scholarly journals High-dimensional regimes of non-stationary Gaussian correlated Wishart matrices

2021 ◽  
pp. 2250006
Author(s):  
Solesne Bourguin ◽  
Thanh Dang
Keyword(s):  
Wasserstein Distance ◽  
High Dimensional ◽  
Wishart Matrix ◽  
Wishart Matrices ◽  
Semicircular Law ◽  
Gaussian Orthogonal Ensemble ◽  
Spectral Distributions ◽  
The Law ◽  
The One ◽  
Functional Setting

We study the high-dimensional asymptotic regimes of correlated Wishart matrices [Formula: see text], where [Formula: see text] is a [Formula: see text] Gaussian random matrix with correlated and non-stationary entries. We prove that under different normalizations, two distinct regimes emerge as both [Formula: see text] and [Formula: see text] grow to infinity. The first regime is the one of central convergence, where the law of the properly renormalized Wishart matrices becomes close in Wasserstein distance to that of a Gaussian orthogonal ensemble matrix. In the second regime, a non-central convergence happens, and the law of the normalized Wishart matrices becomes close in Wasserstein distance to that of the so-called Rosenblatt–Wishart matrix recently introduced by Nourdin and Zheng. We then proceed to show that the convergences stated above also hold in a functional setting, namely as weak convergence in [Formula: see text]. As an application of our main result (in the central convergence regime), we show that it can be used to prove convergence in expectation of the empirical spectral distributions of the Wishart matrices to the semicircular law. Our findings complement and extend a rich collection of results on the study of the fluctuations of Gaussian Wishart matrices, and we provide explicit examples based on Gaussian entries given by normalized increments of a bi-fractional or a sub-fractional Brownian motion.

Preface to the special issue, CMAM 2011, no. 3.

2011 ◽  
Vol 11 (3) ◽  
pp. 272
Author(s):  
Ivan Gavrilyuk ◽  
Boris Khoromskij ◽  
Eugene Tyrtyshnikov
Keyword(s):  
Separation Of Variables ◽  
Numerical Algorithms ◽  
Multilevel Methods ◽  
High Dimensional ◽  
Special Issue ◽  
High Dimensions ◽  
Guiding Principle ◽  
Tensor Methods ◽  
Closed World ◽  
The One

Abstract In the recent years, multidimensional numerical simulations with tensor-structured data formats have been recognized as the basic concept for breaking the "curse of dimensionality". Modern applications of tensor methods include the challenging high-dimensional problems of material sciences, bio-science, stochastic modeling, signal processing, machine learning, and data mining, financial mathematics, etc. The guiding principle of the tensor methods is an approximation of multivariate functions and operators with some separation of variables to keep the computational process in a low parametric tensor-structured manifold. Tensors structures had been wildly used as models of data and discussed in the contexts of differential geometry, mechanics, algebraic geometry, data analysis etc. before tensor methods recently have penetrated into numerical computations. On the one hand, the existing tensor representation formats remained to be of a limited use in many high-dimensional problems because of lack of sufficiently reliable and fast software. On the other hand, for moderate dimensional problems (e.g. in "ab-initio" quantum chemistry) as well as for selected model problems of very high dimensions, the application of traditional canonical and Tucker formats in combination with the ideas of multilevel methods has led to the new efficient algorithms. The recent progress in tensor numerical methods is achieved with new representation formats now known as "tensor-train representations" and "hierarchical Tucker representations". Note that the formats themselves could have been picked up earlier in the literature on the modeling of quantum systems. Until 2009 they lived in a closed world of those quantum theory publications and never trespassed the territory of numerical analysis. The tremendous progress during the very recent years shows the new tensor tools in various applications and in the development of these tools and study of their approximation and algebraic properties. This special issue treats tensors as a base for efficient numerical algorithms in various modern applications and with special emphases on the new representation formats.

Law’s Contradictions

2018 ◽  
Author(s):  
Nimer Sultany
Keyword(s):  
The Other ◽  
Political Actors ◽  
Political Conflicts ◽  
Other Hand ◽  
The Law ◽  
The One

This chapter analyzes concrete Egyptian and Tunisian cases that showcase the interplay between continuity and rupture. These cases illustrate the lack of a systemic relation between law and revolution. On the one hand, the judiciary that interprets and applies the law is part of the very social and political conflicts it is supposed to resolve. On the other hand, the law is incoherent and there are often resources within the legal materials to play it both ways. Thus, the different forces at work use both continuity and rupture to advance their positions. Furthermore, legitimacy discourse mediates the contradictions between law and revolution in the experience of different legal and political actors. This mediation serves an ideological role because it presupposes a binary dichotomy between continuity and rupture, papers over law’s incoherence by reducing it to a singular voice, and reduces revolution to an event rather than a process.

scholarly journals Quantification of Classified Nickel Species in Spent FFC Catalysts

2021 ◽  
Author(s):  
Monica Dapiaggi ◽  
Marco Alloni ◽  
Riccardo Carli ◽  
Nicola Rotiroti ◽  
Giorgia Confalonieri
Keyword(s):  
Zeolite Y ◽  
Complex Matrix ◽  
Spent Catalyst ◽  
Quick Method ◽  
Spent Catalysts ◽  
The Law ◽  
The One ◽  
Nickel Species

Abstract The paper presents a quick method for the quantification of nickel species in spent FFC catalysts; the quantification of known quantities NiO and $$\hbox{NiAl}_2\hbox{O}_{4}$$ NiAl 2 O 4 is first done in a matrix of fresh zeolite Y, and then in a complex matrix, similar to the one of a real spent catalyst. The method is carefully checked and the errors in the quantification are critically evaluated. After the validation of the method with known quantities of NiO, well below the law limit for direct re-use, a set of real spent catalysts (representative of a period of 12 months) is analysed. Graphic Abstract

Insider Trading in Israel and England, Part II

1972 ◽  
Vol 7 (3) ◽  
pp. 373-410
Author(s):  
Aharon Yoran
Keyword(s):  
Insider Trading ◽  
The Other ◽  
Fiduciary Duties ◽  
The Law ◽  
The One

It is submitted that even if the hapless outsider cannot bring an action for damages because of the existing state of the law regarding fiduciary duties and breach of statutory duties, he still has an equitable remedy of rescission of the contract based on quasi-contractual principles. The crime of fraud, under secs. 13 and 54, respectively, would be made the basis of setting the contract (of sale or purchase) aside. To support this proposition we shall explore the quasi-contractual principles which enable one contracting party, the victim of a crime committed by the other party in entering the contract, to defeat this contract.In Browning v. Morris, in an oft-quoted statement by Lord Mansfield, the following principle was declared: But, where contracts or transactions are prohibited by positive statutes, for protecting one set of men from another set of men; the one, from their situation and condition, being liable to be oppressed or imposed upon by the other; there, the parties are not in pan delicto; and in furtherance of these statutes, the person injured, after the transaction is finished and completed, may bring an action and defeat the contract.

Utilitarianism and the Criminal Law in Colonial India: A Study of the Practical Limits of Utilitarian Jurisprudence

1994 ◽  
Vol 28 (4) ◽  
pp. 739-791 ◽  
Author(s):  
Kartik Kalyan Raman
Keyword(s):  
Criminal Justice ◽  
Legal Tradition ◽  
British India ◽  
Local Society ◽  
Colonial India ◽  
Penal Law ◽  
The Law ◽  
Common Observation ◽  
The One

The role of legal tradition in the reformist rhetoric of Benthamite Utilitarianism presents us with a contradiction. On the one hand, there is the common observation that Utilitarian jurisprudence was necessarily ahistorical and rejected the past as a source of concepts for reworking the criminal justice system existing in Britain during the late eighteenth and early nineteenth centuries. For philosophic reformers such as Bentham, contemporary British criminal justice was to be replaced by a scientific jurisprudence, abstract, universal, and secular in outlook, and antipathetic to the more conservative insistence that the foundations of the penal law continue to be tradition-based. ‘If society was to see any improvement, its law must be reformed; if its law was to be reformed it must be burned to the ground and rebuilt according to a new and rational pattern.’ On the other hand, we find that the very same Utilitarian thinkers, in works describing the state of the law in British India, were concerned with local rather than universal conceptions of criminality. In his 1782 Essay on the Influence of Time and Place in Matters of Legislation, Bentham, for instance, urged the philosophic reformer to temper change in India by fitting Utilitarian judgments about the law to the frames of local society.

Preventive Confinement of Dangerous Offenders

2004 ◽  
Vol 32 (1) ◽  
pp. 56-72 ◽  
Author(s):  
Stephen J. Morse
Keyword(s):  
Legal Theory ◽  
The Other ◽  
Legal Issue ◽  
Central Theme ◽  
Sexual Predators ◽  
Dangerous Offenders ◽  
New Form ◽  
The Law ◽  
The One ◽  
Constitutional Regime

How to respond justly to the dangers persistent violent offenders present is a vexing moral and legal issue. On the one hand, we wish to reduce predation; on the other, we want to treat predators fairly. The central theme of this paper is that it is difficult to achieve both goals without compromising one of them, and that both are being seriously undermined. I begin by explaining the legal theory, doctrine and practice governing dangerous offenders (DO) and demonstrate that the law leaves a gap in the ability to confine them. Next I explore the means by which the law has overtly or covertly sought to fill the gap. Many of these measures, especially the new form of civil commitment for sexual predators, dangerously conflate moral and medical categories. I conclude that pure preventive detention is more common than we usually assume, but that this practice violates fundamental assumptions concerning liberty under the American constitutional regime.

STUDI KRITIS JUAL BELI DEKORASI UANG MASKAWIN

Al-MAJAALIS ◽  
2018 ◽  
Vol 6 (1) ◽  
pp. 1-36
Author(s):  
Muhammad Arifin Badri
Keyword(s):  
The Other ◽  
Other Hand ◽  
Business Opportunities ◽  
The Law ◽  
The One ◽  
High Level

This study aims to examine the laws of dowry money decoration that are common in the community. The innovation and soul of art that is channeled through décor of dowry money is proven to produce beautiful and unique works, so as to attract the attention and interest of the wider community. However, because to produce beautiful and unique works, a high level of creativity is needed, so not everyone can do it. On the one hand, this phenomenon opens up quite good business opportunities, but on the other hand, it should be watched out, because in some conditions it contains the practice of buying and selling currencies with nominal differences. Through this study, I would like to uncover the law of buying and selling practices decorating dowry money and decorating services. As I also intend to present an applicative solution for the community so that they can still channel their artistic talents without violating Shari’ah law.

Dismissal with Monetary Consideration under Art. 232, para. 2 of the Labour Code

De Jure ◽  
2019 ◽  
Vol 10 (2) ◽  
Author(s):  
Hristo Banov ◽  
Keyword(s):  
Employment Relationship ◽  
The Other ◽  
Employment Contract ◽  
Other Hand ◽  
Unilateral Termination ◽  
The Law ◽  
The One ◽  
Rules Set ◽  
Final Calculation

The article reviews the main differences between the monetary obligation of the employer under Art. 232, para. 2 of the Labour Code and other payments that the same party owes by law in the employment relationship. Thus, the hypotheses are differentiated, on the one hand, of the unilateral termination of the employment contract by the employer against monetary payment on the grounds of Art. 232, para. 2 of the Labour Code, and, on the other hand, the emergence of an obligation to pay certain compensations – in the true sense of the term – under Art. 213, Art. 214, Art. 219, para. 2 and Art. 225 of the Labour Code. Thereby, the thesis regarding the impossibility of incurring of an obligation on the employer to simultaneously execute the various mentioned monetary considerations, is reasoned. In addition, the rules set out in the law are discussed, both for contracting and for the final calculation of the amount of the employer’s monetary payment, which this study focuses on.

scholarly journals The world market for soybeans: price transmission into Brazil and effects from the timing of crop and trade

Nova Economia ◽  
2007 ◽  
Vol 17 (2) ◽  
pp. 241-270 ◽  
Author(s):  
Mario A. Margarido ◽  
Frederico A. Turolla ◽  
Carlos R. F. Bueno
Keyword(s):  
United States ◽  
Forecast Error ◽  
The United States ◽  
World Market ◽  
Price Transmission ◽  
Long Run ◽  
Cointegration Tests ◽  
The World ◽  
The Law ◽  
The One

This paper investigates the price transmission in the world market for soybeans using time series econometrics models. The theoretical model developed by Mundlack and Larson (1992) is based on the Law of the One Price, which assumes price equalization across all local markets in the long run and allows for deviations in the short run. The international market was characterized by three relevant soybean prices: Rotterdam Port, Argentina and the United States. The paper estimates the elasticity of transmission of these prices into soybean prices in Brazil. There were carried causality and cointegration tests in order to identify whether there is significant long-term relationship among these variables. There was also calculated the impulse-response function and forecast error variance decomposition to analyze the transmission of variations in the international prices over Brazilian prices. An exogeneity test was also carried out so as to check whether the variables respond to short term deviations from equilibrium values. Results validated the Law of the One Price in the long run. In line with many studies, this paper showed that Brazil and Argentina can be seen as price takers as long as the speed of their adjustment to shocks is faster than in the United States, the latter being a price maker.

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