math trig and statistical functions
Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 1
... perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands We apply the ODF regression algorithm and statistical ... commissural, and projection connections and study the inter-subject variability between left and right hemispheres in relation to gender based on this atlas O’Donnell et al [27] and Yushkevich ... generation and HARDI-based statistical INTRODUCTION analysis, is needed for the studies of white matter similarities and differences across large populations 1.2 Research Challenges and Thesis...
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Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 2
... vt = mt , kV mt and the standard fact that energy-minimizing curves coincide with constant-speed length-minimizing curves, one can obtain the metric distance between the template and target shapes, ... initial momentum m0 and the evolving diffeomorphism φt We see that by making a change of variables and obtain the following expression relating mt to the initial momentum m0 and the geodesic φt ... denotes the identity map and vt are the associated velocity vector fields The vector fields vt are constrained to be sufficiently smooth, so that Eq (2.6) is integrable and generates diffeomorphic...
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Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 3
... the neighborhood of xi , and wj is the weight of xj based on the distance between φ1 (xi ) and xj The exponential maps and logarithm maps can be computed via Eq (2.4) and Eq (2.5) respectively ... ORIENTATION DISTRIBUTION FUNCTIONS Figure 3.6: Comparison between the LDDMM-ODF and LDDMM-DTI algorithms Panels (a, b) respectively show the template and target HARDI and their enlarged images, ... vector Property Assume A and B to be two matrices of affine transformations and ψ is a square-root ODF The following property holds true B(Aψ)(s) = (A B)ψ(s), (3.9) where (A B) stands for matrix muliplication...
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Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 4
... and kV respectively as kV Id3×3 and kV Id3×3 , where Id3×3 is a × identity matrix π π and kV and kV are scalars In particular, we assumed that kV and kV are Gaussian with kernel sizes of σV and ... IMAGING 4.4.1 Derivation of Update Equations of σ and m0 in EM We now derive Eqs (4.12) and (4.13) from Q-function in Eq (4.10) for updating values of σ and m0 The reader can skip this subsection ... of the Atlas and the Distribution of Random Diffeomorphisms Figure 4.2: Illustration of the general framework of the Bayesian HARDI atlas estimation 4.2 The Shape Prior of the Atlas and the Distribution...
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Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 5
... relationship of a Ψ-valued random variable Ψ and a non-random variable X ∈ R Such a geodesic relationship cannot be simply written as the summation of the intercept β0 and the scalar variable X ... i ˆ and logψi ψi ˆ ⊥ = logψi ψi − logψi ψi ˆ ˆ , where (·) and (·)⊥ denote components of (·) parallel and orthogonal to ξi respectively 93 GEODESIC REGRESSION OF ORIENTATION DISTRIBUTION FUNCTIONS ... callosum and corticospinal tracts: Panel (a) shows the T1 image of the selected slice and ROIs Panel (b) illustrates the ODFs in the selected ROI and the peaks of each ODF, where blue and red...
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Registration, atlas generation, and statistical analysis of high angular resolution diffusion imaging based on riemannian structure of orientation distribution functions 6
... R R AO Information and accuracy attainable in the estimation of statistical parameters Bull Calcutta Math Soc., 37:81–89, 1945 15 [84] N N C ENCOV Statistical decision rules and optimal inference ... REFERENCES [87] U G RENANDER AND M I M ILLER Computational anatomy: An emerging discipline Quart App Math. , 56(4):617–694, 1998 18, 21 [88] P D UPUIS , U G RENANDER , AND M I M ILLER Variational ... ENGLET, P.M T HOMPSON , AND R V IDAL Estimating Orientation Distribution Functions with Probability Density Constraints and Spatial Regularity In Medical Image Computing and Computer-Assisted Intervention,...
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A new approach to semantic and syntactic functions of English adjectives – A contrastive analysis with their Vietnamese equivalents
... title, aims and objectives, scope, methods and design of the study Chapter II introduces an overview of English adjectives with the definitions of adjectives and their semantic and syntactic functions ... and He wore dirty and old shoes I have a young and beautiful sister When there more than two adjectives, they may be separated by commas and apart from the last adjective which separated by and ... He wore dirty, wet, old and worn shoes But, there are some fixed phrases of adjectives which are often linked by and : old and musty with, a long and winding road, hard and fast rules When the...
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math puzzles and brain 6414
... exciting and promising application of the puzzles would be in a math club where the students can compete and play games that challenge the mind and the creative spirit Teaching and learning mathematics ... dimension: a conceptual understanding and framework To expand the potential power of mathematics, they must enter a third dimension: the intuitive and mind-expanding creative viii Foreword ... difficult math brainteasers and requiring math skills from addition and subtraction to determining probability and algebraic thinking Here are the types of puzzles you will find within these pages: Mathematical...
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Convex sets and convex functions taking the infinity value
... IRn and let f1 , , fm be convex functions Let also and w1 , , wm ≥ Then w1 f1 + · · · + wm fm and max1≤i≤m fi (x) are convex functions More generally, let {fi }i∈I be a family of convex functions ... if and only if S is R convex Moreover, f is proper and convex S ⊆ I n nonempty and convex R =⇒ f + δS is proper and convex dom f ∩ S = ∅ We have a correspondence between convex sets and ... Convex sets and convex functions taking the infinity value Passing from sets to functions A common device to construct convex functions on IRn is to construct a convex set F in IRn+1 and then take...
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Using Local Variables and Creating Functions that Return Results
... "News", channelNames[2] = "Classics", and so on This is important to understand as we progress NOTE For more information on arrays, see Lesson 6, "Creating and Manipulating Data." Let's create ... from a Function Call Not only functions simply execute sets of actions; you can also use them like miniprograms within your movie, processing information sent to them and returning values Take a ... called To understand this, take a look at how this function is called in the following script: var idealCircumstances:Boolean = buyCD(19, "Friday"); if(idealCircumstances == true){ gotoAndPlay("Happiness");...
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Tài liệu Thermodynamics and Statistical Physics doc
... of pressure and temperature at the end of it doing some work then there is no temperature change, i.e Initial temperature and pressure = T and P Final temperature and pressure = T and P 0 0 • ... of a rubber band A rubber band is a collection of long chain polymer molecules In its relaxed state the polymers are high disordered and entangled The amount of disorder is high and so the entropy ... possible we could measure the position and velocity of every particle of the system and calculate the total energy by summing up the individual kinetic and potential energies • • đ W = + PdV...
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Tài liệu AC ANALYSIS AND NETWORK FUNCTIONS doc
... determination of the rms value and the average power MATLAB has two functions, quad and quad8, for performing numerical function integration 6.1.1 MATLAB Functions quad and quad8 The quad function ... domain and by using the Kirchoff voltage and current laws The unknown voltages and currents are solved using matrix techniques Given a network function or transfer function, MATLAB has functions ... than the quad at handling functions with “soft” singularities such as ∫ xdx Suppose we want to find q given as b q = ∫ funct ( x )dx a The general forms of quad and quad8 functions that can...
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Wacky word problems games and activities that make math easy and fun
... English but not math How many students are taking math but not English? How many students are taking math? To solve the problem: a Use paper and a pencil to label one circle math and one circle ... Decimals and Perfect Percents Fabulous Fractions Great Graphs Groovy Geometry Marvelous Multiplication Measurement Mania Magical Math WACKY WORD PROBLEMS Games and Activities That Make Math Easy and ... Lynette Wacky word problems : games and activities that make math easy and fun / Lynette Long p cm —(Magical math) Includes index ISBN 0-471-21061-7 (pbk : alk paper) Mathematical recreations I Title...
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Tài liệu Báo cáo khoa học: "The impact of language models and loss functions on repair disfluency detection" pptx
... disfluencies She identifies and defines three distinct parts of a speech disfluency, referred to as the reparandum, the interregnum and the repair Consider the following utterance: reparandum Related work ... in the past; the work of Johnson and Charniak (2004) first explores such an approach Johnson et al (2004) adds some handwritten rules to the noisy channel model and use a maximum entropy approach, ... Markov Model approach; this is a statistical approach which The reparandum to Boston is the part of the utterance builds up a syntactic analysis of the sentence and that is ‘edited out’; the interregnum...
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Tài liệu Báo cáo khoa học: "Reading Level Assessment Using Support Vector Machines and Statistical Language Models" pdf
... e.g Lee and Myaeng’s (2002) genre and subject detection work and Boulis and Ostendorf’s (2005) work on feature selection for topic classification For our LM classifiers, we followed Boulis and Ostendorf’s ... happened for 10 randomly chosen articles from standard edition of The Washington Post Conclusions and Future Work Statistical LMs were used to classify texts based on reading level, with trigram models ... development and test sets The dev and test sets are the same size and each consist of approximately 5% of the data for each grade level measures For comparison to other methods, e.g Flesch-Kincaid and...
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Tài liệu Báo cáo khoa học: "Japanese OCR Error Correction using Character Shape Similarity and Statistical Language Model " pptx
... was 91% for magazines and introductory textbooks of science and technology (Ito and Maruyama, 1992) used part of speech bigram model and beam search in order to get multiple candidates in their ... data and the test data for handwritten OCR Sentences Words Characters training 192802 4746461 7521293 In the word model, we used 3167 character unigrams and 91198 character bigrams All unigrams and ... accuracy of the first candidate Let c/ be the i-th character in the input, xlj be the j - t h candidate for ci in the output, and p be the probability t h a t the first candidate is correct The...
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Tài liệu Báo cáo khoa học: "Skip N-grams and Ranking Functions for Predicting Script Events" doc
... work (Chambers and Jurafsky, 2008; Chambers and Jurafsky, 2009; McIntyre and Lapata, 2009; McIntyre and Lapata, 2010), these event chains are identified by running a coreference system and a dependency ... The work of McIntyre and Lapata followed in this same paradigm, (McIntyre and Lapata, 2009; McIntyre and Lapata, 2010), collecting chains of events by looking at entities and the sequence of verbs ... Chambers and Jurafsky, which combined a dependency parser with coreference resolution to collect event script statistics and predict script events (Chambers and Jurafsky, 2008; Chambers and Jurafsky,...
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Tài liệu Báo cáo khoa học: "Integrating Symbolic and Statistical Representations: The Lexicon Pragmatics Interface" pot
... (Lascarides and Asher 1993) This framework has already been successful in accounting for other phenomena on the interface between the lexicon and pragmatics, e.g Asher and Lascarides (1995) Lascarides and ... = Z and B = member-of For otherwise the events in (5) are too "disconnected" to support ant" rhetorical relation On the other hand assigning u and B these values allows us to use Subtype and ... incoherent (and we have presupposition failure) The detailed analysis of (3) and (52) involve reasoning about the values of v and B But for reasons of space, we gloss over the details given in Asher and...
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