Invariant Description Research Articles

Structural-functional organization of the visual system in ensuring goal-directed activity

A review of the results of half a century of research into the visual system as a hierarchical structure is presented: a multichannel, multilayer “pyramid”, each layer of which has a different spatiotemporal resolution, but together provides an invariant description of images for their classification, decision making, organization of eye movements and target search. An analysis of the multichannel organization of the human visual system was carried out, as the most effective and most economical. The “periscope and telescopic vision” systems, unique in their morphological and functional characteristics, are identified, providing gaze translation and recognition when searching and achieving a goal. Models of the pyramidal organization of the visual system have justified their existence by having an exceptional influence on the development of engineering solutions for the design of recognition systems operating in real time and the creation of artificial neural networks.

ρ meson magnetic dipole moment from BaBar e+e−→π+π−π0π0 cross section measurement

We obtain the value of the magnetic dipole moment of the ρ meson, using data from the collaboration for the e+e−→π+π−2π0 process. The considered center of mass energy range is from 0.9 to 1.8 GeV. We describe the γ*→4π vertex using a vector meson dominance model, including the intermediate resonant contributions relevant at these energies. We find μρ=2.7±0.3 in e/2mρ units. We improve on the previous extracted value, where preliminary data from the same collaboration was used, by considering definite data, better grounded values of the parameters involved, and an explicit gauge invariant description of the process. Published by the American Physical Society 2024

Perturbative computations of neutron-proton scattering observables using renormalization-group invariant chiral effective field theory up to N3LO

We predict neutron-proton scattering cross sections and polarization observables up to next-to-next-to-next-to-leading order in a renormalization-group invariant description of the strong nucleon-nucleon interaction. Low-energy constants are calibrated to phase shifts, subleading corrections are computed in distorted-wave perturbation theory, and we employ momentum-cutoff values 500 and 2500 MeV. We find a steady order-by-order convergence and realistic descriptions of scattering observables up to a laboratory scattering energy of approximately 100 MeV. We also compare perturbative and nonperturbative calculations for phase shifts and cross sections and quantify how unitarity is gradually restored at higher orders. The perturbative approach offers an important diagnostic tool for any power counting and our results suggest that the breakdown scale in chiral effective field theory might be significantly lower than estimates obtained in nonperturbative calculations. Published by the American Physical Society 2024

Descriptions in V.V. Nabokov’s texts: perfecting techniques in competition with the cinematic language (to the 125th anniversary of the birth)

The article discusses innovative techniques for constructing descriptions in V.V. Nabokov’s texts "Camera Obscura" ("Laughter In The Night") and "The Enchanter". The relevance of the topic is due, on the one hand, to the unsettled issue of identifying invariant description features and attributing the peripheral forms of description. On the other hand, there are no works that fully reveal V.V. Nabokov’s technique of creating descriptions. The research is based on advances in the study of this author’s visual poetics, interest in which has been growing in recent years. The article used lexico-semantic, morphological, syntactic analysis of individual linguistic units. Moreover, linguostylistic text analysis, intertextual and semiotic analysis, content analysis were employed in conjunction with a comparative analysis of the two texts reflecting the dynamics of V.V. Nabokov’s individual style. The study has shown that descriptive fragments in the texts by this author mostly do not have clear boundaries and can overlap or alternate with the narrative even within the same sentence. The article proposes to call this technique "fusion style". It is concluded that one of the important functions of V.V. Nabokov’s descriptions is the embodiment of the film of life mega-metaphor. The language of description borrows techniques from the cinematic language, for instance, montage techniques, double exposure through superimposure, and sound images. The research has identified stylistic devices that can iconically embody cinematic language elements. These include blending, ellipsis, extended allusions, double similes, and paronomasia. The paper concludes that the density of these techniques in V.V. Nabokov’s texts increases as he gains mastery. It is shown that the writer objectifies visual poetics with the help of such linguistic means as embedded structures and absolute constructions, enumerations, groups of nominal sentences.

UCB strategies and optimization of batch processing in a one-armed bandit problem

We consider a Gaussian one-armed bandit problem, which arises when optimizing batch data processing if there are two alternative processing methods with a priori known efficiency of the first method. During processing, it is necessary to determine a more effective method and ensure its preferential use. This optimal control problem is interpreted as a game with nature. We investigate cases of known and a priori unknown variance of income corresponding to the second method. The control goal is considered in a minimax setting, and UCB strategies are used to ensure it. In all the studied cases, invariant descriptions of control on a horizon equal to one are obtained, which depend only on the number of batches into which the data is divided, but not on their full number. These descriptions allow us to determine approximately optimal parameters of strategies using Monte Carlo simulation. Numerical results show the high efficiency of the proposed UCB strategies.

Extended Brauer analysis of some Dynkin and Euclidean diagrams

<p>The analysis of algebraic invariants of algebras induced by appropriated multiset systems called Brauer configurations is a Brauer analysis of the data defining the multisets. Giving a complete description of such algebraic invariants (e.g., giving a closed formula for the dimensions of algebras induced by significant classes of Brauer configurations) is generally a tricky problem. Ringel previously proposed an analysis of this type in the case of Dynkin algebras, for which so-called Dynkin functions were used to study the numerical behavior of invariants associated with such algebras. This paper introduces two additional tools (the entropy and the covering graph of a Brauer configuration) for Brauer analysis, which is applied to Dynkin and Euclidean diagrams to define Dynkin functions associated with Brauer configuration algebras. Properties of graph entropies defined by the corresponding covering graphs are given to establish relationships between the theory of Dynkin functions, the Brauer configuration algebras theory, and the topological content information theory.</p>

Invariant description of static and dynamical Brans–Dicke spherically symmetric models

Invariant description of static and dynamical Brans–Dicke spherically symmetric models

Invariant Description of Control in a Gaussian One-Armed Bandit Problem

Invariant Description of Control in a Gaussian One-Armed Bandit Problem

On hypersymmetry in three dimensions

In this work we presented a number of explicit examples for the cubic vertices describing an interaction of massless spin- frac{5}{2} field with massive boson and fermion including all hypertransformations necessary for the vertices to be gauge invariant. Here we restrict ourselves with the massive bosons with spins s = 2, 1, 0 and massive fermions with spins s = frac{3}{3} , frac{1}{2} . Our general analysis predicted that the vertex must exist for any boson and fermion with the spin difference frac{3}{2} or frac{1}{2} . And indeed it appeared that the vertex exists for all six possible pairs (2, 1, 0) ⊗ ( frac{3}{2} , frac{1}{2} ). As in the case of massive supermultiplets, our construction is based on the gauge invariant description for the massive fields with spins s ≥ 1. Moreover, we have explicitly checked that all the vertices are invariant also under the gauge symmetries of these massive fields.

Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-homogeneous Poisson Structures

We consider multicomponent local Poisson structures of the form {mathcal {P}}_3 + {mathcal {P}}_1, under the assumption that the third-order term {mathcal {P}}_3 is Darboux–Poisson and nondegenerate, and study the Poisson compatibility of two such structures. We give an algebraic interpretation of this problem in terms of Frobenius algebras and reduce it to classification of Frobenius pencils, i.e. linear families of Frobenius algebras. Then, we completely describe and classify Frobenius pencils under minor genericity conditions. In particular,we show that each Frobenuis pencil is a subpencil of a certain maximal pencil. These maximal pencils are uniquely determined by some combinatorial object, a directed rooted in-forest with edges and vertices labelled by numerical marks. They are also naturally related to certain pencils of Nijenhuis operators. We show that common Frobenius coordinate systems admit an elegant invariant description in terms of the corresponding Nijenhuis pencils.

New lower bounds for optimal horoball packing density in hyperbolic n-space for 6 le n le 9

Koszul type Coxeter simplex tilings exist in hyperbolic n-space mathbb {H}^n up to n = 9, and their horoball packings achieve the highest known regular ball packing densities for n = 3, 4, 5. In this paper we determine the optimal horoball packing densities of Koszul simplex tilings in dimensions 6 le n le 9, which give new lower bounds for optimal packing density in each dimension. The symmetries of the packings are given by Coxeter simplex groups, and a parameter related to the Busemann function gives an isometry invariant description of different optimal horoball packing configurations.

Customization of J. Bather UCB strategy for a Gaussian multi-armed bandit

We consider the customization of the UCB strategy, which was first proposed by J. Bather for Bernoulli two-armed bandit, to the case of a Gaussian multi-armed bandit describing batch data processing. This optimal control problem has classical interpretation as a game with nature, in which the payment function of the player is the expected loss of total income caused by incomplete information. The goal is stated in minimax setting. For the considered game with nature, we present an invariant description of the control with a horizon equal to one, which allows to perform computations in two ways: using Monte-Carlo simulations and analytically by dynamic programming technique. For various configurations of the considered game with nature, we have found saddle points, which characterize the optimal control and the worst-case distribution of the parameters of the multi-armed bandit.

Legendrian weaves : N–graph calculus, flag moduli and applications

We study a class of Legendrian surfaces in contact five-folds by encoding their wavefronts via planar combinatorial structures. We refer to these surfaces as Legendrian weaves, and to the combinatorial objects as N-graphs. First, we develop a diagrammatic calculus which encodes contact geometric operations on Legendrian surfaces as multi-colored planar combinatorics. Second, we present an algebraic-geometric characterization for the moduli space of microlocal constructible sheaves associated to these Legendrian surfaces. Then we use these N-graphs and the flag moduli description of these Legendrian invariants for several new applications to contact and symplectic topology. Applications include showing that any finite group can be realized as a subfactor of a 3-dimensional Lagrangian concordance monoid for a Legendrian surface in the 1-jet space of the two-sphere, a new construction of infinitely many exact Lagrangian fillings for Legendrian links in the standard contact three-sphere, and performing rational point counts over finite fields that distinguish Legendrian surfaces in the standard five-dimensional Darboux chart. In addition, the manuscript develops the notion of Legendrian mutation, studying microlocal monodromies and their transformations. The appendix illustrates the connection between our N-graph calculus for Lagrangian cobordisms and Elias-Khovanov-Williamson's Soergel Calculus.

A Pseudoinverse Siamese Convolutional Neural Network of Transformation Invariance Feature Detection and Description for a SLAM System

Simultaneous localization and mapping (SLAM) systems play an important role in the field of automated robotics and artificial intelligence. Feature detection and matching are crucial aspects affecting the overall accuracy of the SLAM system. However, the accuracy of the position and matching cannot be guaranteed when confronted with a cross-view angle, illumination, texture, etc. Moreover, deep learning methods are very sensitive to perspective change and do not have the invariance of geometric transformation. Therefore, a novel pseudo-Siamese convolutional network of a transformation invariance feature detection and a description for the SLAM system is proposed in this paper. The proposed method, by learning transformation invariance features and descriptors, simultaneously improves the front-end landmark detection and tracking module of the SLAM system. We converted the input image to the transform field; the backbone network was designed to extract feature maps. Then, the feature detection subnetwork and feature description subnetwork were decomposed and designed; finally, we constructed a convolutional network of transformation invariance feature detections and a description for the visual SLAM system. We implemented many experiments in datasets, and the results of the experiments demonstrated that our method has a state-of-the-art performance in global tracking when compared to that of the traditional visual SLAM systems.

On massive higher spins in d = 3

In this paper we consider a frame-like gauge invariant description of massive higher spin bosons and fermions in d = 3 and provide for the first time a proof that such formulation does describe just one massive physical degree of freedom with the appropriate helicity. For this purpose we completely fix all the gauge symmetries and show that all other auxiliary components vanish on-shell, while the only remaining highest component satisfies the correct equations. As a bonus, we show that the Lagrangians for the so-called self-dual massive spin-3 and spin-4 fields proposed by Aragone and Khoudeir (as well as their generalization to arbitrary integer and half-integer spins) can be obtained from the gauge invariant ones by the appropriate gauge fixing.

Gauge invariant operators in the SU(2) Higgs model: Ward identities and renormalization

The renormalization properties of two local gauge invariant composite operators $(O,{R}_{\ensuremath{\mu}}^{a})$ corresponding, respectively, to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are analyzed to all orders in perturbation theory by means of the algebraic renormalization in the $SU(2)$ Higgs model, with a single scalar in the fundamental representation, when quantized in the Landau gauge in Euclidean space-time. The present analysis generalizes earlier results presented in the case of the $U(1)$ Higgs model. A powerful global Ward identity, related to an exact custodial symmetry, is derived for the first time, with deep consequences at the quantum level. In particular, the gauge invariant vector operators ${R}_{\ensuremath{\mu}}^{a}$ turn out to be the conserved Noether currents of the above-mentioned custodial symmetry. As such, these composite operators do not renormalize, as expressed by the fact that the renormalization $Z$-factors of the corresponding external sources, needed to define the operators ${R}_{\ensuremath{\mu}}^{a}$ at the quantum level, do not receive any quantum corrections. Using this Ward identity, one can also prove that the longitudinal component of the two-point correlation function $⟨{R}_{\ensuremath{\mu}}^{a}(p){R}_{\ensuremath{\nu}}^{b}(\ensuremath{-}p)⟩$ exhibits only a tree level nonvanishing contribution which, moreover, is momentum independent, thus it is not associated to any physical propagating mode. Finally, we point out that the renowned nonrenormalization theorem for the ghost-antighost-vector boson vertex in Landau gauge remains true to all orders, also in the presence of the Higgs field.

Estimating QCD-factorization amplitudes through SU(3) symmetry in Brightarrow P P decays

We estimate the potential size of the weak annihilation amplitudes in QCD factorization as allowed by experimental data. To achieve this goal, we establish a connection between the amplitudes in the QCD factorization and the so-called topological and SU(3)-invariant descriptions. Our approach is based purely on the analysis of the tensor structure of the decay amplitudes. By focusing on the processes Brightarrow P P and considering data from CP asymmetries and branching fractions, we perform a global fit to the SU(3)-irreducible quantities assuming minimal theoretical bias. Subsequently we translate the outcome to the QCD factorization decomposition, and find that the most constrained weak annihilation amplitudes are below 0.04. However, in view of the large uncertainties in several of the experimental input parameters, values up to sim 0.3 are allowed in certain cases.

THE DISCOURSE OF TOURISM: AN ANALYSIS OF THE ONLINE ARTICLE “10 BEST PLACES TO VISIT IN UKRAINE”

The article shows the fact that the concept of scientific discourse is interpreted as a complex phenomenon that consists of participants in communication, communication situations and the text itself. The conclusion is that discourse is an abstract invariant description of structural and semantic features that are realized in specific texts. Linguists interpret the concept of discourse as a complex communicative phenomenon that includes the speaker and the addressee of the message, the process of proper formation of speech, extralingual factors of communication, social and cultural background. This article presents a critical reading of the text “10 Best places to visit in Ukraine” and its overlook, research study in the field of online tourism promotion, published online in 2021 by one of the world’s largest tourism publishing houses, Touropia. The study aims at revising some of the characteristics of the ongoing tourism discourse through an analysis of the network of people and practices involved in these publications, their textual features and images. The article analyses the way in which various modes to create a virtual brochure with a promotional message from both institutional and commercial positions were combined. In doing this, it studies the organization of the website and its webpage, as well as the lexico-grammatical and visual features of its promotional messages. The analytical framework used includes critical discourse analysis and a corpus-based tool used to interpret different aspects of this tourism discourse. The places advertised as “Top 10” are presented to an all-aged audience that must be interested in discovering new places, appreciated to nature, fond of history and ready to consume national products. Polyparadigmatic nature has led to the active use of these terms in the field of literature, as a result of which scientific studies address issues of artistic concept, artistic discourse, which will always be open to researchers, while not exhausting its relevance.

A Discriminative Target Equation-Based Face Recognition Method for Teaching Attendance

In this paper, we use discriminative objective equations to conduct an in-depth study and analysis of face recognition methods in teaching attendance and use the model in actual teaching attendance. It focuses on the design and implementation of the attendance module, which uses wireless network technology to record students’ access to classrooms in real time, and relies on face recognition technology to identify students’ sign-in images to achieve attendance records of students’ independent attendance sign-in. Real-time detection of student attendance is achieved by combining face detection and face recognition technology through regular camera photography and automatic attendance check-in by the server. Based on the recognition results of the attendance check-in image, an attendance mechanism is proposed, and the attendance score of the student for the current course can be calculated using the attendance mechanism, which realizes the automatic management of student attendance. For the face recognition process, the system uses the Ad boost algorithm based on Hear features to achieve face detection, preprocesses the face samples with gray normalization, rotation correction, and size correction, and uses the method based on LBP features to achieve face recognition. Firstly, a combination of histogram equalization and wavelet denoising is chosen to preprocess the training sample images to obtain the face image light invariance description, and then, the initial dictionary is constructed using the dimensionality reduction performance of the PCA method; next, the initial dictionary is updated, and a new dictionary with representation and discrimination capabilities is obtained using the LC-KSVD algorithm that makes improvements in the dictionary update stage. The sparse coefficients of the feature matrix of the test sample image under the new dictionary are calculated, and the class correlation reconstruction is performed on the feature matrix of the test sample image, and the corresponding reconstruction error is solved; finally, the discriminative classification of the test sample image is achieved according to the solved class correlation reconstruction error. The relevant experiments on the face database prove that the algorithm can improve the recognition accuracy to a certain extent and better solve the influence of changing lighting conditions on the face recognition accuracy.

Lie polynomials and a twistorial correspondence for amplitudes

We review Lie polynomials as a mathematical framework that underpins the structure of the so-called double copy relationship between gauge and gravity theories (and a network of other theories besides). We explain how Lie polynomials naturally arise in the geometry and cohomology of mathcal {M}_{0,n}, the moduli space of n points on the Riemann sphere up to Mobiüs transformation. We introduce a twistorial correspondence between the cotangent bundle T^*_Dmathcal {M}_{0,n}, the bundle of forms with logarithmic singularities on the divisor D as the twistor space, and mathcal {K}_n the space of momentum invariants of n massless particles subject to momentum conservation as the analogue of space–time. This gives a natural framework for Cachazo He and Yuan (CHY) and ambitwistor-string formulae for scattering amplitudes of gauge and gravity theories as being the corresponding Penrose transform. In particular, we show that it gives a natural correspondence between CHY half-integrands and scattering forms, certain n-3-forms on mathcal {K}_n, introduced by Arkani-Hamed, Bai, He and Yan (ABHY). We also give a generalization and more invariant description of the associahedral n-3-planes in mathcal {K}_n introduced by ABHY.