Rank one HCIZ at high temperature: interpolating between classical and free convolutions

We study the rank one Harish-Chandra-Itzykson-Zuber integral in the limit where \frac{N\beta}{2} \to cNβ2→c, called the high-temperature regime and show that it can be used to construct a promising one-parameter interpolation family, with parameter c between the classical and the free convolution. This c-convolution has a simple interpretation in terms of another associated family of distribution indexed by c, called the Markov-Krein transform: the c-convolution of two distributions corresponds to the classical convolution of their Markov-Krein transforms. We derive first cumulant-moment relations, a central limit theorem, a Poisson limit theorem and show several numerical examples of c-convoluted distributions.

Interaction Between Waves and Turbulence Within the Nocturnal Boundary Layer

The presence of waves is proven to be ubiquitous within nocturnal stable boundary layers over complex terrain, where turbulence is in a continuous, although weak, state of activity. The typical approach based on Reynolds decomposition is unable to disaggregate waves from turbulence contributions, thus hiding any information about the production/destruction of turbulence energy injected/subtracted by the wave motion. We adopt a triple-decomposition approach to disaggregate the mean, wave, and turbulence contributions within near-surface boundary-layer flows, with the aim of unveiling the role of wave motion as a source and/or sink of turbulence kinetic and potential energies in the respective explicit budgets. By exploring the balance between buoyancy (driving waves) and shear (driving turbulence), a simple interpretation paradigm is introduced to distinguish two layers, namely the near-ground and far-ground sublayer, estimating where the turbulence kinetic energy can significantly feed or be fed by the wave. To prove this paradigm, a nocturnal valley flow is used as a case study to detail the role of wave motions on the kinetic and potential energy budgets within the two sublayers. From this dataset, the explicit kinetic and potential energy budgets are calculated, relying on a variance–covariance analysis to further comprehend the balance of energy production/destruction in each sublayer. With this investigation, we propose a simple interpretation scheme to capture and interpret the extent of the complex interaction between waves and turbulence in nocturnal stable boundary layers.

Two-loop application of the Breitenlohner-Maison/’t Hooft-Veltman scheme with non-anticommuting γ5: full renormalization and symmetry-restoring counterterms in an abelian chiral gauge theory

We apply the BMHV scheme for non-anticommuting γ5 to an abelian chiral gauge theory at the two-loop level. As our main result, we determine the full structure of symmetry-restoring counterterms up to the two-loop level. These counterterms turn out to have the same structure as at the one-loop level and a simple interpretation in terms of restoration of well-known Ward identities. In addition, we show that the ultraviolet divergences cannot be canceled completely by counterterms generated by field and parameter renormalization, and we determine needed UV divergent evanescent counterterms. The paper establishes the two-loop methodology based on the quantum action principle and direct computations of Slavnov-Taylor identity breakings. The same method will be applicable to nonabelian gauge theories.

A PDE for Smooth Isometric Immersion of an Open Set of the Hyperbolic Plane ℍ 2 into ℝ 4

A simple interpretation of the PDE for isometric immersion of the hyperbolic plane ℍ 2 into ℝ 4 is given. Thus, necessary and sufficient conditions are obtained. And, under natural additional conditions, we show that there are no complete solutions, but we can have special local solutions.

An anti-sum-symmetry model and its orthogonal decomposition for ordinal square contingency tables with an application to grip strength test data

Summary For the analysis of R × R square contingency tables, we need to estimate an unknown probability distribution with high confidence from obtained observations. For that purpose, we need to perform the analysis using a statistical model that fits the data well and has a simple interpretation. This study proposes two original models that have symmetric and asymmetric structures between the probability with which the sum of row and column variables is t, for t = 2, . . ., R, and the probability with which the sum of row and column variables is 2(R + 1) − t. The study also reveals that it is necessary to satisfy the anti-global symmetry model, in addition to the proposed asymmetry model, in order to satisfy the proposed symmetry model. This decomposition theorem is useful to explain why the proposed symmetry model does not hold. Moreover, we show that the value of the likelihood ratio chi-squared statistic of the proposed symmetry model is equal to the sum of those of the decomposed models. We evaluate the utility of the proposed models by applying them to real-world grip strength data.

Introduction

This chapter introduces the basic problem of bhakti’s relationship to caste—the bhakti-caste question—which is an Indic version of a broader question: can theological egalitarianism lead to social equality? Two key stories about saints and eating demonstrate the complexity of the source materials, which defy simple interpretation. When B. R. Ambedkar framed the question as “Did the saints promote social equality?” he answered emphatically, “No.” The chapter highlights the context in which he made this judgment and the anachronism of using the modern idea of social equality to describe the premodern past. The chapter also lays out the plan of the book and its contributions to scholarship. It concludes by clarifying some key but potentially confusing terms that appear throughout the book.

A simple interpretation of undirected edges in essential graphs is wrong

Artificial intelligence for causal discovery frequently uses Markov equivalence classes of directed acyclic graphs, graphically represented as essential graphs, as a way of representing uncertainty in causal directionality. There has been confusion regarding how to interpret undirected edges in essential graphs, however. In particular, experts and non-experts both have difficulty quantifying the likelihood of uncertain causal arrows being pointed in one direction or another. A simple interpretation of undirected edges treats them as having equal odds of being oriented in either direction, but I show in this paper that any agent interpreting undirected edges in this simple way can be Dutch booked. In other words, I can construct a set of bets that appears rational for the users of the simple interpretation to accept, but for which in all possible outcomes they lose money. I put forward another interpretation, prove this interpretation leads to a bet-taking strategy that is sufficient to avoid all Dutch books of this kind, and conjecture that this strategy is also necessary for avoiding such Dutch books. Finally, I demonstrate that undirected edges that are more likely to be oriented in one direction than the other are common in graphs with 4 nodes and 3 edges.

Reciprocal Interaction between Waves and Turbulence within the Nocturnal Boundary-Layer

<p>The presence of waves in the nocturnal boundary layer has proven to generate complex interaction with turbulence. On complex terrain environments, where turbulence is observed in a weak but continuous state of activity, waves can be a vehicle of additional production/loss of turbulence energy. The common approach based on the Reynolds decomposition is unable to disaggregate turbulence and wave motion, thus revealing impaired to explicit the terms of this additional interaction. In the current investigation, we adopt a triple-decomposition approach to separate mean, wave, and turbulence motions within near-surface boundary-layer flows, with the aim of unveiling the role of wave motion as source and/or sink of turbulence kinetic and potential energies in the respective explicit budgets. This investigation reveals that the waves contribute to the kinetic energy budget where the production is not shear-dominated and the budget equation does not reduce to a shear-dissipation balance (e.g., as it occurs close to a surface). Away from the surface, the buoyancy effects associated with the wave motion become a significant factor in generating a three-terms balance (shear-buoyancy-dissipation). Similar effects can be found in the potential energy budget, as the waves affect for instance the production associated with the vertical heat flux. On this basis, we develop a simple interpretation paradigm to distinguish two layers, namely near-ground and far-ground sublayer, estimating where the turbulence kinetic energy can significantly feed or be fed by the wave. To prove this paradigm and evaluate the explicit contributions of the wave motion on the turbulence kinetic and potential energies, we investigate a nocturnal valley flow observed under weak synoptic forcing in the Dugway Valley (Utah) during the MATERHORN Program. From this dataset, the explicit kinetic and potential energy budgets are calculated, relying on a variance-covariance analysis to further comprehend the balance of energy production/loss in each sublayer. With this investigation, we propose a simple interpretation scheme to capture and interpret the extent of the complex interaction between waves and turbulence in nocturnal stable boundary layers.</p>

Answer Evaluation of Short Descriptive Questions

Reforms in the educational system emphasize more on continuous assessment. The descriptive examination test paper when compared to objective test paper acts as a better aid in continuous assessment for testing the progress of a student under various cognitive levels at different stages of learning. Unfortunately, assessment of descriptive answers is found to be tedious and time-consuming by instructors due to the increase in number of examinations in continuous assessment system. In this chapter, an attempt has been made to address the problem of automatic evaluation of descriptive answer using vector-based similarity matrix with order-based word-to-word syntactic similarity measure. Word order similarity measure remains as one of the best measures to find the similarity between sequential words in sentences and is increasing its popularity due to its simple interpretation and easy computation.