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1
Xianwei, Zhou, and Wang Chunjiang, eds. Ren zhi wu xian dian: Renzhi wuxiandian. Beijing Shi: Guo fang gong ye chu ban she, 2008.
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3
Zhi pu xue zai tian ran you ji hua xue zhong di ying yong. Beijing: Ke xue chu ban she, 1987.
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4
Marino, Marcos. Quantum chromodynamics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.32.
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This article focuses on chiral random matrix theories with the global symmetries of quantum chromodynamics (QCD). In particular, it explains how random matrix theory (RMT) can be applied to the spectra of the Dirac operator both at zero chemical potential, when the Dirac operator is Hermitian, and at non-zero chemical potential, when the Dirac operator is non-Hermitian. Before discussing the spectra of these Dirac operators at non-zero chemical potential, the article considers spontaneous symmetry breaking in RMT and the QCD partition function. It then examines the global symmetries of QCD, taking into account the Dirac operator for a finite chiral basis, as well as the global symmetry breaking pattern and the Goldstone manifold in chiral random matrix theory (chRMT). It also describes the generating function for the Dirac spectrum and applications of chRMT to QCD to gauge degrees of freedom.
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Zinn-Justin, Paul, and Jean-Bernard Zuber. Multivariate statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.28.
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This article considers some classical and more modern results obtained in random matrix theory (RMT) for applications in statistics. In the classic paradigm of parametric statistics, data are generated randomly according to a probability distribution indexed by parameters. From this data, which is by nature random, the properties of the deterministic (and unknown) parameters may be inferred. The ability to infer properties of the unknown Σ (the population covariance matrix) will depend on the quality of the estimator. The article first provides an overview of two spectral statistical techniques, principal components analysis (PCA) and canonical correlation analysis (CCA), before discussing the Wishart distribution and normal theory. It then describes extreme eigenvalues and Tracy–Widom laws, taking into account the results obtained in the asymptotic setting of ‘large p, large n’. It also analyses the results for the limiting spectra of sample covariance matrices..
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Borodin, Alexei. Random matrix representations of critical statistics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.12.
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This article examines two random matrix ensembles that are useful for describing critical spectral statistics in systems with multifractal eigenfunction statistics: the Gaussian non-invariant ensemble and the invariant random matrix ensemble. It first provides an overview of non-invariant Gaussian random matrix theory (RMT) with multifractal eigenvectors and invariant random matrix theory (RMT) with log-square confinement before discussing self-unfolding and not self-unfolding in invariant RMT. It then considers a non-trivial unfolding and how it changes the form of the spectral correlations, along with the appearance of a ghost correlation dip in RMT and Hawking radiation. It also describes the correspondence between invariant and non-invariant ensembles and concludes by introducing a simple field theory in 1+1 dimensions which reproduces level statistics of both of the two random matrix models and the classical Wigner-Dyson spectral statistics in the framework of the unified formalism of Luttinger liquid.
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Bouchaud, Jean-Phillipe, and Marc Potters. Asymptotic singular value distributions in information theory. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.41.
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This article examines asymptotic singular value distributions in information theory, with particular emphasis on some of the main applications of random matrices to the capacity of communication channels. Results on the spectrum of random matrices have been adopted in information theory. Furthermore, information theorists, motivated by certain channel models, have obtained a number of new results in random matrix theory (RMT). Most of those results are related to the asymptotic distribution of the (square of) the singular values of certain random matrices that model data communication channels. The article first provides an overview of three transforms that are useful in expressing the asymptotic spectrum results — Stieltjes transform, η-transform, and Shannon transform — before discussing the main results on the limit of the empirical distributions of the eigenvalues of various random matrices of interest in information theory.
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Beenakker, Carlo W. J. Classical and quantum optics. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.36.
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This article focuses on applications of random matrix theory (RMT) to both classical optics and quantum optics, with emphasis on optical systems such as disordered wave guides and chaotic resonators. The discussion centres on topics that do not have an immediate analogue in electronics, either because they cannot readily be measured in the solid state or because they involve aspects (such as absorption, amplification, or bosonic statistics) that do not apply to electrons. The article first considers applications of RMT to classical optics, including optical speckle and coherent backscattering, reflection from an absorbing random medium, long-range wave function correlations in an open resonator, and direct detection of open transmission channels. It then discusses applications to quantum optics, namely: the statistics of grey-body radiation, lasing in a chaotic cavity, and the effect of absorption on the reflection eigenvalue statistics in a multimode wave guide.
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Zabrodin, Anton. Financial applications of random matrix theory: a short review. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.40.
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This article reviews some applications of random matrix theory (RMT) in the context of financial markets and econometric models, with emphasis on various theoretical results (for example, the Marčenko-Pastur spectrum and its various generalizations, random singular value decomposition, free matrices, largest eigenvalue statistics) as well as some concrete applications to portfolio optimization and out-of-sample risk estimation. The discussion begins with an overview of principal component analysis (PCA) of the correlation matrix, followed by an analysis of return statistics and portfolio theory. In particular, the article considers single asset returns, multivariate distribution of returns, risk and portfolio theory, and nonequal time correlations and more general rectangular correlation matrices. It also presents several RMT results on the bulk density of states that can be obtained using the concept of matrix freeness before concluding with a description of empirical correlation matrices of stock returns.
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Eynard, Bertrand. Random matrices and loop equations. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797319.003.0007.
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This chapter is an introduction to algebraic methods in random matrix theory (RMT). In the first section, the random matrix ensembles are introduced and it is shown that going beyond the usual Wigner ensembles can be very useful, in particular by allowing eigenvalues to lie on some paths in the complex plane rather than on the real axis. As a detailed example, the Plancherel model is considered from the point of RMT. The second section is devoted to the saddle-point approximation, also called the Coulomb gas method. This leads to a system of algebraic equations, the solution of which leads to an algebraic curve called the ‘spectral curve’ which determines the large N expansion of all observables in a geometric way. Finally, the third section introduces the ‘loop equations’ (i.e., Schwinger–Dyson equations associated with matrix models), which can be solved recursively (i.e., order by order in a semi-classical expansion) by a universal recursion: the ‘topological recursion’.
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Clark, Terrell A. Assessment and Development of Deaf Children with Multiple Challenges. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780190880545.003.0002.
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The proportion of children who are deaf or hard of hearing and also have other medical, neurodevelopmental, behavioral, or psychosocial conditions is increasing. Prevalence estimates run as high as 50% to 70%. The shifting complexity challenges not only the learners but also the teachers, administrators, and policymakers responsible for the education of deaf students. Documentation of diagnostic profiles contributes to understanding the learning profile of deaf students with concomitant conditions. This may also inform policy decisions, programmatic design, calibration of parental expectations, and implementation of effective teaching strategies. Through illustrative case examples, this chapter explores the principles of differential diagnosis and the implications of various conditions. Topics covered include genetic syndromes, vestibular dysfunction, intrauterine viral infection with associated congenital hearing loss, autism spectrum disorder, reactive attachment disorder, complex medical histories resulting in severe neurologic compromise, intellectual disabilities, cerebral palsy, and nonsyndromic genetic conditions.
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Beenakker, Carlo W. J. Extreme eigenvalues of Wishart matrices: application to entangled bipartite system. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.37.
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This article describes the application of random matrix theory (RMT) to the estimation of the bipartite entanglement of a quantum system, with particular emphasis on the extreme eigenvalues of Wishart matrices. It first provides an overview of some spectral properties of unconstrained Wishart matrices before introducing the problem of the random pure state of an entangled quantum bipartite system consisting of two subsystems whose Hilbert spaces have dimensions M and N respectively with N ≤ M. The focus is on the smallest eigenvalue which serves as an important measure of entanglement between the two subsystems. The minimum eigenvalue distribution for quadratic matrices is also considered. The article shows that the N eigenvalues of the reduced density matrix of the smaller subsystem are distributed exactly as the eigenvalues of a Wishart matrix, except that the eigenvalues satisfy a global constraint: the trace is fixed to be unity.
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Scherer, Nancy. Appointing Federal Judges. Edited by Lee Epstein and Stefanie A. Lindquist. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780199579891.013.26.
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This chapter discusses the historical development of the modern-day lower court appointment process. When lower court judgeships were used as patronage, the process ran smoothly from nomination by the president through confirmation by the Senate. Today, however, these judgeships are used for other political purposes by the president and senators. This is because elites (party leaders and interest groups) associated with each of the two major parties follow the process closely, and they demand that the “right” kind of judges be appointed to the lower federal courts. In turn, presidents and senators now use the lower court appointment process to “score points” with these key party-affiliated elites. Thus, as the two parties cater to interest groups and party bases on the opposite ends of the ideological spectrum, and presidents and senators follow suit, the lower court appointment process has become highly partisan and contentious.
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Bohigas, Oriol, and Hans Weidenmuller. History – an overview. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.2.
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This article discusses the first four decades of the history of random matrix theory (RMT), that is, until about 1990. It first considers Niels Bohr's formulation of the concept of the compound nucleus, which is at the root of the use of random matrices in physics, before analysing the development of the theory of spectral fluctuations. In particular, it examines the Wishart ensemble; Dyson's classification leading to the three canonical ensembles — Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE), and Gaussian Symplectic Ensemble (GSE); and the breaking of a symmetry or an invariance. It also describes how random matrix models emerged from quantum physics, more specifically from a statistical approach to the strongly interacting many-body system of the atomic nucleus. The article concludes with an overview of data on nuclear resonances, many-body theory, chaos, number theory, scattering theory, replica trick and supersymmetry, disordered solids, and interacting fermions and field theory.
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Chan, Felicia. Performing (Comic) Abjection in the Hong Kong Ghost Story. Edinburgh University Press, 2018. http://dx.doi.org/10.3366/edinburgh/9781474424592.003.0007.
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Horror films in Hong Kong cinema have eschewed terror in favour of comedy, where supernatural beings take the form of hopping vampires, wandering spirits and underworld demons rendered in latex masks and movie slime. This chapter explores the comic presentation of these subjects in Hong Kong horror, where the self-reflexive exposure of the cinematic machinery of costume and special effects appear to put it at odds with the spectral affectivity of the Hong Kong ghost story. This chapter returns to two classic films from the mid-1980s, A Chinese Ghost Story (Tsui Hark 1987) and Rouge (Stanley Kwan 1988), films from the ‘second wave’ period long noted to carry ‘Hong Kong’ as a subject of concern in the run up to the British handover of 1997, and revisits their historical positioning in the light of more recent post-1997 incarnations such as Visible Secret (Ann Hui 2001), My Left Eye Sees Ghosts (Johnnie To 2002), and Rigor Mortis (Juno Mak 2013).
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Sogge, Christopher D. Geodesics and the Hadamard parametrix. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160757.003.0002.
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This chapter studies the spectrum of Laplace–Beltrami operators on compact manifolds. It begins by defining a metric on an open subset Ω ⊂ Rn, in order to lift their results to corresponding ones on compact manifolds. The chapter then details some elliptic regularity estimates, before embarking on a brief review of geodesics and normal coordinates. The purpose of this review is to show that, with given a particular Laplace–Beltrami operator and any point y0 in Ω, one can choose a natural local coordinate system y = κ(x) vanishing at y0 so that the quadratic form associated with the metric takes a special form. To conclude, the chapter turns to the Hadamard parametrix.
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Skowronek, Stephen, John A. Dearborn, and Desmond King. Phantoms of a Beleaguered Republic. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780197543085.001.0001.
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As the nation’s chief executive, Donald Trump pitted himself repeatedly against the institutions and personnel of the executive branch. In the process, two once-obscure concepts came center stage in an eerie face-off. On one side was the specter of a “Deep State” conspiracy – administrators threatening to thwart the will of the people and undercut the constitutional authority of the president they elected to lead them. On the other side was a raw personalization of presidential power, one that a theory of “the unitary executive” gussied up and allowed to run roughshod over reason and the rule of law. The Deep State and the unitary executive framed every major contest of the Trump presidency. Like phantom twins, they drew each other out and wrestled to light basic issues of governance long suppressed. Though this conflict reached a fever pitch during the Trump presidency, it is not new. Stephen Skowronek, John A. Dearborn, and Desmond King trace the tensions between presidential power and the depth of the American state back through the decades and forward through the various settlements arrived at in previous eras. Phantoms of a Beleaguered Republic is about the breakdown of settlements and the abiding vulnerabilities of a Constitution that gave scant attention to administrative power. Rather than simply dump on Trump, the authors provide a richly historical perspective on the conflicts that rocked his presidency, and they explain why, if left untamed, the phantom twins will continue to pull American government apart.
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Scaglia, Ilaria. The Emotions of Internationalism. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198848325.001.0001.
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By examining a broad range of individuals and institutions engaged in international cooperation in the Alps in the 1920s and 1930s, this book explains how internationalists constructed and used emotions to attain their goals. It undertakes a journey through the most diverse terrains and venues, from the international art exhibitions and congresses organized by the Union Internationale des Associations d’Alpinisme (also known as UIAA, or the International Mountaineering and Climbing Federation), to the summer camps and schools run by transnational bodies such as the League for Open-Air Education, to the international sanatoria for students, workers, and soldiers healing from tuberculosis in the Swiss village of Leysin. Along the way, this study encounters a broad spectrum of state and non-state actors involved a variety of cross-border endeavors, from large-scale infrastructure projects akin to the tunnel under the Mont Cenis, to the League of Nations and its propaganda efforts, to the plethora of smaller international organizations emulating the League’s work in fields as diverse as leisure, health, and education. Through this metaphorical travel, this book thus argues that starting from the nineteenth century and accelerating in the interwar years emotions became a fundamental feature of internationalism, shaped its development, and constitute an essential dimension of international history to this day.
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Duncan, Anthony, and Michel Janssen. Constructing Quantum Mechanics. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198845478.001.0001.
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This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.