Invariant Description Research Articles

A0 Condensation, Nielsen’s Identity and Effective Potential of Order Parameter

In high temperature SU(2) gluodynamics, the condensation of the zero component gauge field potential A_0 =const and its gauge-fixing dependence are investigated. A_0 is mutually related with Polyakov's loop <L>. The two-loop effective potential W(A_0,xi) is recalculated in the background relativistic R_xi gauge. It depends on the parameter xi, has a nontrivial minimum and satisfies Nielsen's identity. These signs mean gauge invariance of the condensation phenomenon. Following the idea of Belyaev, we express W(A_0,xi) in terms of <L>. The obtained effective potential of order parameter differs from that derived by this author. It is independent of xi and has a nontrivial minimum position. Hence the A_0 condensation follows. We show that the equation relating A_0 and (A_0)|_(classical) coincides with the special characteristic orbit in the (A)$-plain along which the W(A_0,xi) is xi-independent. In this way the link between these two gauge invariant descriptions is established. The minimum value of the Polyakov loop is calculated. Comparison with results of other authors is given.

On massive spin-2 in the Fradkin-Vasiliev formalism. II. General massive case

In this work we apply the Fradkin-Vasiliev formalism based on the frame-like gauge invariant description of the massive and massless spin 2 to the construction of the cubic interactions vertices for massive spin 2 self-interaction as well as its gravitational interaction. In the first case we show that the vertex can be reduced (by field redefinitions) to the set of the trivially gauge invariant terms. There are four such terms which are not equivalent on-shell and do not contain more than four derivatives. Moreover, one their particular combination reproduces the minimal (with no more than two derivatives) vertex. As for the gravitational vertex, we show that due to the presence of the massless spin 2 there exist two abelian vertices (besides the three trivially gauge invariant ones) which are not equivalent to any trivially gauge invariant terms and can not be removed by field redefinitions. Moreover, their existence appears to be crucial for the possibility to reproduce the minimal two derivatives vertex.

Invariants of Linear Control Systems with Analytic Matrices and the Linearizability Problem

The paper continues the authors’ study of the linearizability problem for nonlinear control systems. In the recent work (Sklyar, Syst Control Lett 134:104572, 2019), conditions on mappability of a nonlinear control system to a preassigned linear system with analytic matrices were obtained. In the present paper, we solve more general problem on linearizability conditions without indicating a target linear system. To this end, we give a description of invariants for linear nonautonomous single-input controllable systems with analytic matrices, which allow classifying such systems up to transformations of coordinates. This study leads to one problem from the theory of linear ordinary differential equations with meromorphic coefficients. As a result, we obtain a criterion for mappability of nonlinear control systems to linear control systems with analytic matrices.

Two-armed bandit problem and batch version of the mirror descent algorithm

We consider the minimax setup for the two-armed bandit problem as applied to data processing if there are two alternative processing methods with different a priori unknown efficiencies. One should determine the most efficient method and provide its predominant application. To this end, we use the mirror descent algorithm (MDA). It is well-known that corresponding minimax risk has the order of $N^{1/2$ with $N$ being the number of processed data and this bound is unimprovable in order. We propose a batch version of the MDA which allows processing data by packets that is especially important if parallel data processing can be provided. In this case, the processing time is determined by the number of batches rather than by the total number of data. Unexpectedly, it turned out that the batch version behaves unlike the ordinary one even if the number of packets is large. Moreover, the batch version provides significantly smaller value of the minimax risk, i.e., it considerably improves a control performance. We explain this result by considering another batch modification of the MDA which behavior is close to behavior of the ordinary version and minimax risk is close as well. Our estimates use invariant descriptions of the algorithms based on Gaussian approximations of incomes in batches of data in the domain of ``close'' distributions and are obtained by Monte-Carlo simulations.

Grayscale-inversion and rotation invariant image description with sorted LBP features

Local binary pattern (LBP) is sensitive to inverse grayscale changes. To overcome this problem, several methods map each LBP code and its complement to the minimum one. However, without distinguishing LBP codes and their complements, these methods show limited description ability. In this paper, we introduce a generic histogram sorting method which exploits pattern transition rules to preserve the distribution information of LBP codes and their complements. Based on this method, we develop a series of sorted LBP (SLBP) descriptors, including pairwise sorted ones and fully sorted ones, which are all invariant to grayscale inversion and image rotation. Since SLBP focuses on encoding difference-sign information, it is further generalized to embed difference-magnitude LBP features to obtain complementary representations. We also propose an invariant pyramid pooling strategy to aggregate SLBP features into a pyramid image representation. Experiments on several benchmark texture databases and one newly collected image database (grayscale-inversion images, GII) demonstrate the effectiveness of our descriptors for image classification under (linear or nonlinear) grayscale-inversion and rotation changes. The source code will be available at https://github.com/stc-cqupt/slbp.

On massive spin-3/2 in the Fradkin–Vasiliev formalism

One of the possible approaches to the construction of massive higher spin interactions is to use their gauge invariant description based on the introduction of the appropriate set of Stueckelberg fields. Recently, the general properties of such approach were investigated by Boulanger et al (2018 J. High Energy Phys. JHEP07(2018)021). The main findings of this work can be formulated in two statements. At first, there always exist enough field redefinitions to bring the vertex into abelian form where there are some corrections to the gauge transformations but the gauge algebra is undeformed. At second, with the further (as a rule higher derivative) field redefinitions one can bring the vertex into trivially gauge invariant form expressed in terms of the gauge invariant objects of the free theory. Our aim in this work is to show (using a simple example) how these general properties are realised in the so-called Fradkin–Vasiliev formalism and to see the effects (if any) that the presence of massless field, and hence of some unbroken gauge symmetries, can produce. As such example we take the gravitational interaction for massive spin-3/2 field so we complete the investigation started by Buchbinder et al (2014 Eur. Phys. J. C 74 3153) relaxing all restrictions on the number of derivatives and allowed field redefinitions. We show that in spite of the presence of massless spin-2 field, the first statement is still valid, while there exist two abelian vertices which are not equivalent on-shell to the trivially gauge invariant ones. Moreover, it is one of this abelian vertices that reproduce the minimal interaction for massive spin-3/2.

Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e1g2− e2g1, for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

Determination of the representative volume-of-interest (REVOI) in ceramic replica foams

The investigations on ceramic foams with porous, heterogeneous microstructure are based on the standards and dimensions for dense materials due to the lack of alternatives. It is known that variations in pore size, shape and porosity have a significant effect on the physical properties, however, the considered sample volume is treated here as a secondary interest. To determine the representative volume-of-interest (REVOI), image data from micro tomography measurements of 30,45 and 60 ppi (pore per inch) Al2O3 foams were used. The REVOI is the minimum volume that comprehensively represents the microstructure and can thus be considered a unit volume. The Minkowski functionals allow an invariant microstructure description by single value using stereology approaches. Based on these values of defined volume sets, the REVOI was determined as a novelty in microstructure characterization. Additional analysis of the pore sizes in the 3D volume and determination of tortuosity and permeability at the previously defined volumes allowed validation of the REVOI.

Translation-Invariant Excitons in a Phonon Field

Large-radius excitons in polar crystals are considered. It is shown that translation invariant description of excitons interacting with a phonon field leads to a nonzero contribution of phonons into the exciton ground state energy only in the case of weak or intermediate electron-phonon coupling. A conclusion is made that self-trapped excitons cannot exist in the limit of strong coupling. Peculiarities of the absorption and emission spectra of translation invariant excitons in a phonon field are discussed. Conditions when the hydrogen-like exciton model remains valid in the case of electron-phonon interaction are found.

Polarization singularity analysis of Mueller-matrix invariants of optical anisotropy of biological tissues samples in cancer diagnostics

An approach of azimuthally invariant Mueller-matrix description of the formation of polarization singularities networks of object fields of optically anisotropic biological tissues is proposed. The main formation scenarios of the topological polarization-singular structure of the boundary field of networks of optically anisotropic cylinders are determined by means of computer simulation. In order to assess the polarization-singular structure of the object field of real biological tissues, an original Mueller-matrix method of statistical analysis of the number of L and C points has been developed.

Invariance and attraction properties of Galton–Watson trees

We give a description of invariants and attractors of the critical and subcritical Galton–Watson tree measures under the operation of Horton pruning (cutting tree leaves with subsequent series reduction). Under a regularity condition, the class of invariant measures consists of the critical binary Galton–Watson tree and a one-parameter family of critical Galton–Watson trees with offspring distribution {qk} that has a power tail qk∼Ck−(1+1/q0), where q0∈(1/2,1). Each invariant measure has a non-empty domain of attraction under consecutive Horton pruning, specified by the tail behavior of the initial Galton–Watson offspring distribution. The invariant measures satisfy the Toeplitz property for the Tokunaga coefficients and obey the Horton law with exponent R=(1−q0)−1/q0.

Double field theory algebroid and curved L ∞-algebras

A double field theory algebroid (DFT algebroid) is a special case of the metric (or Vaisman) algebroid, shown to be relevant in understanding the symmetries of double field theory. In particular, a DFT algebroid is a structure defined on a vector bundle over doubled spacetime equipped with the C-bracket of double field theory. In this paper, we give the definition of a DFT algebroid as a curved L∞-algebra and show how implementation of the strong constraint of double field theory can be formulated as an L∞-algebra morphism. Our results provide a useful step toward coordinate invariant descriptions of double field theory and the construction of the corresponding sigma-model.

A complete description of the cohomological invariants of even genus hyperelliptic curves

When the genus g is even, we extend the computation of mod 2 cohomological invariants of \mathcal{H}_g to non algebraically closed fields, we give an explicit functorial description of the invariants and we completely describe their multiplicative structure. In the Appendix, we show that the cohomological invariants of the compactification \overline{\mathcal{H}}_g are trivial, and use our methods to give a very short proof of a result by Cornalba on the Picard group of the compactification \overline{\mathcal{H}}_g and extend it to positive characteristic.

Coupled Attribute Learning for Heterogeneous Face Recognition.

Heterogeneous face recognition (HFR) is a challenging problem in face recognition and subject to large textural and spatial structure differences of face images. Different from conventional face recognition in homogeneous environments, there exist many face images taken from different sources (including different sensors or different mechanisms) in reality. In addition, limited training samples of cross-modality pairs make HFR more challenging due to the complex generation procedure of these images. Despite the great progress that has been achieved in recent years, existing works mainly focus on HFR from only cross-modality image matching. However, it is more practical to obtain both facial images and semantic descriptions about facial attributes in real-world situations, in which the semantic description clues are nearly always obtained during the process of image generation. Motivated by human cognitive mechanisms, we naturally utilize the explicit invariant semantic description, i.e., face attributes, to help address the gap among face images of different modalities. Existing facial attributes-related face recognition methods primarily regard attributes as the high-level features used to enhance recognition performance, ignoring the inherent relationship between face attributes and identities. In this article, we propose novel coupled attribute learning for the HFR (CAL-HFR) method without labeling the attributes manually. Deep convolutional networks are employed to directly map face images in heterogeneous scenarios to a compact common space where distances are taken as dissimilarities of pairs. Coupled attribute guided triplet loss (CAGTL) is designed to train an end-to-end HFR network that can effectively eliminate defects of incorrectly estimated attributes. Extensive experiments on multiple heterogeneous scenarios demonstrate that the proposed method achieves superior performance compared with that of state-of-the-art methods. Furthermore, we make publicly available our generated pairwise annotated heterogeneous facial attribute database for evaluation and promoting related research.

Invariant description for batch version of UCB strategy for multi-armed bandit

We consider a variation of upper confidence bound strategy for multi-armed bandit in batch processing setting. Invariant descriptions with the unit control horizon are obtained for upper bounds in the strategy and for regret. A set of Monte-Carlo simulations are performed for different settings of MABs to determine the minimax regret for multi-armed bandits with different configurations.

Illuminant estimation using pixels spatially close to the illuminant in the rg-chromaticity space

Color constancy algorithms can provide us with illuminant invariant descriptions for a scene, and it is often accomplished by illuminant estimation. Most statistics-based methods estimate the illuminant color from the information provided by all pixels of an image. However, this research reveals that, for most images, the color of many pixels is quite different from the illuminant, and these pixels may severely trim the performance of statistics-based methods. Based on this fact, we propose a color constancy algorithm that finds a subset of image pixels with r, g components similar to those of the illuminant through a shallow neural network, and this subset of pixels is called illuminant close pixels (ICPs). Then the illuminant color is estimated from these pixels by some statistics-based methods. The proposed method has been evaluated and investigated on two benchmark datasets. Compared to using all pixels in an image, these statistics-based methods have been efficiently improved using ICPs.

Vector properties of entanglement in a three-qubit system

We suggest a dynamical vector model of entanglement in a three qubit system based on isomorphism between $su(4)$ and $so(6)$ Lie algebras. Generalizing Pl\"ucker-type description of three-qubit local invariants we introduce three pairs of real-valued $3D$ vector (denoted here as $A_{R,I}$ , $B_{R,I}$ and $C_{R,I}$). Magnitudes of these vectors determine two- and three-qubit entanglement parameters of the system. We show that evolution of vectors $A$, $B$ , $C$ under local $SU(2)$ operations is identical to $SO(3)$ evolution of single-qubit Bloch vectors of qubits $a$, $b$ and $c$ correspondingly. At the same time, general two-qubit $su(4)$ Hamiltonians incorporating $a-b$, $a-c$ and $b-c$ two-qubit coupling terms generate $SO(6)$ coupling between vectors $A$ and $B$, $A$ and $C$, and $B$ and $C$, correspondingly. It turns out that dynamics of entanglement induced by different two-qubit coupling terms is entirely determined by mutual orientation of vectors $A$, $B$, $C$ which can be controlled by single-qubit transformations. We illustrate the power of this vector description of entanglement by solving quantum control problems involving transformations between $W$, Greenberg-Horne-Zeilinger ($GHZ$ ) and biseparable states.

Study of the renormalization of BRST invariant local composite operators in the U(1) Higgs model

The renormalization properties of two local BRST invariant composite operators, $(O,V_\mu)$, corresponding respectively to the gauge invariant description of the Higgs particle and of the massive gauge vector boson, are scrutinized in the $U(1)$ Higgs model by means of the algebraic renormalization setup. Their renormalization $Z$'s factors are explicitly evaluated at one-loop order in the $\overline{\text{MS}}$ scheme by taking into due account the mixing with other gauge invariant operators. In particular, it turns out that the operator $V_\mu$ mixes with the gauge invariant quantity $\partial_\nu F_{\mu\nu}$, which has the same quantum numbers, giving rise to a $2 \times 2$ mixing matrix. Moreover, two additional powerful Ward identities exist which enable us to determine the whole set of $Z$'s factors entering the $2 \times 2$ mixing matrix as well as the $Z$ factor of the operator $O$ in a purely algebraic way. An explicit check of these Ward identities is provided. The final setup obtained allows for computing perturbatively the full renormalized result for any $n$-point correlation function of the scalar and vector composite operators.

Sign Choices for Orientifolds

We analyse the problem of assigning sign choices to O-planes in orientifolds of type II string theory. We show that there exists a sequence of invariant $p$-gerbes with $p\geq-1$, which give rise to sign choices and are related by coboundary maps. We prove that the sign choice homomorphisms stabilise with the dimension of the orientifold and we derive topological constraints on the possible sign configurations. Concrete calculations for spherical and toroidal orientifolds are carried out, and in particular we exhibit a four-dimensional orientifold where not every sign choice is geometrically attainable. We elucidate how the $K$-theory groups associated with invariant $p$-gerbes for $p=-1,0,1$ interact with the coboundary maps. This allows us to interpret a notion of $K$-theory due to Gao and Hori as a special case of twisted $KR$-theory, which consequently implies the homotopy invariance and Fredholm module description of their construction.

Person re-identification using prioritized chromatic texture (PCT) with deep learning

Person re-identification (re-ID) helps to identify a person’s attention in different cameras. But this is not an easy task, due to distance, illumination and lack of dataset. Nowadays, this field attracts many researchers because of its varied applications. Here, the information of both local texture and global color representations are concatenated with an original raw image. This concatenated information is gathered by finding the maximum value of chrominance in terms of HSV, texture in terms of Scale Invariant Local Ternary Pattern (SILTP) for each pixel and original raw image. SILTP is well known for its illumination invariant texture description. Convolutional Neural Network (CNN) is used in the proposed work to extract the features from the concatenated information. The proposed Prioritized Chromatic Texture Image (PCTimg) is concatenated with original raw image and fed into CNN. Here, finally a six dimensionalfeature is fed into CNN to extract the deep features. Cross-view Quadratic Discriminant Analysis (XQDA) similarity metric algorithm is employed to re-identify a person.Multiscale Retinex algorithm is used for pre-processing the images.To address the challenges in terms of view point deflection, a sliding window is formed for describing local details of a person in the SILTP feature extraction phase. The HSV helps to incorporate the human color perception. The triplet loss function is used to learn the similarity and the dissimilarity of the training images. The performance analysis of the proposed work is improvedwhen compared to the existingworks.