Graphs of the Sine and Cosine Functions

Graphs of the Sine and Cosine Functions tài liệu, giáo án, bài giảng , luận văn, luận án, đồ án, bài tập lớn về tất cả c...

Proceedings of the 49th Annual Meeting of the Association for Computational Linguistics, pages 703–711, Portland, Oregon, June 19-24, 2011. c 2011 Association for Computational Linguistics The impact of language models and loss functions on repair disfluency detection Simon Zwarts and Mark Johnson Centre for Language Technology Macquarie University {simon.zwarts|mark.johnson|}@mq.edu.au Abstract Unrehearsed spoken language often contains disfluencies. In order to correctly inter- pret a spoken utterance, any such disfluen- cies must be identified and removed or other- wise dealt with. Operating on transcripts of speech which contain disfluencies, we study the effect of language model and loss func- tion on the performance of a linear reranker that rescores the 25-best output of a noisy- channel model. We show that language mod- els trained on large amounts of non-speech data improve performance more than a lan- guage model trained on a more modest amount of speech data, and that optimising f-score rather than log loss improves disfluency detec- tion performance. Our approach uses a log-linear reranker, oper- ating on the top n analyses of a noisy chan- nel model. We use large language models, introduce new features into this reranker and examine different optimisation strategies. We obtain a disfluency detection f-scores of 0.838 which improves upon the current state-of-the- art. 1 Introduction Most spontaneous speech contains disfluencies such as partial words, filled pauses (e.g., “uh”, “um”, “huh”), explicit editing terms (e.g., “I mean”), par- enthetical asides and repairs. Of these, repairs pose particularly difficult problems for parsing and related Natural Language Processing (NLP) tasks. This paper presents a model of disfluency detec- tion based on the noisy channel framework, which specifically targets the repair disfluencies. By com- bining language models and using an appropriate loss function in a log-linear reranker we are able to achieve f-scores which are higher than previously re- ported. Often in natural language processing algorithms, more data is more important than better algorithms (Brill and Banko, 2001). It is this insight that drives the first part of the work described in this paper. This paper investigates how we can use language models trained on large corpora to increase repair detection accuracy performance. There are three main innovations in this paper. First, we investigate the use of a variety of language models trained from text or speech corpora of vari- ous genres and sizes. The largest available language models are based on written text: we investigate the effect of written text language models as opposed to language models based on speech transcripts. Sec- ond, we develop a new set of reranker features ex- plicitly designed to capture important properties of speech repairs. Many of these features are lexically grounded and provide a large performance increase. Third, we utilise a loss function, approximate ex- pected f-score, that explicitly targets the asymmetric evaluation metrics used in the disfluency detection task. We explain how to optimise this loss func- tion, and show that this leads to a marked improve- ment in disfluency detection. This is consistent with Jansche (2005) and Smith and Eisner (2006), who observed similar Graphs of the Sine and Cosine Functions Graphs of the Sine and Cosine Functions By: OpenStaxCollege Light can be separated into colors because of its wavelike properties (credit: "wonderferret"/ Flickr) White light, such as the light from the sun, is not actually white at all Instead, it is a composition of all the colors of the rainbow in the form of waves The individual colors can be seen only when white light passes through an optical prism that separates the waves according to their wavelengths to form a rainbow Light waves can be represented graphically by the sine function In the chapter on Trigonometric Functions, we examined trigonometric functions such as the sine function In this section, we will interpret and create graphs of sine and cosine functions 1/41 Graphs of the Sine and Cosine Functions Graphing Sine and Cosine Functions Recall that the sine and cosine functions relate real number values to the x- and ycoordinates of a point on the unit circle So what they look like on a graph on a coordinate plane? Let’s start with the sine function We can create a table of values and use them to sketch a graph [link] lists some of the values for the sine function on a unit circle π π sin(x) √2 √3 √3 √2 x π π 2π 3π 5π π Plotting the points from the table and continuing along the x-axis gives the shape of the sine function See [link] The sine function Notice how the sine values are positive between and π, which correspond to the values of the sine function in quadrants I and II on the unit circle, and the sine values are negative between π and 2π, which correspond to the values of the sine function in quadrants III and IV on the unit circle See [link] 2/41 Graphs of the Sine and Cosine Functions Plotting values of the sine function Now let’s take a similar look at the cosine function Again, we can create a table of values and use them to sketch a graph [link] lists some of the values for the cosine function on a unit circle x π π cos(x) √ √ 2 π π 2π − 3π 5π −√ −√ π −1 As with the sine function, we can plots points to create a graph of the cosine function as in [link] The cosine function Because we can evaluate the sine and cosine of any real number, both of these functions are defined for all real numbers By thinking of the sine and cosine values as coordinates of points on a unit circle, it becomes clear that the range of both functions must be the interval [ − 1, 1] 3/41 Graphs of the Sine and Cosine Functions In both graphs, the shape of the graph repeats after 2π, which means the functions are periodic with a period of 2π A periodic function is a function for which a specific horizontal shift, P, results in a function equal to the original function: f(x + P) = f(x) for all values of x in the domain of f When this occurs, we call the smallest such horizontal shift with P > the period of the function [link] shows several periods of the sine and cosine functions Looking again at the sine and cosine functions on a domain centered at the y-axis helps reveal symmetries As we can see in [link], the sine function is symmetric about the origin Recall from The Other Trigonometric Functions that we determined from the unit circle that the sine function is an odd function because sin(−x) = −sin x Now we can clearly see this property from the graph 4/41 Graphs of the Sine and Cosine Functions Odd symmetry of the sine function [link] shows that the cosine function is symmetric about the y-axis Again, we determined that the cosine function is an even function Now we can see from the graph that cos(−x) = cos x Even symmetry of the cosine function A General Note label Characteristics of Sine and Cosine Functions The sine and cosine functions have several distinct characteristics: • They are periodic functions with a period of 2π • The domain of each function is ( − ∞, ∞) and the range is [ − 1, 1] • The graph of y = sin x is symmetric about the origin, because it is an odd function • The graph of y = cos x is symmetric about the y-axis, because it is an even function Investigating Sinusoidal Functions As we can see, sine and cosine functions have a regular period and range If we watch ocean waves or ripples on a pond, we will see that they resemble the sine or cosine 5/41 Graphs of the Sine and Cosine Functions functions However, they are not necessarily identical Some are taller or longer than others A function that has the same general shape as a sine or cosine function is known as a sinusoidal function The general forms of sinusoidal functions are y = Asin(Bx − C) + D and y = Acos(Bx − C) + D Determining the Period of Sinusoidal Functions Looking at the forms of sinusoidal functions, we can see that they are transformations of the sine and cosine functions We can use what we know about transformations to determine the period In the general formula, B is related to the period by P = 2π |B| If |B| > 1, then the period is less than 2π and the function undergoes a horizontal compression, whereas if |B| < 1, then the ...Roles of the SH2 and SH3 domains in the regulation of neuronal Src kinase functions Bradley R. Groveman 1 , Sheng Xue 2 , Vedrana Marin 1 , Jindong Xu 2 , Mohammad K. Ali 1 , Ewa A. Bienkiewicz 1 and Xian-Min Yu 1,2 1 Department of Biomedical Sciences, College of Medicine, Florida State University, Tallahassee, USA 2 Faculty of Dentistry, University of Toronto, Ontario, Canada Introduction Src family kinases (SFKs) are critically involved in the regulation of many biological functions mediated through growth factors, G-protein-coupled receptors or ligand-gated ion channels. As such, SFKs have become important targets for therapeutic treatments [1,2]. Based on crystallographic studies of inactive and active Src, the SH2 and SH3 domains are believed to form a ‘regulatory apparatus’. Binding of the phos- phorylated C-terminus to the SH2 domain and ⁄ or binding of the SH2-kinase linker to the SH3 domain inactivates SFKs [3–6]. It has been shown that mutating Tyr527 to phenylalanine (Y527F) in the Keywords NMDA receptor regulation; phosphorylation; Src; the SH2 domain; the SH3 domain Correspondence X M. Yu, 1115 West Call Street, Tallahassee, FL 32306-4300, USA Fax: +1 850 644 5781 Tel: +1 850 645 2718 E-mail: xianmin.yu@med.fsu.edu (Received 10 September 2010, revised 3 November 2010, accepted 6 December 2010) doi:10.1111/j.1742-4658.2010.07985.x Previous studies demonstrated that intra-domain interactions between Src family kinases (SFKs), stabilized by binding of the phosphorylated C-terminus to the SH2 domain and ⁄ or binding of the SH2 kinase linker to the SH3 domain, lock the molecules in a closed conformation, disrupt the kinase active site, and inactivate SFKs. Here we report that the up-regula- tion of N-methyl- D-aspartate receptors (NMDARs) induced by expression of constitutively active neuronal Src (n-Src), in which the C-terminus tyro- sine is mutated to phenylalanine (n-Src ⁄ Y535F), is significantly reduced by dysfunctions of the SH2 and ⁄ or SH3 domains of the protein. Furthermore, we found that dysfunctions of SH2 and ⁄ or SH3 domains reduce auto- phosphorylation of the kinase activation loop, depress kinase activity, and decrease NMDAR phosphorylation. The SH2 domain plays a greater regu- latory role than the SH3 domain. Our data also show that n-Src binds directly to the C-terminus of the NMDAR NR2A subunit in vitro, with a K D of 108.2 ± 13.3 nM. This binding is not Src kinase activity-dependent, and dysfunctions of the SH2 and ⁄ or SH3 domains do not significantly affect the binding. These data indicate that the SH2 and SH3 domains may function to promote the catalytic activity of active n-Src, which is impor- tant in the regulation of NMDAR functions. Structured digital abstract l MINT-8074560: NR2A (uniprotkb:Q00959) binds (MI:0407)ton-Src (uniprotkb:P05480)by surface plasmon resonance ( MI:0107) l MINT-8074641, MINT-8074668, MINT-8074679, MINT-8074693, MINT-8074813: n-Src (uniprotkb: P05480) and n-Src (uniprotkb:P05480) phosphorylate (MI:0217)byprotein kinase assay ( MI:0424) l MINT-8074576, MINT-8074726, MINT-8074741, MINT-8074777: n-Src (uniprotkb:P05480) phosphorylates ( MI:0217) NR2A (uniprotkb:Q00959)byprotein kinase assay (MI:0424) Abbreviations c-Src, cellular Src; NMDAR, RESEARC H Open Access Schur convexity for the ratios of the Hamy and generalized Hamy symmetric functions Wei-Mao Qian Correspondence: qwm661977@126. com Huzhou Broadcast and TV University, Huzhou 313000, China Abstract In this paper, we present the Schur convexity and monotonicity properties for the ratios of the Hamy and generalized Hamy symmetric functions and establish some analytic inequalities. The achieved results is inspired by the paper of Hara et al. [J. Inequal. Appl. 2, 387-395, (1998)], and the methods from Guan [Math. Inequal. Appl. 9, 797-805, (2006)]. The inequalities we obtained improve the existing corresponding results and, in some sense, are optimal. 2010 Mathematics Subject Classification: Primary 05E05; Secondary 26D20. Keywords: Hamy symmetric function, generalized Hamy symmetric function, Schur convex, Schur concave 1 Introduction Throughout this paper, we denote R n + = {x =(x 1 , x 2 , , x n )|x i > 0, i =1,2, , n} . .For x ∈ R n + , the Hamy symmetric function [1] is defined as F n (x, r)=F n (x 1 , x 2 , , x n ; r)=  1≤i 1 <i 2 <···<i r ≤n ⎛ ⎝ r  j=1 x i j ⎞ ⎠ 1 r , (1:1) where r is an integer and 1 ≤ r ≤ n. The generalized Hamy symmetric function was introduced by Guan [2] as follows F ∗ n (x, r)=F ∗ n (x 1 , x 2 , , x n ; r)=  i 1 +i 2 +···+i n =r  x i 1 1 x i 2 2 x i n n  1 r , (1:2) where r is a positive integer. In [2], Guan proved that both F n (x,r) and F ∗ n (x, r ) are Schur concave in R n + . The main of this paper is to investigate the Schur convexity for the functions F n (x, r) F n ( x, r − 1 ) and F ∗ n (x, r) F ∗ n (x, r − 1) and establish some analytic inequalities by use of the theory of majorization. For convenience of readers, we recall some definitions as follows, which can be found in many references, such as [3]. Qian Journal of Inequalities and Applications 2011, 2011:131 http://www.journalofinequalitiesandapplications.com/content/2011/1/131 © 2011 Qian; licensee Springer. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Definition 1.1.Then-t uple x is said to be majorized by the n-tuple y (in symbols x ≺ y), if k  i =1 x [i] ≤ k  i =1 y [i] , n  i =1 x [i] = n  i =1 y [i] , where 1 ≤ k ≤ n-1, and x [i] denotes the ith largest component of x. Definition 1.2.LetE ⊆ ℝ n be a set. A real-value d function F : E ® ℝ is said to be Schur convex on E if F(x) ≤ F(y)foreachpairofn-tuples x=(x 1 , , x n )andy=(y 1 , , y n )inE, such that x ≺ y. F is said to be Schur concave if -F is Schur convex. The theory of Schur convexity is one of the most important theories in the fields of inequalities. It can be used in combinatorial optimization [4], isoperimetric problems for polytopes [5], theory of statistical experiments [6], graphs and matrices [7], gamma functions [8], reliability and availability [9], optimal designs [10] and other related fields. Our aim in what follows is to prove the following results. Theorem 1.1.Let x ∈ R n + ,2 ≤ r ≤ n is an integer, then the function φ r (x)= F n (x, r) F n ( x, r − 1 ) is Schur concave in R n + and On sum of powers of the Laplacian and signless Laplacian eigenvalues of graphs Saieed Akbari 1,2 Ebrahim Ghorbani 1,2 Jacobus H. Koolen 3,4 Mohammad Reza Oboudi 1,2 1 Department of Mathematical Sciences Sharif University of Technology P.O. Box 11155-9415, Tehran, Iran s akbari@sharif.edu e ghorbani@math.sharif.edu m r oboudi@math.sharif.edu 2 School of Mathematics Institute for Research in Fundamental Sciences (IPM) P.O. Box 19395-5746, Tehran, Iran 3 Department of Mathematics Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea koolen@postech.ac.kr 4 Pohang Mathematics Institute (PMI) Pohang University of Science and Technology (POSTECH) Pohang 790-785, South Korea Submitted: 12 Jan, 2010; Accepted: 27 Jul, 2010; Published: 16 Aug, 2010 Mathematics Subject Classifications: 05C50 Abstract Let G be a graph of order n with signless Laplacian eigenvalues q 1 , . . . , q n and Laplacian eigenvalues µ 1 , . . . , µ n . It is proved that for any real number α w ith 0 < α  1 or 2  α < 3, the inequality q α 1 + ··· + q α n  µ α 1 + ··· + µ α n holds, and for any real number β with 1 < β < 2, the inequality q β 1 + ···+ q β n  µ β 1 + ···+ µ β n holds. In both inequalities, the equality is attained (for α ∈ {1, 2}) if and only if G is bipartite. 1 Introduction Let G be a gra ph with vertex set V (G) = {v 1 , . . . , v n } and edge set E(G) = {e 1 , . . . , e m }. The adjacency matrix of G, A = (a ij ), is an n × n matrix such that a ij = 1 if v i and v j the electronic journal of combinatorics 17 (2010), #R115 1 are adjacent, and otherwise a ij = 0. The incidence matrix of G, denoted by X = (x ij ), is the n ×m matrix, whose rows are indexed by the set of vertices of G and whose columns are indexed by the set of edges of G, defined by x ij :=  1, if e j is incident with v i ; 0, otherwise. If we consider an orientation for G, then in a similar manner as for the incidence matrix, the directed incidence matrix of the (oriented) graph G, denoted by D = (d ij ), is defined as d ij :=    +1, if e j is an incomming edge to v i ; −1, if e j is an outgoinging edge f rom v i ; 0, otherwise. Let ∆ be the diagonal matrix whose entries are vertex degrees of G. The Laplacian matrix of G, denoted by L(G), is defined by L(G) = ∆ − A, and it is easy to see that L(G) = DD ⊤ holds. The signless Laplacian matrix of G, denoted by Q(G), is defined by Q(G) = ∆ + A, and again it is easy to see that Q(G) = XX ⊤ . Since L(G) and Q(G) are symmetric matrices, their eigenvalues are real. We denote the eigenvalues of L(G) and Q(G) by µ 1 (G)  ···  µ n (G) and q 1 (G)  ···  q n (G), respectively (we drop G when it is clear from the context). We call the multi-set of eigenvalues of L(G) and Q(G), the L-spectrum and Q-spectrum of G, respectively. The matrices L and Q are similar if and only if G is bipartite (see, e.g., [5]). The incidence energy IE ( G ) of the graph G is defined as the sum of singular values of the incidence matrix [9]. The directed incidence energy DIE(G) is defined as the sum of singular values of the directed incidence matrix [7]. In other words, IE(G) = n  i=1  q i (G), and DIE(G) = n  i=1  µ i (G). The sum of square roots of Laplacian eigenvalues was also defined as Laplacian-energy like invariant and denoted by LEL(G) in [10]. The connection between IE and Laplacian eigenvalues (for bipartite graphs) was first pointed out in [6]. For more information on IE and DIE/LEL, see [7, 14] and the references therein. In [2], it was conjectured that √ q 1 + ··· + √ q n  √ µ 1 + ··· + √ µ n or equivalently IE(G)  DIE(G). In [1], it is proved that this conjecture is true by showing that for any real number α with 0 < α  1, the following holds: q α 1 + ··· + q α n  µ α 1 + ··· + µ α n . (1) Let G be a graph of order n. In [1], the authors proved that if  n i=0 (−1) i a i λ n−i and  n i=0 (−1) i b i λ n−i are the characteristic polynomials of the signless Laplacian and the Laplacian matrices of G, r INVESTIGATION ON THE CELLULAR AND NEUROPROTECTIVE FUNCTIONS OF NOGO-A/RETICULON 4A TENG YU HSUAN FELICIA (B.Sc. (Hons.)), NUS A THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY DEPARTMENT OF BIOCHEMISTRY NATIONAL UNIVERSITY OF SINGAPORE 2010 Acknowledgements My most sincere thanks goes to my supervisor, A/P Tang Bor Luen, for his guidance, encouragement, criticisms and also financial support throughout these years. I like to also express my appreciation to A/P Marie-Veronique Clement and Dr Deng Lih Wen for being my thesis advisory committee members. Heartfelt thanks goes to the pioneers of this project, Dr Liu Haiping and Dr Cherry Ng Ee Lin, and also my ex-labmates who have worked alongside with me in this project, especially Ms Belinda Ling Mei Tze who has generated some of the Nogo-A truncation constructs, and Ms Low Choon Bing and Ms Selina Aulia who assisted in maintaining our Nogo-deficient mouse colony. I am truly grateful to my fellow colleagues, especially Dr Ng Ee Ling and Ms Chen Yanan for their inspiration, friendship and discussions. I would also like to extend my thanks to my neighbouring lab’s colleagues, especially Dr Sharon Lim, Ms Luo Le, Ms Teong Huey Fern and Dr Michelle Chang Ker Xing, for sharing their expertise and reagents with me. Lastly but most importantly, my deepest gratitude goes to my fantastic husband, my adorable son and my dearest family for their endless support and encouragement. i Table of Contents Acknowledgements i Table of Contents ii Summary ix List of Publications xi List of Figures xii List of Abbreviations xvi Chapter Introduction 1.1 Discovery of Nogo-A: an inhibitor of neuronal regeneration 1.1.1 Neuronal regeneration is limited in adult CNS 1.1.2 The adult CNS environment is non-permissive to neuronal growth and regeneration 1.1.3 1.2 1.3 Nogo-A present in myelin acts as a neurite outgrowth inhibitor Molecular characterization of Nogo-A 1.2.1 Nogo: part of the Reticulon family 1.2.2 The Nogo gene and its splice isoforms 1.2.3 Subcellular localization, topology and structure of Nogo 1.2.4 Tissue distribution of Nogo 10 Functions of Nogo-A 13 1.3.1 13 Role of Nogo-A, after physical injury in adult CNS, as a myelinassociated inhibitor of neuronal regeneration 1.3.1.1 Growth inhibitory domains of Nogo-A 13 1.3.1.2 Nogo-A and its neuronal receptors 14 ii 1.3.1.2.1 NgR 15 1.3.1.2.2 PirB 16 1.3.1.3 The growth-inhibitory signalling pathways elicited by 18 Nogo-A to induce neuronal regeneration inhibition 1.3.1.4 Therapeutic interventions targeting the Nogo-A-NgR 22 signalling axis 1.3.2 1.3.3 Role of Nogo-A in pathological conditions of CNS 25 1.3.2.1 Alzheimer’s disease (AD) 25 1.3.2.2 Amyotrophic lateral sclerosis (ALS) 26 1.3.2.3 Multiple sclerosis (MS) 28 1.3.2.4 Epilepsy 29 1.3.2.5 Schizophrenia 29 Nogo-A and its cell autonomous functions 30 1.3.3.1 Apoptosis 30 1.3.3.2 Organization of endoplasmic reticulum (ER) and 31 formation of nuclear envelope (NE) 1.4 Rationale of my current work 33 Chapter Materials and Methods 35 2.1 General reagents 35 2.2 DNA manipulation 35 2.2.1 Design of constructs 35 2.2.1.1 Nogo-A constructs 35 2.2.1.2 Nogo-B constructs 38 2.2.1.3 Nogo-C constructs 39 iii 2.2.2 2.3 2.2.1.4 Reticulon and constructs (RTN1 and 2) 39 2.2.1.5 Reticulon constructs (RTN3) 40 2.2.1.6 Caspr and Caspr constructs 41 Molecular cloning procedure 42 Protein work 43 2.3.1 43 Sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) 2.4 2.5 2.6 2.3.2 Coomassie Blue staining and destaining of SDS-PAGE gels 45 2.3.3 Western transfer and blotting 45 2.3.4 Production of GST fusion proteins 46 2.3.4.1 Preparation of GST-proteins for antigens 47 2.3.4.2 Preparation of GST-proteins for pull-down assays 48 2.3.5 Purification of antibodies 48 2.3.6 Nuclear-cytosol fractionation 49 Cell culture 50 2.4.1 Mammalian cell culture ... practice with graphs of sine and cosine functions • • • • Amplitude and Period of Sine and Cosine Translations of Sine and Cosine Graphing Sine and Cosine Transformations Graphing the Sine Function.. .Graphs of the Sine and Cosine Functions Graphing Sine and Cosine Functions Recall that the sine and cosine functions relate real number values to the x- and ycoordinates of a point on the. .. reflected about the x-axis [link] shows one cycle of the graph of the function 21/41 Graphs of the Sine and Cosine Functions Using Transformations of Sine and Cosine Functions We can use the transformations