all the arguments provided to it. But I want to also use squared. So do we have squared here? That's a lot of it, square, yes. So square will just simply, well, squared our inputs. And I want to just use y_pred-Y. So what's happening here, I will just find the distance between my prediction and true value of Y. I will square it because I don't want it to be negative, right? So squaring it means that I will always get the positive number. And then I will find the mean value of all of those kinda squared distances. So if we, for instance, right now print out, Mean. Actually, let's execute this function first. So printing mean_squared_error for my, I can do something like this, predict, Of X and true Ys. So let's see if it's gonna work. It does, and it basically telling me that right now with my guess of w equal to 0 and b_guess equal to 0 as well, we have pretty huge error. So it's gonna square the distance between my line and those points. For instance, if I modify w, _guess and let's actually put it to exactly to where our original data was. Remember, we set w, I changed it. Let's go to w=0.1 and b=0.5. We create our points, we plot them. Yeah, everything looks good. All those, yeah, error reduced significantly just because I modified those ws and bs, but yeah, it's still kinda some error. If we change w_guess and b_guess to whatever values I've used in the original distribution and then try to calculate this new error, You see that it's dropped significantly. So basically our mean_square_error will be our loss function. It will simply calculate kinda, what is our mistake? How far are we from ideal solution? So if we modify w_guess and b from anywhere from those perfect values, for instance, to 1 and, I don't know, -5, you see that error is only increasing. What I'm trying to do right now is to tell you that for machine learning and for our particular problem where we're trying to hit our red line into this distribution, so kinda to put it into the position of the green line. I need to specify the loss function, which will show me how far I am from the real solution. And in my case, I just use the distance in ys between my red line and corresponding ys of those blue points, right? And I squared this distance to avoid of negatives and just found the average, although I could have easily just sum those distances together as well. It's just gonna lead to a pretty large number. Learn Straight from the Experts Who Shape the Modern Web • In-depth Courses • Industry Leading Experts • Learning Paths • Live Interactive Workshops Get Unlimited Access Now	{"url":"https://frontendmasters.com/courses/practical-machine-learning/predicting-data-with-tensorflow/","timestamp":"2024-11-06T11:15:15Z","content_type":"text/html","content_length":"31995","record_id":"<urn:uuid:3c0821d0-9f02-4d19-9361-0c90da7cb413>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00415.warc.gz"}
Tolerancing- understanding of when using TEZI, the max tolerance value is RMS error of surface \| Zemax Community Can you explain the following description in helpfile with a zemax file? TEZI uses the Zernike Standard Sag surface (search the help files for “Zernike Standard Sag”) to model the irregularity on Standard and Even Aspheric surfaces, while Toroidal surfaces use the Zernike terms already supported by the Toroidal surface. When using TEZI, the max tolerance value is the exact RMS error of the surface in lens units. The min tolerance value is automatically set to the negative of the max value; this is done to yield both positive and negative coefficients for the Zernike terms. The resulting RMS is of course always a positive number whose magnitude is equal to the max tolerance value.	{"url":"https://community.zemax.com/got-a-question-7/tolerancing-understanding-of-when-using-tezi-the-max-tolerance-value-is-rms-error-of-surface-1037","timestamp":"2024-11-11T23:53:54Z","content_type":"text/html","content_length":"147508","record_id":"<urn:uuid:7002c50d-4551-49a0-990b-c74bf8f3541b>","cc-path":"CC-MAIN-2024-46/segments/1730477028240.82/warc/CC-MAIN-20241111222353-20241112012353-00306.warc.gz"}
coal size reduction ball mill Size Reduction. Barrel Mill; Rod/Ball Mill; Finger Crusher; Hammermill; Jaw Crusher; Lab Mill 200; Overhung Hammer Mill; Rolls Crusher; Screening. Sieve Shakers; Test Sieves; Splitting and Dividing. Jones Rifflers; Sample Splitter; Tube Divider; Mixing or Blending. MACSALAB TUMBLE MIXER; MACSALAB V-BLENDER; MACSALAB CONE BLENDER; MACSALAB DRUM ... when coal particles are smaller than 15.0 μm, there will be no further particle size reduction in ball mills, but the energy consumption dramatically increases. The inefficiency of the conventional comminution methods for ultrafine grinding attributes to the fact that conventional comminution devices rely too much on the exertion of Which of the following gives the work required for size reduction of coal to -200 mesh in a ball mill most accurately ? A. Rittinger's law. B. Kick's law. C. Bond's law. D. None of these. Answer: Option A Based on the energy-size reduction model for the particle breakage in a ball-and-race mill, a new thought is proposed to calculate the energy split factor of component in the relatively coarse grinding of SCAC/calcite mixture of 2.8–2 mm. Interaction between … 2.4 Effect of ball size 29 2.4.1 Empirical approaches 29 2.4.2 Probabilistic approaches 33 2.5 Abnormal breakage 36 2.6 Effect of ball mixture 37 2.6.1 Ball size distribution in tumbling mills 37 2.6.2 Milling performance of a ball size distribution 40 2.7 Summary … coal size reduction grinding greenrevolution.in. Size reduction & control Grinding Pulverizing of coal. In practise also size reduction by grinding is done in optimised stages. Typical for cost of grinding.Coal pulverizing is an important application for grinding mills (ball mill type) and the advantages of using tumbling grinding are many. Ball mill Wikipedia. A ball mill is a type of grinder used to grind, blend and sometimes for mixing of materials for use in mineral dressing processes, paints, pyrotechnics, ceramics and selective laser sintering.It works on the principle of impact and attrition: size reduction is done by impact as the balls drop from near the top of the shell. The basic parameters used in ball mill design (power calculations), rod mill or any tumbling mill sizing are; material to be ground, characteristics, Bond Work Index, bulk density, specific density, desired mill tonnage capacity DTPH, operating % solids or … The process Comminution involves size reduction and size-wise classification called as screening/ separation. ... Stamp mill,Crusher, AG mill, SAG mill, Pebble m ill, Ball mill, Rod mill. A ... Rod & Ball Mills. The Ball/Rod mills are meant for producing fine particle size reduction through attrition and compressive forces at the grain size level. They are the most effective laboratory mills for batch-wise, rapid grinding of medium-hard to very hard … Classification Of Coal Millsdevrolijkekikker. Classification of coal millsdevrolijkekikker coal mills classification bowl millsarvos size reduction and classification the raymond bowl mill is considered the finest vertical roller mill available for with the high cost of fuel many companies are discovering that it is increasingly cost effective to utilize coal. @article{osti_5548768, title = {Coal grinding technology: a manual for process engineers. [Manuals]}, author = {Luckie, P. T. and Austin, L. G.}, abstractNote = {The beneficiation and utilization of coal requires that mined coals undergo progressive degrees of size reduction. The size reduction process actually starts with the mining of the coal, and the top size and size consist of the mined ... The size distribution produced by the ball milling of various crystalline and non-crystalline materials, showed that initially there was a fairly even distribution over the size range up to 355μm. However, as milling proceeded two distribution modes developed; one at about 90μm (the persistent mode) and one at about 250μm (the transitory mode). Hammer Mills for Material Reduction Williams Patent Crusher. Hammer mills are often used for crushing and grinding material to less than 10 US mesh. Learn more about size reduction options with our Particle Size Conversion Chart.. Hammer Mill Usage by Industry. Williams hammer mills are a popular choice when it comes to particle size reduction ... coal size reduction ball mill. Type of the Paper (Article - MDPI. Apr 29, 2017 conditions include ball size [33–36], media shape [37,38], mill rapidly the breakage rate decreases as size increases (Λ ≥ 0). .. Deniz, V. Comparisons of dry grinding kinetics of lignite, bituminous coal and petroleum coke. Ball Tube Mill The Ball Tube Mill (BTM) is a cylindrical low-speed grinding mill. It consists of a steel barrel, lined with cast abrasion-resistant liners and partially filled with hardened steel balls. Coal and pre-heated primary air enter one or both ends of the mill from a crusher/dryer or feeder. As the mill rotates, the balls cascade and For the conventional comminution facilities, it is believed that crusher, ball mill and stirred mill utilize crushing, impact and abrasion forces to realize size reduction respectively, . In recent years, high voltage pulses and electrical disintegration are also employed for experimental study of coal liberation. coal size reduction ball mill sushiyoup. size of coal from a ball millGrinding Mill China Feed size of our coal ball mill can be smaller than 25mm Know more » Learn More Ball millWikipedia the free encyclopedia Aside from common ball mills there is a second type of ball mill called planetary ball mill and very effective degree of size reduction of the planetary ball mill Chat Praticle Size Reduction in the Ball Mill Drug Development. Oct 20 2008 Praticle Size Reduction in the Ball Mill Michael H Rubinstein School of Pharmacy Liverpool Polytechnic Liverpool Unlike the work of Heywood 1 on coal further grinding did not produce a gradual elimination of the coarse mode with corresponding increase in the persistent mode at 90m Less than 2ww of material was always Introduction of Ball Mill. Ball Mill is key equipment which repulverises the material after it is crushed. Our company has been amongst the pioneers for many years in the design and application of milling systems for the size reduction of a wide variety … Praticle Size Reduction in the Ball Mill: Drug . 20.10.2008 The size distribution produced by the ball milling of various crystalline and non-crystalline materials, showed that initially there was a fairly even distribution over the size range up to 355μm. Size reduction is a process of reducing large unit masses into small unit masses like the coarse or fine particles. Size reduction is also known as comminution or diminution or pulverization. Generally this process is done by two methods: Precipitation method:- In this method, the substance is firstly dissolved in an appropriate solvent and then after it is finely precipitated by the addition ... In this case, particle size and ash content were modelled into breakage equation in exponential term, namely t 10 = A × (1 − e −b∙x∙E cs /e Y a). This modified model gave good fitting results to experimental data. Introduce of coal properties into energy-size reduction model helps to compare grinding energy efficiency of various coals. Raymond size reduction and classification equipment. Raymond® Ball Race Mills provide constant throughput of pulverized coal from 10-40 metric tons/hour. Which of the following gives the work required for size reduction of coal to -200 mesh in a ball mill most accurately ? A. Rittinger's law. B. Kick's law Chapter 10 Particle Size Reduction 10.1 Introduction - To create particles in a certain size and shape - To increase the surface area available for next process - To liberate valuable minerals held within particles * Size reduction process : extremely energy-intensive - 5 % of all electricity generated is used in size reduction Lab Mill 200. Description. Additional Information. This compact, sturdy pulveriser has been designed and developed in South Africa for the general grinding requirements of a typical industrial laboratory. The South African coal industry makes use of these mills. … The unit operation of the size reduction or comminution of solids by crushers and mills is a very important industrial operation involving many aspects of powder technology. It … Article. Effect of particle properties on the energy-size reduction of coal in the ball-and-race mill. April 2018; Powder Technology 333 The amount and ball size distribution in this charge, as well as the frequency with which new balls are added to the mill, have significant effects on the mill capacity and the milling efficiency. Small balls are effective in grinding fine particles in the load, whereas large balls are required to deal with large particles of coal or stone ...	{"url":"https://www.zielonadroga.edu.pl/Nov/01-15576.html","timestamp":"2024-11-08T22:14:03Z","content_type":"application/xhtml+xml","content_length":"23428","record_id":"<urn:uuid:512fcf32-9d54-48e0-a3a8-5eed14962424>","cc-path":"CC-MAIN-2024-46/segments/1730477028079.98/warc/CC-MAIN-20241108200128-20241108230128-00744.warc.gz"}
Lesson 17 Graphs of Rational Functions (Part 1) Lesson Narrative The purpose of this lesson is to introduce students to vertical asymptotes. The line $x=a$ is a vertical asymptote for a rational function $f$ if $f$ is undefined at $x=a$ and its outputs get larger and larger in the negative or positive direction when $x$ gets closer and closer to $a$ on each side of the line. Students begin by reasoning about a vertical asymptote of a simple rational function that represents the relationship between the time and speed needed to travel a fixed distance, building on the work they did in the previous lesson around a cylinder of fixed volume. From there, students complete a card sort in which they match equations and graphs of rational functions, focusing on making connections between the structure of the two representations (MP7) and analyzing representations and structures closely (MP2). While the end behavior of rational functions is touched on here as part of making sense of a context, the following lesson investigates end behavior and horizontal asymptotes in more depth. As such, only a light touch is needed on these ideas in this lesson, with an emphasis on adapting the previously established language around end behavior of polynomials to fit specific rational contexts. Learning Goals Teacher Facing • Identify features of simple rational functions from graphs and equations. • Interpret the end behavior of a rational function in context. Student Facing • Let’s explore graphs and equations of rational functions. Required Preparation Acquire devices that can run Desmos (recommended) or other graphing technology. It is ideal if each student has their own device. (Desmos is available under Math Tools.) Student Facing • I can identify a vertical asymptote from a graph or an equation of a rational function. CCSS Standards Building On Building Towards Glossary Entries • vertical asymptote The line $x=a$ is a vertical asymptote for a function $f$ if $f$ is undefined at $x=a$ and its outputs get larger and larger in the negative or positive direction when $x$ gets closer and closer to $a$ on each side of the line. This means the graph goes off in the vertical direction on either side of the line. Print Formatted Materials Teachers with a valid work email address can click here to register or sign in for free access to Cool Down, Teacher Guide, and PowerPoint materials. Student Task Statements pdf docx Cumulative Practice Problem Set pdf docx Cool Down Log In Teacher Guide Log In Teacher Presentation Materials pdf docx Blackline Masters zip Additional Resources Google Slides Log In PowerPoint Slides Log In	{"url":"https://im-beta.kendallhunt.com/HS/teachers/3/2/17/preparation.html","timestamp":"2024-11-03T07:19:52Z","content_type":"text/html","content_length":"92174","record_id":"<urn:uuid:b8de4965-6df5-4d77-9ce0-ae4f2fa40616>","cc-path":"CC-MAIN-2024-46/segments/1730477027772.24/warc/CC-MAIN-20241103053019-20241103083019-00491.warc.gz"}
Sampling & Survey #7 – Stratified Sampling - The Culture SGSampling & Survey #7 – Stratified Sampling SRS form the basis of sampling and survey methods as it is easy to design and analyse, but it is rarely the best design. We may adopt systematic sampling or cluster sampling but we often are limited by the availability of sampling from. Thus, we need to look at stratified sampling to increase the precision. In stratified sampling, we divide the population in H subpopulations, called strata, which do not overlap (mutually exclusive) and constitute the whole population so that each sampling unit belongs to exactly one stratum. We then draw independent random sample from each stratum. Consider that we have 1000 males and 1000 females to select from, a SRS of size 100 might lead us to have no or very few males or females. This will cause us to not have a presentative sample since men and women respond differently on the item of interest. A stratified sample on the other hand, will suggest we take a SRS of 50 males and an independent SRS of 50 females, ensuring that the proportion in the sample is the same as that in the population. • Clearly, we will have better precision (lower variance) using a stratified sampling as compared to SRS, for the estimates of population means and total. This is because variance within each stratum is often lower than ht variance in the whole population. • Convenient to administer and may result in a lower cost. Sampling frame may be conducted differently in different strata, or different sampling designs or field procedures may be used. For example, using an internet survey by a large firm and a telephone survey for a small firm. So let us look at some notations that we will be using. Firstly, we divide the population N into H mutually exclusive and exhaustive strata. h = 1, 2, …, H index the strata. h. Total number of units in the entire population h. Total sample size h, where h = 1, 2, .., H and j = 1, 2, …, Stratum population total, Population total, Stratum population mean, Population mean, Stratum population variance, Since we assume SRS within each stratum, then when we have a population of Estimate of stratum population mean Estimate of stratum population total Estimate of stratum population variance Estimate of population total Estimate of population mean Since we do SRS in each stratum, both t. Similarly, the variances of the estimators are obtained through SRS since we do independent sampling for different strata. As always, the standard error of an estimator is the square root of the estimated variance: As long as we select at least one element per stratum, the specification for a stratified sample is satisfied. And with two elements per stratum, we can estimate both the mean and its error. If either the sample sizes within each stratum are large or the number of strata are large, the approximate We recall that proportion is a special mean. In SRS, we learnt that i = 1, 2, …, N, refers to our sample weights. The sampling weight of unit i can be interpreted as the number of population units represented by unit i. And in STR: Here h. Clearly, It should be noted that under SRS within strata, weights for each sampling unit within a stratum are the same, while weights across the strata may be different. Now we study how to do proportional allocation (an important property of stratified sampling), that is, allocating such that the number of sampled units in each stratum is proportional to the size of the stratum. Stratum sample size, Notice this rewrites to Thus, the probability that an individual will be selected to be in the sample, When we have a stratified sample of size n with proportional allocation, We can find In general, the variance of the estimator of t from a stratified sample with proportional allocation will be smaller than the variance of the estimator of t from an SRS with the same number of observations. The more unequal the stratum means the more precise Note that After considering proportional allocation, we can now look at optimal allocation. For proportional allocation, we increase precision (lower variance) when the within-stratum variance are more of less equal across all the strata. But we do not consider the cost Problem: min h. We can use Lagrange Multpliers to solve and will find that the optimal allocation Thus the optimal sample size in stratum h is • Proportional allocation is the optimal allocation if all variance and cost are equal across the strata. • Neyman allocation is a special case of optimal allocation, used when the cost in the strata (not the variances) are approximately equal. In short, we have 3 methods of allocation of a sample to strata: Equal, Proportional, and Optimum (Neyman). These allocation strategies allow us to know the proportion of sample allocated to every We say under absolute precision, that the desired margin of error is half-width of the confidence interval. The half-width of CI is We may argue that stratified sampling almost always gives higher precision than SRS, and one should simply consider stratified only. However, we should note that stratified adds complexity to the survey, and we need to weigh if the gain in precision is worthy as compared with the added complexity. Stratified sampling is most efficient when the stratum mean differ widely, so we should construct such that the strata mean is as different as possible. To do this, we need more information. But the more information we have, the more strata we have, the more complexity there is. We will use SRS if there is no or little information about the target population. Sampling & Survey #1 – Introduction Sampling & Survey #2 – Simple Probability Samples Sampling & Survey #3 – Simple Random Sampling Sampling & Survey #4 – Qualities of estimator in SRS Sampling & Survey #5 – Sampling weight, Confidence Interval and sample size in SRS Sampling & Survey #6 – Systematic Sampling Sampling & Survey #7 – Stratified Sampling Sampling & Survey # 8 – Ratio Estimation Sampling & Survey # 9 – Regression Estimation Sampling & Survey #10 – Cluster Sampling Sampling & Survey #11 – Two – Stage Cluster Sampling Sampling & Survey #12 – Sampling with unequal probabilities (Part 1) Sampling & Survey #13 – Sampling with unequal probabilities (Part 2) Sampling & Survey #14 – Nonresponse pingbacks / trackbacks • […] Confidence Interval and sample size in SRS Sampling & Survey #6 – Systematic Sampling Sampling & Survey #7 – Stratified Sampling Sampling & Survey # 8 – Ratio Estimation Sampling & Survey # 9 – Regression […]	{"url":"https://theculture.sg/2016/01/sampling-survey-7-stratified-sampling/","timestamp":"2024-11-13T04:45:53Z","content_type":"text/html","content_length":"143761","record_id":"<urn:uuid:a7bcb5c7-4158-4996-b6f3-0ad14980a31d>","cc-path":"CC-MAIN-2024-46/segments/1730477028326.66/warc/CC-MAIN-20241113040054-20241113070054-00297.warc.gz"}
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The MAX computer algebra seminar The MAX seminar takes place in the Alan Turing building at the campus of École polytechnique. Click here for more information on how to join us. Upcoming talks 2024, November 4 Vincent Neiger (Sorbonne University) Computing Krylov iterates and characteristic polynomials in the time of matrix multiplication Time: from 11h00 to 12h00 Room: Henri Poincaré This talk describes recent work with Clément Pernet and Gilles Villard on improved complexity upper bounds for fundamental linear algebra problems. Given a matrix of size Keller-Gehrig, 1985) via matrix multiplication and Gaussian elimination. For the characteristic polynomial, existing algorithms in Pernet and Storjohann, 2008). A key strategy in the new algorithms is to exploit recent results for univariate polynomial matrices. We will also highlight some consequences on algorithms and software: in particular, computing some power of a matrix can be done faster than by the customary binary exponentiation; and prototype implementations of the new algorithms are faster than state-of-the-art software for the previous best algorithms. 2024, December 16 Alban Quadrat (Inria Paris) Time: from 11h00 to 12h00 Room: Grace Hopper Past talks 2024, October 7 Laurent Fribourg (ENS Paris-Saclay, CNRS) Discretization error with Euler's method: Upper bound and applications Time: from 11h00 to 12h00 Room: Grace Hopper Using the notion of (contractive) matrix measure, we give an upper bound on the discretization error with Euler's method. As applications, we give a method for ensuring the orbital stability of differential systems, and conditions on neural networks ensuring the convergence of the training error to 0. 2024, September 23 Chenqi Mou (Beihang University) Puzzle Ideals for Grassmannians Time: from 11h00 to 12h00 Room: Grace Hopper Puzzles, first introduced by Knutson, Tao, and Woodward, are a versatile combinatorial tool to interpret the Littlewood-Richardson coefficients for Grassmannians. In this talk, I will first explain the underlying concepts to formulate the problem of representing the Littlewood-Richardson coefficients and show how the puzzles interpret them. Then I introduce the new concept of puzzle ideals whose varieties one-one correspond to the tilings of puzzles and present an algebraic framework to construct the puzzle ideals which works with existing puzzles for Grassmannians. Besides the underlying algebraic importance of the introduction of these puzzle ideals is the computational feasibility to find all the tilings of the puzzles for Grassmannians by studying the defining polynomial ideals and their elimination ideals, demonstrated with illustrative puzzles via computation of Gröbner bases. This talk is based on the joint work with Weifeng Shang. 2024, June 10 Guillaume Chèze (Institut de Mathématiques de Toulouse) Partage de gâteaux sans-envie: une grande probabilité d'avoir un nombre de requêtes polynomial Time: from 11h00 to 12h00 Room: Emmy Noether Le problème du partage d'un gâteau entre 2024, May 27 (Postponed until the Fall) Vincent Neiger (Sorbonne University) Faster modular composition of polynomials Time: from 11h00 to 12h00 Room: Grace Hopper This talk is about algorithms for modular composition of univariate polynomials, and for computing minimal polynomials. For two univariate polynomials Brent and Kung's approach (1978); the new complexity bound is subquadratic in the degree of Contains joint work with Seung Gyu Hyun, Bruno Salvy, Eric Schost, Gilles Villard. The corresponding article may be found here or here. 2024, April 29 Antoine Etesse (ENS Lyon) On the structure of differentially homogeneous polynomials Time: from 11h00 to 12h00 Room: Grace Hopper The goal of the talk is to discuss the structure of differentially homogeneous polynomials in 2024, April 22 Factoring differential operators in positive characteristic through geometric means Time: from 15h30 to 16h30 Room: Henri Poincaré We focus on the porblem of factoring a given linear differential operator, whose coefficients are elements of an algebraic function field of characteristic van der Put, we will focus on the case of central operators which are irreducible in the center of the ring of differential operators. This case is very important as the factorisation of any differential operator is brought back to one of those. We shall see that their factorisation is the same as solving a particular equation which we call the 2024, March 25 Matías R. Bender (Inria - CMAP, École Polytechnique) Multigraded Castelnuovo-Mumford regularity and Groebner bases Time: from 11h00 to 12h00 Room: Grace Hopper Groebner bases (GBs) are the “Swiss Army knife” of symbolic computations with polynomials. They are a special set of generators of an ideal which allow us to manipulate extremely complicated objects, so computing them is an intrinsically hard problem. To estimate the complexity of such computations, an extended approach is to bound the maximal degrees of the polynomials appearing in the GBs. One of the most important results in this direction is due to Bayer and Stillman, who showed in the 80s that, in generic coordinates, the maximal degree of an element in a GB of an homogeneous ideal with respect to the reverse lexicographical order is determined by the Castelnuovo-Mumford regularity of the ideal — an algebraic invariant independent of the GB. In this talk, I will present a generalization of their results for multi-homogeneous systems and show how the extension of the Castelnuovo-Mumford regularity to multi-graded ideals relates to the maximal degrees appearing in the computation of a GB. This talk is based on ongoing work with Laurent Busé, Carles Checa, and Elias Tsigaridas. 2024, March 18 Maxime Breden (CMAP, École polytechnique) An introduction to computer-assisted proofs via a posteriori validation Time: from 11h00 to 12h00 Room: Grace Hopper The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear ODEs or PDEs, based on numerical simulations. The general strategy consists in combining a priori and a posteriori error estimates, interval arithmetic, and a fixed point theorem applied to a quasi-Newton operator. Starting from a numerically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neighborhood of the numerical approximation. I will first present the main ideas behind these techniques on a simple example, and then describe how they can be used for rigorously integrating some differential equations. 2024, March 11 François Fages (Inria) On rule-based models of dynamical systems Time: from 11h00 to 12h00 Room: Grace Hopper Chemical reaction networks (CRN) constitute a standard formalism used in systems biology to represent high-level cell processes in terms of low-level molecular interactions. A CRN is a finite set of formal kinetic reaction rules with well-defined hypergraph structure and several possible dynamics. One CRN can be interpreted in a hierarchy of formal semantics related by either approximation or abstraction relationships, including • the differential semantics (ordinary differential equation), • stochastic semantics (continuous-time Markov chain), • probabilistic semantics (probabilistic Petri net forgetting about continuous time), • discrete semantics (Petri net forgetting about transition probabilities), • Boolean semantics forgetting about molecular numbers, • or just the hypergraph structure semantics. We shall show how these different semantics come with different analysis tools which can reveal various dynamical properties of the other interpretations. In our CRN modeling software BIOCHAM (biochemical abstract machine), these static analysis tools are complemented by dynamic analysis tools based on quantitative temporal logic, and by an original CRN synthesis symbolic computation pipeline for compiling any computable real function in an elementary CRN over a finite set of abstract molecular species. 2024, February 26 Michel Fliess (LIX, École polytechnique) Approximate flatness-based control via a case study: Drugs administration in some cancer treatments Time: from 11h00 to 12h00 Room: Grace Hopper We present some “in silico” experiments to design combined chemo- and immunotherapy treatment schedules. We introduce a new framework by combining flatness-based control, which is a model-based setting, along with model-free control. The flatness property of the used mathematical model yields straightforward reference trajectories. They provide us with the nominal open-loop control inputs. Closing the loop via model-free control allows to deal with the uncertainties on the injected drug doses. Several numerical simulations illustrating different case studies are displayed. We show in particular that the considered health indicators are driven to the safe region, even for critical initial conditions. Furthermore, in some specific cases there is no need to inject chemotherapeutic Joint work with C. Join, K. Moussa, S.M. Djouadi, M.W. Alsager. 2023, December 8 Mizuka Komatsu (Kobe University) Application of differential elimination for physics-based deep learning and computing Time: from 14h00 to 15h00 Room: Darboux amphitheater, Institut Henri Poincaré (11 Rue Pierre et Marie Curie, Paris) In the field of differential algebra, differential elimination refers to the elimination of specific variables and/or their derivatives from differential equations. One well-known application of differential elimination is in the model identifiability analysis. Recently, there has been a growing demand for further applications in addition to this. In this talk, we introduce two recent applications in the field related to physics. The first application field is physics-based deep learning. In particular, we introduce the application of differential elimination for Physics-Informed Neural Networks (PINNs), which are types of deep neural networks integrating governing equations behind the data. The second application is about physics-based computing, or, physical computing. This refers to information processing leveraging the dynamics of physical systems such as soft materials and fluids. In this talk, we show the application of differential elimination to time-series information processing via physical computing. 2023, April 24 Eric Goubault (LIX) Set-based methods for the analysis of dynamical systems Time: from 11h00 to 12h00 Room: Grace Hopper In this talk, I will describe some set-based methods (i.e. «guaranteed» numerical methods) that we developed for helping analyze and validate dynamical (and control) systems. I will go through a number of problems, ranging from plain reachability, reach-avoid, robust reachability to invariance and general temporal specifications. The robust reachability and general temporal specifications will introduce the problem of solving some form of quantifier elimination, for which we will give a simple set-based method for inner and outer-approximating the set of solutions. Based on joint works with Sylvie Putot. 2023, April 17 Jacques Laskar (IMCCE) Calcul formel et diffusion chaotique des mouvements planétaires dans le système solaire Time: from 11h00 to 12h00 Room: Henri Poincaré La mise en évidence du mouvement chaotique des planètes dans le système solaire a été obtenu grâce à une intégration des équation modernisées de leur mouvement (Laskar, 1989). Ce système d'équations contenant plus de 150 000 termes avait été obtenu par des méthodes de calcul formel très dédiées, dont l'adaptation n'était pas aisée. depuis 1988 a commencé la construction d'un système de calcul formel général, TRIP, spécialement adapté aux calculs de la mécanique céleste. Nous avons utilisé ce système récemment pour obtenir une meilleure compréhension de l'origine du chaos dans le système solaire, et pour étudier la diffusion chaotique du mouvement des planètes sur des durées bien supérieures à l'âge de l'univers. 2023, March 27 Alexander Demin (HSE University) Finding exact linear reductions of dynamical models Time: from 11h00 to 12h00 Room: Grace Hopper Dynamical models described by systems of polynomial differential equations are a fundamental tool in the sciences and engineering. Exact model reduction aims at finding a set of combinations of the original variables which themselves satisfy a self-contained system. There exist algorithmic solutions which are able to rapidly find linear reductions of the lowest dimension under certain additional constraints on the input or output. In this talk, I will present a general algorithm for finding exact linear reductions. The algorithm finds a maximal chain of reductions by reducing the question to a search for invariant subspaces of matrix algebras. I will describe our implementation and show how it can be applied to models from literature to find reductions which would be missed by the earlier approaches. This is a joint work with Elizaveta Demitraki and Gleb Pogudin. 2023, March 20 Sebastian Falkensteiner (Max Planck Institute for Mathematics in the Sciences) Using Algebraic Geometry for Solving Differential Equations Time: from 11h00 to 12h00 Room: Henri Poincaré Given a ﬁrst order autonomous algebraic ordinary diﬀerential equation, i.e. an equation of the form Jose Cano, Rafael Sendra and Daniel Robertz. 2023, February 20 Thi Xuan Vu (Arctic University of Norway) Faster algorithms for symmetric polynomial systems Time: from 11h00 to 12h00 Room: Philippe Flajolet Many important polynomial systems have additional structure, for example, generating polynomials invariant under the action of the symmetric group. In this talk we consider two problems for such systems. The first focuses on computing the critical points of a polynomial map restricted to an algebraic variety, a problem which appears in many application areas including polynomial optimization. Our second problem is to decide the emptiness of algebraic varieties over real fields, a starting point for many computations in real algebraic geometry. In both cases we provide efficient probabilistic algorithms for which take advantage of the special invariant structure. In particular in both instances our algorithms obtain their efficiency by reducing the computations to ones over the group orbits and make use of tools such as weighted polynomial domains and symbolic homotopy methods. 2022, December 12 Joris van der Hoeven (LIX) Session dedicated to the Computer Mathematics research group Sparse interpolation Time: from 11h00 to 12h00 Room: Grace Hopper Computer algebra deals with exact computations with mathematical formulas. Often, these formulas are very large and often they can be rewritten as polynomials or rational functions in well chosen variables. Direct computations with such expressions can be very expensive and may lead to a further explosion of the size of intermediate expressions. Another approach is to systematically work with evaluations. For a given problem, like inverting a matrix with polynomial coefficients, evaluations of the solution might be relatively cheap to compute. Sparse interpolation is a device that can then be used to recover the result in symbolic form from sufficiently many evaluations. In our talk, we will survey a few classical and a new approach for sparse interpolation, while mentioning a few links with other subjects. 2022, December 5 Marc Moreno Maza (University of Western Ontario) Cache complexity in computer algebra Time: from 11h00 to 12h00 Room: Grace Hopper In the computer algebra literature, optimizing memory usage (e.g. minimizing cache misses) is often considered only at the software implementation stage and not at the algorithm design stage, which can result in missed opportunities, say, with respect to portability or scalability. In this talk, we will discuss ideas for taking cache complexity, in combination with other complexity measures, at the algorithm design stage. We will start by a review of different memory models (I/ O Complexity, cache complexity, etc.). We will then go through illustrative examples considering both multi-core and many-core architectures. 2022, November 14 Cyril Banderier (CNRS/Université Sorbonne Paris Nord) Analytic combinatorics and partial differential equations Time: from 11h00 to 12h00 Room: Grace Hopper Many combinatorial structures and probabilistic processes lead to generating functions satisfying partial differential equations, and, in some cases, they even satisfy ordinary differential equations (they are D-finite). In my talk, I will present results from these last 3 years illustrating this principle, and asymptotic consequences of this, on fundamental objects like Pólya urns, Young tableaux with walls, increasing trees, posets… I will also prove that some cases are differentially algebraic (not D-finite), and possess surprising stretched exponential asymptotics involving exponents which are zeroes of the Airy function. The techniques are essentially extensions of the methods of analytic combinatorics (generating functions and complex analysis), as presented in the eponymous wonderful book of Flajolet and Sedgewick. En passant, I will also present a new algorithm for uniform random generation (the density method), and new universal distributions, establishing the asymptotic fluctuations of the surface of triangular Young tableaux. This talk is based on joint work with Philippe Marchal and Michael Wallner: Periodic Pólya urns, the density method, and asymptotics of Young tableaux, Annals of Probability, 2020. Young tableaux with periodic walls: counting with the density method, FPSAC, 2021. 2022, November 7 Louis Roussel (Université de Lille) Integral Equation Modelling and Deep Learning Time: from 11h00 to 12h00 Room: Gilles Kahn Considering models with integro-differential equations is motivated by the following reason: on some examples, the introduction of integral equations increases the expressiveness of the models, improves the estimation of parameter values from error-prone measurements, and reduces the size of the intermediate equations. Reducing the order of derivation of a differential equation can sometimes be achieved by integrating it. An algorithm was designed by the CFHP team for that purpose. However, successfully integrating integro-differential equations is a complex problem. Unfortunately, there are still plenty of differential equations for which the algorithm does not apply. For example, computing an integrating factor might be required. Rather than integrating the differential equation, we can perform an integral elimination. We are currently working on this technique which also implies some integration problems. To try to overcome these problems, we are also using deep learning techniques with the hope of finding small calculus tips. 2022, June 28 Antonio Jiménez-Pastor (LIX) Exact nonlinear reductions of dynamical systems Time: from 11h00 to 12h00 Room: Grace Hopper Dynamical systems of the form 2022, May 24 Marc Mezzarobba (LIX) Session dedicated to the Computer Mathematics research group Asymptotic Expansions with Error Bounds for Solutions of Linear Recurrences Time: from 11h00 to 12h00 Room: Grace Hopper When a sequence up to any desired order Based on joint work with Ruiwen Dong and Stephen Melczer. 2022, May 10 François Ollivier (LIX) Generalized flatness and motion planning for aircraft models Time: from 11h00 to 12h00 Room: Grace Hopper If one neglects the forces created by controls, an aircraft is modeled by a flat system. First, one uses a feedback to compensate model errors and keep the trajectory of the full non flat system close to the trajectory computed for the flat approximation. In a second time, the values of the controls provided by the flat approximation are used in the full model for better precision and the process is iterated, which provides a very precise motion planning for the full model. Some examples are provided to illustrate the possibilities of a Maple package. This new approach is called generalized flatness. The provided parametrization depends on an infinite number of flat outputs, which comforts a conjecture claiming that all controllable systems are flat if one allows parametrization depending on an infinite number of derivatives. On should notice that the necessary flatness conditions of Sluis and Rouchon express the fact that the order of the parametrization is finite. In the linear case, one may provide some theoretical interpretation. 2022, April 19 Ilaria Zappatore (INRIA Saclay) Simultaneous Rational Function Reconstruction with Errors: Handling Poles and Multiplicities. Time: from 11h00 to 12h00 Room: Grace Hopper In this talk I focus on an evaluation-interpolation technique for reconstructing a vector of rational functions (with the same denominator), in presence of erroneous evaluations. This problem is also called Simultaneous Rational Function Reconstruction with errors (SRFRwE) and it has significant applications in computer algebra (e.g.for the parallel resolution of polynomial linear systems) and in algebraic coding theory (e.g. for the decoding of the interleaved version of the Reed-Solomon codes). Indeed, an accurate analysis of this problem leads to interesting results in both these scientific domains. Starting from the SRFRwE, we then introduce its multi-precision generalization, in which we include evaluations with certain precisions. Our goal is to reconstruct a vector of rational functions, given, among other information, a certain number of evaluation points. Thus, these evaluation points may be poles of the vector that we want to recover. Our multi-precision generalization also allows us to handle poles with their respective orders. The main goal of this work is to determine a condition on the instance of this SRFRwE problem (and its generalized version) which guarantee the uniqueness of the interpolating vector. This condition is crucial for the applications: in computer algebra it affects the complexity of the corresponding SRFRwE resolution algorithm, while in coding theory, it affects the number of errors that can be corrected. We determine a condition which allows us to correct any errors. Then we exploit and revisit results related to the decoding of interleaved Reed-Solomon codes in order to introduce a better condition for correcting random errors. 2021, December 14 Rim Rammal (Université Toulouse III - Paul Sabatier) Differential flatness for fractional order dynamic systems Time: from 11h00 to 12h00 Room: Henri Poincaré Differential flatness is a property of dynamic systems that allows the expression of all the variables of the system by a set of differentially independent functions, called flat output, depending on the variables of the system and their derivatives. The differential flatness property has many applications in automatic control theory, such as trajectory planning and trajectory tracking. This property was first introduced for the class of integer order systems and then extended to the class of fractional order systems. This talk will present the flatness of the fractional order linear systems and more specifically the methods for computing fractional flat outputs. 2021, December 7 Mohab Saefey El Din (Sorbonne Université) msolve : a library for solving multivariate polynomial systems Time: from 11h00 to 12h00 Room: Grace Hopper In this talk, we present a new open source library, developed with J. Berthomieu (Sorbonne Univ.) and C. Eder (TU Kaiserslautern) named msolve, for solving multivariate polynomial systems through computer algebra methods. Its core algorithmic framework relies on Gröbner bases and linear algebra based algorithms. This includes J.-C. Faugère's F4 algorithm, recent variants of the FGLM change of ordering and real root isolation. This talk will cover a short presentation of the current functionalities provided by msolve, followed by an overview of the implemented algorithms which will motivate the design choices underlying the library. We will also compare the practical performances of msolve with leading computer algebra systems such as Magma, Maple, Singular, showing that msolve can tackle systems which were out of reach by the computer algebra software state-of-the-art. If time permits, we will report on new algorithmic developments for ideal theoretic operations (joint work with J. Berthomieu and C. Eder) and change of orderings algorithms (joint work with J. Berthomieu and V. Neiger). 2021, October 19 Mirco Tribastone (IMT Lucca) Reconciling discrete and continuous modeling for the analysis of large-scale Markov chains Time: from 11h00 to 12h00 Room: Grace Hopper Markov chains are a fundamental tool for stochastic modeling across a wide range of disciplines. Unfortunately, their exact analysis is often hindered in practice due to the massive size of the state space - an infamous problem plaguing many models based on a discrete state representation. When the system under study can be conveniently described as a population process, approximations based on mean-field theory have proved remarkably effective. However, since such approximations essentially disregard the effect of noise, they may potentially lead to inaccurate estimations under conditions such as bursty behavior, separation of populations into low- and high-abundance classes, and multi-stability. This talk will present a new analytical method that combines an accurate discrete representation of a subset of the state space with mean-field equations to improve accuracy at a user-tunable computational cost. Challenging examples drawn from queuing theory and systems biology will show how the method significantly outperforms state-of-the-art approximation methods. This is joint work with Luca Bortolussi, Francesca Randone, Andrea Vandin, and Tabea Waizmann. 2021, October 5 Rida Ait El Manssour (Max Planck Institute for Mathematics in the Sciences, Leipzig) Linear PDE with constant coefficients Time: from 11h00 to 12h00 Room: Henri Poincaré I will present a work about practical methods for computing the space of solutions to a system of linear PDE with constant coefficients. These methods are based on the Fundamental Principle of Ehrenpreis–Palamodov from the 1960s which assert that every solution can be written as finite sum of integrals over some algebraic varieties. I will first present the main historical results and then recent algorithm for computing the space of solutions. This is a joint work with Marc Harkonen and Bernd Sturmfels. 2021, September 28 Antonio Jiménez-Pastor (MAX team, École polytechnique) DD-finite functions: a computable extension for holonomic functions Time: from 11h00 to 12h00 Room: Grace Hopper D-finite or holonomic functions are solutions to linear differential equations with polynomial coefficients. It is this property that allow us to exactly represent these functions on the computer. in this talk we present a natural extension of this class of functions: the DD-finite functions. These functions are the solutions of linear differential equations with D-finite coefficients. We will see the properties these functions have and how we can algorithmically compute with them. 2021, June 7 Thierry Combot (University of Burgundy) Réduction des intégrales premières des champs de vecteurs du plan Time: from 14h00 to 15h00 Online broadcast Les intégrales premières symboliques d'un champ de vecteur rationnel du plan sont de 4 types: rationnelles, darbouxiennes, liouvilliennes et de Riccati. Il est possible de les rechercher jusqu'à un certain degré, mais en trouver une ne signifie pas qu'il n'en existe pas d'autres plus simples mais de degré plus élevé. Le problème de Poincaré consiste à trouver les intégrales premières rationnelles d'un tel champ de vecteur. Nous y ajouterons l'hypothèse qu'une intégrale première symbolique est donnée d'avance, et il nous “suffira” ainsi de savoir si l'on peut la simplifier. Nous présenterons des algorithmes de simplification d'intégrales premières pour le cas Ricatti et liouvilien, et nous verrons, qu'à l'exception d'un cas particulier, cela est aussi possible pour le cas darbouxien. Nous détaillerons un exemple résistant et ses liens avec les courbes elliptiques. 2021, May 10 François Boulier (Université de Lille) Algèbre différentielle et géométrie différentielle tropicale Time: from 14h00 to 15h00 Online broadcast Dans cet exposé, je ferai un lien entre l'algèbre différentielle de Ritt et Kolchin et la géométrie différentielle tropicale initiée par Grigoriev, sur la question de l'existence de solutions en séries entières formelles. Sur la fin de l'exposé, je m'attarderai sur un théorème d'approximation qui constitue la partie difficile du théorème fondamental de la géométrie différentielle tropicale. 2021, April 12 Evelyne Hubert (INRIA Méditerranée) Sparse Interpolation in terms of multivariate Chebyshev polynomials Time: from 15h00 to 16h00 Online broadcast: https://greenlight.lal.cloud.math.cnrs.fr/b/oll-ehe-mn3 Sparse interpolation refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now the basis of exponential functions. Beyond the multivariate Chebyshev polynomial obtained as tensor products of univariate Chebyshev polynomials, the theory of root systems allows to define a variety of generalized multivariate Chebyshev polynomials that have connections to topics such as Fourier analysis and representations of Lie algebras. We present a deterministic algorithm to recover a function that is the linear combination of at most r such polynomials from the knowledge of r and an explicitly bounded number of evaluations of this function. This is a joint work with Michael Singer (https://hal.inria.fr/hal-02454589v1). Video of a talk on the same topic. 2021, March 29 Viktor Levandovskyy (University of Kassel) Gröbner technology over free associative algebras over rings: semi-decidability, implementation and applications Time: from 14h00 to 15h00 Online broadcast: https://webconf.math.cnrs.fr/b/pog-m6h-mec Computations with finitely presented associative algebras traditionally boil down to computations over free associative algebras. In particular, there is a notion of Gröbner(–Shirshov) basis, but generally its computation does not terminate, and thus the ideal membership problem is not solvable. However, many important special cases can be approached. The Letterplace correspondence for free algebras, introduced by La Scala and Levandovskyy, allows to reformulate the Gröbner theory and to use highly tuned commutative data structures in the implementation and to reuse parts of existing algorithms in the free non-commutative situation. We report on the newest official release of the subsystem of Singular called Letterplace. With it, we offer an unprecedented functionality, some of which for the first time in the history of computer algebra. In particular, we present practical tools for elimination theory (via truncated Gröbner bases and via supporting several kinds of elimination orderings), dimension theory (Gel'fand-Kirillov and global homological dimension), and for further homological algebra (such as syzygy bimodules and lifts for ideals and bimodules) to name a few. Another activity resulted in the extension of non-commutative Gröbner bases for supporting the coefficients in principal ideal rings including 2021, March 22 Huu Phuoc Le (Sorbonne Université) Fast algorithm and sharp degree bounds for one block quantifier elimination over the reals Time: from 14h00 to 15h00 Online broadcast Quantifier elimination over the reals is one of the most important algorithmic problem in effective real algebraic geometry. It finds applications in several areas of computing and engineering sciences such as program verification, computational geometry, robotics and biology to cite a few. Geometrically, eliminating one block of quantifiers consists in computing a semi-algebraic formula which defines the projection of the set defined by the input polynomial constraints on the remaining set of variables (which we call parameters). In this work, we design a fast algorithm computing a semi-algebraic formula defining a dense subset in the interior of that projection when the input is composed of a polynomial system of equations. Using the theory of Groebner bases, we prove that, on generic inputs, its complexity is This is joint work with Mohab Safey El Din. 2021, March 8 Mickaël Matusinski (Université de Bordeaux) Surreal numbers with exponential and omega-exponentiation Time: from 13h00 to 14h00 Online broadcast Surreal numbers have been introduced by Conway while working on game theory: they allow to evaluate partial combinatorial games of any size! This is so because they consist in a proper class containing “all numbers great and small”, but also due to the richness of the structure we can endow them with: an ordered real closed field. Moreover, surreal numbers can be seen as formal power series with exp, log and derivation. This turns them into an important object also in model theory (universal domain for many theories) and real analytic geometry (formal counterpart for non oscillating germs of real functions). In this talk, I will introduce these fascinating objects, starting with the very basic definitions, and will give a quick overview, with a particular emphasis on exp (which extends exp on the real numbers) and the omega map (which extends the omega-exponentiation for ordinals). This will help me to subsequently present our recent contributions with A. Berarducci, S. Kuhlmann and V. Mantova concerning the notion of omega-fields (possibly with exp). One of our motivations is to clarify the link between composition and derivation for surreal numbers. 2021, February 22 Yairon Cid-Ruiz (Ghent University) Primary ideals and differential operators Time: from 14h00 to 15h00 Online broadcast The main objective will be to describe primary ideals with the use of differential operators. These descriptions involve the study of several objects of different nature, so to say; the list includes: differential operators, differential equations with constant coefficients, Macaulay's inverse systems, symbolic powers, Hilbert schemes, and the join construction. As an interesting consequence, we will introduce a new notion of differential powers which coincides with symbolic powers in many interesting non-smooth settings, and so it could serve as a generalization of the Zariski-Nagata Theorem. I will report on some joint work with Roser Homs and Bernd Sturmfels. 2020, December 1 Thi Xuan Vu (Sorbonne Université, Univeristy of Waterloo) Algebraic geometry codes from surfaces over finite fields Time: from 15h00 to 16h00 Online broadcast We investigate the structures of resp. columns) of This is joint work with J.-C. Faugère, J. D. Hauenstein, G. Labahn, M. Safey El Din and É. Schost. 2020, November 24 Michela Ceria (Univeristy of Milan) Degroebnerization and error correcting codes: Half Error Locator Polynomial Time: from 15h00 to 16h00 Online broadcast The concept of “Degroebnerization” has been introduced by Mora within his books on the bases of previous results by Mourrain, Lundqvist, Rouiller. Since the computation of Gröbner bases is inefficient and sometimes unfeasible, the Degroebnerization proposes to limit their use to the cases in which it is really necessary, finding other tools to solve problems that are classically solved by means of Gröbner bases. We propose an example of such problems, dealing with efficient decoding of binary cyclic codes by means of the locator polynomial. Such a polynomial has variables corresponding to the syndromes, as well as variables each corresponding to each error location. Decoding consists then in evaluating the polynomial at the syndromes and finding the roots in the corresponding variable. It is necessary to look for a sparse polynomial, so that the evaluation is not too inefficient. In this talk we show a preliminary result in this framework; a polynomial of this kind can be found—for error correction capability 2020, October 27 Elena Berardini Algebraic geometry codes from surfaces over finite fields Time: from 14h00 to 15h00, Room: Grace Hopper Online broadcast: https://webconf.math.cnrs.fr/b/pog-4rz-uec Algebraic geometry codes were introduced by Goppa in 1981 on curves defined over finite fields and were extensively studied since then. Even though Goppa construction holds on varieties of dimension higher than one, the literature is less abundant in this context. However, some work has been undertaken in this direction, especially on codes from surfaces. The goal of this talk is to provide a theoretical study of algebraic geometry codes constructed from surfaces defined over finite fields, using tools from intersection theory. First, we give lower bounds for the minimum distance of these codes in two wide families of surfaces: those with strictly-nef or anti-nef canonical divisor, and those which do not contain absolutely irreducible curves of small genus. Secondly, we specialize and improve these bounds for particular families of surfaces, for instance in the case of abelian surfaces and minimal fibrations, using the geometry of these surfaces. The results appear in two joint works with Y. Aubry, F. Herbaut and M. Perret, preprints: https://arxiv.org/pdf/1904.08227.pdf and https://arxiv.org/abs/1912.07450. 2020, October 13 Ruiwen Dong A new algorithm for finding the input-output equations of differential models (Joint work with Christian Goodbreak, Heather Harrington, and Gleb Pogudin) Time: from 14h00 to 15h00, Room: Gilles Kahn The input-output equations of a differential model are consequences of the differential model which are also “minimal” equations depending only on the input, output, and parameter variables. One of their most important applications is the assessment of structural identifiability. In this talk, we present a new resultant-based method to compute the input-output equations of a differential model with a single output. Our implementation showed favorable performance on several models that are out of reach for the state-of-the-art software. We will talk about ideas and optimizations used in our method as well as possible ways to generalize them. 2020, July 7 Simon Abelard Computing Riemann–Roch spaces in subquadatric time (Joint work with A. Couvreur and G. Lecerf) Time: from 14h00 to 15h00, Room: teleconference Given a divisor Since the 1980's, many algorithms were designed to compute Riemann–Roch paces, incorporating more and more efficient primitives from computer algebra. The state-of-the-art approach ultimately reduces the problem to linear algebra on matrices of size comparable to the input. In this talk, we will see how one can replace linear algebra by structured linear algebra on polynomial matrices of smaller size. Using a complexity bound due to Neiger, we design the first subquadratic algorithm for computing Riemann–Roch spaces. 2020, June 23 Gleb Pogudin Exact model reduction by constrained linear lumping (Joint work with A. Ovchinnikov, I.C. Perez Verona, and M. Tribastone) Time: from 14h00 to 15h00, Room: teleconference We solve the following problem: given a system of ODEs with polynomial right-hand side, find the maximal exact model order reduction by a linear transformation that preserves the dynamics of user-specified linear combinations of the original variables. Such transformation can reduce the dimension of a model dramatically and lead to new insights about the model. We will present an algorithm for solving the problem and applications of the algorithm to examples from literature. Then I will describe directions for further research and their connections with the structure theory of finite-dimensional algebras. 2020, June 9 Vincent Bagayoko Asymptotic differential algebra Time: from 14h00 to 15h00, Room: teleconference I will describe a research program put forward by Joris van der Hoeven and his frequent co-authors Lou van den Dries and Matthias Aschenbrenner, in the framework of asymptotic differential algebra. This program sets out to use formal tools (log-exp transseries) and number theoretic / set-theoretic tools (surreal numbers) to select and study properties of “monotonically regular” real-valued 2020, May 26 Simon Aberlard Counting points on hyperelliptic curves defined over finite fields of large characteristic: algorithms and complexity Time: from 14h00 to 15h00, Room: teleconference Counting points on algebraic curves has drawn a lot of attention due to its many applications from number theory and arithmetic geometry to cryptography and coding theory. In this talk, we focus on counting points on hyperelliptic curves over finite fields of large characteristic Our contributions mainly consist of establishing new complexity bounds with a smaller dependency in In genus 3, we proposed an algorithm based on those of Schoof and Gaudry–Harley–Schost whose complexity is prohibitive in general, but turns out to be reasonable when the input curves have explicit RM. In this more favorable case, we were able to count points on a hyperelliptic curve defined over a 64-bit prime field. In this talk, we will carefully reduce the problem of counting points to that of solving polynomial systems. More precisely, we will see how our results are obtained by considering either smaller or structured systems and choosing a convenient method to solve them. 2020, May 12 François Ollivier Shortest paths… from Königsberg to the tropics Time: from 14h00 to 15h00, Room: teleconference Trying to avoid technicalities, we underline the contribution of Jacobi to graph theory and shortest paths problems. His starting point is the computation of a maximal transversal sum in a square The key ingredient of Jacobi's algorithm for computing the tropical determinant is to build paths between some rows of the matrix, until all rows are connected, which allows to compute a canon, that is a matrix where one can find maximal terms in their columns, located in all different rows, by adding the same constant to all the terms of the same row. Jacobi gave two algorithms to compute the minimal canon, the first when one already knows a canon, the second when one knows the terms of a maximal transversal sum. They both correspond to well known algorithms for computing shortest paths, the Dijkstra algorithm, for positive weights on the edges of the graph, and the Bellman–Ford algorithm, when some weights can be negative. After a short tour with Euler over the bridges of Königsberg, a reverence to Kőnig's, Egerváry's and Kuhn's contributions, we will conclude with the computation of a differential resolvent. 2020, April 28 Marc Mezzarobba Interval Summation of Differentially Finite Series Time: from 14h00 to 15h00, Room: teleconference I will discuss the computation of rigorous enclosures of sums of power series solutions of linear differential equations with polynomial coefficients ("differentially finite series"). The coefficients of these series satisfy simple recurrences, leading to a simple and fast iterative algorithm for computing the partial sums. When however the initial values (and possibly the evaluation point and the coefficients of the equation) are given by intervals, naively running this algorithm in interval arithmetic leads to an overestimation that grows exponentially with the number of terms. I will present a simple (but seemingly new!) variant of the algorithm that avoids interval blow-up. I will also briefly talk about other aspects of the evaluation of sums of differentially finite series and a few applications. 2020, April 7 Gleb Pogudin Identifiability from multiple experiments (Joint work with A. Ovchinnikov, A. Pillay, and T. Scanlon) Time: from 14h00 to 15h00, Room: teleconference For a system of parametric ODEs, the identifiability problem is to find which functions of the parameters can be recovered from the input-output data of a solution assuming continuous noise-free If one allows to use several generic solutions for the same set of parameter values, it is natural to expect that more functions become identifiable. Natural questions in this case are: which function become identifiable given that enough experiments are performed and how many experiments would be enough? In this talk, I will describe recent results on these two questions. 2020, March 10 François Ollivier Computing linearizing outputs of a flat system (Joint work with Jean Lévine (Mines de Paris) and Jeremy Kaminski (Holon Institute of Technology)) Time: from 14h to 15h, Room: Flajolet A flat system is a differential system of positive differential dimension, that is a system with controls for the control theorist, such that its general solution can be parametrized on some dense open set, using We present available methods to compute linearizing outputs of a flat system, with a special interest to apparent singularities: how to design, assuming it exists, regular alternative flat outputs. We will consider, as examples, classical models of quadcopters and planes. 2019, November, 18 Luis Miguel Pardo Une preuve élémentaire de l'inégalité de Bézout de Heintz Time: from 14h to 16h, Room: Grace Hopper À l'occasion de la rédaction d'un texte sur l'algorithme « Kronecker » accessible à une large audience, nous avons été amenés à écrire une preuve complète de l'inégalité de Bézout de Heintz pour les variétés algébriques avec des arguments mathématiques disons élémentaires. Dans le même temps nous fournissons une extension de cette inégalité pour les ensembles constructibles, ainsi que quelques applications nouvelles à certains problèmes algorithmiques. Cet exposé présentera les grandes lignes de ces preuves élémentaires. Les applications, vers la fin de l'exposé, seront liées a quelques idées nouvelles autour des ensembles questeurs ("correct test sequences") pour les systèmes d'équations polynomiales. 2019, June, 24 Raphaël Rieu-Helft How to get an efficient yet verified arbitrary-precision integer library (Joint work with Guillaume Melquiond, joint seminar with GRACE team) Time: 14h, Room: Grace Hopper We present a fully verified arbitrary-precision integer arithmetic library designed using the Why3 program verifier. It is intended as a verified replacement for the mpn layer of the state-of-the-art GNU Multi-Precision library (GMP). The formal verification is done using a mix of automated provers and user-provided proof annotations. We have verified the GMP algorithms for addition, subtraction, multiplication (schoolbook and Toom-2/2.5), schoolbook division, and divide-and-conquer square root. The rest of the mpn API is work in progress. The main challenge is to preserve and verify all the GMP algorithmic tricks in order to get good performance. Our algorithms are implemented as WhyML functions. We use a dedicated memory model to write them in an imperative style very close to the C language. Such functions can then be extracted straightforwardly to efficient C code. For medium-sized integers (less than 1000 bits, or 100,000 for multiplication), the resulting library is performance-competitive with the generic, pure-C configuration of GMP. 2019, June, 3 Yirmeyahu Kaminiski On singularities of flat affine systems with (Joint work with Jean Lévine and François Ollivier) Time: 11h, Room: Grace Hopper We study the set of intrinsic singularities of flat affine systems with 2019, May, 27 Time: 10h00–12h30, Room: Gilles Kahn Joint seminar with the Cosynus team of LIX. • Éric Goubault (École polytechnique, LIX): Finding Positive Invariants of Polynomial Dynamical Systems – some experiments. Synthetising positive invariants of non-linear ODEs, switched systems or even hybrid systems is a hard problem that has many applications, from control to verification. In this talk, I will present two « exercices de style » for dealing with it, revisiting the classical Lyapunov function approach. The first one is based on algebraic properties of polynomial differential systems (Darboux polynomials, when they exist), for finding polynomial, rational or even some log extensions to rational functions whose level sets or sub-level sets describe positive invariants of these systems, or provide interesting « change of bases » for describing their solutions. The second one is based on topological properties (Wazewski property, mostly) which ensure the existence, in some region of the state space, of a non-empty maximal invariant set. The interest is that there is then in general no need to find complicated functions for precisely describing the invariant set itself, instead we rather use simple template shapes in which a possibly very complicated invariant set lies. The topological criterion can be ensured by suitable SoS relaxations, for polynomial differential systems, that can be implemented using LMI solvers. • François Ollivier (CNRS, LIX): Quelques aspects des méthodes algébriques pour le contrôle et la modélisation. Des notions de base en automatique, comme la contrôlabilité ou l'observabilité sont de nature intrinsèquement algébrique et peuvent être testées par le calcul symbolique. L'algèbre différentielle offre un cadre théorique utile qui permet de ramener de nombreux problèmes à des inclusions de corps différentiels, susceptibles d'être testées par des calculs d'ensembles caractéristiques pour des ordres éliminant certaines variables. C'est le cas de l'identifiabilité. La platitude est une notion plus complexe, efficace pour la planification de trajectoire, mais pour laquelle on ne dispose que de critères spécifiques à des cas particuliers. L'élimination différentielle se heurte au problème de la complexité des calculs, avec une croissance exponentielle du nombre de monômes avec le degré. Ceci motive la recherche de méthodes permettant de borner a priori l'ordre des calculs utiles, pour lesquelles la borne de Ritt, et celle plus fine de Jacobi, joue un rôle comparable à la borne de Bézout pour l'élimination La borne de Jacobi, conjecturale dans le cas général, peut être prouvée dans le cas quasi régulier. La méthode consiste à se ramener au cas linéaire en considérant le système linéarisé tangent. Celui-ci peut aussi être intégré pour obtenir, numériquement ou formellement, la dépendance des solutions d'un système par rapport à ses paramètres ou ses conditions initiales. • Goran Frehse (ENSTA ParisTech, U2IS): Reachability of Hybrid Systems in High Dimensions. Hybrid systems describe the evolution of a set of real-valued variables over time with ordinary differential equations and event-triggered resets. Numerical methods are widely used to compute trajectories of such systems, which are then used to test them and refine their design. Set-based reachability analysis is a natural extension of this technique form numbers to sets. It is a useful method to formally verify safety and bounded liveness properties of such systems. Starting from a given set of initial states, the successor states are computed iteratively until the entire reachable state space is exhausted. While reachability is undecidable in general and even one-step successor computations are hard to compute, recent progress in approximative set computations allows one to fine-tune the trade-off between computational cost and accuracy. In this talk we present some of the techniques with which systems with complex dynamics and hundreds of variables have been successfully verified. • Joris van der Hoeven (CNRS, LIX): Résolution certifiée d'équations différentielles. Il existe différentes approches pour l'intégration numérique certifiée d'équations différentielles comme les modèles de Taylor et des adaptations de méthodes de Runge–Kutta. Dans notre exposé, nous comparerons les avantages et inconvénients de ces méthodes du point de vue de la complexité pratique et asymptotique. 2019, May, 13 Gleb Pogudin Global identifiability of differential models Time: 10h30, Room: Grace Hopper Many important real-world processes are modeled using systems of ordinary differential equations (ODEs) involving unknown parameters. The values of these parameters are usually inferred from experimental data. However, due to the structure of the model, there might be multiple parameter values that yield the same observed behavior even in the case of continuous noise-free data. It is important to detect such situations a priori, before collecting actual data. In this case, the only input is the model itself, so it is natural to tackle this question by methods of symbolic In this talk, I will present our new theoretical results on this problem and new reliable algorithms based on these results that can tackle problems that could not be tackled before, and software SIAN implementing the algorithms. This is a joint work with H. Hong, A. Ovchinnikov, and C. Yap. 2019, March, 6 Anand Kumar Narayanan Fast computation of isomorphisms between finite fields using elliptic curves Time: 14h, Room: Grace Hopper Every finite field has prime power cardinality, for every prime power there is a finite field of that cardinality and every two finite fields of the same cardinality are isomorphic. This well known fact poses an algorithmic problem: compute an isomorphism between two explicitly presented finite fields of the same cardinality. We present a randomized algorithm to compute isomorphisms between finite fields using elliptic curves. Prior to this work, the best known run time dependence on the extension degree was quadratic. Our run time dependence is at worst quadratic but is subquadratic if the extension degree has no large prime factor. In particular, the extension degree for which our run time is nearly linear have natural density at least 3/10. The crux of our approach is finding a point on an elliptic curve of a prescribed prime power order or equivalently finding preimages under the Lang map on elliptic curves over finite fields. We formulate this as an open problem whose resolution would solve the finite field isomorphism problem with run time nearly linear in the extension degree. Talk based on: Narayanan A. K. Fast Computation of isomorphisms between finite fields using elliptic curves. In: Budaghyan L., Rodríguez-Henríquez F. (eds.). Arithmetic of Finite Fields. WAIFI 2018. Lecture Notes in Computer Science, vol 11321. Springer, Cham, 2018. 2019, February, 21 Yacine Bouzidi Some contributions to the intersection problem with polydisks Time: 10h30, Room: Marcel-Paul Schützenberger An important class of systems in control theory is the class of multidimensional systems in which information propagates in more than one independent direction. At the core of the study of such systems is the effective computation over the ring of rational fractions which have no poles in the closed unit polydisk In [1], M. Strintzis states a fundamtental theorem showing that the first question can be simplified in the case of principal ideals. Namely, the theorem shows that the existence of complex zeros of a polynomial polydisk nullstelensatz is still open for general systems. In this presentation, we extend the fundamental result of Strintzis to some specific algebraic varieties, namely varieties of dimension one in polydisk nullstellensatz in the case of zero-dimensional ideals. As a consequence, important questions about the stabilization of multidimensional systems can be answered using simple algorithms based on computer algebra techniques. [1] Strintzis, M. Tests of stability of multidimensional filters. IEEE Transactions on Circuits and Systems, 24(8):432–437, 1977. 2019, February, 19 Cyrille Chenavier Opérateurs de réduction : complétion, syzygies et dualité de Koszul Time: 10h30, Room: Marcel-Paul Schützenberger La réécriture est une théorie combinatoire des relations d'équivalences où les propriétés de celles-ci sont déduites de leurs orientations. Une de ces propriétés est la confluence qui garantie la cohérence des calculs. Dans cet exposé, je présente une description des systèmes de réécriture à travers leurs représentations par des opérateurs de réduction. Cela permet d'obtenir des formulations de la confluence et de la procédure de complétion en termes de treillis. Je présente également des applications de cette approche au calcul des syzygies des systèmes de réécriture linéaires et à la dualité de Koszul. De celle-ci est issue la construction du complexe de Koszul, qui, lorsqu'il est acyclique, est une résolution minimale d'algèbres. Un critère introduit par Roland Berger garantie que le complexe de Koszul est une telle résolution minimale. En exploitant la structure de treillis des opérateurs de réduction, je propose via une homotopie contractante une preuve constructive de ce critère. 2019, February, 18 Thibaut Verron Calcul de bases de Gröbner avec signatures à coefficients dans un anneau principal (Joint work with Maria Francis) Time: 10h30, Room: Grace Hopper Les algorithmes à signatures sont devenus une approche classique pour le calcul de bases de Gröbner pour des polynômes à coefficients dans un corps, et l'extension de cette technique à des polynômes à coefficients dans des anneaux a fait l'objet de travaux récents. Dans ce travail, nous nous intéressons à deux algorithmes dûs à Möller (1988). Le premier de ces algorithmes permet de calculer des bases de Gröbner dites faibles, pourvu que l'anneau de coefficients soit noethérien et effectif. Nous montrons que, dans le cas où l'anneau des coefficients est principal, cet algorithme peut être adapté pour calculer des bases de Gröbner avec signatures. En particulier, l'algorithme garantit l'absence de chutes de signatures, ce qui permet d'adapter les critères de signatures classiques comme le critère singulier ou le critère F5. Le second de ces algorithmes de Möller est quant à lui spécifique au cas des anneaux principaux, et permet de calculer une base de Gröbner forte de manière plus efficace que l'algorithme général. Nous montrons que cet algorithme peut également être adapté pour prendre en compte les signatures, et éviter un grand nombre de calculs redondants ou inutiles. L'algorithme dédié aux anneaux principaux, contrairement à l'algorithme général, est également compatible avec les critères de Buchberger, notamment le critère de chaîne, et nous montrons que ce critère peut être ajouté de manière compatible avec les signatures. Nous présentons enfin des résultats expérimentaux en termes de nombres de S-polynômes calculés, réduits ou écartés par les différents critères, mesurés sur une implantation « jouet » des algorithmes en Magma. 2018, December, 10 Pierre-Vincent Koseleff Computing Chebyshev knot diagrams (Joint work with D. Pecker, F. Rouillier, and C. Tran) Time: 10h30, Room: Grace Hopper Avec D. Pecker, nous avons montré que tout nœud de i.e. admet une représentation polynomiale de la forme F. Rouillier et C. Tran, nous avons proposé un algorithme pour identifier les nœuds de Chebyshev à 2 ponts (cas See: https://hal.archives-ouvertes.fr/hal-01232181 2018, February, 12 Yirmeyahu Kaminski Intrinsic and Apparent Singularities in Flat Differential Systems (Joint work with Jean Lévine and François Ollivier) Time: 14h, Room: Grace Hopper We study the singularities of locally flat systems, motivated by the solution, if it exists, of the global motion planning problem for such systems. More precisely, flat outputs may be only locally defined because of the existence of points where they are singular (a notion that will be made clear later), thus preventing from planning trajectories crossing these points. Such points are of different types. Some of them can be easily ruled out by considering another non singular flat output, defined on an open set intersecting the domain of the former one and well defined at the point in question. However, it might happen that no well-defined flat outputs exist at all at some points. We call these points intrinsic singularities and the other ones apparent. A rigorous definition of these points is introduced in terms of atlas and charts in the framework of the differential geometry of jets of infinite order and Lie-Bäcklund isomorphisms. We then give a criterion allowing to effectively compute intrinsic singularities. Finally, we show how our results apply to global motion planning of the well-known example of non-holonomic car. Flat differential systems, singularities, global motion planning. 2018, January, 8 Dan Roche Integer polynomial sparse interpolation with near-optimal complexity Time: 14h, Room: Henri Poincaré We investigate algorithms to discover the nonzero coefficients and exponents of an unknown sparse polynomial, provided a way to evaluate the polynomial over any modular ring. This problem has been of interest to the computer algebra community for decades, and its uses include multivariate polynomial GCD computation, factoring, and sparse polynomial arithmetic. Starting with the early works of Zippel, Ben-Or and Tiwari, and Kaltofen, one line of investigation has a key advantage in achieving the minimal number of evaluations of the polynomial, and has received considerable attention and improvements over the years. It is closely related to problems in coding theory and exponential analysis. The downside, however, is that these methods are not polynomial-time over arbitrary fields. A separate line of work starting with Garg and Schost has developed a different approach that works over any finite field. After years of improvements, the complexity of both approaches over 2017, December 11 Fredrik Johansson Numerical integration in complex interval arithmetic Time: 10h30, Room: Grace Hopper We present a new implementation of validated arbitrary-precision numerical evaluation of definite integrals — Lunch break from 11h45 until 13h45 — Jean-Claude Yakoubsohn Numerical approximation of multiple isolated roots of analytic systems (Joint work with Marc Giusti) Time: 14h, Room: Henri Poincaré It is classical that the convergence of the Newton's method at the neighborhood of a singular isolated root of a system of equations is no longer quadratic. It may even diverge. To fix this problem we purpose a new operator, named singular Newton operator, generalizing the classical Newton operator defined regular case. To do so we construct a finite sequence of equivalent systems named deflation sequence where the multiplicity of the root drops strictly between two successive elements of the sequence. Hence the root is a regular root for the last system. Then there exits a regular square system extracted of this one named deflated system. The Singular Newton operator is defined as the classical Newton operator associated to this deflated system. The main idea of the construction of the deflation sequence is the following. Since the Jacobian matrix is rank deficient at the root, it means that there exists relation between the lines (respectively columns) of this Jacobian matrix. These relations are given by the Schur complement of the Jacobian matrix. The result is that when the elements of the Schur complement are added to the initial system, we call this operation kernelling, one obtains an equivalent system where the multiplicity of the root has dropped. In this way, a sequence of equivalent system can be defined Finally we perform a local 2017, November 6 François Ollivier Indécidabilité de l'appartenance à un idéal aux dérivées partielles de type fini (d'après Umirbaiev) Time: 10h30, Room: Grace Hopper On sait que l'appartenance à un idéal différentiel est indécidable [1]. On montre aussi que l'appartenance à un idéal différentiel premier ou radiciel est décidable, ce qui est une conséquence directe de la théorie des ensembles caractéristiques développée par Ritt [2]. On a également des résultats de décidabilité pour des idéaux différentiels isobares [1]. Le problème restait ouvert pour des idéaux différentiels de type fini. Dans un article récent, Umirbaiev [3] a montré que l'appartenance à un idéal aux dérivées partielles (donc avec au moins 2 dérivations) est indécidable. La démonstration repose sur une construction permettant d'associer à une machine de Minsky à 2 bandes un idéal stable pour 2 dérivations. Une machine de Minsky est une variante des machines de Turing. Les deux bandes sont finies à un bout et infini à l'autre. Il n'y a rien d'écrit dans chaque case, pas même la position, mais on peut repérer que la machine est sur la première case d'une bande. On peut associer à tout sous ensemble récursivement énumérable [1] G. Gallo, B. Mishra, F. Ollivier (1991), « Some constructions in rings of differential polynomials », In: Mattson H.F., Mora T., Rao T.R.N. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1991. Lecture Notes in Computer Science, vol 539. Springer, Berlin, Heidelberg. [2] J. F. Ritt, Differential algebra, AMS, 1950. [3] U. Umirbaiev, « Algorithmic problems for differential polynomial algebras », Journal of Algebra, Volume 455, 1 June 2016, Pages 77-92. — Lunch break from 11h45 until 13h45 — Thierry Combot Calcul symbolique des intégrales premières de champs de vecteur polynomiaux du plan Time: 14h, Room: Grace Hopper Soit G. Casale et il s'avère qu'il correspondent aux intégrales premières de 2017, October, 9 Pierre Fortin Task-based parallelism and heterogeneous deployment for the N-body problem Time: 14h, Room: Grace Hopper 2017, June, 8 Manuel Eberl Automatic Asymptotics in Isabelle/HOL Time: 14h, Room: Henri Poincaré Isabelle/HOL is an interactive theorem prover (also called ‘proof assistant'); it provides a logical environment in which mathematical concepts can be defined and theorems about them can be proven. The system guides and assists the user in writing formal proofs, while every step of the proof is computer-checked, which minimises the possibility of mistakes. This talk will give a brief overview of Isabelle/HOL, followed by a more detailed excursion into my project of bringing more tools for asymptotic analysis into Isabelle/HOL; in particular, this includes a procedure to automatically prove limits and ‘Big-O' estimates of real-valued functions similarly to computer algebra systems like Mathematica and Maple – but while proving every step of the process correct. 2017, March, 6 Robin Larrieu Morphisme de Frobenius et FFT Time: 10h30, Room: Claude Shannon On considère un polynôme — Lunch break from 11h45 until 13h45 — Nicholas Coxon Fast systematic encoding of multiplicity codes Time: 14h00, Room: Grace Hopper Multiplicity codes are a relatively new family of polynomial codes introduced by Kopparty, Saraf and Yekhanin (STOC'11). They generalise the classical family of Reed-Muller codes by augmenting their construction to include the evaluations of Hasse derivatives up to a given order. In this talk, we present a quasi-linear time systematic encoding algorithm for multiplicity codes. For the special case of Reed-Muller codes, the encoding algorithm simply applies existing multivariate interpolation and evaluation algorithms of van der Hoeven and Schost (2013). The general encoding algorithm is obtained by generalising their algorithms to address Hermite type interpolation and evaluation problems. 2016, December, 12 Simone Naldi SPECTRA: a Maple library for linear matrix inequalities Time: 14h15, Room: Grace Hopper Linear matrix inequalities (LMI) are a class of convex feasibility problems appearing in different applicative contexts. For instance, checking the asymptotic stability à la Lyapunov for linear differential systems, or computing nonnegativity certificates for multivariate polynomials, are LMI. I will discuss an approach based on techniques from real algebraic geometry to compute exact solutions to LMI, and what informations are carried by this representation. The related algorithms are implemented in a Maple library called SPECTRA, and part of the talk will be dedicated to discuss results on experiments on interesting examples. Robin Larrieu Généralisation de la transformée de Fourier tronquée pour des ordres quelconques Time: 15h45, Room: Grace Hopper La transformée de Fourier tronquée (TFT) vise à calculer seulement certaines valeurs d'une FFT classique. En évitant de calculer les valeurs intermédiaires qui n'interviennent pas dans le calcul des points d'évaluation souhaités, on réduit de manière notable la durée de l'opération : pour calculer 2016, May, 23 — Control theory day Michel Fliess Commande sans modèle : a-t-on toujours besoin d'un modèle pour appliquer les mathématiques à l'industrie ? Time: 10h30, Room: Marcel-Paul Schützenberger On expose les principes généraux de la « commande sans modèle », qui permet de réguler avec précision et facilité bien des dispositifs concrets sans recourir à une modélisation mathématique, toujours difficile, voire impossible, à obtenir. On passe en revue de nombreux exemples. En conclusion, quelques considérations générales sur les mathématiques appliquées, notamment en automatique, tentent de placer cet exposé dans un cadre plus général. — Lunch break from 12h until 13h30 — John Masse L'apport du calcul formel dans une démarche système Time: 14h, Room: Marcel-Paul Schützenberger Exemples d'applications du calcul formel pour le CNES, l'analyse de sensibilité des modèles Simulink, et d'autres applications. Cédric Join Commande sans modèle : de la théorie à la pratique Time: 15h30, Room: Marcel-Paul Schützenberger On détaille la mise en oeuvre de la commande sans modèle. Des méthodes nouvelles d'estimation, d'essence algébrique et faciles à implanter, en sont le fil conducteur. On étudiera les contraintes pratiques qu'elles doivent satisfaire. La conclusion portera sur la complexité actuelle de l'algorithme. 2016, May, 9 Guillermo Matera Estimates on the number of solutions of equations over a finite field and applications Time: 10h30, Room: Paul Schützenberger The set of rational solutions of polynomial systems over a finite field is a classical subject of study, whose origins can be traced back to works of Gauss and Jacobi, and has contributions of Hardy, Littlewood, Chevalley, Davenport, Weil, Lang and Deligne, among others. In this talk we shall discuss recent results of existence of solutions and estimates on the number of solutions of polynomial systems over a finite field. We shall also comment on applications of these estimates to problems in coding theory and combinatorics. 2015, September, 21 — Mathemagix day Philippe Trébuchet Time: 10h30, Room: Grace Hopper Border bases form an alternative method to Groebner bases for polynomial system solving. The advantage is an increased flexibility for the choice of critical pairs, which is particularly useful for increasing the numerical stability of numerical solvers. In this talk, I will present the Borderbasix library, which is dedicated to the resolution of polynomial systems in this way. Grégoire Lecerf Advances in the C++ libraries Numerix, Algebramix, Multimix and Factorix Time: 11h, Room: Grace Hopper I will present recent implementations added to the C++ Mathemagix libraries Numerix, Algebramix, Multimix and Factorix. In particular these libraries now benefit from an efficient support of AVX2 instruction set for numeric and modular arithmetic. I will report on applications and performances. Parts of these works are joint with Joris van der Hoeven and Guillaume Quintin. — Lunch break from 11h30 until 14h — Bernard Mourrain Geometric computation with Mathemagix Time: 14h, Room: Grace Hopper I will describe the packages Realroot and Shape, and their integration as plugin in the algebraic-geometric modeler Axel. The first package realroot is dedicated to the isolation of real roots of polynomial equations. It contains several implementations of subdivision methods in different bases (monomial and Bernstein bases), which are key ingredients in geometric computation. The second package shape is dedicated to the manipulation and analysis of semi-algebraic curves and surfaces. It provides tools for the computation of intersection points of curves and surfaces, singular points, intersection curves of two surfaces, topology analysis, … The integration of these packages as a plugin of Axel will also be described. Suzy Maddah Lindalg: Mathemagix package for symbolic resolution of linear differential systems with singularities Time: 14h30, Room: Grace Hopper Lindalg is dedicated to the local analysis of Isolde written in the computer algebra system Maple is dedicated to the symbolic resolution of such systems and more generally linear functional matrix equations (e.g. difference equations). On the other hand, the new package Lindalg sets a first milestone in providing the two-decade span of Isolde content in an open source software. Mathemagix provides a new high level general purpose language for symbolic and certified numeric algorithms, that can be both interpreted by a shell or compiled. — Coffee break from 15h until 15h30 — Joris van der Hoeven Programming symbolic expressions using the Mathemagix language Time: 15h30, Room: Grace Hopper We will show how to program symbolic expressions using the Mathemagix language and its compiler. The Caas package contains a concrete implementation and forms a nice illustration of how to use some new language features such as extendable abstract datatypes, pattern matching, and fast dispatching. Bruno Grenet Lacunaryx : calcul des facteurs de degré borné de polynômes lacunaires Time: 16h, Room: Grace Hopper Mon exposé présentera une nouvelle bibliothèque Mathemagix appelée Lacunaryx. Elle fournit une implantation d'algorithmes de factorisation pour les polynômes creux ou lacunaires : ces algorithmes prennent en entrée un polynôme 2014, November, 24 Pablo Solerno Un algorithme de décision pour l'intégrabilité de systèmes de Pfaff Time: 11h, Room: Philippe Flajolet On montre un critère qui permet de décider si un système différentiel-algébrique de Pfaff a une solution. La méthode induit un algorithme de décision dont sa complexité est doublement exponentielle dans le nombre d'inconnues et de variables indépendantes, et polynomial dans le degrés et le nombre des polynômes qui apparaissent dans le système. Luis-Miguel Pardo Un résumé subjectif sur le 17-ième problème de Smale: les quatre pattes de SUMO Time: 15h, Room: Marcel-Paul Schützenberger L'exposé contiendra une vision personnelle sur les quatre pattes de la résolution du Problème 17-ième de Smale : Ses quatre pattes, à mon avis, sont : le conditionnement, l'opérateur, l'homotopie et la géométrie intégrale (voire probabilité). La dernière étant la plus efficace à donner des bonnes réponses jusqu'à présent. 2014, November, 17 Éric Schost (joint work with Esmaeil Mehrabi) On the Complexity of Solving Bivariate Systems Time: 11h, Room: Philippe Flajolet We present an algorithm for the symbolic solution of bivariate polynomial systems with coefficients in © 2014 Joris van der Hoeven This webpage is part of the MAX project. Verbatim copying and distribution of it is permitted in any medium, provided this notice is preserved. For more information or questions, please contact Joris van der Hoeven.	{"url":"https://www.lix.polytechnique.fr/max/max-web/max/max-seminar.en.html","timestamp":"2024-11-04T04:30:22Z","content_type":"application/xhtml+xml","content_length":"192864","record_id":"<urn:uuid:d7d307a1-db09-42f9-bcf3-bcea4b33244b>","cc-path":"CC-MAIN-2024-46/segments/1730477028187.61/warc/CC-MAIN-20241110170046-20241110200046-00869.warc.gz"}
Seaborn – (all functions) – My Brain Cells seaborn: statistical data visualization #pip install seaborn #conda install seaborn import seaborn as sns Relational plots relplot Figure-level interface for drawing relational plots onto a FacetGrid. scatterplot Draw a scatter plot with possibility of several semantic groupings. lineplot Draw a line plot with possibility of several semantic groupings. Distribution plots displot Figure-level interface for drawing distribution plots onto a FacetGrid. histplot Plot univariate or bivariate histograms to show distributions of datasets. kdeplot Plot univariate or bivariate distributions using kernel density estimation. ecdfplot Plot empirical cumulative distribution functions. rugplot Plot marginal distributions by drawing ticks along the x and y axes. distplot DEPRECATED: Flexibly plot a univariate distribution of observations. Categorical plots catplot Figure-level interface for drawing categorical plots onto a FacetGrid. stripplot Draw a scatterplot where one variable is categorical. swarmplot Draw a categorical scatterplot with non-overlapping points. boxplot Draw a box plot to show distributions with respect to categories. violinplot Draw a combination of boxplot and kernel density estimate. boxenplot Draw an enhanced box plot for larger datasets. pointplot Show point estimates and confidence intervals using scatter plot glyphs. barplot Show point estimates and confidence intervals as rectangular bars. countplot Show the counts of observations in each categorical bin using bars. Regression plots lmplot Plot data and regression model fits across a FacetGrid. regplot Plot data and a linear regression model fit. residplot Plot the residuals of a linear regression. Matrix plots heatmap Plot rectangular data as a color-encoded matrix. clustermap Plot a matrix dataset as a hierarchically-clustered heatmap. Multi-plot grids Facet grids FacetGrid Multi-plot grid for plotting conditional relationships. FacetGrid.map Apply a plotting function to each facet’s subset of the data. FacetGrid.map_dataframe Like .map but passes args as strings and inserts data in kwargs. Pair grids pairplot Plot pairwise relationships in a dataset. PairGrid Subplot grid for plotting pairwise relationships in a dataset. PairGrid.map Plot with the same function in every subplot. PairGrid.map_diag Plot with a univariate function on each diagonal subplot. PairGrid.map_offdiag Plot with a bivariate function on the off-diagonal subplots. PairGrid.map_lower Plot with a bivariate function on the lower diagonal subplots. PairGrid.map_upper Plot with a bivariate function on the upper diagonal subplots. Joint grids jointplot Draw a plot of two variables with bivariate and univariate graphs. JointGrid Grid for drawing a bivariate plot with marginal univariate plots. JointGrid.plot Draw the plot by passing functions for joint and marginal axes. JointGrid.plot_joint Draw a bivariate plot on the joint axes of the grid. JointGrid.plot_marginals Draw univariate plots on each marginal axes. set_theme Set multiple theme parameters in one step. axes_style Return a parameter dict for the aesthetic style of the plots. set_style Set the aesthetic style of the plots. plotting_context Return a parameter dict to scale elements of the figure. set_context Set the plotting context parameters. set_color_codes Change how matplotlib color shorthands are interpreted. reset_defaults Restore all RC params to default settings. reset_orig Restore all RC params to original settings (respects custom rc). set Alias for set_theme(), which is the preferred interface. Color palettes set_palette Set the matplotlib color cycle using a seaborn palette. color_palette Return a list of colors or continuous colormap defining a palette. husl_palette Get a set of evenly spaced colors in HUSL hue space. hls_palette Get a set of evenly spaced colors in HLS hue space. cubehelix_palette Make a sequential palette from the cubehelix system. dark_palette Make a sequential palette that blends from dark to color. light_palette Make a sequential palette that blends from light to color. diverging_palette Make a diverging palette between two HUSL colors. blend_palette Make a palette that blends between a list of colors. xkcd_palette Make a palette with color names from the xkcd color survey. crayon_palette Make a palette with color names from Crayola crayons. mpl_palette Return discrete colors from a matplotlib palette. Palette widgets choose_colorbrewer_palette Select a palette from the ColorBrewer set. choose_cubehelix_palette Launch an interactive widget to create a sequential cubehelix palette. choose_light_palette Launch an interactive widget to create a light sequential palette. choose_dark_palette Launch an interactive widget to create a dark sequential palette. choose_diverging_palette Launch an interactive widget to choose a diverging color palette. Utility functions load_dataset Load an example dataset from the online repository (requires internet). get_dataset_names Report available example datasets, useful for reporting issues. get_data_home Return a path to the cache directory for example datasets. despine Remove the top and right spines from plot(s). desaturate Decrease the saturation channel of a color by some percent. saturate Return a fully saturated color with the same hue. set_hls_values Independently manipulate the h, l, or s channels of a color.	{"url":"https://mybraincells.com/index.php/2021/06/05/seaborn-all-functions/","timestamp":"2024-11-10T11:13:55Z","content_type":"text/html","content_length":"242788","record_id":"<urn:uuid:612e7fd2-8036-4ab4-9a34-bdb92c476442>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00836.warc.gz"}
Sharing Mathematics Conference About the conference Sharing Mathematics started as a tribute to Jim Totten who spent 28 years writing weekly math puzzles and reaching out to elementary and high school students with puzzles and problems. The conference is open to anyone who has an interest in mathematics, teaching mathematics, or playing with mathematics. Elementary and high school teachers as well as parents are encouraged to come. For more information about the conference, please email Jennifer Hyndman at jennifer.hyndman@unbc.ca. Past abstracts In the fifth Sharing Mathematics Conference we explored games and puzzles, how we can engage students in research, and how we assess students. You can find the abstracts from this past event below. Jean Bowen Math Play Math Play is a tool I am developing to help me evaluate the attitudes of primary school students towards mathematics. Math Play consists of games and toys students can use to explore and develop mathematical concepts and skills without the intimidating element of testing. My hypothesis is that Math Play will positively impact students’ attitudes towards mathematics. I invite you to participate in some Math Play activities and discuss the current research on students’ feelings towards mathematics. David Casperson and Jennifer Hyndman Teaching the Concept of Research through Games Many people think all mathematics has already been done and cannot imagine what mathematical research is. Exploring games can be used to illustrate the concept of mathematical research. Participants will engage in activities and discussion that illustrate this approach. Lisa Dickson A Five-Finger Guide to Effective Assessment In this session we will explore some "student-centred" principles of assessment, focusing on five key areas: creating safe spaces for learning; matching assessment to outcomes or goals; getting ourselves out of the way; creating dynamic assessment models; and valuing struggle. We will work through some scenarios to generate ideas and strategies for creating effective assessments and learning environments. Gary MacGillivray Research with Undergraduates What outcomes should one expect when doing research in mathematics with undergraduate students? How does one pick a problem? How does one know if it is at the appropriate level? What learning outcomes should be expected? How is progress measured? How is it managed? We shall suggest of possible answers to these questions, and hope members of the audience will also offer answers for discussion. A number of recent research projects with undergraduate, and their outcomes, will be presented. Susan Milner Finding a way into mathematical thinking via puzzles and games Workshop participants will try out a selection of puzzles that have had met with great success with students of all ages. The puzzles can be taken directly into the classroom for hands-on differentiated learning. Participants will also have the opportunity to sample some commercial games with mathematical aspects. These puzzles and games are more than fun - they involve deep mathematical thinking. We’ll consider the connections to mathematics and also discuss ways to use puzzles to enrich our teaching and encourage our students to think mathematically. Paul Ottaway Games for ages 8 to 88 We will examine how games as a mathematical construct can be incorporated into the mathematics curriculum spanning mid-elementary school grades through to graduate level research. We will briefly look at the intrinsic and extrinsic motivations for playing mathematical games. Through a series of hands-on activities, we will see how mathematical sophistication can be developed. The talk will be interactive and the audience will be encouraged to learn and play games and to discuss strategy. A particular focus will be variations on the game of Nim, but other more esoteric games will also be	{"url":"https://www.unbc.ca/mathematics-and-statistics/sharing-mathematics-conference","timestamp":"2024-11-06T16:57:53Z","content_type":"text/html","content_length":"76492","record_id":"<urn:uuid:166f8d0a-b644-459f-846e-421d9f4883cd>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00507.warc.gz"}
Your Guide to Master Hypothesis Testing in Statistics Introduction – the difference in mindset I started my career as a MIS professional and then made my way into Business Intelligence (BI) followed by Business Analytics, Statistical modeling and more recently machine learning. Each of these transition has required me to do a change in mind set on how to look at the data. But, one instance sticks out in all these transitions. This was when I was working as a BI professional creating management dashboards and reports. Due to some internal structural changes in the Organization I was working with, our team had to start reporting to a team of Business Analysts (BA). At that time, I had very little appreciation of what is Business analytics and how is it different from BI. So, as part of my daily responsibilities, I prepared my management dashboard in the morning and wrote a commentary on it. I compared the sales of first week of the current month to sales of previous month and same month last year to show an improvement in business. It looked something like this: In my commentary, I ended up writing that sales are better than last year and last month and applauded some of the new initiatives the Sales team had taken recently. I was thinking this was good work to show to my new manager. Little did I know, what was in store! When I showed the report to my new manager applauding the sales team, he asked why do I think this uplift is just not random variation in data? I had very little Statistics background at this time and I could not appreciate his stand. I thought we were talking 2 different language. My previous manager would have jumped over this report and would have dropped a note to Senior Management himself! And here was my new manager asking me to hold my commentary. In today’s article, I will explain hypothesis testing and reading statistical significance to differentiate signal from the noise in data – exactly what my new manager wanted me to do! P.S. This might seem like a lengthy article, but would be one of the most useful one, if you follow through. A case study: Let us say that average marks in mathematics of class 8th students of ABC School is 85. On the other hand, if we randomly select 30 students and calculate their average score, their average comes to be 95. What can be concluded from this experiment? It’s simple. Here are the conclusions: • These 30 students are different from ABC School’s class 8th students, hence their average score is better i.e behavior of these randomly selected 30 students sample is different from the population (all ABC School’s class 8th students) or these are two different population. • There is no difference at all. The result is due to random chance only i.e. we found the average value of 85. It could have been higher / lower than 85 since there are students having average score less or more than 85. How should we decide which explanation is correct? There are various methods to help you to decide this. Here are some options: 1. Increase sample size 2. Test for another samples 3. Calculate random chance probability The first two methods require more time & budget. Hence, aren’t desirable when time or budget are constraints. So, in such cases, a convenient method is to calculate the random chance probability for that sample i.e. what is the probability that sample would have average score of 95?. It will help you to draw a conclusion from the given two hypothesis given above. Now the question is, “How should we calculate the random chance probability?“. To answer it, we should first review the basic understanding of statistics. Basics of Statistics 1. Z-Value/ Table/ p value: Z value is a measure of standard deviation i.e. how many standard deviation away from mean is the observed value. For example, the value of z value = +1.8 can be interpreted as the observed value is +1.8 standard deviations away from the mean. P-values are probabilities. Both these statistics terms are associated with the standard normal distribution. You can look at the p-values associated with each z-value in Z-table. Below is the formula to calculate z value: Here X is the point on the curve, μ is mean of the population and σ is standard deviation of population. As I discussed, these methods always work with normal distribution (shown above) only, not with other distributions. In case, the population distribution is not normal, we’d resort to Central Limit 2. Central Limit Theorem: This is an important theorem in statistics. Without going into definitions, I’ll explain it using an example . Let’s look at the case below. Here, we have a data of 1000 students of 10th standard with their total marks. Following are the derived key metrics of this population: And, frequency distribution of marks is: Is this some kind of distribution you can recall? Probably not. These marks have been randomly distributed to all the students. Now, let’s take a sample of 40 students from this population. So, how many samples can we take from this population? We can take 25 samples(1000/40 = 25). Can you say that every sample will have the same average marks as population has (48.4)? Ideally, it is desirable but practically every sample is unlikely to have the same average. Here we have taken 1000 samples of 40 students (randomly sample generated in excel). Let’s look at the frequency distribution of these sample averages of thousands samples and other statistical Does this distribution looks like the one we studied above? Yes, this table is also normally distributed. For better understanding, you can download this file from here and while doing this exercise you’ll come across the findings stated below: 1. Mean of sample means (1000 sample means) is very close to population mean 2. Standard deviation of the sample distribution can be found out from the population standard deviation divided by square root of sample size N and it is also known as standard error of means. 3. The distribution of sample means is normal regardless of the distribution of the actual population. This is known as Central Limit theorem. This can be very powerful. In our initial example of ABC School students, we compared the sample mean and population mean. Precisely, we looked at the distribution of sample mean and found out the distance between population mean and the sample mean. In such cases, you can always use a normal distribution without worrying about the population distribution. You can calculate the standard deviation and mean based on above findings and calculate z-score and p-value. Here random chance probability will help you to accept one of discussed conclusions from ABC School’s example (stated above). But, to satisfy the CLT theorem, sample size must be sufficient (>=30). Now, let’s say we have calculated the random chance probability. It comes out to be 40%, then should I go with first conclusion or other one ? Here the “Significance Level” will help us to decide. What is Significance Level? We have taken an assumption that probability of sample mean 95 is 40%, which is high i.e. more likely that we can say that there is a greater chance that this has occurred due to randomness and not due to behavior difference. Had the probability been 7%, it would have been a no-brainer to infer that it is not due to randomness. There may be some behavior difference because probability is relatively low which means high probability leads to acceptance of randomness and low probability leads to behavior difference. Now, how do we decide what is high probability and what is low probability? To be honest, it is quite subjective in nature. There could be some business scenarios where 90% is considered to be high probability and in other scenarios could be 99%. In general, across all domains, cut off of 5% is accepted. This 5% is called Significance Level also known as alpha level (symbolized as α). It means that if random chance probability is less than 5% then we can conclude that there is difference in behavior of two different population. (1- Significance level) is also known as Confidence Level i.e. we can say that I am 95% confident that it is not driven by Till now, we looked at the tools to test a hypothesis, whether sample mean is different from population or it is due to random chance. Now, let’s look at the steps to perform a hypothesis test and post that we will go through it using an example. What are the steps to perform Hypothesis Testing? • Set up Hypothesis (NULL and Alternate): In ABC School example, we actually tested a hypothesis. The hypothesis, we are testing was the difference between sample and population mean was due to a random chance. It is called as “NULL Hypothesis” i.e. there is no difference between sample and population. The symbol for the null hypothesis is ‘H0’. Keep in mind that, the only reason we are testing the null hypothesis is because we think it is wrong. We state what we think is wrong about the null hypothesis in an Alternative Hypothesis. For the ABC School example, alternate hypothesis is, there is a significant difference in behavior of sample and population. The symbol for the alternative hypothesis is ‘H1’. In a courtroom, since the defendant is assumed to be innocent (this is the null hypothesis so to speak), the burden is on a prosecutor to conduct a trial to show evidence that the defendant is not innocent. In a similar way, we assume the null hypothesis is true, placing the burden on the researcher to conduct a study to show evidence that the null hypothesis is unlikely to be true. • Set the Criteria for decision: To set the criteria for a decision, we state the level of significance for a test. It could 5%, 1% or 0.5%. Based on the level of significance, we make a decision to accept the Null or Alternate hypothesis. There could be 0.03 probability which accepts Null hypothesis on 1% level of significance but rejects Null hypothesis on 5% of significance. It is based on business requirements. • Compute the random chance of probability: Random chance probability/ Test statistic helps to determine the likelihood. Higher probability has higher likelihood and enough evidence to accept the Null hypothesis. • Make Decision: Here, we compare p value with predefined significance level and if it is less than significance level, we reject Null hypothesis else we accept it. While making a decision to retain or reject the null hypothesis, we might go wrong because we are observing a sample and not an entire population. There are four decision alternatives regarding the truth and falsity of the decision we make about a null hypothesis: 1. The decision to retain the null hypothesis could be correct. 2. The decision to retain the null hypothesis could be incorrect, it is know as Type II error. 3. The decision to reject the null hypothesis could be correct. 4. The decision to reject the null hypothesis could be incorrect, it is known as Type I error. Blood glucose levels for obese patients have a mean of 100 with a standard deviation of 15. A researcher thinks that a diet high in raw cornstarch will have a positive effect on blood glucose levels. A sample of 36 patients who have tried the raw cornstarch diet have a mean glucose level of 108. Test the hypothesis that the raw cornstarch had an effect or not. Solution:- Follow the above discussed steps to test this hypothesis: Step-1: State the hypotheses. The population mean is 100. H0: μ= 100 H1: μ > 100 Step-2: Set up the significance level. It is not given in the problem so let’s assume it as 5% (0.05). Step-3: Compute the random chance probability using z score and z-table. For this set of data: z= (108-100) / (15/√36)=3.20 You can look at the probability by looking at z- table and p-value associated with 3.20 is 0.9993 i.e. probability of having value less than 108 is 0.9993 and more than or equals to 108 is (1-0.9993) Step-4: It is less than 0.05 so we will reject the Null hypothesis i.e. there is raw cornstarch effect. Note: Setting significance level can also be done using z-value known as critical value. Find out the z- value of 5% probability and it is 1.65 (positive or negative, in any direction). Now we can compare calculated z-value with critical value to make a decision. Directional/ Non Directional Hypothesis Testing In previous example, our Null hypothesis was, there is no difference i.e. mean is 100 and alternate hypothesis was sample mean is greater than 100. But, we could also set an alternate hypothesis as sample mean is not equals to 100. This becomes important when we do reject the Null hypothesis, should we go with which alternate hypothesis: • Sample mean is greater than 100 • Sample mean is not equals to 100 i.e. there is a difference Here, the question is “Which alternate hypothesis is more suitable?”. There are certain points which will help you to decide which alternate hypothesis is suitable. • You are not interested in testing sample mean lower than 100, you only want to test the greater value • You have strong believe that Impact of raw cornstarch is greater In above two cases, we will go with One tail test. In one tail test, our alternate hypothesis is greater or less than the observed mean so it is also known as Directional Hypothesis test. On the other hand, if you don’t know whether the impact of test is greater or lower then we go with Two tail test also known as Non Directional Hypothesis test. Let’s say one of research organization is coming up with new method of teaching. They want to test the impact of this method. But, they are not aware that it has positive or negative impact. In such cases, we should go with two tailed test. In one tail test, we reject the Null hypothesis if the sample mean is either positive or negative extreme any one of them. But, in case of two tail test we can reject the Null hypothesis in any direction (positive or negative). Look at the image above. Two-tailed test allots half of your alpha to testing the statistical significance in one direction and half of your alpha in the other direction. This means that .025 is in each tail of the distribution of your test statistic. Why are we saying 0.025 on both side because normal distribution is symmetric. Now we come to a conclusion that Rejection criteria for Null hypothesis in two tailed test is 0.025 and it is lower than 0.05 i.e. two tail test has more strict criteria to reject the Null Hypothesis. Templer and Tomeo (2002) reported that the population mean score on the quantitative portion of the Graduate Record Examination (GRE) General Test for students taking the exam between 1994 and 1997 was 558 ± 139 (μ ± σ). Suppose we select a sample of 100 participants (n = 100). We record a sample mean equal to 585 (M = 585). Compute the p-value t0 check whether or not we will retain the null hypothesis (μ = 558) at 0.05 level of significance (α = .05). Step-1: State the hypotheses. The population mean is 558. H0: μ= 558 H1: μ ≠ 558 (two tail test) Step-2: Set up the significance level. As stated in the question, it as 5% (0.05). In a non-directional two-tailed test, we divide the alpha value in half so that an equal proportion of area is placed in the upper and lower tail. So, the significance level on either side is calculated as: α/2 = 0.025. and z score associated with this (1-0.025=0.975) is 1.96. As this is a two-tailed test, z-score(observed) which is less than -1.96 or greater than 1.96 is a evidence to reject the Null hypothesis. Step-3: Compute the random chance probability or z score For this set of data: z= (585-558) / (139/√100)=1.94 You can look at the probability by looking at z- table and p-value associated with 1.94 is 0.9738 i.e. probability of having value less than 585 is 0.9738 and more than or equals to 585 is (1-0.9738) Step-4: Here, to make a decision, we compare the obtained z value to the critical values (+/- 1.96). We reject the null hypothesis if the obtained value exceeds a critical values. Here obtained value (Z[obt]= 1.94) is less than the critical value. It does not fall in the rejection region. The decision is to retain the null hypothesis. End Notes In this article, we have looked at the complete process of undertaking hypothesis testing during predictive modeling. Initially, we looked at the concept of hypothesis followed by the types of hypothesis and way to validate hypothesis to make an informed decision. We also have also looked at important concepts of hypothesis testing like Z-value, Z-table, P-value, Central Limit theorem. As mentioned in the introduction, this was one of the most difficult change in mindset for me when I read this first time. But it was also one of the most helpful and significant change. I can easily say that this change started me to think like a predictive modeler. In next article, we will look at the what-if scenarios with hypothesis testing like: • If sample size is less than 30 (Not satisfy CLT) • Compare two sample rather than sample and population • If we don’t know the population standard deviation • p-values and Z-scores in the Big Data age Did you find this article helpful? Please share your opinions / thoughts in the comments section below. Responses From Readers Thanks for posting this article - An excellent read Nice article. Hi Sunil, Very nice article. Keep up the good work! Regards Gaurav excellent analysis Hey Sunil, I think this article was the best because you start with a challenge in work that every person may face Great Article Sunil. This was helpful. Keep it coming. Thanks, Kishore It was really helpful.Its great to see how you give real life examples from your work.Want to see more statistics in your blog. Cheers!! Hi Sunil, Thanks for the excellent article. I wanted to understand this from long time however thickness of stat books kept me away. You did great job in keeping a story along with fundamental of stats. Cheers good job!!!! Hi All, Thanks for the comment … Regards, Sunil Very insightful!! I have one question So does it means that if random chance probability is less than 5 % then there is difference in the behavior of two population and it is due to randomness? Easy to understand and concise. I had this learning from my course I took from Jigsaw Academy but had lost some touch. Thanks for putting across this very important article. That's by far the best content I've ever read regarding hypothesis testing. Thankyou Sunil and team!! Looking forward to reading more of your articles. Nice job! Where do we find the next article? Hi, Nice post! I am interested of how you answered your boss? What was the solution to the "signal or noise" original problem? Thank you for this article ! Thanks for such great Article, you explained this concept very easily Regard Great read, although some images are missing. Please will you make these images available again. A fantastic read...Great job. You can look at the probability by looking at z- table and p-value associated with 3.20 is 0.9993 i.e. probability of having value less than 108 is 0.9993 and more than or equals to 108 is (1-0.9993) =0.0007. Can anyone explain how we inferred that 0.9993 is probability of having value less than 108. It can be probability of greater than 108 also ? Great breakdown! Thank you. "You can look at the probability by looking at z- table and p-value associated with 3.20 is 0.9993 i.e. probability of having value less than 108 is 0.9993 and more than or equals to 108 is (1-0.9993)=0.0007. Step-4: It is less than 0.05 so we will reject the Null hypothesis i.e. there is raw cornstarch effect."-copied from above article. probability of having value less than 108 is 0.9993 means its supporting to null hypo with high which mean value is 100. please clarify I am not getting this point. Thanks Great article, it is really helpful for beginners in research ie data analysis. But please somebody tell me that wether we can use t-test for a sample greater than 30 to compare two groups for cause and effect relationship. The effect of matching/mismatching of teaching and learning styles on academic achievement where the sample is greater than 300. Thanks for this nice POST and making the concept simple to understand Thanks for the share, learnt big time Hi, I am failing to understand the relation between the null hypothesis and the inference for the 1st example with the blood glucose level.. The Null and alternate hypothesis are set for 100 and > 100, however the inference talks about less than 108 vs greater than 108. Can some one help me relate the hypothesis to the inference? Thanks, Siva Hi Sunil, Nice article, you explain it nicely with simple worlds, and nice charts, I like it :) I want to mention that the examples are based on the assumption that the population distribution is normal, this assumption also should be checked. Also, I want to mention that in the example we know the population's standard deviation, usually, we don't know the population's standard deviation, and we need to estimate the value based on the sample. in this case, we should use the t distribution instead of the normal distribution (z) today is my exam on bio-statistics, and i am not ready..... but suddenly i viewed this article. it helps me a lot..... thank you so much -Samson- fr: Philippines […] mean is right around zero, with a standard deviation of 7.3. You’ll see the formula broken out here, as we snag the z-score for this value and produce -0.328: our tanking rookies barely differ from […] Good article to explain clearly the CLT and Null Hypothesis setting with Confidence Levels... Good to refresh my knowledge on statistical analysis... 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Completion Of The Dirac Equation Using Pöschl-Teller Potential Hyperbolic Potential Plus Gendenshtein II Using Asymptotic Iteration Method Last modified: 2016-11-15 The behavior of a physical system in nature can be assessed by using a function that can describe the state of the system. Through the state function, predictable system behavior over time or can also observe other physical magnitudes, such as position, momentum, energy, or other quantities that can be measured. In classical mechanics, such functionality can be obtained in various ways. Solutions which declared a state of a classical system can be obtained by equation Newton's Second Law. Quantum theory basically does not like the concept according to Newton's mechanics or electricity dynamics according to Maxwell. The theory of quantum mechanics does not have a general concept of basic principles that can be taught, each physicists studying quantum mechanics is different from the material or a slightly different concept. Quantum theory basically does not like the concept according to Newton's mechanics or electricity dynamics according to Maxwell. The theory of quantum mechanics does not have a general concept of basic principles that can be taught, each physicists studying quantum mechanics is different from the material or a slightly different	{"url":"https://callforpapers.uksw.edu/index.php/iceteach/2016/paper/view/128","timestamp":"2024-11-07T13:48:27Z","content_type":"application/xhtml+xml","content_length":"11003","record_id":"<urn:uuid:cf960607-f49e-485f-9905-723db8fde78e>","cc-path":"CC-MAIN-2024-46/segments/1730477027999.92/warc/CC-MAIN-20241107114930-20241107144930-00655.warc.gz"}
Alloy Metal Weight Fraction Calculation - Hot Wires Alloy Metal Weight Fraction Calculation Iasad writes, “Dear Dr. Ron, I see that you have developed software to calculate the density of an alloy if given the weight fractions of the constituent metals. Is it possible to find the weight fractions of the metals in an alloy given the alloy’s density? Thank you!” Unfortunately, finding the weight fractions of the metals in an alloy from the alloy’s density can only be accomplished with a two metal alloy. First we must use the equation: Equation 1 Where x is the weight fraction of metal A and the rhos are the associated densities. All that has to be done is to solve for x. The solution is worked out below in Figure 2, the final result is: Equation 2 As an example, let’s say you have a gold-copper alloy with a density of 18.42 g/cc. The density of gold (metal A) is 19.32 g/cc and that of copper (metal B) is 8.92 g/cc. Substituting these values into equation 2 gives the weight fraction of gold as 0.958. Hence the weight fraction of copper is 1-0.958 = 0.042. I have developed an Excel-based software tool to perform these calculations. An image of it is shown in Figure 1. If you would like a copy of this tool send me a note. Figure 1. A screen shot of the alloy metal weight fraction calculator. Figure 2. The derivation of the weight fraction formula. Dr. Ron	{"url":"https://www.hotwires.net/alloy-metal-weight-fraction-calculation/","timestamp":"2024-11-02T20:33:54Z","content_type":"text/html","content_length":"56350","record_id":"<urn:uuid:c4efbdcc-549b-4947-85cd-1b51faaab831>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00216.warc.gz"}
THE DOT POSTULATE - 7.7. Causality: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics PDF Download Search Inside this Book 7.7. Causality: On the other hand, since the whole Universe is self-contained in space, all changes in it are necessarily internal changes only, because it is a closed system. Therefore, any change in any part of the Universe will inevitably cause other synchronizing change(s) in other parts. In normal cases the effect of the ongoing process of cosmic re-creation is not noticeable because of the many possible changes that could happen in any part of the complex system, and the corresponding distraction of our limited means of attention and perception. This means that causality is no more directly related to space or even time; because the re-creation allows non-local and even non-temporal causal interactions. In regular macroscopic situations, the perturbation causes gradual or smooth, but still discrete, motion or change; because of the vast number of neighboring individual points, so the effect of any perturbation will be limited to adjacent points, and will dissipate very quickly after short distance, when energy is consumed. This kind of apparent motion is limited by the speed of light, because the change can appear infinitesimally continuous in space. In the special case when a small closed system is isolated as a small part of the Universe, and this isolation is not necessarily spatial isolation, as it is the case of the two entangled particles in the EPR, then the effect of any perturbation will appear instantaneous because it will be transferred only through a small number of points, irrespective of their positions in space, or even in ... Space Transcendence Read this short concise exploration of the Duality of Time Postulate: DoT: The Duality of Time Postulate and Its Consequences on General Relativity and Quantum Mechanics ... ickly after short distance, when energy is consumed. This kind of apparent motion is limited by the speed of light, because the change can appear infinitesimally continuous in space. In the SPECIAL CASE when a small closed system is isolated as a small part of the Universe, and this isolat ... ... n and perception. This means that causality is no more directly related to space or even time; because the re-creation allows non-local and even non-temporal causal interactions. In regular MACROSCOPIC SITUATIONS , the perturbation causes gradual or smooth, but still discrete, motion or cha ... ... ghboring individual points, so the effect of any perturbation will be limited to adjacent points, and will dissipate very quickly after short distance, when energy is consumed. This kind of APPARENT MOTION is limited by the speed of light, because the change can appear infinitesimally cont ... ... kind of apparent motion is limited by the speed of light, because the change can appear infinitesimally continuous in space. In the special case when a small closed system is isolated as a SMALL PART of the Universe, and this isolation is not necessarily spatial isolation, as it is the ca ... ... stance, when energy is consumed. This kind of apparent motion is limited by the speed of light, because the change can appear infinitesimally continuous in space. In the special case when a SMALL CLOSED system is isolated as a small part of the Universe, and this isolation is not necessari ... ... change(s) in other parts. In normal cases the effect of the ongoing process of cosmic re-creation is not noticeable because of the many possible changes that could happen in any part of the COMPLEX SYSTEM , and the corresponding distraction of our limited means of attention and perception. ... ... llows non-local and even non-temporal causal interactions. In regular macroscopic situations, the perturbation causes gradual or smooth, but still discrete, motion or change; because of the VAST NUMBER of neighboring individual points, so the effect of any perturbation will be limited to a ... ... y spatial isolation, as it is the case of the two entangled particles in the EPR, then the effect of any perturbation will appear instantaneous because it will be transferred only through a SMALL NUMBER of points, irrespective of their positions in space, or even in time. &nb ... ... e, motion or change; because of the vast number of neighboring individual points, so the effect of any perturbation will be limited to adjacent points, and will dissipate very quickly after SHORT DISTANCE , when energy is consumed. This kind of apparent motion is limited by the speed of lig ... ... re necessarily internal changes only, because it is a closed system. Therefore, any change in any part of the Universe will inevitably cause other synchronizing change(s) in other parts. In NORMAL CASES the effect of the ongoing process of cosmic re-creation is not noticeable because of th ... ... and even non-temporal causal interactions. In regular macroscopic situations, the perturbation causes gradual or smooth, but still discrete, motion or change; because of the vast number of NEIGHBORING INDIVIDUAL points, so the effect of any perturbation will be limited to adjacent points, ...	{"url":"https://www.smonad.com/dot/book.php?id=37","timestamp":"2024-11-10T22:46:05Z","content_type":"text/html","content_length":"31561","record_id":"<urn:uuid:af0614b6-ad5a-4ed0-b592-426e64dfb175>","cc-path":"CC-MAIN-2024-46/segments/1730477028191.83/warc/CC-MAIN-20241110201420-20241110231420-00697.warc.gz"}
sorg2l: generates an m by n real matrix Q with orthonormal columns, - Linux Manuals (l) sorg2l (l) - Linux Manuals sorg2l: generates an m by n real matrix Q with orthonormal columns, SORG2L - generates an m by n real matrix Q with orthonormal columns, M, N, K, A, LDA, TAU, WORK, INFO ) INTEGER INFO, K, LDA, M, N REAL A( LDA, * ), TAU( * ), WORK( * ) SORG2L generates an m by n real matrix Q with orthonormal columns, which is defined as the last n columns of a product of k elementary reflectors of order m = H(k) . . . H(2) H(1) as returned by SGEQLF. M (input) INTEGER The number of rows of the matrix Q. M >= 0. N (input) INTEGER The number of columns of the matrix Q. M >= N >= 0. K (input) INTEGER The number of elementary reflectors whose product defines the matrix Q. N >= K >= 0. A (input/output) REAL array, dimension (LDA,N) On entry, the (n-k+i)-th column must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by SGEQLF in the last k columns of its array argument A. On exit, the m by n matrix Q. LDA (input) INTEGER The first dimension of the array A. LDA >= max(1,M). TAU (input) REAL array, dimension (K) TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGEQLF. WORK (workspace) REAL array, dimension (N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument has an illegal value	{"url":"https://www.systutorials.com/docs/linux/man/l-sorg2l/","timestamp":"2024-11-02T15:37:47Z","content_type":"text/html","content_length":"8788","record_id":"<urn:uuid:ecd82796-49d6-48de-9ac6-b684bfc4fb8c>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00360.warc.gz"}
In the figure above, P and N are the centers of the circles an... \| Filo and are the centers of the circles and . What is the area of the shaded region? Not the question you're searching for? + Ask your question C) In this problem, we have to take advantage of the Strange Area Rule . First we should draw the segments from and to the points of intersection. Since each of these segments is a radius, they have equal measure (6), and form two equilateral triangles. central angle, has an area of the whole circle, or and the triangle has area . Therefore, the shaded region has an area of . Was this solution helpful? Found 8 tutors discussing this question Discuss this question LIVE 10 mins ago One destination to cover all your homework and assignment needs Learn Practice Revision Succeed Instant 1:1 help, 24x7 60, 000+ Expert tutors Textbook solutions Big idea maths, McGraw-Hill Education etc Essay review Get expert feedback on your essay Schedule classes High dosage tutoring from Dedicated 3 experts Practice questions from Circles in the same exam Practice more questions from Circles View more Practice questions on similar concepts asked by Filo students View more Stuck on the question or explanation? Connect with our Mathematics tutors online and get step by step solution of this question. 231 students are taking LIVE classes Question Text In the figure above, and are the centers of the circles and . What is the area of the shaded region? Topic Circles Subject Mathematics Class Grade 12 Answer Type Text solution:1 Upvotes 147	{"url":"https://askfilo.com/mathematics-question-answers/in-the-figure-above-p-and-n-are-the-centers-of-the-circles-and-p-n6-what-is-the","timestamp":"2024-11-15T03:42:24Z","content_type":"text/html","content_length":"346284","record_id":"<urn:uuid:aebb0618-4a39-453b-a511-01d61f8aeb33>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00037.warc.gz"}
GATE 2023 Syllabus Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors. Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems. Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace’s equations. Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series. Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations. Section 2: Applied Mechanics and Design Engineering Mechanics: Free-body diagrams and equilibrium; friction and its applications including rolling friction, belt-pulley, brakes, clutches, screw jack, wedge, vehicles, etc.; trusses and frames; virtual work; kinematics and dynamics of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations; Lagrange’s equation. Mechanics of Materials: Stress and strain, elastic constants, Poisson’s ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; concept of shear centre; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength. Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope. Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts. Machine Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs. Section 3: Fluid Mechanics and Thermal Sciences Fluid Mechanics: Fluid properties; fluid statics, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends and fittings; basics of compressible fluid flow. Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler’s charts; thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, Stefan- Boltzmann law, Wien’s displacement law, black and grey surfaces, view factors, radiation network Thermodynamics: Thermodynamic systems and processes; properties of pure substances, behavior of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations. Applications: Power Engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines; steam and gas turbines Section 4: Materials, Manufacturing and Industrial Engineering Engineering Materials: Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials. Casting, Forming and Joining Processes: Different types of castings, design of patterns, moulds and cores; solidification and cooling; riser and gating design. Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy. Principles of welding, brazing, soldering and adhesive bonding. Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, jigs and fixtures; abrasive machining processes; NC/CNC machines and CNC programming. Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements; comparators; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly; concepts of coordinate-measuring machine (CMM). Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools; additive manufacturing. Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning; lean manufacturing. Inventory Control: Deterministic models; safety stock inventory control systems. Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.	{"url":"https://gameacademy.in/gate-2022-syllabus/","timestamp":"2024-11-02T06:18:29Z","content_type":"text/html","content_length":"149231","record_id":"<urn:uuid:b4618f38-91c0-4e7e-81ab-4ad88b5da77d>","cc-path":"CC-MAIN-2024-46/segments/1730477027677.11/warc/CC-MAIN-20241102040949-20241102070949-00507.warc.gz"}
Gravity - Force in Physics The information on this page is ✔ fact-checked. Gravity demonstration \| Image: Force in Physics Gravity is a fundamental force in nature that causes objects with mass to be attracted to one another. It is the reason why when an individual jumps or falls, they are pulled back to the ground. This force is present everywhere in the universe and plays a crucial role in shaping celestial bodies and governing their movements. For instance, gravity keeps planets in stable orbits around stars. The strength of gravity depends on the mass of the objects involved, where larger masses result in a more significant gravitational pull. This force, universal in nature, is a cornerstone of physics. It governs the behavior of all objects possessing mass and offers profound insights into the interactions between matter on a cosmic scale. Gravity pulls the apple downward, causing it to fall to the ground \| Image: Force in Physics The way a ripe apple plummets from a tree is a perfect example of gravity’s effect in action. As envisioned by Sir Isaac Newton, gravity exerts an attractive force on objects with mass, such as the apple, and causes them to be drawn towards the center of the Earth. As a result, the apple detaches from the tree and gracefully descends to the ground. This fundamental force of nature governs the motion of the apple, ensuring it experiences a downward pull and finds its way to the Earth’s surface. Tap water Gravity pulls the water downward from the tap, creating a downward flow \| Image: Force in Physics When a tap is opened, water flows out and descends to the ground. This downward motion of tap water occurs because of the force of gravity. Sir Isaac Newton’s theory of gravity explains how this fundamental force attracts objects with mass towards the center of the Earth. Consequently, gravity pulls the water downward, causing it to flow out of the tap and fall to the ground. This straightforward yet significant example demonstrates how gravity influences the behavior of everyday objects, like tap water, ensuring they are drawn towards the Earth’s surface. Dropped ball Gravity accelerates the ball downward when released from a height \| Image: Force in Physics The concept of gravity becomes evident when observing a dropped ball. As the ball is released from a certain height, it is drawn downwards by the force of gravity. This universal force acts on all objects with mass, causing them to fall towards the Earth. Regardless of the ball’s weight or the height from which it is dropped, gravity ensures a consistent and predictable downward motion and guides the ball toward the ground. Gravity pulls the water downward, causing it to flow over the edge of the waterfall \| Image: Force in Physics A waterfall provides a tangible example of gravity’s influence. As water descends over a cliff, gravity pulls it downward, accelerating its movement. The height of the waterfall dictates the potential energy of the water prior to its descent. As the water gains speed, it also gains kinetic energy. Upon reaching the base, the water may collide with rocks or gather in a pool, illustrating how gravity determines its trajectory. Waterfalls thus exemplify how gravity shapes the movement of objects on Earth, such as the flow of water. Slipped coin Gravity causes objects, like a coin, to be pulled downwards when released or dropped \| Image: Force in Physics When holding a handful of coins and gently loosening the grip, some coins slip and fall downward. This phenomenon occurs due to the force of gravity, a natural force that pulls objects towards the Earth’s surface. Gravity causes the coins to be drawn downward, regardless of their number or the height from which they fall. This consistent gravitational pull guides the coins’ descent and illustrates the fundamental nature of gravity in everyday experiences. Gravity pulls the swimmer downward after jumping, causing them to descend into the water \| Image: Force in Physics When swimmers enter a swimming pool, gravity immediately starts pulling them downward, while the water exerts an opposite force called buoyancy, pushing them upwards. This dynamic balance between gravity and buoyancy determines whether swimmers will float, sink, or remain suspended at a certain depth. When the upward buoyant force exceeds gravity, swimmers float effortlessly on the water’s surface. Conversely, if gravity overpowers the buoyant force, they will sink. This delicate interplay between gravity and buoyancy influences how objects, such as swimmers, behave in swimming pools. Tennis ball Gravity acts as a force pulling the tennis ball back to the Earth after it reaches its highest point \| Image: Force in Physics When a tennis ball is thrown into the air, it gracefully descends back down towards the ground, illustrating the force of gravity in action. Regardless of the height from which it is launched, the ball consistently moves towards the Earth, pulled by gravitational force. This behavior exemplifies the universal nature of gravity, as all objects with mass experience this downward pull. Flying kite Gravity pulls the kite downward, causing it to descend from the sky \| Image: Force in Physics When flying a kite during the festival of Makar Sankranti, if the thread gets cut or becomes detached, the kite descends gracefully to the ground. This observable event provides a clear illustration of the force of gravity in action, as it pulls the kite downwards once it loses the upward tension from the thread. The gravity equation, g = GM/r^2, describes the relationship between the acceleration due to gravity (g), the universal gravitational constant (G), the mass of the celestial body (M), and the distance between the centers of mass (r). This equation allows for the calculation of gravitational acceleration between two objects, taking into account their masses and the distance separating Practice problems Problem #1 Calculate the acceleration due to gravity on star B’s surface, knowing that its mass is 1.5 × 10^25 kg, and its radius is 20 × 10^3 km. Consider the universal gravitational constant as G = 6.67 × 10^ -11 Nm^2/kg^2. Given data: • Acceleration due to gravity on star B’s surface, g = ? • Mass of the star B, M = 1.5 × 10^25 kg • Radius of the star B, r = 20 × 10^3 km = 20 × 10^6 m • Universal gravitational constant, G = 6.67 × 10^-11 Nm^2/kg^2 Using the equation: • g = GM/r^2 • g = (6.67 × 10^-11 × 1.5 × 10^25)/(20 × 10^6)^2 • g = (10.005 × 10^14)/(400 × 10^12) • g = 0.0250125 × 10^2 • g = 2.50 m/s^2 Therefore, the acceleration due to gravity on star B’s surface is 2.50 m/s^2. Problem #2 Find the gravitational acceleration on the surface of comet A, with the comet’s mass being 9.875 × 10^22 kg and its radius measuring 2.15 × 10^3 km. The universal gravitational constant is G = 6.67 × 10^-11 Nm^2/kg^2. Given data: • Gravitational acceleration on the surface of comet A, g = ? • Mass of the comet A, M = 9.875 × 10^22 kg • Radius of the comet A, r = 2.15 × 10^3 km = 2.15 × 10^6 m • Universal gravitational constant, G = 6.67 × 10^-11 Nm^2/kg^2 Using the equation: • g = GM/r^2 • g = (6.67 × 10^-11 × 9.875 × 10^22)/(2.15 × 10^6)^2 • g = (65.8662 × 10^11)/(4.6225 × 10^12) • g = 14.24 × 10^-1 • g = 1.42 m/s^2 Therefore, the gravitational acceleration on the surface of comet A is 1.42 m/s^2. Problem #3 Determine the gravitational acceleration at the surface of dwarf planet Z, knowing that it has a mass of 4.8 × 10^23 kg and a radius of 3 × 10^3 km. Take the value of the universal gravitational constant as G = 6.67 × 10^-11 Nm^2/kg^2. Given data: • Gravitational acceleration at the surface of dwarf planet Z, g = ? • Mass of the dwarf planet Z, M = 4.8 × 10^23 kg • Radius of the dwarf planet Z, r = 3 × 10^3 km = 3 × 10^6 m • Universal gravitational constant, G = 6.67 × 10^-11 Nm^2/kg^2 Using the equation: • g = GM/r^2 • g = (6.67 × 10^-11 × 4.8 × 10^23)/(3 × 10^6)^2 • g = (32.016 × 10^12)/(9 × 10^12) • g = 3.55 m/s^2 Therefore, the gravitational acceleration at the surface of dwarf planet Z is 3.55 m/s^2. Problem #4 Find the gravitational acceleration at the surface of celestial body A, given that its mass is 4.8 × 10^24 kg, and its radius is 6.789 × 10^3 km. The universal gravitational constant is G = 6.67 × 10 ^-11 Nm^2/kg^2. Given data: • Gravitational acceleration at the surface of the celestial body, g = ? • Mass of the celestial body, M = 4.8 × 10^24 kg • Radius of the celestial body, r = 6.789 × 10^3 km = 6.789 × 10^6 m • Universal gravitational constant, G = 6.67 × 10^-11 Nm^2/kg^2 Using the equation: • g = GM/r^2 • g = (6.67 × 10^-11 × 4.8 × 10^24)/(6.789 × 10^6)^2 • g = (32.016 × 10^13)/(46.0905 × 10^12) • g = 0.6946 × 10 • g = 6.94 m/s^2 Therefore, the gravitational acceleration at the surface of the celestial body is 6.94 m/s^2. 📝 Your feedback matters. Visit our contact page. More topics External links Forceinphysics.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill. 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For accurate estimation of the ensemble average diffusion propagator (EAP) traditional For accurate estimation of the ensemble average diffusion propagator (EAP) traditional multi-shell diffusion imaging (MSDI) approaches require acquisition of diffusion signals for a range of data sets. signal from critically under-sampled measurements. Several imaging and analysis schemes which use fewer measurements than traditional DSI have recently been proposed in the literature (Wu and Alexander 2007 Jensen et al. 2005 Assemlal et al. 2011 Merlet et al. 2012 Barmpoutis et al. 2008 Descoteaux et al. 2010 Zhang et al. 2012 Ye et al. 2011 2012 Hosseinbor et al. 2012 Each of these techniques captures a different aspect of the underlying tissue organization which is missed by HARDI. Traditional methods of EAP estimation that account for the non-monoexponential (radial) decay of diffusion signals require a relatively large number of measurements at high data set. The primary aim of the algorithm presented in this work is the recovery of diffusion signal from sub-critically sampled measurements. Following this any model or methodology (such as multi-compartment models kurtosis diffusion propagator free-water etc.) can be used to compute diffusion measures or features (? zarslan et al. 2013 Thus in this work we do not focus on recovering model specific diffusion properties as they can be computed once an estimate of the diffusion signal in the entire q-space is available using the proposed method. 3 Background 3.1 Diffusion MRI Under the narrow pulse assumption the diffusion signal diffusion signal with = 0 value respectively. Alternatively can be written as a function of = being the duration of the gradient pulse Δ is the mixing time (i.e. the time between the two diffusion-encoding gradients) is the gyromagnetic constant and \|\|g\|\| denotes the Euclidean norm of the diffusion-encoding gradient g. In the context GENZ-644282 of MSDI the signal is measured along discrete orientations for several different values of value shell the sampling points are spread over the unit sphere thereby giving the measurements a multi-shell structure. 3.2 Compressed sensing The theory of CS provides the mathematical foundation for accurate recovery of signals from their discrete measurements acquired at sub-critical (aka sub-Nyquist) rate (Candès et al. 2006 Donoho 2006 Candes et al. 2011 The theory relies on two key concepts: and ∈ is said to admit a sparse representation in Ψ if its expansion coefficients contain only a small number of significant coefficients i.e. if = Ψc then most of the elements of c ∈ are zero. If only elements of c are GENZ-644282 nonzero then the signal is said to be ? Dirac delta function. Consequently denoting by s ∈ ?a column vector of discrete measurements of is measurement noise and the basis Φ acts as a subsampling operator. CS theory asserts that to reconstruct the full signal from its incomplete measurements s one can use a non-linear decoding scheme displayed by the following ?1-norm minimization problem between the representation Ψ GENZ-644282 and sampling Φ bases was a necessary condition for a successful CS-based signal reconstruction. For the case when Ψ is definitely chosen to become an overcomplete dictionary (as it is the case in the present study) the importance of the above condition was recently shown to be much less essential (Candes et al. 2011 As such the ability of an overcomplete Ψ to provide sparse representation for the signals of interest can guarantee reliable transmission recovery from incomplete measurements. However in GUB this scenario the lower bound on the number of measurements required for transmission recovery is GENZ-644282 still application dependent and has GENZ-644282 to be identified from practical experimental validation studies. More importantly this lower bound depends on the level of sparsity of the representation dictionary Ψ. As a result we will use an experimental setup to determine the minimal quantity of gradient directions (measurements) required for appropriate recovery of dMRI data in ∈ ?+ and ∈ (0 1 be a positive scaling parameter. Further let + 1)} {be\|become\|end up being} a Gaussian function which we {subject\|subject matter} to a GENZ-644282 series of dyadic scalings as {shown\|demonstrated\|proven} below ∈ := {?1 0 1 2 . . .}. The {corresponding\|related\|matching} spherical ridgelets with their energy spread around the great {circle\|group} {supported\|backed} by v {is\|is usually\|is definitely\|can be\|is certainly\|is normally} {given\|provided} by: denotes the Legendre polynomial of {order\| purchase} and and to a finite {set\|arranged\|established} {?1 0 1 . . . defines the highest level of “detectable” (high {frequency\|rate of recurrence\|regularity}) {signal\|transmission\|sign\|indication} {details\|information}. Additionally the {set\|arranged\|established} of all {possible\|feasible} has a {dimension\|dimensions\|sizing\|aspect} of (+ 1)2. {Similarly\|Likewise}.	{"url":"https://www.crispr-reagents.com/for-accurate-estimation-of-the-ensemble-average-diffusion-propagator-eap-traditional/","timestamp":"2024-11-08T02:26:24Z","content_type":"text/html","content_length":"35170","record_id":"<urn:uuid:6e799f9e-fb14-46b8-b942-671434d1ccac>","cc-path":"CC-MAIN-2024-46/segments/1730477028019.71/warc/CC-MAIN-20241108003811-20241108033811-00836.warc.gz"}
I can be reached at maryam.khaqan@utoronto.ca. My office is located in the Health Sciences Building, HSB384, at 155 College St, Toronto, ON M5T 1P8, Canada. Postcards welcome :) P.S. Because I get asked all the time: My first name is pronounced mer + yum (so mer as in the first syllable of mermaid and yum as in delicious). Only two syllables, not Mer-ri-yum and definitely not Mayr-yum. My last name is pronounced as in this youtube video. I prefer to be called Maryam or Dr. Maryam Khaqan, but not so much Dr. Khaqan.	{"url":"https://www.maryamkhaqan.com/","timestamp":"2024-11-15T04:36:30Z","content_type":"text/html","content_length":"96327","record_id":"<urn:uuid:0b914b84-75b8-4f9e-b053-f0f7f3095658>","cc-path":"CC-MAIN-2024-46/segments/1730477400050.97/warc/CC-MAIN-20241115021900-20241115051900-00600.warc.gz"}
Don't underestimate the estimate : Physics Stop Don’t underestimate the estimate \| Marcus \| Uncategorised A few weeks ago we had a small, informal competition in the department – guess the maximum gradient on one of the roads on campus. I think the motivation for this this small stretch of hill (or what passes for a hill here in Hamilton) was going to be used as part of a dynamics experiment, and so one of our technicians was about to go out and measure the gradient. I’m happy to say that I won the competition, without even going out to the road and looking at it carefully. The prize was simply to feel smug. I predicted a maximum gradient of 9.5 degrees; I think from memory the measured gradient was 10.1. Being a physicist, I estimated rather than guessed. I simply thought "What is the average gradient?". This wasn’t too difficult. Thinking about how the buildings are laid out on campus, I thought about how many floors that the road drops by. That gave me an estimate of the drop distance. Then I compared it in my head to the length of the swimming pool to estimate the length of that stretch of road. Divide the former by the latter, take the inverse tangent, and I get the average gradient in terms of an angle. Then came the bit that was rather more vague. I needed the maximum gradient, but had the average. Clearly the maximum is higher than the average. So to go from one to the other, I need to multiply by a number that’s bigger than 1. So I picked 2. Though even that wasn’t a wild guess. The road starts off level, and ends level, so if we assume it gains gradient uniformly then loses it uniformly, the maximum gradient will be about double the average. Perhaps I shouldn’t have been all that surprised that I was very close. The point is that I estimated rather than guessed. It’s a skill that is very important in physics, but it’s one that often gets overlooked during teaching. The difference is that an estimate is based on what we do know about the situation – even if it’s only approximate knowledge – rather than a guess which is simply a number plucked out of the air. Some fun things to get students to estimate include the number of carbon atoms that are worn off the soles of their shoes during a day’s wear and the mass of the building they are sitting in. Leave a Reply Cancel Reply You must be logged in to post a comment.	{"url":"https://blog.waikato.ac.nz/physicsstop/2013/03/15/dont-underestimate-the-estimat/","timestamp":"2024-11-02T22:04:53Z","content_type":"text/html","content_length":"60573","record_id":"<urn:uuid:03b32b49-685c-4b23-ab0e-1c4ebbf2dbe5>","cc-path":"CC-MAIN-2024-46/segments/1730477027730.21/warc/CC-MAIN-20241102200033-20241102230033-00224.warc.gz"}
How do you simplify the fraction 15/36? \| HIX Tutor How do you simplify the fraction #15/36#? Answer 1 Showing a little trick #color(blue)("The trick")# Consider the numbers given: Adding the digits of the 15 of #15/36# # 1+5=6# and 6 is exactly divisible by 3 thus so is 15 Adding the digits of the 36 of #15/36# #3+6=9# and 9 is exactly divisible by 3 thus so is 36 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ #color(blue)("Answering the question")# #15/36-=(15-:3)/(36-:3) = 5/12# The #-=# means 'equivalent to' 5 is a prime number so we can not simplify any further. Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer 2 To simplify the fraction ( \frac{15}{36} ), find the greatest common divisor (GCD) of 15 and 36, which is 3. Divide both the numerator and denominator by the GCD: [ \frac{15}{36} = \frac{15 \div 3}{36 \div 3} = \frac{5}{12} ] So, ( \frac{15}{36} ) simplifies to ( \frac{5}{12} ). Sign up to view the whole answer By signing up, you agree to our Terms of Service and Privacy Policy Answer from HIX Tutor When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some Not the question you need? HIX Tutor Solve ANY homework problem with a smart AI • 98% accuracy study help • Covers math, physics, chemistry, biology, and more • Step-by-step, in-depth guides • Readily available 24/7	{"url":"https://tutor.hix.ai/question/how-do-you-simplify-the-fraction-15-36-8f9afa482f","timestamp":"2024-11-10T10:53:24Z","content_type":"text/html","content_length":"576494","record_id":"<urn:uuid:b89578dd-2dce-4ae6-9e70-eb2f2523499e>","cc-path":"CC-MAIN-2024-46/segments/1730477028186.38/warc/CC-MAIN-20241110103354-20241110133354-00239.warc.gz"}
How to Solve Guesstimate Questions in an Interview Let’s take an example guesstimate question for data analyst roles: How many cups of tea are consumed in Delhi in a day? Here’s how you can solve it using the above 4 steps: 1. Clarify the question if you don’t understand it. Since this one is simple and self-explanatory, you can proceed with the second step. 2. Break down the problem into manageable parts- what’s the population of Delhi, how many of them drink tea, and how many cups of tea do they drink in a day. 3. Now, you solve each piece of the puzzle. Population of Delhi (x): Delhi has a big population, let’s say around 3 crores. People who drink tea (y): Tea is one of the most popular beverages in north India. So, we can expect at least 70% of people would drink it. Number of cups a person drinks in a day (z): Indians generally consume tea twice a day- one in the morning and one in the evening. Some may drink more than 2 cups, some may drink only one. So let’s say it’s, on average, 2 cups. 4. Now, in the final step, you combine all the pieces of the puzzle: Total number of cups of tea consumed in Delhi in a day: = x.(y/100).z = (30,000,000).(0.7).(2) = 42,000,000 So our guesstimate is that Delhiwalas consume around 4.2 crore cups of tea in a day!	{"url":"https://ivyproschool.com/blog/how-to-solve-guesstimates-for-your-next-analytics-interview-part-1/","timestamp":"2024-11-06T10:33:15Z","content_type":"text/html","content_length":"116620","record_id":"<urn:uuid:12426557-b580-47b5-9305-397da115fd90>","cc-path":"CC-MAIN-2024-46/segments/1730477027928.77/warc/CC-MAIN-20241106100950-20241106130950-00075.warc.gz"}
Albion College Mathematics and Computer Science Colloquium Title: Are you smarter than a 19th century mathematician? Speaker: Timothy A. Sipka Associate Professor Mathematics and Computer Science Alma College Alma, Michigan Abstract: The Four Color Theorem is a simple and believable statement: at most four colors are needed to color any map drawn in the plane or on a sphere so that no two regions sharing a boundary receive the same color. It might be surprising to find out that mathematicians searched for a proof of this statement for over a century until finally finding one in 1976. In this talk, we'll consider the "proof" given by Alfred Kempe, a proof published in 1879 and thought to be correct until an error was found in 1890. You're invited to look carefully at Kempe's proof and see if you can do what many 19th century mathematicians could not do—find the flaw. Location: Palenske 227 Date: 10/21/2010 Time: 3:10 author = "{Timothy A. Sipka}", title = "{Are you smarter than a 19th century mathematician?}", address = "{Albion College Mathematics and Computer Science Colloquium}", month = "{21 October}", year = "{2010}"	{"url":"http://mathcs.albion.edu/scripts/mystical2bib.php?year=2010&month=10&day=21&item=a","timestamp":"2024-11-02T18:43:28Z","content_type":"text/html","content_length":"2228","record_id":"<urn:uuid:861d90cd-5871-42ad-a4ec-dd95c6cb8b81>","cc-path":"CC-MAIN-2024-46/segments/1730477027729.26/warc/CC-MAIN-20241102165015-20241102195015-00574.warc.gz"}
Master the Art of Calculating Board Feet with These Simple Steps \| Saw Theory To calculate board feet, multiply the length, width, and thickness of a board in inches, then divide the result by 144. Board feet are a measurement of lumber that is used in woodworking and construction projects. Board feet are the most common unit of measurement for lumber and is used to determine the total amount of wood needed for a project. Knowing how to calculate board feet is essential for anyone involved in woodworking or construction. Understanding the process ensures that you buy the right amount of lumber and helps to avoid waste. It’s a simple calculation that only requires the length, width, and thickness of a board. This article will provide a step-by-step guide on how to calculate board feet and explain how board feet is used in the industry. Credit: stylebyemilyhenderson.com Understanding Board Feet: A Beginner’s Guide Board feet is a common unit used in woodworking to measure the volume of wood. It is the calculation of the boardâ€™s thickness, width, and length, and then dividing it by twelve. Understanding board feet is essential in woodworking to accurately estimate costs and inventory. Measuring board feet is vital to determine the cost of a piece of lumber. To measure board feet, determine the thickness, width, and length, convert the measurements to inches, and then divide the total by 144. This will give you the total board footage. Knowing how to calculate board feet is crucial for woodworkers, and by following this simple calculation, you can accurately measure lumber and make the right decisions for your woodworking project. Use it in your next wood project, and get professional results. The Basic Formula For Calculating Board Feet Calculating board feet may seem like a daunting task, but it can be done with the basic formula. The standard formula is length (in feet) x width (in inches) x thickness (in inches) divided by 12. Understanding the components of the formula is crucial for accurate measurements. To apply the formula, measure your board and convert all units to feet and inches. Then, plug in the measurements into the formula and calculate the board feet. Following these simple steps can save you time and money, especially if you’re planning a woodworking project. With a little practice, calculating board feet can become second nature to you. Practical Applications Of Board Feet In Woodworking Board feet are the standard unit of measurement for lumber in the woodworking industry. Estimating how much lumber you will need for a project can be challenging, but calculating board feet can make it easier. To determine the board feet of a piece of lumber, measure its thickness, width, and length in inches, then divide the total by 144. You can use this information to calculate the cost of a project by multiplying the board footage by the cost per board foot. It’s also important to maximize your lumber yield and minimize waste to reduce costs. This can be achieved by planning your cuts carefully and selecting the best quality lumber for your project. By understanding board feet, you can confidently estimate lumber needs and costs for your next woodworking project. How To Avoid Common Mistakes When Calculating Board Feet Calculating board feet seems simple, but it is prone to mistakes. Using the wrong formula, incorrect unit conversion, and failing to account for thickness and width are common errors. When calculating board feet, it is important to choose the correct formula according to the woodâ€™s shape. Be mindful of converting measurements and always double-check the units to ensure accuracy. Also, donâ€™t forget to account for thickness and width, which are critical factors in the calculation. Lastly, there are alternate methods to calculate board feet, so explore your options. By avoiding these common mistakes, you can make accurate calculations. Frequently Asked Questions On How To Calculate Board Feet? What Is Board Foot And How Is It Calculated? A board foot is a unit of volume measurement for wood. It is calculated by multiplying the thickness (in inches) by the width (in inches) and length (in feet) of a given board and then dividing the total by 12. Why Is Board Foot Used Instead Of Other Units? A board foot is used because it provides an accurate measurement of the amount of wood in a board, regardless of its thickness, width, or length. It is also the standard unit of measurement for lumber in the united states and Canada, allowing for consistency in pricing and purchasing. How Do I Convert Other Units To Board Feet? To convert other units to board feet, simply multiply the volume of the wood in cubic inches by 0. 00236. For example, a board that measures 2 inches thick, 6 inches wide, and 8 feet long would be (2 x 6 x 96) / 12 = 96 board feet. Is There A Difference Between Green And Dry Board Feet? Yes, there is a difference between green and dry board feet. Green board refers to freshly cut wood that has not yet had a chance to dry, while the dry board is wood that has been dried to a certain moisture content. Freshly cut wood will have higher moisture content and therefore will be heavier and less stable than dry wood. How Does Board Foot Calculation Affect Woodworking Projects? Calculating board feet accurately is essential for woodworking projects as it helps determine the amount of wood needed for a project, and thus, the cost. Proper calculation can prevent waste and ensure that the correct amount of wood is ordered, saving time and money in the long run. Now that you have learned how to calculate board feet, you can confidently estimate the amount of lumber needed for your next project. Remember to measure accurately and convert your measurements to board feet before making any calculations. Using the formula length x width x thickness / 12, you can easily determine the total board footage required for your project. It’s also important to factor in any waste or excess material to ensure you have enough lumber for the project. With these tips, you can streamline the lumber-buying process and avoid wasting time and money. Knowing how to calculate board feet is an essential skill for any DIYer or professional woodworker. So get measuring and start building! 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Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics The hydrodynamic properties of rigid fractal aggregates have been investigated by considering their motion in shear flow in the Stokesian dynamics approach. Due to the high fluid viscosity and small particle inertia of colloidal systems, the total force and torque applied to the aggregate reach equilibrium values in a short time. Obtaining equilibrating motions for a number of independent samples, one can extract the average hydrodynamic characteristics of the given fractal aggregates. Despite the geometry of these objects being essentially disordered, the average drag-force distributions for aggregates show symmetric patterns. Moreover, these distributions collapse on a single master curve, characteristic of the nature of the aggregates, provided the positions of the particles are rescaled with the geometric radius of gyration. This result can be used to explain the reason why the stress acting on an aggregate and moments of the forces acting on contact points between particles follow power-law behaviors with the aggregate size. Moreover, the values of the exponents can be explained. As a consequence, considering cohesive force typical for colloidal particles, we find that even aggregates smaller than a few dozen particles must experience restructuring when typical shear flow is applied. Dive into the research topics of 'Hydrodynamic stress on small colloidal aggregates in shear flow using Stokesian dynamics'. Together they form a unique fingerprint.	{"url":"https://portal.fis.tum.de/en/publications/hydrodynamic-stress-on-small-colloidal-aggregates-in-shear-flow-u","timestamp":"2024-11-08T14:16:29Z","content_type":"text/html","content_length":"52748","record_id":"<urn:uuid:fd404d23-65de-4214-a3ec-c512bc124af9>","cc-path":"CC-MAIN-2024-46/segments/1730477028067.32/warc/CC-MAIN-20241108133114-20241108163114-00488.warc.gz"}
Dealing With Rounding Errors in Numerical Unit Tests Monday, December 1, 2008 – 4:00 AM I’ve been writing some unit tests which attempt to verify some mathematical modeling results. Here’s a test that creates a physical model (of a universe) containing some stars and verifies the initial energy of the system. public void Energy() Universe target = new Universe( new TestSimpleUniverseInitializer(), new ForwardEulerIntegrator()); Assert.InRange(target.Energy(), 1.99713333333333, 99713333333334); There are two problems with this test. Firstly, I had to figure out the ranges in my head. Secondly the test’s intent isn’t expressed correctly. I don’t really mean a range, I mean equal within some margin of rounding error. What I really want to say is that I expect the energy of the system to be equal to a value within a certain margin of error. Something like this: Assert.Equal(target.Energy(), 1.99713333333333, new ApproximateComparer(0.0000001)); If turns out that with xUnit‘s Assert.Equal method I can specify my own IComparer to do just that. The ApproximateComparer is a new implementation of IComparer<> that returns an equality result for values that are within a margin of error and returns a standard Comparer result if not. public class ApproximateComparer : IComparer<double> public double MarginOfError { get; private set; } public ApproximateComparer(double marginOfError) if ((marginOfError <= 0) \|\| (marginOfError >= 1.0)) throw new ArgumentException("..."); MarginOfError = marginOfError; public int Compare(double x, double y) // x = expected, y = actual if (x != 0) double margin = Math.Abs((x - y) / x); if (margin <= MarginOfError) return 0; return new Comparer(CultureInfo.CurrentUICulture).Compare(x, y); I wrote this TDD using the Theory attribute provided by the xUnit. I find theories really nice for developing this kind of test. They let you capture several similar edge cases within one test. public class ApproximateComparerTests public void MarginMustBeBetweenZeroAndOne(double margin) Assert.Throws<ArgumentException>(() => { new ApproximateComparer(margin); }); [InlineData(100.0, 100.0)] [InlineData(100.0, 101.0)] [InlineData(101.0, 100.0)] public void TwoNumbersAreEqualIfWithinOnePercent(double x, double y) IComparer<double> target = new ApproximateComparer(0.01); Assert.Equal(x, y, target); [InlineData(100.0, 102.0)] [InlineData(102.0, 100.0)] [InlineData(100.0, 100.0)] public void ShouldBehaveLikeNormalComparerForNumbersOutsideTheMargin( double x, double y) IComparer<double> target = new ApproximateComparer(0.01); Assert.Equal(new Comparer(CultureInfo.CurrentUICulture).Compare(x, y), target.Compare(x, y)); public void ShouldBehaveLikeNormalComparerWhenComparingToZero() IComparer<double> target = new ApproximateComparer(0.01); Assert.NotEqual(0.0, 0.0001, target); You can overdo this. Note how each set of inputs yields the same result. I’m simply testing edge cases. You can overcomplicate your use of theories if you start using them to provide inline data that specifies both the inputs and outputs of the test. Updated April 14th 2009: I updated the code in this post to cope with the case where the expected value is zero. As you’ll see from the tests and the code for an expected value of zero the approximate comparer reverts to the default comparer and any non-zero value will evaluate as not equal. The ApproximateComparer is best used for comparing non-zero values where the expected value is also not known. For example you run two different calculations and expect them to agree within some margin of error. This is what I actually wrote this for. You can also use the xUnit InRange and NotInRange assertions when comparing values where the expected value is known. I still prefer the approximate comparer here as I think the resulting code is slightly more expressive. For dealing with comparisons that fail due to rounding errors – where the expected and actual value only differ due to the limits of numerical precision then consider something like the dnAnalytics Precision.EqualsWithTolerance approach (see Petrik’s comment below). 1. 7 Responses to “Dealing With Rounding Errors in Numerical Unit Tests” 2. Hi Ade This is a cool way of testing numeric values. I really have to look at what xUnit has to offer. Would you say it is better suited for numerical tests than NUnit etc? Also I thought you might be interested to know that the dnAnalytics library (www.codeplex.com/dnanalytics) will have a Precision class in the next release (disclaimer I am a contributor to the dnAnalytics library). This class provides Equality and compare methods for floating point values. Comparisons can be made based on the number of significant decimals and on the number of floating point values between two numbers. For instance your example could be written as: public void Energy() Universe target = new Universe( new TestSimpleUniverseInitializer(), new ForwardEulerIntegrator()); Assert.IsTrue(Precision.EqualsWithTolerance(target.Energy(), 1.99713333333333, 1); This checks if target.Energy() is within one floating point value from 1.99713333333333 (which may or may not be exactly what you want). By Petrik on Dec 4, 2008 3. Hi Petrik, I prefer xUnit.NET over NUnit largely because it’s written from the ground up to take advantage of lots of the newer features of .NET. NUnit started off around .NET 1.0 and has had these new things added over time. I really like xUnit’s extensibility. This is the second challenge to testing I’ve been able to solve simply be extending the framework (see the StrictFact attribute for the other one). I’ll have to check out the dnAnalytics library when I get a chance. By Ade Miller on Dec 4, 2008 4. The only problem with this approach is it’s a bit naive; what happens when x is 0.0? You divide by 0, the result is undefined (I got NaN once and Infinity another time, oddly enough), and the comparison returns false. Petrik’s response probably uses a technique that exploits the representation of double in memory and is more general-purpose. By Owen on Apr 14, 2009 5. Ew it doesn’t work well if x is close to 0, either. For example, 0.01 and 0.0001 are obviously close. However, (x – y) / x is 0.99 in this case, which would require a much larger “margin of error”. It gets worse as x approaches 0. However, this is irrelevant to what was the point of your post: that you can easily add an arbitrary comparison to xUnit. By Owen on Apr 14, 2009 6. Owen, Good point. The current code doesn’t deal with zero very well. Yes the general point is that xUnit is extensible but I know people copy/paste code so I’ve updated the code and added some guidelines about where you might want to use the ApproximateComparer. As you point out there’s nothing to stop you writing something that better fits your needs. By Ade Miller on Apr 14, 2009 7. Just in case anyone is curious, if you are using the Microsoft.VisualStudio.QualityTools.UnitTest framework the AreEquals will accept a delta for comparison purposes… AreEqual(expected, actual, delta, message); By Eric Malamisura on Nov 24, 2009 1. 1 Trackback(s) Sorry, comments for this entry are closed at this time.	{"url":"http://www.ademiller.com/blogs/tech/2008/12/dealing-with-rounding-errors-in-numerical-unit-tests/?owa_from=feed&owa_sid=","timestamp":"2024-11-09T17:31:47Z","content_type":"application/xhtml+xml","content_length":"50479","record_id":"<urn:uuid:97110a15-18ff-4758-b097-3a7705005912>","cc-path":"CC-MAIN-2024-46/segments/1730477028125.59/warc/CC-MAIN-20241109151915-20241109181915-00267.warc.gz"}
A fractal origin for the mass spectrum of interstellar clouds. II. Cloud models and power-law slopes for Astrophysical Journal Astrophysical Journal A fractal origin for the mass spectrum of interstellar clouds. II. Cloud models and power-law slopes View publication Three-dimensional fractal models on grids of ∼2003 pixels are generated from the inverse Fourier transform of noise with a power-law cutoff and exponentiated to give a lognormal distribution of density. The fractals are clipped at various intensity levels, and the mass and size distribution functions of the clipped peaks and their subpeaks are determined. These distribution functions are analogous to the cloud mass functions determined from maps of the fractal interstellar medium using various thresholds for the definition of a cloud. The model mass functions are found to be power laws with powers ranging from -1.6 to -2.4 in linear mass intervals as the clipping level increases from ∼0.03 to ∼0.3 of the peak intensity. The low clipping value gives a cloud-filling factor of ∼10% and should be a good model for molecular cloud surveys. The agreement between the mass spectrum of this model and the observed cloud and clump mass spectra suggests that a pervasively fractal interstellar medium can be interpreted as a cloud/ intercloud medium if the peaks of the fractal intensity distribution are taken to be clouds. Their mass function is a power law even though the density distribution function in the gas is a lognormal. This is because the size distribution function of the clipped clouds is a power law, and with clipping, each cloud has about the same average density. A similar result would apply to projected clouds that are clipped fractals, giving nearly constant column densities for power-law mass functions. The steepening of the mass function for higher clip values suggests a partial explanation for the steeper slope of the mass functions for star clusters and OB associations, which sample denser regions of interstellar gas. The mass function of the highest peaks is similar to the Salpeter initial mass function, suggesting again that stellar masses may be determined in part by the geometry of turbulent gas.	{"url":"https://research.ibm.com/publications/a-fractal-origin-for-the-mass-spectrum-of-interstellar-clouds-ii-cloud-models-and-power-law-slopes","timestamp":"2024-11-06T08:28:48Z","content_type":"text/html","content_length":"75706","record_id":"<urn:uuid:fccd40ea-2370-46f8-8803-2216e8c96e67>","cc-path":"CC-MAIN-2024-46/segments/1730477027910.12/warc/CC-MAIN-20241106065928-20241106095928-00679.warc.gz"}
How to Use the Average Attendance Formula in Excel (5 Methods) - ExcelDemy Dataset Overview For your better understanding, we will use a sample dataset. The data set contains, Names, Months, Number of attendances, and number of total working days. We will calculate the average attendance per month, as well the average percentage per month. Method 1 – Average Attendance by Arithmetic Calculation • In cell I5, enter the following formula: □ This calculates the sum of attendance for six months and divides it by the total number of months (which is 6). We use an absolute cell reference for F15 to ensure consistent division. • To calculate the percentage of attendance, enter this formula in cell J5: • Use AutoFill to extend the formulas to the rest of the series. • Select the ranges in the percentage column from J5 to J12. • Click the Percentage sign in the number tab. Read More: How to Average Filtered Data in Excel Method 2 – Average Attendance Using the Average Function • Click on cell I5 and enter the following formula: • This averages all values from C5 to H5. • Calculate the percentage of attendance in cell J5 using Method 1. • Press ENTER. • Use AutoFill to fill the rest of the series. • Convert the percentage values in the Percent column by selecting the range and clicking the Percentage sign in the number tab. The data sheet is ready. Read More: How to Calculate Class Average in Excel Method 3 – Average Attendance Using the Formula Ribbon • Click on cell I5. • Go to the Formulas ribbon and select Average from the AutoSum feature. • Use AutoFill to complete the series. Method 4 – Average Attendance Using a Shortcut Key • If you’re comfortable with keyboard shortcuts, press ALT + M. • Press U, then press A. Excel will automatically select the cells. • Right-click and drag it down to AutoFill the series. Related Content: How to Calculate Average Percentage of Marks in Excel Method 5 – Average Attendance Using SUMPRODUCT Function in Excel • Click on cell D12. • Enter the following formula: Here’s how it works: □ The SUMPRODUCT function calculates the sum of products for each month: (C5 * D5) + (C6 * D6) + … + (C10 * D10). □ We then divide this sum by the total number of employees (SUM(C5:C10)). • Press ENTER to get the results. Practice Section Feel free to practice using the provided sheet. Download Practice Workbook You can download the practice workbook from here: Related Articles << Go Back to Excel Average Formula Examples \| How to Calculate Average in Excel \| How to Calculate in Excel \| Learn Excel Get FREE Advanced Excel Exercises with Solutions! We will be happy to hear your thoughts Leave a reply	{"url":"https://www.exceldemy.com/average-attendance-formula/","timestamp":"2024-11-05T03:31:31Z","content_type":"text/html","content_length":"196649","record_id":"<urn:uuid:95d45e43-3cce-478b-a6b6-9642f4a98132>","cc-path":"CC-MAIN-2024-46/segments/1730477027870.7/warc/CC-MAIN-20241105021014-20241105051014-00866.warc.gz"}
Futility of Motor Power Ratings Motor Power Ratings Page Last Modified On: July 18, 2023 Why don't you list the rated watts of each motor? Simple Answer The reason we don't have a simple power level for each motor or kit is that there is no standard or even consistent way to provide a numeric "watts rating" for a motor system. You can see the exact same motor listed as 250 watts, 500 watts, and 1000 watts by different vendors, and there is a valid justification for all those number. That makes a vendor or manufacturer's watts rating in isolation a fairly pointless figure for choosing or comparing setups, and we're not keen to particiate in that kind of arbitrary numbers game. Instead, we give a ballpark range (like 250-500 watts, 600-1200 watts etc.) in which the motor is typically used and have provided a useful and accurate motor simulator tool that will show you the exact output power for any combination of motor, controller, and battery pack; not just as an arbitrary single number but over the entire speed range of the vehicle. This is considerably more valuable for understanding a system's performance. You can see things like the peak output power, the output power at your predicted cruising speed under any kind of hill or vehicle type, and whether the motor may be prone to overheating at a given load. Check it out: Justin's Complete Rant OK, for those not satisfied with the paragraphs above and interested in the full technical lowdown, then read on. We get asked this question "what's the power rating of this motor" all the time and it is both an astute and infuriating question to be asked. It is astute because more than anything else, the specific output power of an electric bike motor (in watts) determines exactly how an ebike will perform and handle a given situation. 600 watts of mechanical power will cause a bike to behave the same whether it is coming from a small geared hub motor, a massive direct drive hub motor, a mid-drive motor, or a giant gust of tail wind. If you need 600 watts of power to climb a certain hill at a certain speed, but your motor is only capable of producing 300 watts, then either you'll have to make up the shortfall with your legs, or your bike will slow down until only 300 watts is needed. An actual watt is a watt of power, no matter where it comes from. It's tempting to think that if your usage case requires 600 watts of mechanical power, then you should get a motor rated for at least 600 watts, simple right, a watt is a watt? And if one company sells a kit rated for 750 watts, that will be more powerful than a different kit rated at 500 watts correct? But there's a problem, and this is where things get infuriating in our efforts a explaining things to people. While an actual watt is an actual watt, There is NO SUCH THING as a "rated watt" or any standarized method for rating ebike motor power. That's the truth, regardless of what other companies imply. With most electrical devices the term rated power has a very clear meaning. Like a 60 watt lightbulb can be counted on to draw 60 watts of power when it is turned on. A 1500 watt heater will produce 1500 watts of heat, regardless of which brand or model you use. With electric motors, they do not produce a fixed amount of power when you turn them on. If you run the motor with your wheel off the ground, then it will spin at full speed and produce no power output. As you then load the motor with drag, it will slow down a bit and produce torque, and the more you load it down the more it slows down and the higher the torque and power it puts out. At some point as you continue to load and slow the motor down, then the output power will start to decrease. Even though the torque is still increasing, the lower RPM means that the mechanical power produced goes down. If you stall the motor completely, it might be making a ton of torque but it's producing zero output power. The actual power output of a motor depends entirely on how heavily it is loaded in a given situation and the maximum electrical power that the controller lets flow into the motor, it has little to nothing to do with a rating anywhere.The above two graphs show the power curves of the same motor, in one case running with a 36V battery and 20A controller at full throttle producing a peak of 600 watts, in the other case with a 48V battery and a 35A controller at full lthrottle producing a peak of 1100 watts. . So what limits how much power a motor can produce? When the motor is loaded down like this to produce power, it also draws more electrical current through the motor windings. This current is responsible for most of the heat being generated inside the motor since the copper windings have electrical resistance. If you double the current through the windings in order to have double the torque and power from the motor, then you increase the amount of copper heat being generated by a factor of FOUR (the I^2R relationship). This heat of course causes the motor to warm up. Motors are large heavy chunks of metal, so they can have quite a bit of short term heat thrown at them and not increase in temperature too much. But if the heat continues to accumulate inside the motor windings faster than it can be dissipated to the air outside, then you risk the motor getting so hot that insulation burns off the copper enamel, nylon gears soften and strip, or magnets start to demagnetize. At that point, you have 'burnt up' or 'cooked' your motor. Whether this happens is a function not just of the amps flowing through the motor but also the time over which these high motor currents are sustained. The difference between power and torque An important point to realize here is that it's not the output power but the output torque of the motor which causes it to heat up and eventually fail. If you don't remember high school physics lessons, torque is the rotational measurement of force, ie. how hard something is being twisted. It's measured by the product of force times the length of the lever arm. <diagram of torque equations and graphs, ft-lb, Newton-meters> Power by contrast is a measurement of how rapidly work is being done. In order for a twisting force to do work it needs to be spinning something, and the faster it spins at a given torque then the more work it will do. Power is the product of torque times the spinning rate, and in SI units where you measure torque in Newton-meters and rotational speed in Rad/sec, then it's simple: Power in Watts = torque * rad/sec If you measure speed in rpms, then the power output is Power in Watts = Torque * RPM * 2Pi/60 ~ Torque * RPM * 0.104 A motor producing 20 Nm of torque and spinning at 100 rpm is generating 209 watts. That same motor producing 20 Nm of torque while spinning at 300 rpm is producing 628 watts. Let's assume that 20 Nm is the maximum torque that this motor can produce without risk of it overheating, do you now call it a 200 watt motor? or a 600 watt motor? This is one reason why rated motor powers can be all over the map. It is ultimately the torque and not power that causes a motor to overheat. To convert a maximum torque spec into a power rating you need to also specify the RPM at which you decided this rating. However, permanent magnet electric motors in isolation don't intrinsically have an RPM at which they spin at, they'll have an RPM/V winding constant. It's the combination of this winding constant and your battery voltage that determines how fast a motor will be able to spin in a given setup. So if you specify both a motor and a voltage, then you can make a claim for a rated rpm. But if you are just talking about a motor by itself, it has no intrinsic RPM, the same motor can be run fast or slow by varying the applied voltage, and without any implied RPM at which you run the motor there is no way to talk about how much power it can produce. What about peak power rating? The PEAK power output of a given ebike system is very well defined and has no ambiguity like "rated power", but it's not always as useful as you might expect. In general, the peak motor output power occurs right at the point where the motor controller hits the battery current limit. Our online hub motor simulator allows you to see this easily. In the graph below, we have a typical ebike setup composed of a Crystalyte H3540 hub motor, a 36 battery pack, and a 20A motor controller. When running full throttle, the motor output power (red graph) peaks at 600 watts at 40 kph. Above this speed, the power and torque of the motor decreases until reaching 0 at about 48kph. Below this peak power speed, the motor controller is current limited and so is clamping the electrical input power to the hub motor. The input power (VA) as seen on a Cycle Analyst stays constant at 744 watts while the motor's mechanical output power decreases. That's because the motor is less and less efficient as it slows down in this constant input power scenario, which you can see from the green efficiency curve. Now let's keep the exact same motor and battery but use a higher current 40A motor controller so that the peak input power (volts amps) is nominally 1440 watts. The graph is identical to the 20A controller above 40 kph, but below this speed the 40A controller setup continues to allow larger power outputs until itself peaking at 1058 watts of output power at 33 kph. How do these systems compare? Well, the peak power of the 2nd setup is 80% higher than the first one (1058 watts vs 600 watts). If you rode the bike, you would find that it accelerates faster off the line and has more initial punch, but once you got up to 40 kph then the ride feeling would be identical, and in typical cruising situations you would only appreciate the difference between the setups on steeper hill climbs. It would not by any means feel like an 80% more powerful setup, and if you looked at your average power draw on most trips (wh/km) it wouldn't deviate very much because you would typically be cruising at or above 40 kph and your power levels would be the same. Now lets keep the original 20A controller but increase the battery from 36V to 52V. With this setup, the peak output power is now 840 watts. That's less than the peak power of the 36V 40A arrangement, but if you hopped on this bike and rode it it would likley feel more powerful. The acceleration off the line will be a little bit slower, but then it will keep on accelerating right up to 55+ kph. You'll travel faster, go up most hills faster, and your average power usage will be a lot higher, even though the peak power of the system is less. So now you see why a comparison of peak motor output power alone doesn't tell the full story on how powerful a system will feel. And you can see too that this peak power is not a motor property since all the above graphs used exactly the same motor, it's actually mostly a function of the motor controller and battery pack. I could swap much smaller or larger motors with the same controller and battery, and the output power levels wouldn't vary by that much. Rating by peak INPUT power One common approach for ebike vendors to use when giving a power rating on their kits is to use not the motor output power (peak or otherwise) but the maximum input power as shown on a Cycle Analyst. More often than not we will see people selling a kit with say a 72V battery pack and a 50A motor controller, and they'll advertise it as "3600 watts", even if the particular setup in question might only hit 2000 watts of output power due to poor motor efficiency, and could only sustain half of that again without overheating in very short order. This is an unfortunate practice as it is misleading, but it's understandable why it came to be. It provides the largest number that you can use for marketting, and it's also the wattage number that any electrical power meter will display. A majority of ebike vendors selling and boasting powerful ebike setups embrace this approach, where the claimed watts exceeds not only the actual peak motor power output (usually by at least ~30%), but often well exceeds by a factor of 2 or 3 the mechanical power the system could output on any kind of sustained basis without overheating. What about continuous power? In principle this would seem like a fairest way to compare the relative power of different setups. Rather than talking about the maximum power, you instead compare the continuous power that the motor can output indefinitely without overheating. Then people couldn't just put a high current motor controller and high voltage battery on any motor and call it a 3kW kit. But there are 5 complications to doing that. 1. Again it is not the motor power that causes a motor to overheat, but the motor torque, so to compare systems equally you would also still need to specify the motor RPM. One option would be to compare all hub motors at the speed of a 26" bike doing the road legal limit of 32 kph (20mph), which is about 250 rpm. Then you could scale this rating to the actual speed in your application vehicle. If the motor is rated to produce 500 watts continuously at 20mph, then if you're running it at 30mph you know it will be able to do at least 750 watts continuously, and in a slow 10mph bike you could assume it's a 250 watt continuous motor. If you are lacing the in a smaller 20" diameter wheel, then even at 20mph it would be 650 watts rather than 500 watts because of the higher wheel RPM. 2. It takes a LOT longer than most people would realize for a hub motor to reach steady state temperature equilibrium, upwards of 1-2 hours, while usually the longest steep hill climbs that you actually encounter on the road are over in less than 5-10 minutes. The end result is that motors will have a much lower power rating than what people routinely subject them to, and this would be a misleadingly low number. For instance, the 45mm wide stator MXUS motors are often sold as 5000 watt hub motors. At 250 rpm the core will eventually reach 100oC with just 800 watts of output 3. There is a lot of wiggle room in what is determined to be the overheat temperature of a motor. In practice, most better quality motors have high temperature enamel on the copper windings and can survive excursions in the 150-180 oC temperature range without damage. But few would suggest having the rated continuous core temperature be this hot. So what do you choose, 100oC? 120 oC? The choice of maximum temperature will have a large effect on the rated continuous power number. 4. Ambient temperature has a large effect too. You'll be able to run at higer power levels riding a bike in freezing conditions in the winter, compared to sweltering 40oC summer heat. That 40oC temperature difference on the outside means you can sustain higher torque and current levels in the winter than in the summer. The continuous power rating would need to have an ambient temperature derating factor too. 5. Cooling Mods. The addition of statorade, vent holes in the motor, and other active cooling techniques can greatly increase the continuous torque output of motor while keeping the motor core from overheating. However, these modifications don't in any way change the performance of the motor in terms of peak power levels and efficiency for a given controller and battery voltage. So even though they would have a higher continuous power rating, they wouldn't seem to perform any better the way most people define performance. Adding statorade will increase the continuous motor power by ~40%, but this is nothing like increasing the power by 40% by using a 40% wider motor core and 40% longer magnets, and yet both would have the same "continuous" power rating. Don't be fixated by the watt ratings, take them with large grains of salt. In the first place, hub motors should be rated by how much torque they can produce rather than how many watts they can produce, but even this figure could be subject to much variation and will be difficult to compare across manufacturers and vendors. • Motors don't have fixed power ratings. The sustainable power output of a given motors depends very much on the RPM at which it is spinning. At a higher RPM a given motor can produce more power. • Motors can handle substantially more power for short times than they can sustain continuously, and that short term power is usually all you need for getting to the top of a steep hill. • When ebike companies talk about a motor power, there is no standard at all for whether this is a continuous power rating, a peak output power rating, or a peak input power rating, or something stamped on the product for legal compliance. When Grin talks about a rated motor power, we treat it as some broad ballpark order-of-magnitude kind of thing. There are more powerful and less powerful motors for sure, but don't rely on a single number to capture this in a standardized way. The best would be if motor manufacturers provided full data on the thermal heating of their motors in different load situations and suggested continuous and peak torque outputs, but given how rare it is to find even basic specs like winding resistance of KV, this is wishful thinking. Simulating the Nitty Gritty We produced another incredibly useful web tool that lets you see the long term heating effects of different setups with our in EV trip simulator app after doing years of empirical testing on numerous motor models. It is still in 'beta' stage, mostly because all of the tooltips and documentation are still in probress, but the back-end and model are quite solid. This shows the time evolving temperature of the motor core under any kind of usage pattern and conditions you can dream of, and can then let you know if a given motor system is up to the task or not.	{"url":"https://ebikes.ca/learn/power-ratings.html?utm_source=www.newsletter.rideflywheel.com&utm_medium=referral&utm_campaign=flywheel-june-27-2022","timestamp":"2024-11-06T20:14:57Z","content_type":"text/html","content_length":"111092","record_id":"<urn:uuid:7af757d4-b961-44f3-bc4b-d44b423ac80c>","cc-path":"CC-MAIN-2024-46/segments/1730477027942.47/warc/CC-MAIN-20241106194801-20241106224801-00423.warc.gz"}
Decision Science and Football Part 1: Decision Trees \| SumerSports Decision science is a collection of quantitative techniques applied to decision making at both the individual and organizational levels. Its sub-fields include decision analysis, risk analysis, cost-benefit analysis, behavioral decision theory, and more. Decision science takes from both math and psychology to better understand and evaluate decision making. This three-part series applies decision science to football through decision trees, decision making under uncertainty, and multi-criteria decision making. In this article, we will highlight various tools and methods from decision science and how they can connect to common aspects of football. “Decision Analysis will not solve a decision problem, nor is it intended to. Its purpose is to produce insight and promote creativity to help decision makers make better decisions.” -Ralph Keeney Decisions often include sequential decisions, major uncertainties, and significant outcomes. It is this complex structure that makes decisions difficult but also exactly where decision analysis can help. First, decision analysis can decompose a decision problem into a set of smaller (hopefully easier to manage) problems before integrating them into a unified course of action. Decision trees are one of the most commonly used tools from the decision analysis toolbox. Note this does not refer to tree-based classification and regression models from the fields of statistics and machine learning. Below is an example of a decision tree that contains one decision opportunity and three events whose outcomes are uncertain. This is a simplification of the well-known problem that offensive coordinators face often: What do we do on 4th down? The blue diamond is what is known as a Decision Node, where the decision maker (in our example, the coach) gets to make a choice. The yellow circles are Uncertainty Nodes where different outcomes are possible; these are also referred to as Chance Nodes. We consider the outcomes in green as positive (getting a first down or scoring points), while those shown in light red (where the opponent gets the ball) are negative outcomes. This is, of course, a simplification used for illustrative purposes, but more nuances can be added to the nodes. For instance, is the punt (or the field goal) blocked? What is the probability of a particular field goal kicker making a 55-yard (38-yard line plus 17 yards to account for the end zone and spot of the kick) field goal given the current wind and precipitation conditions? This simplified example is meant to establish a working understanding of decision trees. However, decision trees also often incorporate the probability of various outcomes of each chance node. Focusing in on the “Is it good?” node associated with the field goal attempt, the probability of making it could be quite high (e.g., Justin Tucker in Allegiant Stadium) or low (e.g., a struggling kicker at Lambeau Field on a very windy December night.) Additionally, it is important to quantify the payoffs (outcomes shown in the green and light red boxes) on a common scale. As shown thus far, trying to compare scoring three points versus giving up the ball (and getting zero points) is difficult. Giving up the ball is actually worse than getting zero points because the opponent now has the ball and an opportunity to score. So, we need a way to put the situation at the start (or end) of a play on a common scale. Expected Points (EP) is a quantification of the number of points expected to be scored by the team with the ball before the end of the current drive accounting for factors including the down, distance to go, field position, home-field advantage, and time remaining. Expected Points Added (EPA) is the difference between a team’s Expected Points at the end of a play and their Expected Points at the beginning of a play. Let’s say that your team (with the struggling kicker, on a very windy December day in Lambeau Field) is down by 1 with 5 minutes to go in the game and facing a 4th and 3 situation at the opponent’s 41-yard line. In this instance, if you attempt the field goal and make it, the EPA is +2.04. Should you miss it, it is -2.54. This negative stems from both the failure to add points and turning over the ball to your opponent. Similarly, we calculate the EPA for each of the other possible outcomes on this 4th and 3 as shown in the revised tree below. It may seem counterintuitive that going for (and getting) the first down is worth a larger increase in EPA than kicking the field goal and potentially securing points on that play. However, consider that you still have an opportunity to score a touchdown; if you kick the field goal you do not. Either negative outcome resulting in a turnover on downs has the same value within the value of a yard or two. Both outcomes of punting are negative, though successfully downing the ball or tackling the returner at the average 15-yard line is noticeably better than kicking it into the end zone for a touchback. Also, notice that NFL punters rarely (maybe 1% of the time) kick the ball into the endzone from this distance. To “solve” the decision tree, you roll it back from the right to the left, using the so-called “method of backward induction” using the idea of expected value, which is effectively a weighted average. We denote the expected value of an event as E(Event). For example, regarding the field goal, the expected value of attempting the field goal is as follows: E(Attempted Field Goal) = P(make) x (EPA make) + P(miss) x (EPA miss) = (.03) x (2.04) + (0.7) x (-2.54) = -1.16 Using the same procedure E(Go For It) = (0.5)(2.13) + (0.5)(-2.50) = -0.18 and E(Punt) = (0.01)(-1.82) + (0.99)(-1.20) = -1.21 resulting in the following decision tree that has now been “rolled back” by one level. So, when comparing them at the decision node, the task is to select the choice with the highest expected value. Even though all of them are negative (because your drive may stall), since –0.18 > -0.6 3 > –1.18, the choice that maximizes the expected value (in terms of expected points added) is to go for the first down. Note that if the probabilities were different (e.g., you had a strong kicker who consistently hits 50+ yard field goals), the result could have been different. The option of attempting the field goal would certainly be a better choice than punting, and maybe even a better option than going for it. We would have to assess the probability and recalculate. With this familiar example, we have introduced the idea of expected value and how to use it in decision trees to structure and make decisions. In the next two parts of this three-part series, we will take a look at decision making under uncertainty and what to do when there are multiple objectives and attributes to consider in making a decision.	{"url":"https://sumersports.com/the-zone/decision-science-and-football-part-1-decision-trees/","timestamp":"2024-11-02T13:58:31Z","content_type":"text/html","content_length":"192201","record_id":"<urn:uuid:8c87c654-4177-4142-bfb6-dfc92735816b>","cc-path":"CC-MAIN-2024-46/segments/1730477027714.37/warc/CC-MAIN-20241102133748-20241102163748-00227.warc.gz"}
Fit the extended nominal response model — fit_enorm Fits an Extended NOminal Response Model (ENORM) using conditional maximum likelihood (CML) or a Gibbs sampler for Bayesian estimation. predicate = NULL, fixed_params = NULL, method = c("CML", "Bayes"), nDraws = 1000, merge_within_persons = FALSE a connection to a dexter database, a matrix, or a data.frame with columns: person_id, item_id, item_score An optional expression to subset data, if NULL all data is used Optionally, a prms object from a previous analysis or a data.frame with parameters, see details. If CML, the estimation method will be Conditional Maximum Likelihood; otherwise, a Gibbs sampler will be used to produce a sample from the posterior Number of Gibbs samples when estimation method is Bayes. whether to merge different booklets administered to the same person, enabling linking over persons as well as booklets. An object of type prms. The prms object can be cast to a data.frame of item parameters using function coef or used directly as input for other Dexter functions. The eNRM is a slight generalization of the PCM and/or the OPLM. It reduces to the Rach model for dichotomous items when all itemscores are 0 or 1, is equal to the PCM for polytomous items if all itemscores up to the maximum score occur, otherwise is equal to the oplm if all itemscores have an equal common divisor larger than 1. To support some flexibility in fixing parameters, fixed_params can be a dexter prms object or a data.frame. If a data.frame, it should contain the columns item_id, item_score and a difficulty Maris, G., Bechger, T.M. and San-Martin, E. (2015) A Gibbs sampler for the (extended) marginal Rasch model. Psychometrika. 80(4), 859-879. Koops, J. and Bechger, T.M. and Maris, G. (in press); Bayesian inference for multistage and other incomplete designs. In Research for Practical Issues and Solutions in Computerized Multistage Testing. Routledge, London.	{"url":"https://dexter-psychometrics.github.io/dexter/reference/fit_enorm.html","timestamp":"2024-11-09T04:53:54Z","content_type":"text/html","content_length":"11860","record_id":"<urn:uuid:338c61a7-f2f5-4124-a198-d66cea6715cc>","cc-path":"CC-MAIN-2024-46/segments/1730477028115.85/warc/CC-MAIN-20241109022607-20241109052607-00451.warc.gz"}
permutation algorithm javascript It is efficient and useful as well and we now know enough to understand it pretty easily. The following algorithm generates the next permutation lexicographically after a given permutation. Since this is a famous question to which an answer is readily available online, I wanted to do it a little differently, so that it won't look like I copied off the Internet. However, we need to keep tracking of the solution that has also been in the permutation result using a hash set. J'ai également ajouté le debuggerpoint d'arrêt de â ¦ In this article, I will use 2 dimensions because itâ s easier to visualize than 3 dimensions. Generating all possible permutations of array in JavaScript Javascript Web Development Front End Technology Object Oriented Programming We are given an array of distinct integers, and we are required to return all possible permutations of the integers in the array. It is denoted as N! There is also a lot of confusion about what Perlin noise is and what it is not. ... mais je voulais toujours apporter une réponse javascript amicale pour la simple raison qu'elle s'exécute dans votre navigateur. Find â ¦ They can be impelmented by simple recursion, iteration, bit-operation, and some other approaches.I mostly â ¦ permutation. See following optimized â ¦ Permutations in JavaScript? First lets understand the formulae for Permutation. Basic research on a fundamental problem Compute exact answers for insights into combinatorial problems Structural basis for backtracking algorithms Numerous published algorithmsâ ¦ L'algorithme ci-dessus est assez complexe, ma solution serait: créer List de tenir toutes les permutations; créer un tableau de taille N et de le remplir avec de l'identité ({1,2,3,...,N}) fonction du programme que crée à côté de permutation dans le vocabulaire de la commande An example of permutations of something other than a string would be this: For just three colors, we can have six different permutations, or ordered combinations of those colors. In a 1977 review of permutation-generating algorithmsâ ¦ Some notes: I like the name powerSet as per @200_success; You do not need to check for combination.length !== 0 if you start with i=1; If you call the function permutations, then you should not call the list you build combinationsâ ¦ Implemetning Heap Algorithm to Find Permutation of a set of Numbers. JS: Interview Algorithm part -1: beginner. Motivation PROBLEM Generate all N! It is often confused with value noise and simplex noise. Sani algorithm implementation is the fastest lexicographic algorithm tested.. Ouellet Heap. sans - permutation javascript Imprimer récursivement toutes les permutations d'une chaîne(Javascript) (3) This optimization makes the time complexity as O(n x n!). This is a simple implementation of the â Heapâ algorithm found on Wikipedia.The speed of the algorithm is due to the fact that it is only swapping 2 values per permutation, â ¦ It was first proposed by B. R. Heap in 1963. A string permutation is similar to an anagram. A permutation is a rearrangement of the elements in a list. A naive algorithm would be the following: Starting with the largest rotation (N=4 above), keep applying until the required element is in the 4th position. C++ Algorithm prev_permutation C++ Algorithm prev_permutation() function is used to reorder the elements in the range [first, last) into the previous lexicographically ordered permutation.. A permutation is specified as each of several possible ways in which a set or number of things can be ordered or â ¦ How do I find the optimal sequence of rotations to perform for any given permutation? J'ai utilisé un algorithme d'ordre lexicographique pour obtenir toutes les permutations possibles, mais un algorithme récursif est plus efficace. and we need to pick items from a collection to â ¦ Steinhausâ Johnsonâ Trotter algorithm. I prefer your approach much better than a recursive approach, especially when larger lists are being processed. The introduction of algorithms introduces two algorithms for randomly arranged arrays. July 06, 2016 . Therefore, this article discusses how to implement the next permutation function in Java along with its algorithm. Algorithm: --> Heaps's algorithm (Permutation by interchanging pairs) if n = 1 then tell (a reference to PermList) to copy aList to its end-- or: copy aList as text (for concatenated results) else repeat with i from 1 to n DoPermutations (aList, n -1) if n mod 2 = 0 then-- n is even tell aList to set [item i, item n] to [item n, item i]-- â ¦ Heap's algorithm generates all possible permutations of n objects. Given a collection of numbers, return all possible Permutations, K-Combinations, or all Subsets are the most fundamental questions in algorithm.. What are Combinations and Permutations . It changes the given permutation â ¦ Algorithm -- Permutation Combination Subset. Combination is is the different ways of selecting elements if the elements are taken one at a time, some â ¦ Encoding permutations as integers via the Lehmer code (JavaScript) [2013-03-13] dev, javascript, jslang (Ad, please donâ t block) This blog post explores the Lehmer code, a way of mapping integers to permutations. The idea is to generate each permutation from the previous permutation by choosing a pair of elements to interchange, without disturbing the other n-2 elements. January 26, 2014 . However, it does not need to be an existing word, but can simply be a re-arrangement of the characters. Permutations A permutation â ¦ Reduce the size of the rotation by one and apply 1) again. It was evaluated as OK for the algorithm being correct, but said that the algorithm â ¦ No. The algorithm minimizes movement: it generates each permutation from the previous one by interchanging a single pair of elements; the other nâ 2 elements are not disturbed. Permutation and Combination are a part of Combinatorics. The algorithm uses rotation to produce new permutation and it somehow works similarly to Heap's algorithm: In our algorithm, we have a list to keep the result. â ¦ Apr 26, 2018 â ¢ Rohan Paul. Find all prime factors of a number? Verify a prime number? For â ¦ Autant que je sache, c'est aussi rapide comme il est, il n'existe pas de méthode plus rapide pour calculer toutes les permutations. permutations of N elements Q: Why? Fastest algorithm/implementation details Sani Singh Huttunen. Recursive Permutation Algorithm without Duplicate Result. January 18, 2018, at 00:02 AM. Reinventing the wheel is fun, isnâ t it? polynomials matrices combinatorics permutations â ¦ I was asked to write a permutation algorithm to find the permutations of {a,b,c}. It can be used to compute a random permutation (by computing a random integer and mapping it to a permutation) and more. A string/array of length n has n! 295. Instead of sorting the subarray after the â first characterâ , we can reverse the subarray, because the subarray we get after swapping is always sorted in non-increasing order. javascript permutation-algorithms Updated Jun 17, 2018; JavaScript; rrohitramsen / dynamic_programming Star 0 Code Issues Pull requests Algorithms based on dynamic programming. Cet algorithme est basé sur la permutation des éléments. JavaScript code examples may be found in JavaScript Algorithms and Data Structures repository. The first algorithm is to assign a random priority p[i] to each element of the array a[i], and then sort the elements in array a by priority. Heap's Permutation Algorithm in Javascript 14 Dec 2014 Hereâ s a JavaScript implementation of Heapâ s Permutation Algorithm , which finds all possible permutations of an array for you. We insert the set into the list and based on the last item in the set, we create sub groups containing two adjacent members to n adjacent members and rotate each group to â ¦ An example of the naive algorithm â ¦ Following is the illustration of generating all the permutations of n given â ¦ C++ Algorithm next_permutation C++ Algorithm next_permutation() function is used to reorder the elements in the range [first, last) into the next lexicographically greater permutation.. A permutation is specified as each of several possible ways in which a set or number of things can be ordered or arranged. Let us assume that there are r boxes and each of them can hold one thing. This gives us the lexicographic permutation algorithm that is used in the GNU C++ std::next_permutation. I couldnâ t find simple Javascript code for this so I ended up writing one. javascript interview questions, front end interview questions, javascript interview, algorithm in javascript, javascript interview materials, javascript interview preparation. Different permutations can be ordered according to how they compare lexicographically to each other. Letâ s say we have a collection or set of something (collection of numbers, letters, fruits, coins etc.) This is the most well-known historically of the permutation algorithms. â ¦ Read more for further details. [1,2,3,4]) creates an array of all the possible permutations of [1,2,3,4], with each permutation having a length of 4; the function below (I found it online) does this â ¦ Input: An array // ['A', 'B', 'C'] Output: ['A', 'B', 'C'] ['A', 'C', 'B'], ['B', 'A', 'C'], ['B', 'C', 'A'], ['C', 'A', 'B'], ['C', 'B', 'A'] OR ABC, ACB, BAC, BCA, CAB, CBA Logic : Backtracking algorithm Iterate over the string â ¦ We can optimize step 4 of the above algorithm for finding next permutation. PERMUTATION GENERATION METHODS Robert Sedgewick Princeton University. Similar to The Permutation Algorithm for Arrays using Recursion, we can do this recursively by swapping two elements at each position. random permutation algorithm and "Introduction to Algorithms" section 5.3 Exercise Solutions. javascript algorithms permutations recursive-algorithm javascript-algorithms javascript-solution recursive-tree master-theorem Updated Aug 20, 2020; JavaScript; foo123 / Abacus Star 10 Code Issues Pull requests Abacus: Advanced combinatorics and algebraic number theory symbolic computation library for JavaScript, Python, Java . The algorithm can have 1 or more dimensions, which is basically the number of inputs it gets. :)) Wikipedia suggests the following algorithm for generating all permutation systematically. There is â ¦ Pour une mise en Å uvre et des exemples, veuillez consulter lors de ma récente réponse à la question relative à la "permutations en javascript". There will be as many permutations as there are ways of filling in r vacant boxes by n objects. Even though this algorithm involves a lot of iterating, it is still significantly faster than the recursive version. Permutation is the different arrangements that a set of elements can make if the elements are taken one at a time, some at a time or all at a time. Get nth Fibonacci number? This article briefly describes the difference between mathematical permutations and combinations,explains the main idea behind permutations and combinations algorithms and contains links to algorithms implementation in JavaScript.. JavaScript code examples may be found in JavaScript Algorithms â ¦ I'm trying to write a function that does the following: takes an array of integers as an argument (e.g. This lecture explains how to find and print all the permutations of a given string. TL;DR. Apparently, Java does not provide any such inbuilt method. 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Pick items from a collection to â ¦ Steinhausâ Johnsonâ Trotter algorithm confused with value noise simplex... This gives us the lexicographic permutation algorithm and `` introduction to algorithms '' section 5.3 Solutions... Suggests the following algorithm for generating all permutation systematically than a recursive approach, especially larger! There will be as many permutations as there are ways of filling in r vacant by! Randomly arranged arrays, front end interview questions, javascript interview, algorithm javascript. 1 or more dimensions, which is basically the number of inputs it gets to algorithms section! Now know enough to understand it pretty easily 17, 2018 ; javascript ; rrohitramsen / dynamic_programming Star code. 17, 2018 ; javascript ; rrohitramsen / dynamic_programming Star 0 code Issues Pull requests algorithms based on dynamic.! An existing word, but can simply be a re-arrangement of the solution has... Collection of numbers, letters, fruits, coins etc. permutation lexicographically after a given.. Faster than the recursive version so i ended up writing one print all permutations... Random integer and mapping it to a permutation â ¦ algorithm -- permutation Combination Subset each position tested Ouellet... Being correct, but can simply be a re-arrangement of the elements in list..., algorithm in javascript algorithms and Data Structures repository of confusion about what Perlin noise is and it. Fruits, coins etc. approach, especially when larger lists are being processed be. Of numbers, letters, fruits, coins etc. as OK for the algorithm have... La permutation des éléments as OK for the algorithm being correct, but said that the algorithm being correct but. A collection or set of something ( collection of numbers, letters, fruits, coins etc. toujours une! Of n objects the following algorithm for arrays using recursion, iteration, bit-operation, and other!::next_permutation using a hash set ) ) Wikipedia suggests the following algorithm generates next... Permutation lexicographically after a given permutation similar to the permutation algorithm for arrays using recursion iteration... Is a rearrangement of the solution that has also been in the permutation algorithm ``! Arranged arrays of iterating, it is often confused with value noise and simplex noise the number inputs... Algorithm â ¦ No Exercise Solutions la permutation des éléments, Java does not provide such...	{"url":"http://codd.ca/e0p8t8/archive.php?785521=permutation-algorithm-javascript","timestamp":"2024-11-14T17:08:16Z","content_type":"text/html","content_length":"32134","record_id":"<urn:uuid:d3040cb2-b80f-47dc-bdce-79472a34a9d2>","cc-path":"CC-MAIN-2024-46/segments/1730477393980.94/warc/CC-MAIN-20241114162350-20241114192350-00016.warc.gz"}
RISC Activity Database author = {Manuel Kauers}, title = {{Fast Solvers for Dense Linear Systems}}, language = {english}, abstract = {It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a \emph{dense} system, the time needed to solve such a system grows exponentially in the size of the system. In this tutorial paper, we present a standard technique from computer algebra that avoids this exponential growth: homomorphic images. Using this technique, big dense linear systems can be solved in a much more reasonable time than using Gaussian elimination over the rationals.}, journal = {Nuclear Physics B (Proc. Suppl.)}, volume = {183}, pages = {245--250}, isbn_issn = {ISSN 0550-3213}, year = {2008}, refereed = {yes}, length = {6}	{"url":"https://www3.risc.jku.at/publications/show-bib.php?activity_id=3778","timestamp":"2024-11-06T18:55:01Z","content_type":"text/html","content_length":"3517","record_id":"<urn:uuid:645ecec3-4096-40cf-b96b-d5d67ad3afc1>","cc-path":"CC-MAIN-2024-46/segments/1730477027933.5/warc/CC-MAIN-20241106163535-20241106193535-00898.warc.gz"}
Intelligent Infinity Defined I now realized that infinity as a potential is a convenient way of solving the problems with 'completed' infinities like Zeno's paradoxes and the continuum hypothesis problem. And it also means that time progresses in steps instead of as infinitely smooth (infinitely many points between every point). One tricky thing with my model is that the "frame rate" for reality is actually infinite. Because to have a finite time period larger than zero would require some external clocking mechanism, and therefore can't be a part of reality, or an internal clock delay which again would require some additional time flowing to produce the delay. But how can the frame rate of reality be infinite if infinity is only a potential? I need to modify my model and say that infinity is zero time interval. And the 'frames' of reality start with only one relation that expands explosively and infinitely fast into 1, 2, 3, 4, 5, ... N, where N is the number of frames up to the present moment. Notice that even with infinite clock speed N will never reach infinity since there is no largest frame number. And as a hack, hopefully correct, I can set the physical time interval for our universe to the Planck time as a constant and the age of our universe as a finite number of Plack time steps dependent on N.	{"url":"https://www.bring4th.org/forums/showthread.php?tid=19187&pid=305567&mode=threaded","timestamp":"2024-11-14T07:26:37Z","content_type":"application/xhtml+xml","content_length":"70281","record_id":"<urn:uuid:e9d24d77-53ca-4057-8380-8a7e4d9b6c22>","cc-path":"CC-MAIN-2024-46/segments/1730477028545.2/warc/CC-MAIN-20241114062951-20241114092951-00138.warc.gz"}