• From eq.(3.4), we can set the sufficient statistic <math>t\left(x \right)</math> and parameters <span
    17 KB (2,590 words) - 10:45, 22 January 2015
  • where I is some open interval of the real number set <math>\mathbb{R}</math>. This is called a `parametric representation' of th ...to parametrize a graph described by y = f(x) is to choose a parameter and set it equal to x, then express y in terms of that parameter. For example, the
    10 KB (1,752 words) - 17:02, 14 May 2015
  • | <math> (i.e.,\ |a|R=\ the\ set\ of\ points\ {|a|z}\ for\ z\ in\ R)\ </math> | <math> R^{1/k}\ (i.e.,\ the\ set\ of\ points\ z^{1/k},\ </math>
    7 KB (1,018 words) - 08:55, 6 March 2015
  • *Definition of a set **[[Practice_Question_definition _set_ECE302S13Boutin|Do these signals form a set?]]
    7 KB (960 words) - 18:17, 23 February 2015
  • ...t Analysis is a process of extracting useful information from a noisy data set. Complex data sets may hid significant relationship between variables, and ...at a set frequency. We live in a three dimensional world, so we decide to set up three cameras in a rather random directions to collect the data on the m
    6 KB (1,043 words) - 12:45, 3 March 2015
  • Let <math class="inline">\left\{ t_{k}\right\}</math> be the set of Poisson points corresponding to a homogeneous Poisson process with param
    5 KB (780 words) - 01:25, 9 March 2015
  • This question is a set of short-answer questions (no proofs):
    5 KB (729 words) - 00:51, 10 March 2015
  • ...h> . The event space <math class="inline">\mathcal{F}</math> is the power set of <math class="inline">\mathcal{S}</math> , and the probability measure <m
    5 KB (735 words) - 01:17, 10 March 2015
  • ...ex as a function of <math class="inline">q</math> (the probability that a set of twins are identical.)
    5 KB (748 words) - 01:01, 10 March 2015
  • ...ent of' 'the set of real numbers' 'for all' n 'which are elements of' 'the set of natural numbers'. ...implies that <math>ln(x)</math> must be <math>< 0</math>), we arbitrarily set <math>s = -ln(x)</math> or <math>-s = ln(x)</math>, which leaves us with:
    3 KB (512 words) - 15:14, 1 May 2016
  • ...utilized the property that ''arctan(-x)'' = ''-arctan(x)''. Explicitly, I set a 'negative flag' if the ''arctan'' to be calculated had a negative argumen ...utput at a macro scale (ie not by counting assembly instruction cycles), I set the conditionals in the code such that the longest logical processing path
    8 KB (1,176 words) - 15:15, 1 May 2016
  • ...the 4 signs of the set of voltage equations, as well rule that bounds the set of possible sign configurations.
    3 KB (474 words) - 15:17, 1 May 2016
  • % set params
    2 KB (289 words) - 15:14, 1 May 2016
  • ...ydrogen and Carbon, it is redundant and needs to be removed. A sign that a set of vectors is a basis is that any vector you add to it from vector space V ...o generate every color and don't have any redundant colors among their own set, then they serve as a basis for all colors.
    14 KB (2,247 words) - 13:09, 3 March 2015
  • ...tes. Since <math>\phi</math> was allowed to be any scalar function, we can set <math>\phi = \theta</math> to obtain
    19 KB (3,027 words) - 12:01, 24 February 2015
  • ...late, then, that the transformation from one set of coordinates to another set is merely ...ansformation T, T is the Transformation from C1 to C2 and C2 is the second set of coordinates.
    18 KB (2,894 words) - 12:17, 3 March 2015
  • ...> <br /> where, <math>n</math> is the number of events (cardinality of the set <math>\{A_{i}\}</math>) in the sample space and, <math>i = 1, 2, ..., n</ma
    14 KB (2,241 words) - 10:42, 22 January 2015
  • ...e global maximum. So we take the derivative w.r.t. <math>\beta</math>, and set it equal to zero to find the maximum.
    13 KB (2,062 words) - 10:45, 22 January 2015
  • ...near separation, which is a hyperplane. The hyperplane can be defined by a set of points which are equidistant to <math>\mu_1</math> and <math>\mu_2</math
    19 KB (3,255 words) - 10:47, 22 January 2015
  • ...orthonormal transformations to convert the observed correlated data into a set of linearly uncorrelated data, which are the so-called principle components &nbsp; &nbsp; In this section, I will just use PCA on a simple data set to help you gain some intuition of PCA, the question of "why does it work"
    22 KB (3,459 words) - 10:40, 22 January 2015
  • ...atrix '''Σ'''. This is either known or it can be estimated from your data set. We assume that '''Σ''' is positive definite. We also assume wlog that ''' Then, '''Y''' is a set of <math>n</math> data points drawn from an uncorrelated bivariate Gaussian
    17 KB (2,603 words) - 10:38, 22 January 2015
  • ...="texhtml">θ</span>&nbsp;is a fixed, unknown constant<br>belonging to the set&nbsp;<math>\Theta \subset \mathbb{R}^{n}</math>. business of making predictions based on a set of solid assumptions, then we would be
    25 KB (4,187 words) - 10:49, 22 January 2015
  • ...hich means that the density function is estimated locally based on a small set of neighboring samples. Because of this locality, local (nonparametric) den
    15 KB (2,345 words) - 10:52, 22 January 2015
  • ...nbsp; Let D = {x<sub>1</sub>,x<sub>2</sub>,...,x<sub>N</sub>}&nbsp;to be a set of iid samples from the Gaussian distribution with μ and Σ unknown.&nbsp;
    7 KB (1,177 words) - 10:47, 22 January 2015
  • ...ndom variable X and the parameter θ can be vector-valued. Now we obtain a set of independent observations or samples S = {x<sub>1</sub>,x<sub>2</sub>,... ...he distribution p(θ ). Then the probability density function of X given a set of observations S can be estimated by<br>
    15 KB (2,273 words) - 10:51, 22 January 2015
  • ...f the most useful method to represent pattern classifiers is in terms of a set of '''''discriminant functions ''''' <math>g_i(\mathbf{x}), i=1,2,...,c</ma
    14 KB (2,287 words) - 10:46, 22 January 2015
  • ...the infinity. We set <math>P = \lim_{n \to \infty}P_n(e)</math>. Then, we set infinite sample conditional average probability of error as <math>P(e|x)</m ...in previous section can be utilized to get the upper error bound. First we set
    14 KB (2,313 words) - 10:55, 22 January 2015
  • ...nbsp;&nbsp; &nbsp; We divide the sample data into training set and testing set. Training data is used to estimate the model parameters, and testing data i Given a data set
    9 KB (1,382 words) - 10:47, 22 January 2015
  • Now, assume that a set of <math>N</math> independent samples were obtained from a certain class <m ...math>\theta</math> both the information in priori and the information from set <math>\mathcal{D}</math> of n samples <math>x_1, x_2, ... , x_n</math> need
    10 KB (1,625 words) - 10:51, 22 January 2015
  • ...e of discriminant functions as a means of classifying data. That is, for a set of classes <math> \omega_c </math>, we choose to classify a sample <math>\v
    16 KB (2,703 words) - 10:54, 22 January 2015
  • ...lambda \textbf{c}</math> also separates the data. One solution might be to set <math>|\textbf{c}|=1</math>. Another solution is to introduce a bias denote ...Other than the parameters in the optimization problem, the SVM has another set of parameters called hyperparameters, including the soft margin constant, <
    14 KB (2,241 words) - 10:56, 22 January 2015
  • ...' = 3. Column 4 - 7 gives the records counts with the threshold value''t'' set to the probability of current record. Accordingly, TPR and FPR can be compu
    11 KB (1,823 words) - 10:48, 22 January 2015
  • Given a set of training data in a region <math>\Re^n</math>, and a point <math>x_0</mat
    12 KB (2,086 words) - 10:54, 22 January 2015
  • ...iven as <math>(x_i,y_i)</math> where i is the index number of the training set, and <math>x_i</math> is hair length in inches and <math>y_i=1</math> indic If we set the above equation to zero, there is no close form solution, so we are goin
    9 KB (1,540 words) - 10:56, 22 January 2015
  • # Prior selection : How to set priors?
    18 KB (2,852 words) - 10:40, 22 January 2015
  • Therefore, when both of the parameters are unknown for a set of Gaussian distributed random vector, the ML estimator of covariance matri
    19 KB (3,418 words) - 10:50, 22 January 2015
  • ...ith corresponding labels <math> y_{1}, y_{2}, ..., y_{N} </math> from some set of <math> C </math> classes <math> w_1,w_2,...w_C</math>. Together these are often called the training set, because they are used to "train" the classifier.
    9 KB (1,604 words) - 10:54, 22 January 2015
  • The KNN method begins with a set of labeled training data (points) in the feature space. Note that it is ess <br> Number of total points in the training set: <span class="texhtml">''N''</span> <br>
    6 KB (1,013 words) - 10:55, 22 January 2015
  • ...um value of likelihood, which means is the most likely to observe the data set samples.<br> &nbsp; Suppose we have a set of n independent and identically destributed observation samples. Then dens
    13 KB (1,966 words) - 10:50, 22 January 2015
  • =<math>\Sigma^{-1}\sum\limits_{j=1}^{N}(x_j-\mu)</math> set to be 0 \end{bmatrix}</math> set to be 0
    11 KB (2,046 words) - 10:51, 22 January 2015
  • = Set up and Tricks = There are a number of tricks that are used in the set up for LDA. The first and most important is the concatenation trick. This t
    10 KB (1,666 words) - 10:56, 22 January 2015
  • ...l wish to discover some form of underlying structure in an unlabelled data set. Such a task falls under the category of unsupervised learning. ...points in multidimensional space. For example, consider the following data set:
    8 KB (1,350 words) - 10:57, 22 January 2015
  • ...series which may or may not converge. The domain for this function is the set of all ''x'''s for which the series converges.
    9 KB (1,632 words) - 18:19, 27 February 2015
  • The discrete-time Fourier transform (DTFT) of a discrete set of real or complex numbers x[n] with n=all integers, is a Fourier series, w
    3 KB (515 words) - 20:02, 16 March 2015
  • The result of this function is a set of time-shifted impulses whose amplitudes match those of the input signal x
    4 KB (734 words) - 18:56, 16 March 2015
  • ...above equation we can see that if we were to have <math>{\omega}</math> be set to <math>{\omega}_{o}</math> we get
    5 KB (862 words) - 20:02, 16 March 2015
  • Using the Nyquist condition to set the sampling period <math>T</math>:<br><math>\frac{1}{T} > 2f_M \ or \ T <
    10 KB (1,650 words) - 19:04, 16 March 2015
  • ...ed signal. Essentially, the comb is grabbing points on the graph x(t) at a set interval, T. <math>
    2 KB (335 words) - 09:57, 14 March 2015
  • ...a specific <math>\theta</math>. Repeating over many <math>\theta</math>, a set of data like that shown in Figure 2 will be obtained. All the data will be
    8 KB (1,252 words) - 19:26, 9 February 2015
  • Let <math class="inline">\left\{ t_{k}\right\}</math> be the set of Poisson points corresponding to a homogeneous Poisson process with param
    4 KB (700 words) - 17:48, 13 March 2015
  • This question is a set of short-answer questions (no proofs): 1. The set <math class="inline">\left\{ \mathbf{X}\leq x\right\}</math> is an event
    2 KB (287 words) - 00:52, 10 March 2015
  • ...ex as a function of <math class="inline">q</math> (the probability that a set of twins are identical.)
    1 KB (187 words) - 01:03, 10 March 2015
  • ...h> . The event space <math class="inline">\mathcal{F}</math> is the power set of <math class="inline">\mathcal{S}</math> , and the probability measure <m
    4 KB (698 words) - 01:35, 10 March 2015
  • An '''equivalence class''' is the set of numbers that are all equivalent under modulo operation. In the above exa ...es for the modulus 4. This means we are living in a universe which is this set {0,1,2,3}.
    6 KB (886 words) - 05:16, 24 June 2015
  • Finite Field/Galois Field: a finite set together with operations + and * with the following properties: 1. The set forms an additive group with neutral element 0
    6 KB (1,012 words) - 11:15, 29 June 2015
  • ...he question does not say what set the equation is under. I assume that the set is under all natural numbers greater than or equal to 1 since excluding the
    7 KB (1,244 words) - 09:36, 18 December 2015
  • ...is to create a set of target notes in order of their occurrence. How this set is formatted is based on the windowing size and tempo. These concepts will ...s for a 1 second long note, ten of that note are needed in the target note set. These windows are examined to determine the energy of the window, the numb
    9 KB (1,777 words) - 23:23, 21 November 2015
  • T_sampling = 0.001; % set according to parameters in modulation scheme
    4 KB (546 words) - 19:34, 29 November 2015
  • ...signal, we would get impulses at -1Hz and 1Hz. There is no other possible set of frequencies that can produce the above signal. If asked to draw a function to fit the discrete set of points, most people will draw the 1Hz cosine above. This is not incorrec
    12 KB (2,004 words) - 20:37, 2 December 2015
  • a = 0.3; % set the attenuation factor D = delay*fs; % set the delay time in s
    2 KB (362 words) - 22:18, 29 November 2015
  • a = 0.3; % set the attenuation factor D = delay*fs; % set the delay time in s
    3 KB (405 words) - 23:49, 29 November 2015
  • We know that <math>Z(t)</math> can only take on the values 0 and 1, so we set out to find the probability that <math>Z(t)</math> = 0; if we subtract this
    6 KB (973 words) - 00:57, 1 February 2016
  • ...ot form a circle and also with the minimize cost to join the selected edge set. (A Tree is a connected graph with no cycle) ...to our selected edge set we consider if it will cause a circle of the edge set.
    10 KB (1,524 words) - 23:36, 24 April 2016
  • ...he solved this problem by his theorem, which is also in his paper, "For a set of added edges it is necessary and sufficient to be an optimal solution for
    9 KB (1,403 words) - 20:45, 24 April 2016
  • A social network is a social structure that made up of a set of nodes (individuals or organizations) connected by edges (relationships). A graph is a set of nodes and a set of links.<br />
    14 KB (2,465 words) - 20:07, 24 April 2016
  • Lastly, we cannot have a set of precedence relations that form a cycle. In other words, we cannot have ( •''Project''-A set of tasks to be completed
    7 KB (1,196 words) - 21:33, 24 April 2016
  • A set of these particles is known as the ''swarm'' and they will all exist inside Set the position as a random point inside the search space
    14 KB (2,177 words) - 11:28, 24 April 2016
  • ...t until all vertices have been visited). If we are able to find a spanning set of the graph without using one environmentally impactful edge, we are done. ...e of its vertices is in the current tree and add it back into the modified set; if the graph is now spanned, we are done. If the graph is still not spanne
    5 KB (975 words) - 22:15, 7 March 2016
  • % This code tests BayesErrorMonteCarlo.m using a data set with known
    3 KB (392 words) - 18:50, 11 February 2016
  • * ''Arc-set'': A list of all the arcs in a digraph. ...one point and a loss counts as no points. This is achieved by sorting the set of outdegrees in nondecreasing order.
    6 KB (1,066 words) - 13:06, 24 April 2016
  • ...where to build streets connecting the houses. Modeling this as selecting a set of pairs of houses to connect so that all houses in the end have a connecte ...ing this network, given the costs <math>\alpha(\cdot,\cdot)</math> and the set <math>E</math> of environmentally sensitive pairs <math>(x,y)</math>. Sketc
    5 KB (766 words) - 22:18, 7 March 2016
  • <math>\bullet</math> We set <math>d(A,A)</math> = 0 and all other distances <math>d(\cdot,\cdot)</math> <math>\bullet</math> Following edges from <math>A</math>, we set <math>d(A,B)=1,\, d(A,C)=0</math>, and <math>d(A,D)=2</math>.
    2 KB (375 words) - 22:29, 7 March 2016
  • ...ons on the availability of resources form what is known as a '''constraint set'''. ...> be the number of shipments from district ''i'' to landfill ''j''. We can set up the minimization like so:
    15 KB (2,613 words) - 22:35, 24 April 2016
  • ...ing at NP-complete problems. The NP-complete set of problems comprise of a set of problems, to each of which any other NP-problem can both be reduced to b Next, we look at NP-hard problems. These problems comprise at set of problems that are at the minimum as difficult to solve as NP problems. H
    11 KB (2,028 words) - 20:48, 24 April 2016
  • ...set of vertices (or "dots") in the graph and <math>\ E_{G} </math> is the set of edges (or "lines") for the graph.
    13 KB (2,051 words) - 22:06, 24 April 2016
  • ...istance value so the first node is set to zero and all the other nodes are set to infinity. Starting at the initial node we consider all if its unvisited ...ted (or add it to the visited list) and remove it from the unvisited list. Set the unvisited node marked with the smallest tentative distance as the next
    14 KB (2,351 words) - 23:21, 24 April 2016
  • ...igure out what they are. By comparing the unknown data with the whole data set of the known data, we would predict the unknown data is the same as certain ...rs are machine printed or similar to that. It is because the training data set contains only a particular letter style. So maybe some machine printed test
    8 KB (1,405 words) - 22:56, 27 November 2016
  • *Set <math>x[n]=\delta[n]</math> to get the unit impulse response h[n] of the sy *Set <math>x[n]=\delta[n]</math> to get the unit impulse response h[n] of the sy
    9 KB (1,559 words) - 14:33, 24 November 2016
  • ...ssian filtering is used to counter this effect. The image is taken in as a set of discrete pixels. Normally, blurring can be achieved on a normal image by
    2 KB (258 words) - 04:20, 28 November 2016
  • :As threads are out-of-sync, the working set for the cache increases. This can be addressed potentially with a shared (b ...k of lock step. Solution #2's approach aims to solve the increased working set for the caches. Solution #2's use of a victim buffer is a little unclear, h
    20 KB (3,337 words) - 15:32, 25 April 2017
  • ...image were scanning from left to write, we can see that if the filter was set at (2,2) in the image above, it would have a value of 400 and therefore wou
    7 KB (1,184 words) - 20:31, 23 April 2017
  • ...sum allows a continuous function to be represented by a sum of a discrete set of values. The concepts of region of convergence and translating a discrete
    6 KB (931 words) - 23:40, 23 April 2017
  • ...t was hard, even as a native English speaker, to understand how the IPA is set up [3]. In essence, it was difficult to get through the literature and unde
    3 KB (576 words) - 23:56, 23 April 2017
  • <math>\quad The \quad set\quad is\begin{Bmatrix} <math>\quad \therefore \quad The \quad set\quad is\begin{Bmatrix}
    6 KB (742 words) - 07:16, 17 May 2017
  • ...such that each edge of the graph is incident to at least one vertex of the set. The problem of finding a minimum vertex cover is a classical optimization ...e in the set <math>s</math> may have multiple expertise. We will model the set of <math>t</math> applicants as <math>V</math> vertices, and each specialti
    6 KB (995 words) - 16:05, 23 August 2017
  • ...hile taking advantage of a very powerful engine with a superior supporting set of libraries (called Toolboxes). Think of Matlab as giving you the ability
    5 KB (799 words) - 20:12, 9 December 2017
  • ...e discussing them within real numbers. When a set of numbers match another set of numbers by a particular definition, a function forms. Therefore, if we a
    6 KB (1,070 words) - 23:06, 21 November 2017
  • ...exact" in science is defined as "using accurate measurements and following set rules". Here is another intuitive explanation from the perspective of langu Set <math>\frac{∂F}{∂x}=f=xy</math>, then do the integration <math>F=\int x
    10 KB (1,764 words) - 14:31, 17 November 2017
  • To set the record straight before we begin, infinity does not work like any other
    7 KB (1,344 words) - 01:36, 1 November 2017
  • To set the record straight before we begin, infinity does not work like any other
    15 KB (2,678 words) - 04:42, 14 February 2020
  • ...em, an equilibrium point is going to be a solution of a pair of constants. Set all of the differential terms equal to <math>0</math> to find the equilibri In the example in 6.0, we set <math>\frac{dx}{dt}=\frac{dy}{dt}=0</math>, hence <math>x(1-2x-3y)=2y(3-x-2
    10 KB (1,613 words) - 23:16, 21 November 2017
  • '''Solution:''' Set the particular solution <math>y_p = u_1 (2t+1) + u_2 e^{2t} </math>, Set '''<math>\frac{du_1}{dt} (2t+1) + \frac{du_2}{dt} e^{2t} = 0</math>''' to b
    7 KB (1,254 words) - 19:49, 22 November 2017
  • ...given a feedback system, the steps involved in determining the output are set up the transfer function, get it in the form of Y(Z) = H(Z)X(Z) and use the
    396 B (64 words) - 15:33, 3 December 2017
  • ...hile taking advantage of a very powerful engine with a superior supporting set of libraries (called Toolboxes). Think of Matlab as giving you the ability
    5 KB (799 words) - 00:59, 4 December 2017
  • %set 10 as treshold %set 10 as treshold
    4 KB (462 words) - 16:35, 10 December 2017
  • Question Set 1: Energy Conversion and Reference Frame Theory
    1 KB (182 words) - 13:47, 16 January 2018
  • Question Set 1: Energy Conversion and Reference Frame Theory
    1 KB (159 words) - 00:52, 11 January 2018
  • Question Set 1: Energy Conversion and Reference Frame Theory
    1 KB (172 words) - 18:21, 16 January 2018
  • Question Set 1: Energy Conversion and Reference Frame Theory
    1 KB (166 words) - 16:00, 19 January 2018
  • ...state conditions. The only information affecting the three-phase, balanced set of circuit variables is the RMS value and initial phase angle. These are th
    9 KB (1,373 words) - 14:16, 19 February 2018

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Alumni Liaison

Basic linear algebra uncovers and clarifies very important geometry and algebra.

Dr. Paul Garrett