Renormalizable and Unitary Lorentz Invariant Model of Quantum Gravity

We analyze the R+R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

Suite by A. Beloshitsky “From the Depths of Centuries” in dialogue with the genre tradition of national-historical ballads

Рассматривается эволюция романтической баллады в баянном искусстве. Впервые обозначены три стадии ее жанровой эволюции. В качестве материала анализа избрана сюита для готово-выборного баяна А. Белошицкого «Из глубины веков». Цель исследования - атрибуция жанрово-балладных элементов в названном произведении. Использованы методы теоретической поэтики, целостного и жанрового музыковедческого анализа. В задачи работы входит установление соотношений между балладной моделью-инвариантом и ее реализацией в названном опусе, для чего даны критерии жанровой идентификации национально-исторической баллады. К ним относятся жанровый код - «Человек и историческая трагедия народа», генеральная интонация жанра - Nordic sublime, балладные персонажи - бард, воин и возлюбленная - и канонический мотивный тезаурус, лежащий в основе ее композиционно-драматургической модели. Делается вывод, что движение от баллады к балладности в сюите соответствует третьей стадии жанровой эволюции, связанной с разрушением «твердой жанровой формы», а ее реактуализация в ХХ веке способна выступить инструментом мифологизации прошлого. This work examines the evolution of romantic ballad in accordion art. For the first time, three stages of its genre evolution are identified. A suite for the converter accordion by A.Beloshitsky “From the Depths of Centuries” was chosen as the analysis material. The purpose of the article is to attribute genre-ballad elements in the named work. Methods of theoretical poetics, holistic and genre musicological analysis were used. The tasks of the work include establishing relationships between the ballad invariant model and its implementation in the named opus, for which the criteria for genre identification of a national-historical ballad are given. These include the genre code - «Man and the historical tragedy of the people», the general intonation of the genre - Nordic sublime, ballad characters - bard, warrior and beloved and canonical motive thesaurus, which underlies its composition and drama model. It is concluded that the movement from ballad to balladness in suite corresponds to the third stage of genre evolution associated with the destruction of the “true genre form” and its reactualization in the twentieth century is able to act as an instrument for the mythologization of the past.

Co-clustering of Time-Dependent Data via the Shape Invariant Model

Multivariate time-dependent data, where multiple features are observed over time for a set of individuals, are increasingly widespread in many application domains. To model these data, we need to account for relations among both time instants and variables and, at the same time, for subject heterogeneity. We propose a new co-clustering methodology for grouping individuals and variables simultaneously, designed to handle both functional and longitudinal data. Our approach borrows some concepts from the curve registration framework by embedding the shape invariant model in the latent block model, estimated via a suitable modification of the SEM-Gibbs algorithm. The resulting procedure allows for several user-defined specifications of the notion of cluster that can be chosen on substantive grounds and provides parsimonious summaries of complex time-dependent data by partitioning data matrices into homogeneous blocks. Along with the explicit modelling of time evolution, these aspects allow for an easy interpretation of the clusters, from which also low-dimensional settings may benefit.

Renormalizable and Unitary Lorentz Invariant Model of Quantum Gravity

We analyze the R + R2 model of quantum gravity where terms quadratic in the curvature tensor are added to the General Relativity action. This model was recently proved to be a self-consistent quantum theory of gravitation, being both renormalizable and unitary. The model can be made practically indistinguishable from General Relativity at astrophysical and cosmological scales by the proper choice of parameters.

Pattern formation in a 2-population homogenized neuronal network model

We study pattern formation in a 2-population homogenized neural field model of the Hopfield type in one spatial dimension with periodic microstructure. The connectivity functions are periodically modulated in both the synaptic footprint and in the spatial scale. It is shown that the nonlocal synaptic interactions promote a finite band width instability. The stability method relies on a sequence of wave-number dependent invariants of $2\times 2$ 2 × 2 -stability matrices representing the sequence of Fourier-transformed linearized evolution equations for the perturbation imposed on the homogeneous background. The generic picture of the instability structure consists of a finite set of well-separated gain bands. In the shallow firing rate regime the nonlinear development of the instability is determined by means of the translational invariant model with connectivity kernels replaced with the corresponding period averaged connectivity functions. In the steep firing rate regime the pattern formation process depends sensitively on the spatial localization of the connectivity kernels: For strongly localized kernels this process is determined by the translational invariant model with period averaged connectivity kernels, whereas in the complementary regime of weak and moderate localization requires the homogenized model as a starting point for the analysis. We follow the development of the instability numerically into the nonlinear regime for both steep and shallow firing rate functions when the connectivity kernels are modeled by means of an exponentially decaying function. We also study the pattern forming process numerically as a function of the heterogeneity parameters in four different regimes ranging from the weakly modulated case to the strongly heterogeneous case. For the weakly modulated regime, we observe that stable spatial oscillations are formed in the steep firing rate regime, whereas we get spatiotemporal oscillations in the shallow regime of the firing rate functions.

Some Implications of a Scale Invariant Model of Statistical Mechanics to Boltzmann versus Shannon Entropy in Thermodynamics and Information Theory

A scale invariant model of statistical mechanics is applied for a comparative study of Boltzmann’s entropy in thermodynamics versus Shannon’s entropy in information theory. The implications of the model to the objective versus subjective aspects of entropy as well as Nernst-Planck statement of the third law of thermodynamics are also discussed