Invariant Transform Research Articles

COLOROMETRIC ANALYSIS OF THE IMAGE OF THE BUILDING SITE

The paper considers the approach to the formalization of the colorimetric (color) atlas of the construction site (СABS), which is determined by the subject area at the intersection of disciplines: materials science, structural mechanics and machine mechanics, technical condition control, photogrammetry, pattern recognition theory. Each of the above applied areas contains its own knowledge base, various information technologies that take into account the characteristics of each of them. The procedure of forming the concept of color atlas of the construction site in the intellectual information environment in construction, its features and composition, the difference from the usual procedures of forming the knowledge system, as well as the proposed and described approach to its study, the information interaction of the intellectual environment of the object object of construction. The possibility of constructing different formalizations of СABS on the basis of ontological and semantic graphs and the graph of the construction site image is shown. The problems that arise in the process of formalization and analysis of СABS in order to search for image elements are identified and described. The substantive structure of СABS and the equivalence of СABS graphs are determined, taking into account the possibility of introducing similarity measures. СABS in terms of pragmatic classification is a specialized finding of elements on construction sites. The work is performed in the framework of cluster analysis and focuses on the development of methods for constructing algorithms for recognition and identification of construction sites. For the described transformations, research was conducted on their observation in digital images, as well as the possibility of observing the invariants of transformations. The work was performed for СABS in order to determine the possibility of building its information model, taking into account the development of methods for constructing algorithms for recognition and identification on construction sites. The possibility of constructing СABS on the basis of a set of images is investigated, the possibility of corresponding visualizations of СABS СABS as a means of categorization is established.

Computation of bio-nano-convection power law slip flow from a needle with blowing effects in a porous medium

Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transfer external to a needle in a porous medium have many biomedical engineering applications (e.g. hypodermic needles used in hemotology). It is also used to design many biomedical engineering equipment's and coating flows with bio-inspired nanomaterials. Coating flows featuring combinations of nanoparticles and motile micro-organisms also constitute an important application area. A model for convective flow of a power-law nanofluid containing gyrotactic micro-organisms past a needle in a Darcy porous medium is developed. Multiple slips and Stefan blowing effects at the needle boundary are considered. The model features a reduced form of the conservation of equations with appropriate coupled boundary conditions. The governing equations are converted to similarity equations using appropriate invariant transformations. The transformed equations have been solved numerically using the in-built Matlab bvp4c function. The influence of the emerging parameters on the flow characteristics, friction, heat, mass, and micro-organism transfers are discussed in detail. Note that velocity decreases whilst temperature, concentration, and density of motile micro-organism increase with an increase in blowing parameter for shear thinning, Newtonian, and shear thickening fluids. All physical quantities are decreasing with increasing blowing, Darcy, power law and needle size parameters.

Structure and properties of phases in the Cu2-ХSe-Sb2Se3 system. The Cu2-XSe-Sb2Se3 phase diagram

The phase diagram of the Cu2−XSe-Sb2Se3 system is revisited to clarify ambiguity/disagreement in previously reported data. Ternary Cu3SbSe3 and CuSbSe2 compounds were obtained. In order to confirm that the phases have been identified correctly, crystal structures were solved, and the energy band gaps measured. For the sample containing 75 mol% Sb2Se3 and 25 mol% Cu1.995Se the temperature range of the stability of the high-temperature CuSb3Se5 phase was determined for the first time. This phase is formed at 445 °С, decomposes following a peritectic reaction at 527 °С, and can be quenched. A high-temperature X-ray diffraction study of a sample containing 75 mol% Sb2Se3 and 25 mol% Cu2Se allowed us to measure the thermal expansion of the CuSbSe2 and Sb2Se3 phases present in the sample. The anisotropy of thermal expansion of CuSbSe2 is similar to that of As2S3 (orpiment); thermal expansion of Sb2Se3 is similar to that of AsS (realgar). The 6 balance equations of the invariant phase transformations involving all the ternary compounds existing in the Cu2−XSe-Sb2Se3 system were suggested for the first time. The temperature and the enthalpies of all these transformations were measured. A phase diagram of the Cu2−XSe-Sb2Se3 system was found for the first time in all the range of concentrations at temperatures from ambient to the complete melting. This diagram takes into consideration the phase equilibria that involve all the ternary compounds that are possible in this system. The liquidus of the Cu2−XSe-Sb2Se3 system was calculated according to Redlich-Kister equation; it agrees with the experimental data within 1–17 °С.

Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches

By taking advantage of three different computational analytical methods: the Lie symmetry analysis, the generalized Riccati equation mapping approach, and the modified Kudryashov approach, we construct multiple new analytical soliton solutions to the nonlinear convection-diffusion-reaction equation (NCDR) with power-law nonlinearity and density-dependent diffusion. Lie symmetry analysis is one of the powerful techniques that reduce the higher-order partial differential equation into an ordinary differential equation by reduction of independent variables. By the Lie group technique, we obtain one-parameter invariant transformations, determining equations and corresponding vectors for the considered convection-diffusion-reaction equation. By treating the parameters of the governing equation as constants, the applied methods yield a variety of new closed-form solutions, including inverse function solutions, periodic solutions, exponential function solutions, dark solitons, singular solitons, combo bright-singular solitons, and the combine of bright-dark solitons and dark-bright solitons. Moreover, using the Bäcklund transformation of the generalized Riccati equation and modified Kudryashov method, we can construct multiple solitons and other solutions of the considered equation. The obtained new solutions of this work demonstrate that the used approaches are powerful and effective in dealing with nonlinear equations, and that these solutions are required to explain many biological and physical phenomena. Comparing our obtained solutions of this paper with the ones obtained in the literature, we see that our solutions are new and not reported elsewhere. These newly formed soliton solutions will be more beneficial in the various disciplines of ocean engineering, plasma physics, and nonlinear sciences.

NP-Difficult Tasks: Automatic Proof of Theorems and Turings Machine

It is offered to use for solving NP-complete (difficult) tasks a modification of methods for satisfying the constraint (CS) by including automatic proof of theorems (APT), and programming in constraints — generation of Turing's machine (TM). Currently, CS uses AP in a truncated form (logical programming), and it is suggested using the method of invariant transformations (MIT), which is a full-fledged APT. In addition, it is offered to use CS methods to generate TM solving NP-difficult tasks recorded on the TM tape, which is an extension of programming capabilities in constraints.

On analytic series solutions and conserved fluxes of the time fractional (2+1)-dimensional Burger's system via invariant approach

The article investigates some new properties such as invariant transformations, conserved vectors, and closed-form series solutions of (2+1) dimensional nonlinear coupled Burger system, a model of the evolution of the scaled volume concentration or sedimentation of the two kinds of particles in fluid suspensions of colloids, under the effect of gravity, with fractional temporal evolution by the Lie symmetry method. It is worth noting that the series solutions of (2+1) or higher-dimensional system is not much explored. Moreover, nonlocal conservation laws, one of the important aspects of symmetries, are constructed by the generalized Noether theorem.

Decoupling of second order systems via linear time invariant transformations

Decoupling of linear time invariant (LTI) systems of second order ordinary differential equations (ODEs) with real matrix coefficients via LTI transformations in the configuration space is revisited. Necessary and sufficient conditions for the existence of such transformations are presented, as well as methods to construct transformation matrices. Matrix series and general matrix function formulas for the system’s matrix coefficients which enable decoupling are also discussed. Systems with non-symmetric and symmetric matrices are considered. Situations when systems degenerate into second order ODEs and lower order ODEs, including differential algebraic equations (DAEs), are analyzed as well.

Equivalent polyadic decompositions of matrix multiplication tensors

Invariance transformations of polyadic decompositions of matrix multiplication tensors define an equivalence relation on the set of such decompositions. In this paper, we present an algorithm to efficiently decide whether two polyadic decompositions of a given matrix multiplication tensor are equivalent. With this algorithm, we analyze the equivalence classes of decompositions of several matrix multiplication tensors. This analysis is relevant for the study of fast matrix multiplication as it relates to the question of how many essentially different fast matrix multiplication algorithms there exist. This question has been first studied by de Groote, who showed that for the multiplication of 2 ×2 matrices with 7 active multiplications, all algorithms are essentially equivalent to Strassen’s algorithm. In contrast, the results of our analysis show that for the multiplication of larger matrices (e.g., 2 ×3 by 3 ×2 or 3 ×3 by 3 ×3 matrices), two decompositions are very likely to be essentially different. We further provide a necessary criterion for a polyadic decomposition to be equivalent to a polyadic decomposition with integer entries. Decompositions with specific integer entries, e.g., powers of two, provide fast matrix multiplication algorithms with better efficiency and stability properties. This condition can be tested algorithmically and we present the conclusions obtained for the decompositions of small/medium matrix multiplication tensors.

Application of the form invariance transformations of the scalar cosmological model in inflation theory

In this work, it is shown that the equations of motion of the scalar field for spatially flat, homogeneous, and isotropic space-time Friedmann-Robertson-Walker have a form-invariance symmetry, which is arising from the form invariance transformation. Form invariance transformation is defined by linear function ρ = n 2 ρ in general case. It is shown the method of getting potential and the scalar field for the power law scale factor. The initial model is always stable at exponent of the scale factor α > 1, but stability of the transformation model depends on index n. Slow roll parameters and spectral induces is obtained and at large α they agree with Planck observation data.

Bloch waves and non-commutative tori of magnetic translations

We review the Landau problem of an electron in a constant uniform magnetic field. The magnetic translations are the invariant transformations of the free Hamiltonian. A Kähler polarization of the plane has been used for the geometric quantization. Under the assumption of quasi-periodicity of the wavefunction, the Zak’s magnetic translations in the Bravais lattice generate a non-commutative quantum torus. We concentrate on the case when the magnetic flux density is a rational number. The Bloch wavefunctions form a finite-dimensional module of the noncommutative torus of magnetic translations as well as of its commutant, which is the non-commutative torus of magnetic translations in the dual Bravais lattice. The bi-module structure of the Bloch waves is shown to be the connecting link between two Morita equivalent non-commutative tori. The main focus of our review is the Kähler structure on the Hilbert space of Bloch waves and its inherent quantum toric geometry. We reveal that the metaplectic group Mp(2,R) of the automorphisms of magnetic translation algebras is represented by the quantum optics squeezing operators.

Leaf Identification Based on Shape, Color, Texture and Vines Using Probabilistic Neural Network

The importance of the plant for the human being and the environment led to deeply been studied and classified in detail. The advancement of the technology is the main factor in finding many ways for plant identification process. Some kind of initial intelligence systems in order to identify plant, followed by many theories and concepts using methods like; Moment Invariant (MI), Zernike Moments (ZM) and Polar Fourier Transform (PFT), and technologies for classification like; Neural Network (NN), K-Nearest Neighbor Classifier (KNN) and Support Vector Machine (SVM), were used by many researchers through past years. In this paper is Centroid-Radii (C-R) combined with geometric features of the leaves, in order to cover most of shape feature of the leaves, color moments and Grey-Level Co-occurrence Matrix (GLCM) to improve the accuracy of the system identification. in addition to the above features, Veins also involved in the method been used plus Principal Component Analysis (PCA), which is used to convert features into orthogonal features and the results were inputted to the classifiers that used Probabilistic Neural Network (PNN). Two datasets have been used for test, first dataset is created especially for this work and collected from 24 kinds of plants and second dataset is called Flavia which contains 32 kinds. The results were clearly improved to identify the plants. the maximum accuracy reached up to %98.50 when using the first data set and 98.16% for the second dataset.

TIF-Reg: Point Cloud Registration with Transform-Invariant Features in SE(3).

Three-dimensional point cloud registration (PCReg) has a wide range of applications in computer vision, 3D reconstruction and medical fields. Although numerous advances have been achieved in the field of point cloud registration in recent years, large-scale rigid transformation is a problem that most algorithms still cannot effectively handle. To solve this problem, we propose a point cloud registration method based on learning and transform-invariant features (TIF-Reg). Our algorithm includes four modules, which are the transform-invariant feature extraction module, deep feature embedding module, corresponding point generation module and decoupled singular value decomposition (SVD) module. In the transform-invariant feature extraction module, we design TIF in SE(3) (which means the 3D rigid transformation space) which contains a triangular feature and local density feature for points. It fully exploits the transformation invariance of point clouds, making the algorithm highly robust to rigid transformation. The deep feature embedding module embeds TIF into a high-dimension space using a deep neural network, further improving the expression ability of features. The corresponding point cloud is generated using an attention mechanism in the corresponding point generation module, and the final transformation for registration is calculated in the decoupled SVD module. In an experiment, we first train and evaluate the TIF-Reg method on the ModelNet40 dataset. The results show that our method keeps the root mean squared error (RMSE) of rotation within 0.5 and the RMSE of translation error close to 0 m, even when the rotation is up to [−180, 180] or the translation is up to [−20 m, 20 m]. We also test the generalization of our method on the TUM3D dataset using the model trained on Modelnet40. The results show that our method’s errors are close to the experimental results on Modelnet40, which verifies the good generalization ability of our method. All experiments prove that the proposed method is superior to state-of-the-art PCReg algorithms in terms of accuracy and complexity.

Radar Life Signal Processing Algorithm Based on Improved EEMD

Non-contact measurement of human vital signs is of great significance to the construction of smart homes and hospitals. The vital signal extracted from the FMCW radar contains a lot of noise. In order to reduce the noise impact and improve the life signal detection results accuracy, Ensemble Empirical Mode Decomposition (EEMD) algorithm is studied, and a new method based on the combination of EEMD and Translation Invariant Wavelet Transform (TIWT) is proposed. This method firstly decomposes the original signal using EEMD to obtain several Intrinsic Mode Function (IMF) components, and then changes the arrangement order of IMF by Translation Invariant Wavelet Transform to change the position of the singularity in the whole signal to reduce or eliminate the oscillations. Finally, signal screening is completed and life signals are reconstructed. Experiments show that, the proposed method has better detection accuracy in detecting vital signs collected by radar.

Exact Anti-Self-Dual four-manifolds with a Killing symmetry by similarity transformations

We study the group properties and the similarity solutions for the constraint conditions of anti-self-dual null Kähler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply the theory of Lie symmetries to determine all the infinitesimal generators of the one-parameter point transformations which leave the system invariant. We use these transformations to define invariant similarity transformations which are used to simplify the differential equations and find the exact form of the spacetime. We show that the constraint equations admit an infinite number of symmetries which can be used to construct an infinite number of similarity transformations.

ПРИМЕНЕНИЕ НЕЙРОННЫХ СЕТЕЙ ДЛЯ РАСПОЗНАВАНИЯ ПРИНЦИПИАЛЬНЫХ УСЛОВНО-ГРАФИЧЕСКИХ ЭЛЕКТРИЧЕСКИХ ОБОЗНАЧЕНИЙ

The article discusses the issue of using artificial neural networks for recognizing the conditionally graphical designations of electrical engineering, in particular, the convolutional neural networks and the R-CNN object recognition model, which is most suitable for solving the task at hand. Recognition of images of a specific picture is a task set for the complex information processing systems, as well as control and decision-making systems. The classification of various technological or natural objects, analog and digital signals is developed by a set of specific characteristics and properties. Defining the type and features of an object finds its application in different branches of science: machine learning, diagnostics, meteorology, video surveillance and security systems, in virtual reality systems and image search. However, research has not yet been carried out for solving the applied problems and achieving the required parameters (e.g. in recognizing conditional graphical symbols of electrical engineering). The neural networks have been found to have the highest quality and most promising among all mathematical models and methods of pattern recognition. As for the interactivity, the output result of image recognition work is a necessary and sufficient answer, which does not have a stable work on the variability of objects within categories and their invariant transformations. The scheme of the model R-CNN has been studied in detail, the importance of the training sample and its influence on the quality of pattern recognition by the neural network have been grounded. The application of the RoI Pooling method for object recognition in the image is shown in general, due to which there have been selected several regions of interest indicated through the bounding boxes.

Physical invariance in neural networks for subgrid-scale scalar flux modeling

In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data, state-of-the-art neural networks, such as convolutional neural networks, may not preserve well known physical priors, which may in turn question their application to real case-studies. To address this issue, we investigate hard and soft constraints into the model based on classical transformation invariances and symmetries derived from physical laws. From simulation-based experiments, we show that the proposed transformation-invariant NN model outperforms both purely data-driven ones as well as parametric state-of-the-art subgrid-scale models. The considered invariances are regarded as regularizers on physical metrics during the a priori evaluation and constrain the distribution tails of the predicted subgrid-scale term to be closer to the DNS. They also increase the stability and performance of the model when used as a surrogate during a large-eddy simulation. Moreover, the transformation-invariant NN is shown to generalize to regimes that have not been seen during the training phase.

Analysis of the geometric features of T-x-y diagrams with melt immiscibility for silicate systems

Analysis of the geometric structure of phase diagrams for ternary systems with the two immiscible liquids has been carried out. T-x-y diagrams with the both types of the monotectic equilibriums (univariant and invariant ones) have been analyzed. Three-dimensional computer models of T-x-y diagrams for the four silicate systems with mono- and invariant equilibriums and different variants of the immiscibility surfaces location have been built. T-x-y diagram of the ZrO2-SiO2-Al2O3 system includes one immiscibility cupola, located in the ZrO2 crystallization field, which adjoins the ZrO2-SiO2 side. The 3D model of T-x-y diagram includes four invariant transformations: peritectic P: L+ZrO2+SiO2→R2, quasi-peritectic Q: L+ZrO2 →R1+R2, two eutectic E1: L→ZrO2+Al2O3+R1, E2: L→SiO2+R1+R2. Five surfaces of liquidus, which correspond to the beginning of primary crystallization of three initial components and two binary compounds R1=3Al2O3·2SiO2 and (congruently melting) and R2=ZrO2·SiO2 (decomposed without liquid) are formed in the system. T-x-y diagram TiO2-ZrO2-SiO2 is characterized by one eutectic E: L→TiO2+SiO2+ZrO2·TiO2 and one quasi-peritectic Q: L+ZrO2→SiO2+ZrO2·TiO2 transformations and includes two immiscibility surfaces from the sides of TiO2-SiO2 and ZrO2-SiO2 binary systems. FeO-SiO2-Fe2O3 system with common immiscibility cupola, that prolongs from the system FeO-SiO2 to the system SiO2-Fe2O3, is characterized by three invariant transformations of eutectic type, and one metatectic transformation V: B1 →L+B2+C, which corresponds to the transfer from high-temperature allotropy of silica (B1 - cristobalite) to the low-temperature one (B2 – tridymite). T-x-y diagram KAlSi2O6-Fe2SiO4-SiO2 has two immiscibility surfaces: one of them adjoins to the Fe2SiO4-SiO2 binary system and the second one is located on the Fe2SiO4 and tridymite liquidus surfaces, dividing the univariant curve on their boundary into two parts, and has three points of the maximum and three points of the minimum. Using of the computer models of T-x-y diagrams allows you to take into account different variants of the geometric structure of the investigated silicate systems.

Capsule neural nets for graph objects classification

A new way to solve the graph classification problem is addressed. The main method utilized is the application of a capsule neural network on graphs. The results achieved include, firstly, the enhancement of the base algorithm for training a capsule network with the possibility of using graphs as an input (a stage of training for permutation invariants of graph vertices’ transformation matrices is included as well as a memory block for trained matrices), and secondly, a proposition of a training set of labeled graph objects, transformed from the MNIST dataset. This opens a perspective for a better classification of graph objects due to preserving of their structure and transformation invariance between layers.

Energy conservation of nanofluids from a biomagnetic needle in the presence of Stefan blowing: Lie symmetry and numerical simulation

Thermal energy management associated with the transmission of heat is one of the main problems in many industrial setups (e.g. pharmaceutical, chemical and food) and bio-engineering devices (e.g. hospital ventilation, heating, cooling devices, heat exchanger and drying food, etc). The current study aims to examine thermo-bioconvection of oxytactic microorganisms taking place in a nanofluid-saturated needle with the magnetic field. Stefan-blowing is applied. The leading equations of continuity, momentum and energy, species transport equations for oxygen concentration and population density of microorganisms are reduced dimensionless and Lie symmetry group transformations are used to generate appropriate invariant transformations. The resulting similarity boundary value problem (in which the blowing parameter is coupled with concentration) have been simulated using MATLAB (2015a) bvp5c built in function. The impact of the emerging factors on the nondimensional velocity, temperature, nanoparticle concentration and motile microorganism density functions and their slopes at the wall, are pictured and tabulated. Justification with published results are included. It is found that all physical quantities decrease with Stefan blowing and increase with power law index parameter. With elevation in magnetic field parameter i.e., Lorentzian drag force, the friction factor reduces while the local Nusselt number, local Sherwood number, and the local motile microorganism density wall gradient increase. Present study could be used in food and pharmaceutical industries, chemical processing equipment, fuel cell technology, enhanced oil recovery, etc.

On group symmetries of the hydrodynamic equations for rarefied gas

<p style='text-indent:20px;'>The invariant group transformations of three-dimensional hydrodynamic equations derived from the Boltzmann equation are studied. Three levels (with respect to the Knudsen number) of hydrodynamic description are considered and compared: (a) Euler equations, (b) Navier-Stokes equations, (c) Generalized Burnett equations (GBEs), which replace the original (ill-posed) Burnett equations. The main attention is paid to group analysis of GBEs in their most general formulation because this and related questions have not been studied before in the literature. The results of group analysis of GBEs and, for comparison, of similar results for Euler and Navier-Stokes equations are presented in two theorems and discussed in detail. It is remarkable that the use of computer code greatly simplifies the proof of the results for GBEs, which are very cumbersome equations with many undetermined parameters.