Block Representation Research Articles

Non-Contact Multi-Subject Human Gait Analysis Using A State-Space Method With Enhanced 1-D Block Representation

A stepped-frequency continuous-wave (SFCW) radar system with adequate pulse repetition frequency (PRF) is developed to track relatively fast motions from various parts of the human body, separately. Robust signal processing technique is utilized, where a 1-D block processing technique, based on state-space method (SSM) is developed in two dimensions to form an enhanced Hankel matrix to track human motions from two-dimensional (2-D) data collected using the developed SFCW radar system in single- or multi-subject motion scenarios. Experimental datasets are used to track body parts' motions and velocities with high accuracy. The significant improvement, besides de-noising the data, is due to the fact that applying the 1-D block processing technique to 2-D dataset matrix accounts for the correlation between motion's estimates from consecutive frames. Results agree well with our reference, the human Boulic model.

Trinion conformal blocks from topological strings

In this paper we investigate the relation between conformal blocks of Liouville CFT and the topological string partition functions of the rank one trinion theory T2. The partition functions exhibit jumps when passing from one chamber in the parameter space to another. Such jumps can be attributed to a change of the integration contour in the free field representation of Liouville conformal blocks. We compare the partition functions of the T2 theories representing trifundamental half hypermultiplets in N = 2, d = 4 field theories to the partition functions associated to bifundamental hypermultiplets. We find that both are related to the same Liouville conformal blocks up to inessential factors. In order to establish this picture we combine and compare results obtained using topological vertex techniques, matrix models and topological recursion. We furthermore check that the partition functions obtained by gluing two T2 vertices can be represented in terms of a four point Liouville conformal block. Our results indicate that the T2 vertex offers a useful starting point for developing an analog of the instanton calculus for SUSY gauge theories with trifundamental hypermultiplets.

The Invertibility of U-Fusion Cross Gram Matrices of Operators

Finding matrix representations is an important part of operator theory. Calculating such a discretization scheme is equally important for the numerical solution of operator equations. Traditionally in both fields, this was done using bases. Recently, frames have been used here. In this paper, we apply fusion frames for this task, a generalization motivated by a block representation, respectively, a domain decomposition. We interpret the operator representation using fusion frames as a generalization of fusion Gram matrices. We present the basic definition of U-fusion cross Gram matrices of operators for a bounded operator U. We give necessary and sufficient conditions for their (pseudo-)invertibility and present explicit formulas for the (pseudo-)inverse. More precisely, our attention is on how to represent the inverse and pseudo-inverse of such matrices as U-fusion cross Gram matrices. In particular, we characterize fusion Riesz bases and fusion orthonormal bases by such matrices. Finally, we look at which perturbations of fusion Bessel sequences preserve the invertibility of the fusion Gram matrix of operators.

DSSR-enabled innovative schematics of 3D nucleic acid structures with PyMOL.

Sophisticated analysis and simplified visualization are crucial for understanding complicated structures of biomacromolecules. DSSR (Dissecting the Spatial Structure of RNA) is an integrated computational tool that has streamlined the analysis and annotation of 3D nucleic acid structures. The program creates schematic block representations in diverse styles that can be seamlessly integrated into PyMOL and complement its other popular visualization options. In addition to portraying individual base blocks, DSSR can draw Watson-Crick pairs as long blocks and highlight the minor-groove edges. Notably, DSSR can dramatically simplify the depiction of G-quadruplexes by automatically detecting G-tetrads and treating them as large square blocks. The DSSR-enabled innovative schematics with PyMOL are aesthetically pleasing and highly informative: the base identity, pairing geometry, stacking interactions, double-helical stems, and G-quadruplexes are immediately obvious. These features can be accessed via four interfaces: the command-line interface, the DSSR plugin for PyMOL, the web application, and the web application programming interface. The supplemental PDF serves as a practical guide, with complete and reproducible examples. Thus, even beginners or occasional users can get started quickly, especially via the web application at http://skmatic.x3dna.org.

Facial Expression Recognition with Active Local Shape Pattern and Learned-Size Block Representations

Facial expression recognition has been studied broadly, and several works using local micro-pattern descriptors have obtained significant results. There are, however, open questions: how to design a discriminative and robust feature descriptor?, how to select expression-related most influential features?, and how to represent the face descriptor exploiting the most salient parts of the face? In this article, we address these three issues to achieve better performance in recognizing facial expressions. First, we propose a new feature descriptor, namely Local Shape Pattern (LSP), that describes the local shape structure of a pixel’s neighborhood based on the prominent directional information by analyzing the statistics of the neighborhood gradient, which allows it to be robust against subtle local noise and distortion. Furthermore, we propose a selection strategy for learning the influential codes being active in the expression affiliated changes by selecting them exhibiting statistical dominance and high spatial variance. Lastly, we learn the size of the salient facial blocks to represent the facial description with the notion that changes in expressions vary in size and location. We conduct person-independent experiments in existing datasets after combining above three proposals, and obtain an improved performance for the facial expression recognition task.

Solving fuzzy linear systems by a block representation of generalized inverse: the core inverse

This paper presents a method for solving fuzzy linear systems, where the coefficient matrix is an $$n\times n$$ real matrix, using a block structure of the Core inverse, and we use the Hartwig–Spindelbock decomposition to obtain the Core inverse of the coefficient matrix A. The aim of this paper is twofold. First, we obtain a strong fuzzy solution of fuzzy linear systems, and a necessary and sufficient condition for the existence strong fuzzy solution of fuzzy linear systems are derived using the Core inverse of the coefficient matrix A. Second, general strong fuzzy solutions of fuzzy linear systems are derived, and an algorithm for obtaining general strong fuzzy solutions of fuzzy linear systems by Core inverse is also established. Finally, some examples are given to illustrate the validity of the proposed method.

“Avoiding the mistakes of the past”

AbstractA powerful dystopian imaginary dominates political and cultural representations of Britain's postwar tower blocks, which continue to be linked to social dysfunction and alienation despite extensive empirical research that challenges such claims. This article asks what contested declarations of failure “do” by examining how “tower block failure” is discursively deployed by placemaking professionals—planners, architects, housing managers, regeneration practitioners—engaged in the construction of a “model” mixed-tenure neighborhood in London's Olympic Park. Examining how the aesthetic figure of the “failed” high-rise housing estate is configured in relation to the normative models of citizenship and community that infuse social and spatial policy, I argue “failure” is entangled with a speculative, future-oriented economy of risk management, which refracts wider questions about the nonobvious forms that power takes in the neoliberal city.

Fast computation of Hahn moments on gray images using block representation

The moments constitute a well-known tool for image analysis and recognition tasks. The family of moments that has the most advantages is the discrete orthogonal moments. A set of these moments is the Hahn moments, as they have a great number of advantages in comparison with other sets of moments. The main disadvantage of moments, including Hahn moments, is the high computational cost, which is increased as higher order moments are involved in the computations, so the real-time analysis is hard to be done. We propose an effective approach for the computation of Hahn moments. The gray image is decomposed in a set of binary images that are named as bitplanes. The most significant bitplanes are represented using image block representation and their moments are computed fast using block techniques. The least significant binary images are substituted by a constant ideal image called “half-intensity” image, which has known Hahn moment values. The proposed method has low computational error, low computational complexity, and under certain conditions is able to achieve real-time processing rates.

Procedural knowledge and function blocks for smart process planning

In the age of digital manufacturing there is a need to elicit and transfer procedural knowledge between humans and machines. Having proper knowledge is essential in decision-making. The more the knowledge, the better decisions are made. To capture experiences and turn them into knowledge is fundamental in learning processes and knowledge development. Knowledge engineering and knowledge management have been subject for research for decades and several concepts about knowledge and knowledge transfer have been introduced, but a functional approach to exploit knowledge efficiently in manufacturing is still missing. In the era of Industry 4.0, humans and machines must be able to collaborate in such way that both can exploit the best abilities of each other in a manufacturing process. This paper introduces a procedural knowledge process (PKP) approach to capturing and defining unexpected events, while a process step is able to perform its required functions and transfer that information as machine-understandable knowledge about a failure mode. Function blocks (FBs), as per the IEC-61499 standard, have been proposed as a way to achieve distributed process planning in which the manufacturing process can adapt itself to runtime conditions, e.g. machine availability, etc. However, FBs are event-driven systems and the approach is limited to work under well-known runtime conditions, e.g. machine configurations and states, or deviations which are impossible to foresee in advance, for instance the outcome of a process failure mode effects analysis (PFMEA). The PKP introduced in this paper, aims at bridging this gap by integrating at runtime an expert operator’s solution based on root cause analysis (RCA) in an FB architecture, making the FB knowledge-driven systems, for further executions of the same without redesigning it. Natural language representations of procedural knowledge blocks (PKBs) allow to transfer procedural knowledge to human operators, i.e. explain the process flow of a machine decision, while machine representations of PKBs allow to embed procedural knowledge that is elicited from expert operators upon unexpected events into the FBs process. The resulting PKP enhances the FBs for smart industrial applications, such as the process planning use case described in this paper.

Parallel implementation of the Image Block Representation using OpenMP

Herein, a parallel implementation in OpenMP of the Image Block Representation (IBR) for binary imagesis investigated. The IBR is a region-based image representation scheme that represents the binary image as a set of non-overlapping rectangular areas with object level, called blocks. The IBR permits the execution of operations on image areas instead of image points and therefore leads to a substantial reduction of the required computational complexity. The experimental and the analytically derived results from parallel implementation in OpenMP, on a multicore computer, proved that a very good overall performance can be achieved.

Structural block driven enhanced convolutional neural representation for relation extraction

In this paper, we propose a novel lightweight relation extraction approach of structural block driven convolutional neural learning. Specifically, we detect the essential sequential tokens associated with entities through dependency analysis, named as a structural block, and only encode the block on a block-wise and an inter-block-wise representation, utilizing multi-scale Convolutional Neural Networks (CNNs). This is to (1) eliminate the noisy from irrelevant part of a sentence; meanwhile (2) enhance the relevant block representation with both block-wise and inter-block-wise semantically enriched representation. Our method has the advantage of being independent of long sentence context since we only encode the sequential tokens within a block boundary. Experiments on two datasets i.e., SemEval2010 and KBP37, demonstrate the significant advantages of our method. In particular, we achieve the new state-of-the-art performance on the KBP37 dataset; and comparable performance with the state-of-the-art on the SemEval2010 dataset.

Reversible causal graph dynamics: invertibility, block representation, vertex-preservation

Causal Graph Dynamics extend Cellular Automata to arbitrary time-varying graphs of bounded degree. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of symmetries: shift-invariance (it acts everywhere the same) and causality (information has a bounded speed of propagation). We add a further physics-like symmetry, namely reversibility. In particular, we extend two fundamental results on reversible cellular automata, by proving that the inverse of a causal graph dynamics is a causal graph dynamics, and that these reversible causal graph dynamics can be represented as finite-depth circuits of local reversible gates. We also show that reversible causal graph dynamics preserve the size of all but a finite number of graphs.

Propagator identities, holographic conformal blocks, and higher-point AdS diagrams

Conformal blocks are the fundamental, theory-independent building blocks in any CFT, so it is important to understand their holographic representation in the context of AdS/CFT. We describe how to systematically extract the holographic objects which compute higher-point global (scalar) conformal blocks in arbitrary spacetime dimensions, extending the result for the four-point block, known in the literature as a geodesic Witten diagram, to five- and six-point blocks. The main new tools which allow us to obtain such representations are various higher-point propagator identities, which can be interpreted as generalizations of the well-known flat space star-triangle identity, and which compute integrals over products of three bulk-to-bulk and/or bulk-to-boundary propagators in negatively curved spacetime. Using the holographic representation of the higher-point conformal blocks and higher-point propagator identities, we develop geodesic diagram techniques to obtain the explicit direct-channel conformal block decomposition of a broad class of higher-point AdS diagrams in a scalar effective bulk theory, with closed-form expressions for the decomposition coefficients. These methods require only certain elementary manipulations and no bulk integration, and furthermore provide quite trivially a simple algebraic origin of the logarithmic singularities of higher-point tree-level AdS diagrams. We also provide a more compact repackaging in terms of the spectral decomposition of the same diagrams, as well as an independent discussion on the closely related but computationally simpler framework over p-adics which admits comparable statements for all previously mentioned results.

On conformal blocks, crossing kernels and multi-variable hypergeometric functions

In this note, we present an alternative representation of the conformal block with external scalars in general spacetime dimensions in terms of a finite summation over Appell fourth hypergeometric function F4. We also construct its generalization to the non-local primary exchange operator with continuous spin and its corresponding Mellin representation which are relevant for Lorentzian spacetime. Using these results we apply the Lorentzian inversion formula to compute the so-called crossing kernel in general spacetime dimensions, the resultant expression can be written as a double infinite summation over certain Kampé de Fériet hypergeometric functions with the correct double trace operator singularity structures. We also include some complementary computations in AdS space, demonstrating the orthogonality of conformal blocks and performing the decompositions.

Structure and block representation for circulant quantum processes

We study a family of quantum Markov semigroups with circulant structure. We obtain a complete description of the spectral representation for the Lindbladian and, putting it together with some purely probabilistic properties of a classical associated process, we can study asymptotic properties, invariant states, quantum-detailed balance conditions and reducibility. In particular, in the reducible case, we can construct a generator on a lower-dimensional space which can fully describe the original circulant semigroup.

Representation of atmospheric blocking in the new global non-hydrostatic weather prediction model ICON

Representation of atmospheric blocking in the new global non-hydrostatic weather prediction model ICON

Block rank sparsity-aware DOA estimation with large-scale arrays in the presence of unknown mutual coupling

With the development of massive multiple-input mutiple-output (MIMO) technique, high-resolution direction-of-arrival (DOA) estimation has attracted great attention. A novel sparse signal reconstruction method based on the inherent block rank sparsity of the sub-matrix is proposed for high resolution DOA estimation with large-scale arrays under the condition of unknown mutual coupling. In the proposed method, by taking advantage of the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM), a novel block representation model is firstly formulated by parameterizing the steering vector. Then, exploiting the inherent block sparsity characteristics of the sub-matrix, a reweighted nuclear norm minimization algorithm is proposed to reconstruct the sparse matrix, in which the weighted matrix is designed by using the spectrum of MUSIC-Like algorithm. Finally, the DOAs are achieved by searching the non-zeros blocks of the recovered matrix. The proposed method not only makes full use of the block rank sparsity characteristics of the sub-matrix and weighted matrix for enhancing the sparse solution, but also avoids the array aperture loss. Thus, the proposed method has superior estimation performance than the state-of-the-art algorithms under the condition of unknown mutual coupling. Especially, in the case of large-scale antennas, the advantage of the proposed method is more obvious. Some computer simulation results are performed to verify the advantage of our proposed method.

Video intra prediction using convolutional encoder decoder network

Intra prediction is an effective method for video coding to remove the spatial redundancy of content. Classical intra prediction method usually creates a prediction block by extrapolating the encoded pixels surrounding the target block. However, existing methods cannot guarantee the prediction efficiency for rich textural structure, especially when weak spatial correlation exists between the target block and reference pixels. To remedy this issue, this paper proposes a novel intra prediction method via convolutional encoder-decoder network, which we term IPCED. IPCED can learn and extract the internal representation of reference blocks, and progressively generate a prediction block from this representation. IPCED is a data-driven method, which represents an improvement over hand-crafted methods, and is capable of improving the accuracy of intra prediction. Extensive experimental results demonstrate that IPCED can generate higher-quality intra prediction results, achieves 3.41%, 3.07% and 3.44% bitrate saving for the Y/Cb/Cr channel compared with HEVC baseline, which is significantly beyond existing methods.

Renormalization of gravitational Wilson lines

We continue the study of the Wilson line representation of conformal blocks in two-dimensional conformal field theory; these have an alternative interpretation as gravitational Wilson lines in the context of the AdS3/CFT2 correspondence. The gravitational Wilson line involves a path-ordered exponential of the stress tensor, and its expectation value can be computed perturbatively in an expansion in inverse powers of the central charge c. The short-distance singularities which occur in the associated stress tensor correlators require systematic regularization and renormalization prescriptions, whose consistency with conformal Ward identities presents a subtle problem. The regularization used here combines dimensional regularization and analytic continuation. Representation theoretic arguments, based on SL(2, ℝ) current algebra, predict an exact result for the Wilson line anomalous dimension and, by building on previous work, we verify that the perturbative calculations using our regularization and renormalization prescriptions reproduce the exact result to order 1/c3 included. We also discuss a related, but somewhat simpler, Wilson line in Wess-Zumino-Witten models that yields current algebra conformal blocks, and we emphasize the distinction between Wilson lines constructed out of non-holomorphic and purely holomorphic currents.

THE STUDY OF STATISTICAL PROPERTIES OF THE MODEL BLOCK REPRESENTATION FOR SET OF DESCRIPTORS OF KEY POINTS OF IMAGES

Context. The multidimensional nature of the processed data in modern computer vision systems requires new approaches to theconstruction of effective feature spaces that simplify processing by summarizing the available information. Structural methods ofimage recognition use descriptions of visual objects in the form of sets of key point descriptors as sets of numerical vectors of highdimension. The main tool for reducing the dimension is the presentation of data in the form of a system of their blocks and a statisticalstudy of such data structures, which in terms of recognition should display the generalized properties of an object as a set of itsfragments. In this connection, there is problem of studying the features of the applied application and the characteristics of the blockrepresentation model in the aspect of its use to determine the relevance of descriptions and classify data within the base of referenceimages.Objective. Perform statistical estimation of the importance of making classification decisions on the basis of the calculation ofthe relevance of object descriptions for the model of block representation of descriptors of key points of images.Method. Methods are proposed for distinguishing descriptions based on the application of the block representation model of thedata descriptors of key points of images using the criteria of mathematical statistics and information theory tools.Results. The main result of the article is the confirmation that the use of classical statistical criteria for analyzing empirical datain the form of structural descriptions of images makes it possible to determine the quality factor of the constructed feature space fordistinguishing visual objects when they are recognized in computer vision systems. The introduction of the block representationmodel and statistical analysis for the values of descriptors of key features of images contributes to the efficiency of the process ofrecognizing visual objects, which is confirmed by the improvement in the level of difference by increasing the fragment size in theconstructed description chain structure.Conclusions. The use of a variety of statistical criteria gave an identical effect on the significance of the differences in the empiricaldescriptions of visual objects in the constructed feature space, which underlines the objectivity of the study. The implementedmodel of block representation of data retains the distinguishing properties of a structural description with the effect of a significantimprovement in the speed of classification decision making.The scientific novelty of the study is the improvement and statistical substantiation of models for making decisions about theclass of visual objects based on the calculation of the relevance of their descriptions with references using a block representation ofdescriptors of key points of images.The practical significance of the work is confirming the advisability of introducing a block structure for the block description ofan object as an effective approach to solving the problem of recognition with examples of images for implementation in computervision systems.