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3. m∠2 = m∠3 given 4. m∠1 = m∠2 substitution Angle C and angle D are corresponding angles, both having 70 degrees. If corresponding angles are equal, then the lines are parallel. This information can be used to determine that angles 2 and 8 are congruent because m ∠ 2 = m ∠ 6 = m ∠ 8. Missing angles (CA geometry) Our mission is to provide a free, world-class education to anyone, anywhere. and are equal to each other. 1. l||m if lines are ||, corresponding angles are equal. Math. Note: These shapes must either be similar or congruent. Furthermore, for a similar triangle, the corresponding sides lengths are also in direct proportion. Why? Play this game to review Geometry. The corresponding sides of similar shapes are not necessarily congruent. Alternate exterior angles are always congruent, so the answer is c. 271. d Angles … Corresponding angle: If lines are parallel, the angles are equal. - 5160681 1. This can be proven for every pair of corresponding angles in the same way as outlined above. The Z-shape shows alternate interior angles. CORRESPONDING ANGLES ARE EQUAL ALTERNATE ANGLES ARE EQUAL ANGLES IN A TRIANGLE ANGLES IN A TRIANGLE a c b A B E C D b Angle BCE = Angle ABC (Alternate angles) a Angle ... – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 461f9b-MWJhO In similar Polygons, corresponding sides are ___ and corresponding angles are ___. A line that passes through two distinct points on two lines in the same plane is called a transversal. Therefore, we can say that angles 1 and 2 are corresponding angles. Equal C. Supplementary - edu-answer.com Question 2: If l is any given line an P is any point not lying on l, … However, angles 2 and 6 are corresponding, so their measures are equal. You know that, when two lines are parallel, then a transversal gives rise to equal corresponding angles, equal alternate interior angles, and co-interior angles being supplementary. Now that we have understood the definition of corresponding angles, we can figure out whether any two given angles are corresponding or not in any given diagram. So if the ration is 1/2 for one pair, then it is the saeme fore all pairs.) (a) When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel. Asked 8/13/2012 10:15:58 AM. The two angles marked in each diagram below are called alternate angles. Corresponding angle are equal. Solved Examples for You. Similar triangles have all corresponding angles equal. Checking for parallel lines. Uses of congruent angles. However, corresponding angles in a transversal of two nonparallel lines are never equal. Identify corresponding, alternate and co-interior angles when two straight lines are crossed by a transversal. 2. m∠1 = m∠3 vertical angles are equal. 3 + 7, 4 + 8 and 2 + 6. Step-by-step explanation: If two parallel lines are intersected by a transversal, then each pair of angles so formed . In addition to calculating angles, we also use vertical angles, corresponding angles, and alternate angles in many situations in mathematics, such as proofs of congruence or similarity. Updated 21 days ago|12/28/2020 5:20:12 AM. 1. (Fill in the blanks) That is what gives them the same shape. asked Oct 7, 2020 in Triangles by Anika01 ( … Given that the lines are parallel, corresponding angles are congruent proof. “Two quadrilaterals are similar, if their corresponding angles are equal”. Assuming corresponding angles, let's label each angle α and β appropriately. Missing angles (CA geometry) Up Next. So, the angles are corresponding angles. The three angles are still equal but they are not congruent. Understand: That angles can be classified by their location of intersection. When a transversal crossed two non-parallel lines, the corresponding angles are not equal. Khan Academy is a 501(c)(3) nonprofit organization. 3. Angles 6 and 8 are vertical, so their measures are also equal. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs e.g. In the example below, the corresponding angles are equal, but all of the sides are in equal proportions. Angle relationships with parallel lines. In fact, angles 2 and 8 are called alternate exterior angles. So what's interesting is these three smaller triangles, they all have the exact same angles, 30, 60, 90, and the exact same side lengths. 2. One of the angles in the pair is an exterior angle and one is an interior angle. 30. Do: Corresponding angles are pairs of angles that lie on the same side of the transversal in matching corners. ★★★ Correct answer to the question: Corresponding angles are A. Complementary B. Just think of one triangle. Thy are equal in size. Two triangles are _____ if corresponding angles are equal and the lengths of the corresponding sides are proportional. They are SIMILAR. Corresponding angles are equal. The sides of similar figures are in equal ratios. Say that angle A is 30˚. Log in Join now 1. s. Expert answered|uxiali|Points 449| Log in for more information. The corresponding angles as well as the corresponding sides are defined as appearing in the same sequence, so for example if in a polygon with the side sequence abcde and another with the corresponding side sequence vwxyz we have vertex angle A appearing between sides a and b then its corresponding vertex angle V must appear between sides v and w Alternate angles are equal. By the straight angle theorem, we can label every corresponding angle either α or β. Corresponding angles of similar or congruent triangles/polygons/etc. Is the following statement true? Congruent angles can also be denoted without using specific angle measures by an equal number of arcs placed around the vertices of two angles, as shown below. (b) When a transversal cuts two lines such that pairs of alternate interior angles are equal, then the lines have to be parallel. The F-shape shows corresponding angles. (Similar means that all pairs of corresponding sides are in the same proportion. The two angles marked in this diagram are called corresponding angles. Note: Similar figures are congruent if there is one to one correspondence between the figures. Instructor: Malcolm M. Malcolm has a Master's Degree in education and holds four teaching certificates. Now **shrink it** withoiut changing its shape. Step 2: Since we know that corresponding angles are equal, we can give the answer with its reason. Look at the pictures below to see what corresponding sides and angles look like. The angles of similar figures are equal. Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. find the ratio of their corresponding heights. If the two lines are parallel, the corresponding angles are equal. 0 Answers/Comments. This angle is 90 degrees, and this angle here is 30. For example, angle A and angle B are corresponding angles, both having 50 degrees. Site Navigation. Alternate angles are equal. LO: To identify corresponding, alternate and co-interior angle Know: That angles are created when two lines intersect each other. 5 points Are corresponding angles equal?? or Z angles. Donate or volunteer today! Alternate angle: If lines are parallel, the angles are equal. It is clear that our corresponding angles definition seems to be fulfilled. Corresponding angles don't add up to 90 or 180 degrees, because corresponding angles will have the same angle measures as each other. The angles which occupy the same relative position at each intersection where a straight line crosses two others. (corresp s; ) If you use the property of angles on parallel lines, you need to state which lines are parallel in the reason. ... Two polygons are said to be similar when their corresponding angles are congruent. So angle say AC-- or say, angle ABE, so this whole angle we see is 60 degrees. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher. Solution: False Which of the following statements is false? Complete the proof for theorem 3-13. Hence you only have to prove 2 equal then the 3rd ones will automatically be equal by the theorem involving the sum of the interior angles of a triangle. The angles are in matching positions, and make an "F " shape. Equal. (c) When a transversal cuts two lines such that pairs of interior angles on … Are corresponding angles equal?? Angles that are in the area between the parallel lines like angle 2 and 8 above are called interior angles whereas the angles that are on the outside of the two parallel lines like 1 and 6 are called exterior angles. The interior angles formed on the same side of the transversal are supplementary. Corresponding angles. When two shapes are similar, it means that their angles are equal and their sides are in the same ratio. Log in Join now Secondary School. A transversal forms four pairs of corresponding angles. Any two squares are similar since corresponding angles are equal and lengths are proportional. are always equal; as are corresponding angles in a transversal of parallel lines. So this-- or not the outer angles, or these combined angles. Vertically opposite angles are equal. Hence, the same side interior angle theorem is proved. Since $$\angle 5$$ and $$\angle 4$$ forms linear pair, \begin{align}\angle 5 + \angle4 &= 180^\circ & \rightarrow (2) \end{align} From (1) and (2), $\angle 1 = \angle 5$ Thus, a pair of corresponding angles is equal, which can only happen if the two lines are parallel. If corresponding angles are equal, the lines are parallel. AAS (Angle-Angle-Side): If two pairs of angles of two triangles are equal in measurement, and a pair of corresponding non-included sides are equal in length, then the triangles are congruent. Their sums differ. Question. <= Assume corresponding angles are equal and prove L and M are parallel. ∴ From above we deduce: Any two triangles are similar, if their (i) Corresponding angles are equal [since, all corresponding angles are equal] Hence, ∆QPR is not similar to ∆TSM, since correct correspondence is P ↔ T, Q ↔ S and R ↔ M. Question 6. Corresponding sides and angles are a pair of matching angles or sides that are in the same spot in two different shapes. 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# Kerodon

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proved that cascading chaotic maps can increase the Lyapunov exponent, and many chaotic maps can be generated with the cascade model. Dunn and Harman presented the Graphics User Interface (GUI) features of MATLAB in designing. f (z) is zero when z is less than zero and f (z) is equal to z when z is above or equal to zero. The numerical analysis shows that the generated binary sequences have good cryptographic properties and can pass the well-known statistical tests. Top free barang logistic downloads. can u plse help me with the code which u have tried for logistic map. Visualize data with high-level plot commands in 2D and 3D. Make sure to label your graphs. The second portion of the code is the portion that is denoting that the generated figure is a mesh plot. Plotting from a for loop- discrete maps. m: 11/19(R) 5. edu/~seibold [email protected] The first page of the array indicates the red component for each color, the second page indicates the. Chaos can involve multi-dimensional systems. 3: Structures and Execution. Note that there are two key parts to the code below:. For example, to create a vector whose entries are 0, 2 , 4, 6, and 8, you can type in the following line: >> 0:2:8 ans = 0 2 4 6 8. Since, it is used in almost all the convolutional neural networks or deep learning. In other words, the logistic regression model predicts P. 4 The objective of this project is to make available an open-source version of our Multifactor Dimensionality Reduction (MDR) software. – Love affairs (an example of a linear 2d system), Strogatz section 5. But these make the math work out nicely, so let’s stick with them. pashaie and farhat: self-organization in a parametrically coupled logistic map network 607 Fig. This implies holding a vector that corresponds to the $$r$$ values you are considering, and a vector corresponding to the various orbits, and with one line of code you can update all the values in the. Learn more about image processing, image analysis, plot, subplot, plotting, image acquisition. Select a Web Site. 5 # Seed value for x in (0, 1) spacing =. %Image reconstruction by combining 8,7,6 and 5 bit planes. Plots are easy to create in MATLAB. How to create a 3D Terrain with Google Maps and height maps in Photoshop - 3D Map Generator Terrain - Duration: 20:32. % BifurDiag. It is a method for classification. A Population Example. The first map is the Chepyshev chaotic map, which is used for the permutation of the pixels of the image. Imaging and EISCAT radar measurements of an auroral prebreakup event. Privacy Policy | Contact Us | Support © 2020 ActiveState Software Inc. 1d systems. The 2D logistic map is defined in Eq. It has powerful plotting capabilities that allow one to plot 2D and 3D graphs, contour plots, vector plots, slices etc. Vlsi matlab -titles-2014-15 A Novel Partial Image Encryption using Chaotic Logistic Map. 4,500000)\n%\n% modification of code in. The principle of the design consists of combining 2D and 1D chaotic systems. We will use 5-fold cross-validation to find optimal hyperparameters. Specifically, the control parameters of the 2D Logistic map, 2D Sine Logistic modulation map (2D-SLMM) , 2D Logistic-adjusted-Sine map (2D-LASM) , and 2D-LSCM are set as 1. 1 Linear stability analysis of ﬁxed points Suppose that we are studying a map xn+1 = f(xn): (1) A ﬁxed point is a point for which xn+1 =xn =x = f(x ), i. 6 pages, 7 figures. As an example, here is the IFS code for generating a fern and watching the evolution of the plot. Plotting from a for loop- discrete maps. A Population Example. 11 AM-1 PM Lab. The roughness can arise from polishing marks, machining marks, marks left by rollers, dust or other particles and is basically shaped by the full history of the surface from the forming stages (casting, sintering, rolling, etc. Let us use a matrix u(1:m,1:n) to store the function. I shall be highly thankful for the kind help and guidance. combines between 1D-Logistic maps and 2D Cat Mapping to encrypt the color image. Fraser lab; The pendulum lab of F-J Elmer. oscillator 93. A “for loop” loops some code a set number of times, and a “while loop” loops until a certain condition is met. %-----write data to excell-----y = transpose(y); z = transpose(z);. Fixed-point iteration Method for Solving non-linear equations in MATLAB(mfile) 21:59 MATLAB PROGRAMS % Fixed-point Algorithm % Find the fixed point of y = cos(x). In the resulting model the population grows exponentially. This means that '. MATLAB is widely used in universities and college introductory and advanced courses in applied mathematics, science and in engineering. Logistic Map Bifurcation Diagram Matlab Code Whats New Logistic map bifurcation diagram matlab code. map2geosofttbl. 2d systems - local analysis near fixed points. 2 Equilibrium points and periodic solutions of the logistic map. Basic Concepts in M atlab, provides a short overview of M atlab. This game turns the task of constructing a cobweb diagram with the logistic map into a game. Top free barang logistic downloads. In this case, we have to tune one hyperparameter: regParam for L2 regularization. Learn more about. A growing number of features in MATLAB offer automatic parallel support, including multi-gpu support, without requiring any extra coding. 2(c) and (d), an inverse bifurcation diagram is shown by. 2d systems - Limit cycles. 1 Ouverture Firstly, create a folder (directory) in your Windows system of name mas2106. Change the code to compute the sine map (see text problem 10. In the previous section we discussed a model of population growth in which the growth rate is proportional to the size of the population. (b) Graphical representation of the iteration of (2. Matlab/C toolbox for least squares support vector machines. m % 1D map analysis % clear % removes all variables from the workspace global r; % control parameter clf; % deletes from the current figure all graphics objects r_min=3; r_max=4. Imaging and EISCAT radar measurements of an auroral prebreakup event. Sukhadia University, Udaipur-313001, Rajasthan, India. In many applications, the map is a model for the dynamics of a population, and xnis the population of the nth generation. Fixed-point iteration Method for Solving non-linear equations in MATLAB(mfile) 21:59 MATLAB PROGRAMS % Fixed-point Algorithm % Find the fixed point of y = cos(x). This report provides a summary of several different header compression tec. m with code such as:. calculate lyapunov of the logistic map lyap=zeros(1,1000); j=0; for (r=3:0. I figured that one more demonstration wouldn’t hurt so I coded it up in SAGE – a free open source mathematical package that has a level of power on par with Mathematica or MATLAB. Regularization is extremely important in logistic regression modeling. (The MATLAB output is fairly long, so I've omitted it here. How to Make 3D Plots Using MATLAB. 2D Graphics; check the distribution of points for the logistic map x -> 4*x*(1-x) 3D graphics; mesh plot; contour plot; 2D Graphics. 7, 1] Tent map exhibit chaos behavior and hence the property of sensitive dependence so it can used for image cryptosystem for r[0. 2,2) will graph the 2nd iterate of the logistic map with a=3. 4) some other code that cumulatively adds the images to build up a map of where the spark has been*. AMATH 383 Spring 2017 Problem Set 1 Due: Thursday 4/6 at noon Note: Submit electronically to Canvas. 5 at increments of 0. In our study, the two-dimensional logistic map with complicated basin structures and attractors are first used for image encryption. Step 3: Theoretical PDF: The given code snippets above, already include the command to plot the theoretical PDF by using the ‘pdf’ function in Matlab. Nan stands for 'not a number'. not a scrambled one. A graphical user interface (GUI) provides various visualization tools, such as heat maps and 2D plots. Numerical Solution using MATLAB. For details, see Run MATLAB Functions with Automatic Parallel Support. Cryptography is the encoding approach used to convert the raw information in encoded form so that the data integrity over the network is improved. 2 Equilibrium points and periodic solutions of the logistic map. 1 Logistic Regression. How to make 3D surface plots in MATLAB ®. "FNN: MATLAB function to calculate corrected false nearest neighbors," Statistical Software Components T7415010, Boston College Department of Economics. m, it is a function, which can be called where the argument m is the delay step; e. Download Logistic Regression Software Advertisement Multifactor Dimensionality Reduction v. An encryption standard based on the chaotic properties of the logistic map function. Journal of Bifurcation and Chaos 14(10):3613---3624 Google Scholar Cross Ref; Pareek NK, Patidar V, Sud KK (2006) Image encryption using chaotic logistic map. Let us assume that this population can take a maximum value Pmax. Cross Lab; B. We concluded that the encryption algorithm has shown good results in terms of PSNR, MSE,NPCR and , UACI. Macquarie University. The green ball shows the current iterate; past iterates are marked on the curve by smaller points. Matlab Introduction 4: Creating and using matrices. In the chaotic regime, the points converge to a strange attractor similar to the one found for the Duffing equation. Use of Semicolon (;) in MATLAB. The logit function is the natural log of the odds that Y equals one of the categories. n the figure below, we repeat from Part 2 a plot of the actual U. 65, you'll ﬁnd out the dramatic ending to these investigations (so don't keep going if you don't want to spoil the surprise. matlab neural network 43 case analysis" source code & Data. F urthermore, the 2D logistic map even has a. Lecture notes. Semicolon (;) indicates end of statement. Demonstration Software for Gaussian Processes by David MacKay (in OCTAVE). m - this MATLAB file simulates the logistic difference equation u(n+1)=a u(n) (1-u(n)) and carries out a bifurcation analysis by varying a. to find factorial using gui in matlab. Department of Applied Mathematics Engineering Center, ECOT 225 526 UCB Boulder, CO 80309-0526. php on line 143 Deprecated: Function create_function() is deprecated in. The 2D logistic map is defined in Eq. Nonlinear Dynamics in Complex Systems: Matlab code for download: Mandelbrot Set Bifurcation Diagram Logistic Map Fractal Fern Lorenz (Roessler) attractor. How to make 3D surface plots in MATLAB ®. I'm new to MATLAB and I'm trying to plot the logistic map x = λx(1-x) for λ in [0,4] and the initial condition from [0,1]. And, matlab giving me the value of f(x)=0. Every generation, the population of fish in a lake grows by 10%. Plot3D[f, {x, xmin, xmax}, {y, ymin, ymax}] generates a three-dimensional plot of f as a function of x and y. Figures and Tables Fig1: Block Digram of the proposed algorithm Fig:2 Results. In a very special case, sometimes these 2D points are considered as their 1D-projections to obtain a 1D map. Goal: trying to map a short signal onto a long signal, not caring that the mapping distance between each data point is equal. Nonlinear Discrete Dynamical Systems 2. I only skimmed the paper in question, to be honest I was assuming OP had already seen it and was looking for something else anyways. Site Map About. Descriptions of the sort given at the end of the prevous page are unnatural and clumsy. This algorithm is used for the dependent variable that is Categorical. It has powerful plotting capabilities that allow one to plot 2D and 3D graphs, contour plots, vector plots, slices etc. Site Map About. 1d systems. com/39dwn/4pilt. Matlab Image Encryption Code - Free download as Word Doc (. For example, 'help plot'. To solve the logistic equation numerically in MATLAB we must begin by writing a function which represents the right-hand-side of the logistic equation, which the MATLAB program will then use in the numerical solution. Logistic regression with Spark and MLlib¶ In this example, we will train a linear logistic regression model using Spark and MLlib. 2(c) plots their LD distributions where we shift parameter r of the 2D Logistic map to provide a better visual comparison. Authors: Narendra K. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register This video project is done by. The cobweb diagram is a geometric way of showing the behavior of the logistic map. Click record or press 'R' to start/stop recording (max. , Mathematics, Bogazi˘ci University, 2007 Submitted to the Institute for Graduate Studies in. Hello, I have assignment to make, a logistic map simulation in simulink using Discrete State Space and Math Function (square), and to be honest I have no idea how to do it. Again, this is to save myself a few minutes rather than googling it around the internet. LoopCurrentMagneticMoment. m Lyapunov exponents for logistic map Code to iterate general functions f:. It follows a very basic approach and is dependent on ultrasonic sensors and a digital compass. The present excercise introduces some basic matlab tools for ploting 2D graphs, as well as shows how to use MATLAB function ode23 for numerical solution of initial value problems. Cellular automata (in one and two dimensions). In this blog post I did a few experiments with t-SNE in R to learn about this technique and its uses. I want to get every value of X for each a value but the array editor only shows one value of x for each a. The logistic map which is a simple dynamic nonlinear equation with complex chaotic behaviour is one of the famous 1D chaotic maps. We need the output of the algorithm to be class variable, i. Logistic map attractor by. WE REMAIN OPEN FOR BUSINESS AND ARE SHIPPING PRODUCTS DAILY Give $10, Get$10 Toggle navigation. The logistic map is a polynomial mapping (equivalently, recurrence relation) of degree 2, often cited as an archetypal example of how complex, chaotic behaviour can arise from very simple non-linear dynamical equations. In summary, the iteration values ( x i , y i ) of 2D-SLMM fall into most regions of its 2D phase plane. The file ex2data1. The green ball shows the current iterate; past iterates are marked on the curve by smaller points. In this experiment, we are going to explore another built-in function in Scilab intended for curve fitting or finding parameters or coefficients. 5 at increments of 0. I suspect the problem Rita and Michael were having is that their data describes a decreasing logistic and the program is set up to do an increasing logistic. I've applied circular hough tranform for identifing the circlular objects in an image and i got the results. 4) Poincaré Maps and Sections Lorenz ODE to cusp map Rössler ODE to logistic map (pp. m-- Graphical display of solutions for Discrete Logistic with delay. Why is the logistic map be-havior so much richer than of the continuous logistic equation, Poincare section and the relation between maps and continuous systems. ) For example, at these RGB Color websites, you will be given R=255, G=0, B=0 for red. encryption algorithm based on three chaotic maps is discussed. a ﬁxed point is an equilibrium point of a map. calculate lyapunov of the logistic map lyap=zeros(1,1000); j=0; for (r=3:0. Determine λ values for the onset of: 2-cycle, 4-cycle,. Below you can see the code creating desired sequence and an instance of Plotter class. Perform limited autonomous navigation and plot a 2D map of the environment. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register This video project is done by. This is a high-level matrix/array language with ﬂow control, functions, data 3. Matlab References. H is the combined rotation and translation matrix required to map the co-ordinates from the one image to the other. I assume the set of images are not related and will answer the question using the traditional approach. The 2D logistic map is defined in Eq. You can use directly log(x) in MATLAB to do this. Please hand in cleanly handwritten or typed (preferably with LATEX) homeworks. As is often the case in dynamical systems theory, the action of the logistic map can not only be represented algebraically, as in Eq. In this exercise, we will implement a logistic regression and apply it to two different data sets. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register. 2002 % The logistic map is x[t+1] = r*x[t]*(1-x[t]) where 0 < r < 4 is a parameter % value and 0 < x[t] < 1 is a variable. (The MATLAB output is fairly long, so I've omitted it here. by Marco Taboga, PhD. The model itself can be numerically solved using finite difference methods. This proposed technique aims to increase PSNR and reduce the noise in the received image. From Figure 2(a), it can be seen that the logistic map is chaotic only when $\mathrm { r } \in [ 3. RANDOM NUMBER GENERATION USING CHAOTIC DYNAMICAL MAPS by Ali R za Oz oren B. 2d systems - Limit cycles. Chaotic Logistic Map Cipher v0. Donnay et al. Fixed-point iteration Method for Solving non-linear equations in MATLAB(mfile) 21:59 MATLAB PROGRAMS % Fixed-point Algorithm % Find the fixed point of y = cos(x). Using plot() In this case we need to specify the functions for x and y separately. (1,4,0,1,200)\n% bifurf(3. 5 Applications 2. Numerical Solution using MATLAB. Finds a rotated rectangle of the minimum area enclosing the input 2D point set: minEnclosingCircle: Finds a circle of the minimum area enclosing a 2D point set: minEnclosingTriangle: Finds a triangle of minimum area enclosing a 2D point set and returns its area. Sharpen your programming skills while having fun!. For the matrix-free implementation, the coordinate consistent system, i. Specifically, the control parameters of the 2D Logistic map, 2D Sine Logistic modulation map (2D-SLMM) , 2D Logistic-adjusted-Sine map (2D-LASM) , and 2D-LSCM are set as 1. It simply returns the value of the derivative dx/dt. It is useful to plot complex numbers as points in the complex. Corresponding largest Lyapunov exponent (LE) is provided in Fig. We consider a very simple model for this evolution. The behaviour and properties of one-dimensional discrete mappings are explored by writing Matlab code to iterate mappings and draw graphs. logistic map to control three kinds of typical two-dimensional chaotic maps, but do not show the performances of their parameter-varied chaotic maps. Montoya, M. A practical Time -Series Tutorial with MATLAB Michalis Vlachos IBM T. Learn more about. 4) Poincaré Maps and Sections Lorenz ODE to cusp map Rössler ODE to logistic map (pp. Contribute to pengsun/MatlabCNN development by creating an account on GitHub. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register This video project is done by. Department of Applied Mathematics Engineering Center, ECOT 225 526 UCB Boulder, CO 80309-0526. Download Logistic Regression Software Advertisement Multifactor Dimensionality Reduction v. logistic map, and I don' seem to understand what the purpose of this block of code. In the resulting model the population grows exponentially. I shall be highly thankful for the kind help and guidance. , from an oscilloscope). This was the first I had heard of it. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register This video project is done by. Step 3: Theoretical PDF: The given code snippets above, already include the command to plot the theoretical PDF by using the ‘pdf’ function in Matlab. Simply plot national and US state boundaries, with or without Matlab's Mapping Toolbox. I only skimmed the paper in question, to be honest I was assuming OP had already seen it and was looking for something else anyways. To solve the logistic equation numerically in MATLAB we must begin by writing a function which represents the right-hand-side of the logistic equation, which the MATLAB program will then use in the numerical solution. org) taught by Prof. Hint 2: (Code takes forever) If your code is running very slowly, you should consider updating all the orbits (one for each $$r$$ value) at once. However, from the Fig. Given a point xn, the graph of the logistic map provides y = f(xn). Contribute to pengsun/MatlabCNN development by creating an account on GitHub. Plotting 3D Surfaces. plots the Feigenbaum diagram of the logistic map in Matlab: to calculate the heat transfer in a 2D plate. Matlab is more than a glorified calculator. Logistic Regression is a Machine Learning classification algorithm that is used to predict the probability of a categorical dependent variable. plots the Feigenbaum diagram of the logistic map in Matlab: to calculate the heat transfer in a 2D plate. Plotting the bifurcation diagram of a chaotic dynamical system. image enhancement in image processing , image enhancement algorithms , image enhancement code in matlab , image enhancement example , image enhancement gamma correction , image edge enhancement matlab. So, to find the 2nd bifurcation value, I need to apply secant method. This project focusses on development of a robot that can autonomously navigate and plot a 2D map. The Octave syntax is largely compatible with Matlab. m Usage: logiter(3. The 1-dimensional logistic map. to the logistic map. But when i used the code into an app designer, insted of ploting the circles into the image where the centers are marked its ploting the circle in a different figure. Let's take a program which plots the standard logistic map: to create a finite element solver for Poisson's equation in 2D and check the performance differences. Orbit diagram: Code. Make sure to label your graphs. This indeed vindicates our hypothesis that stream of bits obtained from orbits of logistic map using perturbation and Bernoulli shift map exhibits randomness. It is one of the simplest nonlinear chaotic discrete. The evaluation and comparison results of LE, LD and KE show that 2D-SLMM has more complex chaotic behaviors and better unpredictability than existing chaotic maps. This is not the most efficient use of Matlab, but shows the basic apsects of programming. (the logistic map) - Duration: MATLAB code for solving Laplace's equation using the Jacobi method - Duration:. It needs the following codes, vect. Code for the quadratic regression. sin C: Math. The bifurcation diagram is a numerical method for showing the asymptotic behavior of the logistic map for various values of the parameter, r. Similar algortihm works well in MATLAB but in OPENCV i am getting original image as it is. Perform limited autonomous navigation and plot a 2D map of the environment. An algorithm for manifold learning and dimension reduction. c: A 1920x1080 canvas. For the 2D Logistic map, 2D-SLMM, Hénon map and 2D-LASM, Fig. Let us use a matrix u(1:m,1:n) to store the function. You can adapt this for the cobwebbing analysis of other difference equations. 2 Fixed Points and Periodic Orbits 2. Data in 2D and 3D. Logistic regression with Spark and MLlib¶ In this example, we will train a linear logistic regression model using Spark and MLlib. by Marco Taboga, PhD. Math 1280: Ordinary Differential Equations II Spring 2017 Instructor: David Swigon Office: Thackeray 511, 412-624-4689, [email protected] The ebook and printed book are available for purchase at Packt Publishing. So complexity is higher than the normal 2D logistic map method. Lecture 11. - Download scanned notes Nonlinear maps: the logistic map. It is called the logistic map because it maps the population value at any time step to its value at the next time step: xt+1 = r xt (1 xt). As stated in the question, I want to find the topological entropy of the logistic map on the interval$[0,1]$for a "nice" range of the parameter$\mu$, namely$\mu \in (1,3)$. First of all, on the basis of Logistics mapping to join an iteration variable, form 2D - Logistic discrete dynamical system to enhance the sensitivity of the original algorithm. MATLAB 1 Matlab basics 1. So here is the logistic map:$$x_{i+1} = f(x_i) \qquad \text{where} \ Matlab code for logistic map bifurcation. 2(a) and (b), fix q = 0. 1 Linear stability analysis of ﬁxed points Suppose that we are studying a map xn+1 = f(xn): (1) A ﬁxed point is a point for which xn+1 =xn =x = f(x ), i. Matlab Programs rk2 rk4 logistic map Euler scheme circle map lorenz lorenz w manifolds henon pendulum standard map pendulum w forcing Links Online "Labs": The Physics Lab by E. Please help and provide the sample matlab code (for any discrete 2D chaotic map) if anyone is having it. We will wrap up this series with a look at the fascinating Lorenz Attractor. This is a high-level matrix/array language with ﬂow control, functions, data 3. 1 Ouverture Firstly, create a folder (directory) in your Windows system of name mas2106. The plot shows the curve and the points ( ). This paper first proposes a new 2D chaotic map, called the 2D Logistic-adjusted-Sine map (2D-LASM). (Self-similarity of period doubling bifurcations) For a map of the form x n+1 = rg(x n) undergoing a period-doubling transition to chaos, de ne r i as the value of rat which the ithperiod bifurcation occurs. Change the code to compute the sine map (see text problem 10. Questions about Walker et al 2012 Evolutionary Transitions and Top -Down Causation by the logistic map in the JIDT generated Matlab code x = logistic(2,. Lecture 2: 2D approximations of the HH model. Sign up Simple program for producing bifurcation plot of logistic map. Step2: Convert the segmented HSZ 3D images to 2D gray color images. ; Turunen, T. The logistic map is discussed in many references. This is a model of a 2-D cellular automaton where each cell's state can take a real value between 0 and 1 and the state-updating rule consists of a coupled chaotic map (in this case the logistic map). Use this function to numerically integrate the HH model in Matlab (e. The second portion of the code is the portion that is denoting that the generated figure is a mesh plot. txt contains the dataset for the first part of the exercise and ex2data2. c which uses malloc to create a vector, mmatrix. In the following code the sunspot data, which comes with Matlab, is plotted using a delay plot. We will use 5-fold cross-validation to find optimal hyperparameters. However, this is an artificial way of reducing the 2D map by dropping one of the variables. 4 The objective of this project is to make available an open-source version of our Multifactor Dimensionality Reduction (MDR) software. The logistic and tent map are topologically conjugate for and respectively. The population sequence for N1=100 is: 100, 110. In this experiment, we are going to explore another built-in function in Scilab intended for curve fitting or finding parameters or coefficients. I am trying to generate a bifurcation diagram for a predator prey interaction but I am struggling to find a way to plot it. Here we explore the route into chaotic behaviour using the Logistic Difference Equation (LDE) as a model. I have a 4 DOF robot with variables t1,t2,d3 and t4. Image Encryption and Decryption using Chaotic Key Sequence Generated by Sequence of Logistic Map and Sequence of States of Linear Feedback Shift Register. 2D Logistic Map (Chaotic Map): In normal 2D logistic map method key will be random generated but in our case we take the hash as a key so more security we will obtain. Please help and provide the sample matlab code (for any discrete 2D chaotic map) if anyone is having it. Designing such a default map is not easy, because they should handle a lot of different things (Moreland, 2009): – The map yields images that are aesthetically pleasing – The map has a maximal perceptual resolution. How to make 3D surface plots in MATLAB ®. m-- Graphical display of solutions for Discrete Logistic with delay. Matlab codes for 2D Convolutional Neural Network. in image encryption, an encryption algorithm of self-adaptive image is proposed based on 2D - Logistics chaotic mapping. The model itself can be numerically solved using finite difference methods. 1 Satellite 2D Logistic Image Encryption (S2LIE) Algorithm Step1: Apply the Region -of Interest (ROI) [16] on the HSZ of Google map images to perform segmentation. 1 Section 1. m function [x]=MapDerivate(x) % logarithm of the map derivative % r is a global parameter global r; % logistic map x=log(abs(r. Macquarie University. Shapour Mohammadi, 2009. In other words, the behaviour of the tent map for is the same as that of the logistic map when. matlab code - different steps of the solution, matlab code - webgraph only Exercise: Period doubling in your pocket J. respectively, for four initial conditions x0=0. The next program is Target Practice Game. Specifically, the control parameters of the 2D Logistic map, 2D Sine Logistic modulation map (2D-SLMM) , 2D Logistic-adjusted-Sine map (2D-LASM) , and 2D-LSCM are set as 1. – Logistic map: ﬁxed points, stability, oscillations, chaos. How can i generate chaos sequence. I am trying to generate a bifurcation diagram for a predator prey interaction but I am struggling to find a way to plot it. Questions about Walker et al 2012 Evolutionary Transitions and Top -Down Causation by the logistic map in the JIDT generated Matlab code x = logistic(2,. I don't think it's supposed to be like this. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. To show the actual behaviors of chaotic systems in stable state, we plot the iteration points from 5000 to 35,000 in each trajectory. As is often the case in dynamical systems theory, the action of the logistic map can not only be represented algebraically, as in Eq. The Henon map discrete time dynamical system. The logistic map, period-doubling and universal constants We consider the discrete time dynamical system known as the logistic map x n+1 = µx n(1−x n) See R. HH_stimulate. dat files, other the Logistic regression was implemented in MATLAB language files m the program source file. Finally we concluded the paper in Section 5. Invariant measure in the case a=3. The Hénon map takes a point (x n, y n) in the plane and maps it to a new point {+ = − + + =. Example 5 The logistic map. A 2D discrete chaotic map has two LEs. I have generated a world map by plotting coastlat and coastlon. These IPython Notebooks show more. As you may have noted, gnuplot and Matlab have different default color maps. Please help and provide the sample matlab code (for any discrete 2D chaotic map) if anyone is having it. J Image Vis Comp 24(9):926---934 Google Scholar Cross Ref. 2d systems - local analysis near fixed points. – Love affairs (an example of a linear 2d system), Strogatz section 5. The permuted image is subjected to the diffusion process using the improved Quadratic map in an efficient encryption algorithm which its key is related to the original image. A=imread ('coins. Based on your location, we recommend that you select:. m is a Matlab program to construct a bifurcation diagram for the logistic map % to allow exploring the period doubling route to Chaos. Single Remote Sensing Image De-hazing. e 0-no, 1-yes. Cryptography is the encoding approach used to convert the raw information in encoded form so that the data integrity over the network is improved. Performance evaluations show that 2D-LASM has a wider chaotic range, better ergodicity and unpredictability than several existing chaotic. It would be nice to have a simple measure that could discriminate among the types of orbits in the same manner as the parameters of the harmonic oscillator. I'm using the code below in matlab to produce a bifurcation diagram for the logistic map. Also, the control parameters of shuffling are randomly generated by employing 2D coupled Logistic map. Here we explore the route into chaotic behaviour using the Logistic Difference Equation (LDE) as a model. Note that there are two key parts to the code below:. β1, β2, γ1 and γ2 are system control parameters. The basic usage for MATLAB's solver ode45 is ode45(function,domain,initial condition). moments: Calculates all of the moments up to the third order of a polygon or. Please help and provide the sample matlab code (for any discrete 2D chaotic map) if anyone is having it. Functions for reading and writing colour maps in various formats. Matlab code: Histogram equalization without using histeq function It is the re-distribution of gray level values uniformly. I used linspace to generate values for the variables, and also I calculated the positions, resulting 90x90x90 matrices (for X, Y and Z). LoopCurrentMagneticMoment. The user specifies the following:. Plotting the bifurcation diagram of a chaotic dynamical system. Technological breakthroughs, patience, and refined skills will get us there, but the first step is. Why is the logi stic map be-havior so much richer than of the continuous logistic equation, Poincare section and the relation between maps and continuous systems. txt contains the dataset for the first part of the exercise and ex2data2. Watson Research Center Hawthorne, NY, 10532 Tutorial | Time-Series with Matlab 2 About this tutorial The goal of this tutorial is to show you that time-series research (or research in general) can be made fun, when it involves visualizing ideas, that can be achieved with. Logistic Chaos-bit Generator - Convert any data to high entoropy state by logistic map c cryptography original logistic-map Updated Apr 12, 2019. View Homework Help - AMATH383_S17_HW1 from AMATH 383 at University of Washington. -- Contributed to: X Spanish Meeting on Cryptology and Information Security (Salamanca, Spain, Sep 2-5, 2008). The Matlab function for refraction at a plane interface takes as input height y of the ray at the interface, slope 𝑢= tan𝜃, thickness of the lens, index of refraction n, and vector z, which is used to plot the ray in air (back of lens). These programs demonstrates different chaotic maps,bifurcations,hybrid chaotic maps,highly secure maps,auto correlations,cross correlations and their extreme sensitivity to initial conditions or bifurcation parameters. The Curve Fitting Toolbox for use with MATLAB provides a user interface and command line functionality for previewing and preprocessing, as well as creating, comparing, analyzing and managing models. Also, the control parameters of shuffling are randomly generated by employing 2D coupled Logistic map. I have deleted most of this text since it was about the logistic map or about the mandelbrot set, but not about bifurcation diagrams and most of its contents was already contained under logistic map. So, to find the 2nd bifurcation value, I need to apply secant method. The next program is Target Practice Game. Vinod Patidar. I have done it because I want to plot some data that I have over said map. The tent map is a piecewise linear, one-dimensional map. Viewed 3k times 0. U-sequence. Without further ado: from pylab import show, scatter, xlim, ylim from random import randint iter = 1000 # Number of iterations per point seed = 0. 3D Maps & Alcohol Consumption with Python. We will wrap up this series with a look at the fascinating Lorenz Attractor. Selective Image Encryption using Confusion Technique The security of multimedia data in digital distribution networks is commonly provided by encryption, i. Matlab Programs rk2 rk4 logistic map Euler scheme circle map lorenz lorenz w manifolds henon pendulum standard map pendulum w forcing Links Online "Labs": The Physics Lab by E. 1 Eleftherios "Lefty" Ioannidis 1 How it works The Chaotic Logistic Map cipher, hereby refered as CLM, utilizes the pseudo-random properties of the logistic map, a simple recurence relation of degre 2 with interesting properties: x n+1 = rx n(1 x n) where x n 2[0;1] and r 2[1;4]. 98, one can find that a normal bifurcation diagram is derived in the Fig. m Usage: logistic(0. map2geosofttbl. chaotic economic map [6], variable length codes that are based on Collatz conjecture [7], 2D discrete wavelet transform and Arnold mapping [8], logistic mapped convolution and cellular automata [9], cat map [10], 2D Chebyshev-sine map [11], 2D Sine Logistic modulation map [12], one-dimensional. The algorithm works as follows: Beginning with a certain values for x and r, find n. I just uploaded a non-GUI fit_logistic function and at first it failed with Rita's data, too. in image encryption, an encryption algorithm of self-adaptive image is proposed based on 2D - Logistics chaotic mapping. Nn is the population of generation n. Is tere a way to make Discrete State Space to calculate x(i+1) using square function like x(i)(1-x(i)) not just x(i). 85 , a0 = 0. This example shows how to run MATLAB code on multiple GPUs in parallel, first on your local machine, then scaling up to a cluster. The plot shows the curve and the points ( ). Dismiss Join GitHub today. I only skimmed the paper in question, to be honest I was assuming OP had already seen it and was looking for something else anyways. Click record or press 'R' to start/stop recording (max. Goal: trying to map a short signal onto a long signal, not caring that the mapping distance between each data point is equal. Cryptographic of Chaotic Map This section discusses the methodical procedure of the proposed image encryption as well as decryption process using two chaotic logistic maps [12]. The basic logistic-map is formulated as: (1) X +1 =μX −Xn (1) where μ represents the parameter of chaotic map. LOGISTIC MAP The Logistic map presents a polynomial map of degree two. 2d MLG Home. 8 2D maps: Poincaré sections + Hénon map + Sink, sources and saddles + Linear maps + Real evals + Repeated evals + Complex evals +. pdf), Text File (. Chaos & Fractals : Practical Examples and Homeworks (MATLAB) slopefield1D 2Dvectorfield LimitCycle Poincare Section Matlab code: Seminar_code. Finds a rotated rectangle of the minimum area enclosing the input 2D point set: minEnclosingCircle: Finds a circle of the minimum area enclosing a 2D point set: minEnclosingTriangle: Finds a triangle of minimum area enclosing a 2D point set and returns its area. ; Manninen, J. How to create a function in matlab. With today's computers even a for-loop in a scripting language like R takes only a few seconds. This support lets you integrate algorithm development with rapid prototyping, implementation, and verification workflows. Neumann; M. Here you can download matlab code & images. Œ Examples of projects: bugs, birds and leaves from Strogatz; love affairs;. 2D phase portraits: phase trajectories from clicking on a figure window: Code Numerical computation of Jacobians: Code Limit cycles: finding them using root find, Poincare maps, and stability: Code Parametric excitation: Mathieu's equations, tongues of instability: Code Chaos in the logistic map. com/39dwn/4pilt. Arnold's cat map is a particularly well-known example of a hyperbolic toral automorphism, which is an automorphism of a torus given by a square unimodular matrix having no eigenvalues of absolute value 1. This implies holding a vector that corresponds to the $$r$$ values you are considering, and a vector corresponding to the various orbits, and with one line of code you can update all the values in the. 6 MATLAB Commands 2. Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. plots the Feigenbaum diagram of the logistic map in Matlab: to calculate the heat transfer in a 2D plate. The surface plot uses Z for height and CO for color. First of all, on the basis of Logistics mapping to join an iteration variable, form 2D - Logistic discrete dynamical system to enhance the sensitivity of the original algorithm. The values are estimated by the formula from J. From the Start button, select All programs, Scientific software and Matlab2010b. , Mathematics, Bogazi˘ci University, 2007 Submitted to the Institute for Graduate Studies in. Matlab Image Encryption Code - Free download as Word Doc (. Old versions of Octave do not. Giacinto Gelli e Francesco Verde. This is a high-level matrix/array language with ﬂow control, functions, data 3. In the chaotic regime, the points converge to a strange attractor similar to the one found for the Duffing equation. Dana Kester, Oct. m: 11/19(R) 5. m Usage: logiter(3. Curve Fitting with Matlab Matlab has a curve fitting toolbox (installed on machines in Hicks, but perhaps not elsewhere on campus - as of Sept. Edit and draw graphs of your 2D or 3D Data. ; Lyatsky, W. - Download scanned notes Nonlinear maps: the logistic map. a) 1 2 sin x x x r x b) x (x 2 e rx)(r x ) c) x xe x r 2 sin x 2 d) Atypical bifurcation. I remember, it took the little computer the whole night to produce the bifurcation chart. Discrete one-dimensional chaotic maps are simple iterative or recurrence relations of the form x n + 1 = f (x n), which is a function of a single variable and one or few parameters, which are easy to simulate or implement. It worthwhile to note that all following source code is written under MATLAB and that files may call built-in functions from specific toolbox(es). The logit function is the natural log of the odds that Y equals one of the categories. It you do not have access to this function, you could use the following equation for computing the theoretical PDF. ) Since x and y are. to the logistic map. First of all, on the basis of Logistics mapping to join an iteration variable, form 2D - Logistic discrete dynamical system to enhance the sensitivity of the original algorithm. To evaluate x at an arbitrary value, see version 3 of this code. The chaos game sierpinski triangle, nonlinear dynamics matlab logistic map code, chaos test file exchange matlab central, a practical test for noisy chaotic dynamics sciencedirect, solving odes in matlab 12 lorenz attractor and chaos, matlab file chaos game, matlab code for chaos free open source codes codeforge com, chaos based. to find factorial using gui in matlab. ) Hard coding data into the MATLAB code file. Simply plot national and US state boundaries, with or without Matlab's Mapping Toolbox. 2d systems - Linstedt Poincare method. In the chaotic regime, the points converge to a strange attractor similar to the one found for the Duffing equation. 1D Logistic Mapping The one-dimensional Logistic map is proposed by R. Specify the colors using truecolor, which uses triplets of numbers to stand for all possible colors. edu March 31, 2008 1 Introduction On the following pages you ﬁnd a documentation for the Matlab. Project #3: Maps, period doubling, chaos, and Lyapunov exponents (Due Dec 4 ) Here is Matlab code for plotting the bifurcation diagram associated with the logistic map. 001 , n = 100 ). The first map is the Chepyshev chaotic map, which is used for the permutation of the pixels of the image. To start up Matlab, go to a university computer cluster and login to your account. Note, in particular, the way it folds back on itself. Since, it is used in almost all the convolutional neural networks or deep learning. How to Make 3D Plots Using MATLAB. Rk2 Matlab Code. Logistic map May's 1976 nature paper Li-Yorke's "period 3 implies chaos" Chaos Theory: Matlab: time series (Malthus logistic) cobweb (Malthus logistic Bellows) bifurcation (logistic Bellows) 11/17(T) 5. This solution was in fact contributed by a student (Robert Castillo) who took this class in 2011. 5 As noted above, negative values of λ here indicate stability in the logistic map. The map x->4x(1-x). Given a point xn, the graph of the logistic map provides y = f(xn). 2 Equilibrium points and periodic solutions of the logistic map. Matlab commands. Sign up Simple program for producing bifurcation plot of logistic map. It is called the logistic map because it maps the population value at any time step to its value at the next time step: xt+1 = r xt (1 xt). (In a later post I discuss a cleaner way to calculate the Lyapunov exponent for maps and particularly the logistic map, along with Mathematica code. 0 it behaves the same as Matlab. I used linspace to generate values for the variables, and also I calculated the positions, resulting 90x90x90 matrices (for X, Y and Z). Based on your location, we recommend that you select:. Deprecated: Function create_function() is deprecated in /www/wwwroot/dm. On the other side, the neighborhood is defined as a convolution-like kernel for the map around the winner. Hello everyone. chaotic economic map [6], variable length codes that are based on Collatz conjecture [7], 2D discrete wavelet transform and Arnold mapping [8], logistic mapped convolution and cellular automata [9], cat map [10], 2D Chebyshev-sine map [11], 2D Sine Logistic modulation map [12], one-dimensional. Learn more about matlab function, logistic map MATLAB. logistic map, and I don' seem to understand what the purpose of this block of code. Oberbroeckling, Fall 2014. Logistic regression with Spark and MLlib¶ In this example, we will train a linear logistic regression model using Spark and MLlib. 25, 2018) Homework submission. Its name is ' datafit '. Here we use a function plot in MATLAB library. Each cell 'reads' its own state and the state of each of its four neighbours and updates its state accordingly. pashaie and farhat: self-organization in a parametrically coupled logistic map network 607 Fig. The basic logistic-map is formulated as: (1) X +1 =μX −Xn (1) where μ represents the parameter of chaotic map. map2ermapperlutfile. In many applications, the map is a model for the dynamics of a population, and xnis the population of the nth generation. 5 As noted above, negative values of λ here indicate stability in the logistic map. https://www. Sign up Simple program for producing bifurcation plot of logistic map. J Image Vis Comp 24(9):926---934 Google Scholar Cross Ref. Functions for reading and writing colour maps in various formats. History Awards Leaders Units. Based on your location, we recommend that you select:. All rights reserved. *x); plot (x,y,'g') We can notice by looking at the graph above how both graphs are close to being identical. map <- function(r, x, N, M){ ## r: bifurcation. (Strogatz, 1994, 10. In summary, the iteration values ( x i , y i ) of 2D-SLMM fall into most regions of its 2D phase plane. The logistic map is one dimensional chaotic system with X output and input variable and two initial conditions X0 and α (Patidar et al, 2009; Yong et al. The 2D coupled logistic map is given by the equations ,. Logistic Map In order to understand the chaotic behavior, logistic map is presented in this section. 99, respectively. 2(c) plots their LD distributions where we shift parameter r of the 2D Logistic map to provide a better visual comparison. Agent based models. J Image Vis Comp 24(9):926---934 Google Scholar Cross Ref. Matlab's image processing toolkit provides functions for reading and writing DICOM medical image files, but it does not provide a full DICOM toolkit for networking, structured reports, etc. WE REMAIN OPEN FOR BUSINESS AND ARE SHIPPING PRODUCTS DAILY Give$10, Get \$10 Toggle navigation. Since John von Neumann suggested utilizing Logistic map as a random number generator in 1947, a great number of encryption schemes based on Logistic map and/or its variants have been proposed. One can now think about 2D maps, like the henon map. However, this is an artificial way of reducing the 2D map by dropping one of the variables. Wiring diagram is a technique of describing the configuration of electrical equipment installation, eg electrical installation equipment in the substation on CB, from panel to box CB that covers telecontrol & telesignaling aspect, telemetering, all aspects that require wiring diagram, used to. It is a simple Algorithm that you can use as a performance baseline, it is easy to implement and it will do well enough in many tasks. 10 secs) Click capture to take a screenshot. The principle of the design consists of combining 2D and 1D chaotic systems. 11 AM-1 PM Lab. Learn more about matlab function, logistic map MATLAB. An elementary treatment of chaos theory and its applications concentrating on discrete dynamical systems. Guide to get Matlab running random walk codes in both 1D (EXrandomWalk1D. Time Series of Logistic Map Equation. By applying this criterion, show that the two-cycle for the logistic map is stable for 3 < µ < 1+ √ 6. Vcsel Matlab Code. Based on your location, we recommend that you select:. Sprott, 2003 (Chaos and time-series analysis, volume 69. Provide details and share your research! But avoid … Asking for help, clarification, or responding to other answers. 1, but also geometri-cally. ‘bitset’ is used to set a bit at a specified position. These files were voted MATLAB Central Pick of the Week in July 2013. lat, lon — Geolocation array M-by-N matrix | M-element vector. png 1,200 × 900; 8 KB. For instance, I would feel fine putting a 3×3 matrix into my code. The cobweb diagram is a geometric way of showing the behavior of the logistic map. Nonlinear Dynamics in Complex Systems: Matlab code for download: Mandelbrot Set Bifurcation Diagram Logistic Map Fractal Fern Lorenz (Roessler) attractor. And, matlab giving me the value of f(x)=0. 4) some other code that cumulatively adds the images to build up a map of where the spark has been*. A=imread ('coins. In summary, the iteration values ( x i , y i ) of 2D-SLMM fall into most regions of its 2D phase plane. References G. m is a Matlab program to construct a bifurcation diagram for the logistic map % to allow exploring the period doubling route to Chaos. The other day I found some old basic code I had written about 15 years ago on a Mac Classic II to plot the Feigenbaum diagram for the logistic map. Logistic map is developed to give a chaos function can be. 3 Chaos in the logistic map. which is positive and confirms the chaotic nature of the logistic map at [lambda] = 4. I am not an expert on dynamical systems, so I hope someone else can write the appropriate article for this title. The simulation results and the performance analysis show that the algorithm has large secret-key space, high security, fast encryption speed and strong robustness. Click record or press 'R' to start/stop recording (max. This support lets you integrate algorithm development with rapid prototyping, implementation, and verification workflows. f (z) is zero when z is less than zero and f (z) is equal to z when z is above or equal to zero. I've applied circular hough tranform for identifing the circlular objects in an image and i got the results. HH_stimulate. Perform limited autonomous navigation and plot a 2D map of the environment. map <- function(r, x, N, M){ ## r: bifurcation. 2: 1b, 1e, 2c, 2d, 3, 4, 17 (skip part (i)). The principle of the design consists of combining 2D and 1D chaotic systems. Here, we’re running the logistic map for 4,000 generations across 50 growth rate parameters in the chaotic regime between r=3. GitHub is home to over 40 million developers working together to host and review code, manage projects, and build software together. Learn more about matlab function, logistic map MATLAB. 2(c) and (d), an inverse bifurcation diagram is shown by. Logistic map became very popular after it was exploited in 1979 by the biologist Robert M. Performance evaluations show that 2D-LASM has a wider chaotic range, better ergodicity and unpredictability than several existing chaotic.
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# hyperref autoref capitalization problems with babel

I have already read some similar qustions, but the solution over there does not work if I add the 'babel' package. The thing is change the autorefname of one specific, say Figure, and I just want to change the way that it is written, say capital case. Everything is fine but if I uncomment the package babel, so the command is ignored.

\documentclass[11pt]{book}

%\usepackage[english]{babel}
\usepackage{hyperref}
\def\figureautorefname{FIGURE}

\begin{document}
\begin{figure}
\centering
\rule{1cm}{1cm}
\caption{foo}\label{fig:foo}
\end{figure}
As shown in \autoref{fig:foo}~\dots
\end{document}

probably is a easy questions, but I don't find it.

-

The manual of hyperref contains an example for this case:

Example for a redefinition if babel is used:

\usepackage[ngerman]{babel}
\def\subsectionautorefname{Unterkapitel}%
}

\usepackage[english]{babel}

 Sorry, but it doesn't work, I have already seen the example in the manual, and it works perfectly, but changing the language as well as the command extrasngerman by captionsenglish, it does not. – Gitano Jan 22 at 16:22 Answer fixed: \extrasenglish instead of \captionsenglish. – Heiko Oberdiek Jan 22 at 16:33 Thanks, it works perfectly. – Gitano Jan 22 at 17:02


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# zbMATH — the first resource for mathematics

Higher order influence functions and minimax estimation of nonlinear functionals. (English) Zbl 05556804
Nolan, Deborah (ed.) et al., Probability and statistics: Essays in honor of David A. Freedman. Institute of Mathematical Statistics Collections 2. Beachwood, OH: IMS, Institute of Mathematical Statistics. 335-421 (2008).
Summary: We present a theory of point and interval estimation for nonlinear functionals in parametric, semi-, and non-parametric models based on higher order influence functions (Robins (2004), Section 9; Li et al. (2004), Tchetgen et al. (2006), Robins et al. (2007)). Higher order influence functions are higher order U-statistics. Our theory extends the first order semiparametric theory of Bickel et al. (1993) and van der Vaart (1991) by incorporating the theory of higher order scores considered by Pfanzagl (1990), Small and McLeish (1994) and Lindsay and Waterman (1996). The theory reproduces many previous results, produces new non-$$\sqrt n$$ results, and opens up the ability to perform optimal non-$$\sqrt n$$ inference in complex high dimensional models. We present novel rate-optimal point and interval estimators for various functionals of central importance to biostatistics in settings in which estimation at the expected $$\sqrt n$$ rate is not possible, owing to the curse of dimensionality. We also show that our higher order influence functions have a multi-robustness property that extends the double robustness property of first order influence functions described by Robins and Rotnitzky (2001) and van der Laan and Robins (2003).
For the entire collection see [Zbl 1159.60006].

##### MSC:
 62G05 Nonparametric estimation 62C20 Minimax procedures in statistical decision theory
Full Text:


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Precise Large Deviation for the Difference of Non-Random Sums of NA Random Variables

DOI：10.3770/j.issn:2095-2651.2016.06.013

 作者 单位 华志强 内蒙古民族大学数学学院, 内蒙古 通辽 028043 宋立新 大连理工大学数学科学学院, 辽宁 大连 116024

研究形如$\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}$的非随机和的差的精确大偏差, 其中$\{X_{1j},j\geq 1\}$是一列服从共同分布$F_{1}(x)$ 的负相协随机变量序列, $\sum_{j=1}^{n_1(t)}X_{1j}$是$\{X_{1j},j\geq 1\}$的非随机和, $\{X_{2j},j\geq 1\}$是一列服从独立同分布的随机变量序列, $\sum_{j=1}^{n_2(t)}X_{2j}$是$\{X_{2j},j\geq 1\}$的非随机和, $n_1(t)$和$n_2(t)$是两个取正整数的函数. 在一些其它的条件下,得到了如下一致渐近关系$$\lim_{t\rightarrow\infty}\sup_{x\geq\gamma (n_{1}(t))^{p+1}}|\frac{P(\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}-(\mu_{1}n_{1}(t)-\mu_{2}n_{2}(t))>x)}{ n_{1}(t)\bar{F_{1}}(x)}-1|=0.$$

In this paper, we study precise large deviation for the non-random difference $\sum_{j=1}^{n_1(t)}X_{1j}$ $-\sum_{j=1}^{n_2(t)}X_{2j}$, where $\sum_{j=1}^{n_1(t)}X_{1j}$ is the non-random sum of $\{X_{1j},j\geq 1\}$ which is a sequence of negatively associated random variables with common distribution $F_{1}(x)$, and $\sum_{j=1}^{n_2(t)}X_{2j}$ is the non-random sum of $\{X_{2j},j\geq 1\}$ which is a sequence of independent and identically distributed random variables, $n_1(t)$ and $n_2(t)$ are two positive integer functions. Under some other mild conditions, we establish the following uniformly asymptotic relation $$\lim_{t\rightarrow\infty}\sup_{x\geq\gamma (n_{1}(t))^{p+1}}\Big|\frac{P(\sum_{j=1}^{n_1(t)}X_{1j}-\sum_{j=1}^{n_2(t)}X_{2j}-(\mu_{1}n_{1}(t)-\mu_{2}n_{2}(t))>x)}{n_{1}(t)\bar{F_{1}}(x)}-1\Big|=0.$$


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## $$*$$-product on the tangent bundle of the group $$U(n)$$. (Produit $$*$$ sur le fibré tangent du groupe $$U(n)$$.)(French)Zbl 0930.22010

Séminaire de mathématique de Luxembourg. Luxembourg: Centre Universitaire de Luxembourg. Trav. Math. 10, 1-14 (1998).
For the complex connected reductive Lie group $$G$$ the diffeomorphism $$K \times A^* \times N^+ \to G; (k,a,n) \mapsto kan,$$ associated with the Iwasawa decomposition is well-known. Because of the existence of a nondegenerate bilinear Killing form on reductive groups one can identify the tangent space $$T_kK$$ to $$K$$ at a point $$k\in K$$ with the sum $$i{\mathfrak a} + \mathfrak n^+$$ and therefore identify $$G$$ with $$TK$$ (§3.1).
Equipping $$TK$$ with the group structure of $$G$$, the authors associate the *-product to $$TK$$ from $$G$$. In particular, for the case $$G=GL_n(\mathbb C)$$, $$K= U(n)$$, the authors obtain a $$U(n)$$-equivariant *-product on $$TU(n) \cong GL_n(\mathbb C)$$.
For the entire collection see [Zbl 0910.00035].

### MSC:

 2.2e+28 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)


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How vcftools calculate Fst value?
0
0
Entering edit mode
3.4 years ago
seta ★ 1.7k

Hi all,

I used vcftools for calculation the Fst value between two populations (pop1 and pop2) using the below command:

./vcftools --vcf file.vcf --weir-fst-pop population_1.txt --weir-fst-pop population_2.txt  --out pop1_vs_pop2

However, some Fst value sounds strange to me. For example, please consider the allele frequency of some variants in two pops and the obtained Fst value:

SNP AF_pop1     AF_pop2     Fst value
snp1    0.74    0.43    0.037
snp2    0.33    0.79    0.423
snp3    0.69    0.03    0.42

As you see, the frequency of snp1 and snp2 is similar between the two populations, but there is a huge difference in the related Fst values. Similarly, while the allele frequency of snp2 and snp3 is very different between populations, the related Fst values are similar. I'm confused with such an output. Could you please let me know your idea about it, is it reasonable to you?

Fst vcftools populations • 4.2k views
0
Entering edit mode

You may contact one of the developers of VCFtools (Adam Auton) in order to understand what is exactly happening. You should be able to find his contact online.


text:
### Best rational approximation to the $p$ th root

A landmark result of rational approximation theory states that the pth root $x^{1/p}$ on $[0,1]$ can be approximated by type $(n,n)$ rational functions with root-exponential accuracy. (By contrast, polynomials can only converge algebraically.) Specifically, there exist rational functions $r_n$ of type $(n,n)$ such that asymptotically as $n\rightarrow \infty$,

$$\max_{x \in [0,1]} |r_n(x)-x^{1/p}| \sim 4^{1+1/p}\sin(\pi/p)\exp( -2\pi \sqrt{n/p} ),$$

where the constants were worked out by Stahl [3].

For example, here is the error curve of the minimax rational approximant of type $(5,5)$ to the cube root, shown on a semilogx scale. It has the famous equioscillation property at $5+5+2=12$ points:

p = 3;
f = chebfun(@(x)x^(1/p),[0 1],'splitting','on');
[~,~,r] = minimax(f,5,5);
xx = logspace(-15,0,1000)';
semilogx(xx,f(xx)-r(xx)), grid on
title('absolute error of type (5,5) minimax approximant')

### Approximation by composite rational functions

In [1], Gawlik examined rational approximations of $x^{1/p}$ obtained by composing rational functions of lower degree. One example is the function $f_k(x)$ defined recursively by

$$f_{k+1}(x) = \frac{1}{p}\left( (p-1)\mu_k f_k(x) + \frac{x}{\mu_k^{p-1} f_k(x)^{p-1}} \right), \quad f_0(x) = 1,$$

$$\alpha_{k+1} = \frac{p \alpha_k}{(p-1)\mu_k + \mu_k^{1-p}\alpha_k^p}, \quad \alpha_0 = \alpha,$$

where $\alpha \in (0,1)$ is a parameter and

$$\mu_k = \left( \frac{\alpha_k - \alpha_k^p}{(p-1)(1-\alpha_k)} \right)^{1/p}.$$

$f_k$ is a rational function of type $(3^{k-1},3^{k-1}-1)$, and the scaled function $\widetilde{f}_k(x)=2\alpha_k f_k(x)/(1+\alpha_k)$ has the property that the relative error $x^{-1/p}(\widetilde{f}_k(x)-x^{1/p})$ equioscillates at $2^k+1$ points on $[\alpha^p,1]$. For details, see [1,2]. Here is an illustration.

alp = 0.03; alpini = alp; % approximation on $[alp^p,1]$
rr = @(x)1;
for kk = 1:3
mu = ((alp-alp^p)/((p-1)*(1-alp)))^(1/p);
rr = @(x) 1/p*((p-1)*mu*rr(x) + x./(mu*rr(x)).^(p-1));
alp = p*alp / ((p-1)*mu + mu^(1-p)*alp^p);
end
y = @(x)2*alp/(1+alp)*rr(x);
xx = logspace(log10(alpini^p),0,1000);
relerr = (y(xx)-f(xx))./(f(xx));
semilogx(xx,relerr), grid on
title(['relative error of composite approximant, k=3, \alpha=',num2str(alpini)])

Instead of the relative error, we might be interested in the absolute error, for example when approximation at or near $x=0$ is of interest. How does it look? Here is a plot including much smaller values of $x$.

xx = logspace(-15,0,1000);
abserr = y(xx)-f(xx);
semilogx(xx,abserr),grid on

LS = 'linestyle'; IN = 'interpreter'; LT = 'latex';
CO = 'color'; FS = 'fontsize'; MS = 'markersize';
line([alpini^p alpini^p],norm(abserr,inf)*[-1 0.5],LS,'--',CO,'r')
text(alpini^p*1.1,-norm(abserr,inf),'$\alpha^p$',IN,LT,FS,18,CO,'r')
title(['absolute error of composite approximant, k=3, \alpha=',num2str(alpini)])

The error is oscillating with growing amplitude on $[\alpha^p,1]$ as expected, and it takes the smallest values near $x=\alpha^p$. On $[0,\alpha^p]$, the error grows towards $x=0$, but stays bounded.

The picture looks quite different if we start with a different value of $\alpha$. For example with a larger $\alpha$,

alp = 0.1; alpini = alp;
rr = @(x)1;
for kk = 1:3
mu = ((alp-alp^p)/((p-1)*(1-alp)))^(1/p);
rr = @(x) 1/p*((p-1)*mu*rr(x) + x./(mu*rr(x)).^(p-1));
alp = p*alp / ((p-1)*mu + mu^(1-p)*alp^p);
end
y2 = @(x)2*alp/(1+alp)*rr(x);

xx = logspace(-15,0,1000);
abserr2 = y2(xx)-f(xx);
hold off, semilogx(xx,abserr2), grid on

line([alpini^p alpini^p],norm(abserr,inf)*[-1 0.5],LS,'--',CO,'r')
text(alpini^p*1.1,-norm(abserr,inf),'$\alpha^p$',IN,LT,FS,18,CO,'r')
title(['absolute error of composite approximant, k=3, \alpha=',num2str(alpini)])

Here is a run with a smaller $\alpha$.

alp = 0.01; alpini = alp;
rr = @(x)1;
for kk = 1:3
mu = ((alp-alp^p)/((p-1)*(1-alp)))^(1/p);
rr = @(x) 1/p*((p-1)*mu*rr(x) + x./(mu*rr(x)).^(p-1));
alp = p*alp / ((p-1)*mu + mu^(1-p)*alp^p);
end
y3 = @(x)2*alp/(1+alp)*rr(x);

xx = logspace(-15,0,1000);
abserr3 = y3(xx)-f(xx);
hold off, semilogx(xx,abserr3), grid on

line([alpini^p alpini^p],norm(abserr,inf)*[-1 0.5],LS,'--',CO,'r')
text(alpini^p*1.1,-norm(abserr,inf),'$\alpha^p$',IN,LT,FS,18,CO,'r')
title(['absolute error of composite approximant, k=3, \alpha=',num2str(alpini)])

The maximum absolute error is attained at either $x=0$ or $x=1$. In [2] we showed that by balancing the errors at these endpoints we obtain a good composite rational approximant to $x^{1/p}$. How does the convergence compare with minimax? With respect to the degree, it is of course worse. The rational approximants are of type $(3^{k-1},3^{k-1}-1)=(9,8)$. For example, let's compare minimax with the first approximant above.

[~,~,r,err] = minimax(f,9,8);

minimaxerr = r(xx)-f(xx);
hold off, semilogx(xx,abserr), grid on
hold on
semilogx(xx,minimaxerr)

text(xx(20),abserr(1)+4e-3,'composite',IN,LT,CO,'b')
text(xx(20),minimaxerr(1)+4e-3,'minimax',IN,LT,CO,'r')
title('composite vs. minimax approximants type (9,8), absolute error')
hold off
Trial interpolant too far from optimal...
Trying AAA-Lawson-based initialization...

It can be shown that with respect to the degree, the composite rational approximant converges almost "pth root exponentially", that is, the error scales roughly like $\exp(-cn^{1/p})$ where $n$ is the degree. More precisely, we obtain the bound

$$\max_{x \in [0,1]} |f_k(x)-x^{1/p}| \leq \exp( -b n^c ),$$

where $b$ is a positive constant depending on $p$, $n=p^{k-1}$ is the degree of $f_k$, and

$$c = \frac{ \log \left(\frac{p}{p-1}\right) \log 2 }{ \log \left(\frac{2p}{p-1}\right) \log p }.$$

But we claim that composite approximants are still interesting, because they can be generated using very few parameters---only $O(k)$ parameters are used to express a rational function of degree $3^k$. For example, here is a convergence comparison with respect to the degrees of freedom. With a double exponential convergence with respect to $k$, composite rational approximants eventually outperform minimax.

k = 10; % max. number of compositions
n = 1:30;
stahl = exp(-2*pi*sqrt(n))*4^(1+1/p)*sin(pi/p); % Stahl's minimax estimate
semilogy(2*n,stahl,'.-',MS,12)
grid on, hold on
nn = p.^(0:k);
exponent = log(p/(p-1))*log(2) / (log(2*p/(p-1))*log(p)); % exponent obtained in [2]
b = 3;  % experimental constant
semilogy(p*(1:k+1),exp(-b*nn.^exponent)*10,'.-',MS,12);
xlabel('degrees of freedom'), ylabel('error')
text(p*(k/2),exp(-b*nn(1)^(1/exponent)),'composite',FS,12)
text(40,stahl(end)*10,'minimax',FS,12)

This makes composite rational approximants attractive in e.g. computing functions at a matrix argument, for which the efficiency gain can be exponential as compared to the minimax approximant. For details, see [2].

### References

[1] E. S. Gawlik, Rational minimax iterations for computing the matrix $p$ th root, arXiv:1903.06268, 2019.

[2] E. S. Gawlik and Y. Nakatsukasa, Approximating the $p$ th root by composite rational functions, arXiv:1906.11326, 2019.

[3] H. Stahl. Best uniform rational approximation of $x^\alpha$ on $[0, 1]$, Acta Math., 190 (2003), 241-306


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Question in the appendixes A of O'Neill book

I'm reading appendixes A of O'Neill's book, "Semi-riemannian geometry" and I don't understand a something.

I don't understand at the last theorem, how we construct a universal cover for $M$ and why is that (if it is) a manifold.

• The construction is not described in the paragraph you quote. He only claims that it is legit to discuss the simply connected covering, as opposed to a simply connected covering. – Amitai Yuval Aug 14 '18 at 17:52
• Yeah, sure but i put the whole paragraph to show the lack of explanation and as a reference for someone who might use this as a tool for the proof. So my question becomes where can I find a proof for this theorem? – Hurjui Ionut Aug 14 '18 at 18:55
• If you’re willing to invest some time it’s in chapter 3 of Peter May book math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf – Elad Aug 15 '18 at 8:58


text:
Tag Archives: zariski topology

Commutative Algebra 36

In this article, we will study the topology of Spec A when A is noetherian. For starters, let us consider irreducible topological spaces in greater detail. Irreducible Spaces Recall that an irreducible topological space is a non-empty space X satisfying any of the … Continue reading

Commutative Algebra 23

Localization and Spectrum Recall that the ideals of correspond to a subset of the ideals of A. If we restrict ourselves to prime ideals, we get the following nice bijection. Theorem 1. The above gives a bijection between Useful trick If … Continue reading

Commutative Algebra 14

Basic Open Sets For , let , an open subset of Spec A. Note that . Proposition 1. The collection of over all forms a basis for the topology of . Proof Let be an open subset of Spec A. Suppose … Continue reading

Commutative Algebra 13

Zariski Topology for Rings In this article, we generalize earlier results in algebraic geometry to apply to general rings. Recall that points on an affine variety V correspond to maximal ideals . For general rings, we have to switch to … Continue reading


text:
- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnlilne Submission ㆍMy Manuscript - For Reviewers - For Editors
 On congruences involving the generalized Catalan numbers and harmonic numbers Bull. Korean Math. Soc. 2019 Vol. 56, No. 3, 649-658 https://doi.org/10.4134/BKMS.b180454Published online May 31, 2019 Sibel Koparal, Ne\c{s}e \"{O}m\"{u}r Kocaeli University; Kocaeli University Abstract : In this paper, we prove some congruences involving the generalized Catalan numbers and harmonic numbers modulo $p^{2},$ one of which is \begin{align*} \sum\limits_{k=1}^{p-1}k^{2}B_{p,k}B_{p,k-d} \equiv &\ 4\left( -1\right) ^{d}\left\{ \frac{1}{3}d\left( 2d^{2}+1\right) \left( 4pH_{d}-1\right) \right. \\ &\ \left. -p\left( \frac{26}{9}d^{3}+\frac{4}{3}d^{2}+\frac{7}{9}d+\frac{1}{2} \right) \right\}\pmod{p^{2}}, \end{align*} where a prime number $p>3$ and $1\leq d\leq p.$ Keywords : congruences, harmonic numbers and binomial coefficients MSC numbers : Primary 11B50, 11A07, 11B65 Full-Text :


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# FO-definability of the integers in (Q, +, <)

With $Q$ the set of rational numbers, I'm wondering:

Is the predicate "Int($x$) $\equiv$ $x$ is an integer" first-order definable in $(Q, +, <)$ where there is one additional constant symbol for each element of $Q$?

I know this in the case if multiplication is allowed. I guess the fact that $<$ is dense would imply a negative answer to this question, via an EF game maybe; is there a similar structure with a dense order but with Int($x$) FO-definable?

-
I don't see how Int is definable even when multiplication is allowed. Do you have a source ? – mercio May 22 '11 at 6:56
@chandok: this is a famous result of Julia Robinson. JSTOR link – Chris Eagle May 22 '11 at 7:08

First, I claim that the theory of the structure $\langle\mathbb{Q},+,\lt\rangle$ admits elimination of quantifiers. That is, every formula $\varphi(\vec x)$ in this language is equivalent over this theory to a quantifier-free formula. This can be proved by a brute-force hands-on induction over formulas. Allow me merely to sketch the argument. It is true already for the atomic formulas, and the property of being equivalent to a quantifier-free formulas is preserved by Boolean connectives. So consider a formula of the form $\exists x\varphi(x,\vec z)$, where $\varphi$ is quantifier-free. We may put $\varphi$ in disjunctive normal form and then distribute the quantifier over the disjunct, which reduces to the case where $\varphi$ is a conjunction of atomic and negated atomic formulas. We may assume that $x$ appears freely in each of these conjuncts (since otherwise we may remove it from the scope of the quantifier). If a formula of the form $x+y=z$ appears in $\varphi$, then we may replace all occurences of $x$ with $z-y$ and thereby eliminate the need to quantify over $x$ (one must also subsequently eliminate the minus sign after the replacing, but this is easy by elementary algebraic operations). We may do this even if $x$ appears multiply, as in $x+x+y=z$, for then we replace $x$ everywhere with $(z-y)/2$, but then clear both the $2$ and the minus sign by elementary algebraic manipulations. Thus, we may assume that equality atomic assertions appear only negatively in $\varphi$. All the other assertions merely concern the order. Note that a negated order relation $\neg(u\lt v)$ is equivalent to $v\lt u\vee v=u$, and we may distribute the quantifier again over this disjunct. So negated order relations do not appear in $\varphi$. The atomic order formulas have the form $x+y\lt u+v$ and so on. We may cancel similar variables on each side, and so $x$ appears on only one side. By allowing minus, we see that every conjunct formula in $\varphi$ says either that $a\cdot x\neq t$, or that $b\cdot x\lt s$ or that $u\lt c\cdot x$, for some terms $t,s,u$, in which $+$ and $-$ may both appear, and where $a$, $b$ and $c$ are fixed positive integer constants. By temporarily allowing rational constant coefficients, we may move these coefficients to the other side away from $x$. Thus, the assertion $\exists x\,\varphi(x,\vec t,\vec s,\vec u)$ is equivalent to the assertion that every $\frac{1}{c}u$ is less than every $\frac 1b s$. We may then clear the introduced rational constant multiples by multiplying through (which means adding that many times on the other side). Clearly, if such an $x$ exists, then this will be the case, and if this is the case, then there will be $x$'s in between, and so infinitely many, so at least one of them will be unequal to the $t$'s. This final assertion can be re-expressed without minus, and so the original assertion is equivalent to a quantifier-free assertion. So the theory admits elimination of quantifiers.