Multi-Channel Local Binary Pattern Guided Convolutional Neural Network for Breast Cancer Classification

Background: The advancement in convolutional neural network (CNN) has reduced the burden of experts using the computer-aided diagnosis of human breast cancer. However, most CNN networks use spatial features only. The inherent texture structure present in histopathological images plays an important role in distinguishing malignant tissues. This paper proposes an alternate CNN network that integrates Local Binary Pattern (LBP) based texture information with CNN features. Methods: The study propagates that LBP provides the most robust rotation, and translation-invariant features in comparison with other texture feature extractors. Therefore, a formulation of LBP in context of convolution operation is presented and used in the proposed CNN network. A non-trainable fixed set binary convolutional filters representing LBP features are combined with trainable convolution filters to approximate the response of the convolution layer. A CNN architecture guided by LBP features is used to classify the histopathological images. Result: The network is trained using BreKHis datasets. The use of a fixed set of LBP filters reduces the burden of CNN by minimizing training parameters by a factor of 9. This makes it suitable for the environment with fewer resources. The proposed network obtained 96.46% of maximum accuracy with 98.51% AUC and 97% F1-score. Conclusion: LBP based texture information plays a vital role in cancer image classification. A multi-channel LBP futures fusion is used in the CNN network. The experiment results propagate that the new structure of LBP-guided CNN requires fewer training parameters preserving the capability of the CNN network’s classification accuracy.

Quantum Walks: Schur Functions Meet Symmetry Protected Topological Phases

This paper uncovers and exploits a link between a central object in harmonic analysis, the so-called Schur functions, and the very hot topic of symmetry protected topological phases of quantum matter. This connection is found in the setting of quantum walks, i.e. quantum analogs of classical random walks. We prove that topological indices classifying symmetry protected topological phases of quantum walks are encoded by matrix Schur functions built out of the walk. This main result of the paper reduces the calculation of these topological indices to a linear algebra problem: calculating symmetry indices of finite-dimensional unitaries obtained by evaluating such matrix Schur functions at the symmetry protected points $$\pm 1$$ ± 1 . The Schur representation fully covers the complete set of symmetry indices for 1D quantum walks with a group of symmetries realizing any of the symmetry types of the tenfold way. The main advantage of the Schur approach is its validity in the absence of translation invariance, which allows us to go beyond standard Fourier methods, leading to the complete classification of non-translation invariant phases for typical examples.

Frequency domain of weakly translation invariant frame MRAs

Frequency domain of bandlimited frame multiresolution analyses (MRAs) plays a key role when derived framelets are applied into narrow-band signal processing and data analysis. In this study, we give a characterization of frequency domain of weakly translation invariant frame scaling functions [Formula: see text] with frequency domain [Formula: see text]. Based on it, we further study convex and ball-shaped frequency domains. If frequency domain of bandlimited frame scaling function [Formula: see text] is convex and completely symmetric about the origin, then it must be weakly invariant and [Formula: see text]. If [Formula: see text] has a ball-shaped frequency domain, the ball radius must be bounded by [Formula: see text]. These frequency domain characters are owned uniquely by frame scaling functions and not by orthogonal scaling functions.

An Azimuth Signal-Reconstruction Method Based on Two-Step Projection Technology for Spaceborne Azimuth Multi-Channel High-Resolution and Wide-Swath SAR

Azimuth non-uniform signal-reconstruction is a critical step for azimuth multi-channel high-resolution wide-swath (HRWS) synthetic aperture radar (SAR) data processing. However, the received non-uniform signal has noise in the actual azimuth multi-channel SAR (MCSAR) operation, which leads to the serious reduction in the signal-to-noise ratio (SNR) of the results processed by a traditional reconstruction algorithm. Aiming to address the problem of reducing the SNR of the traditional reconstruction algorithm in the reconstruction of non-uniform signal with noise, a novel signal-reconstruction algorithm based on two-step projection technology (TSPT) for the MCSAR system is proposed in this paper. The key part of the TSPT algorithm consists of a two-step projection. The first projection is to project the given signal into the selected intermediate subspace, spanned by the integer conversion of the compact support kernel function. This process generates a set of sparse equations, which can be solved efficiently by using the sparse equation solver. The second key projection is to project the first projection result into the subspace of the known sampled signal. The secondary projection can be achieved with a digital linear translation invariant (LSI) filter and generate a uniformly spaced signal. As a result, compared with the traditional azimuth MCSAR signal-reconstruction algorithm, the proposed algorithm can improve SNR and reduce the azimuth ambiguity-signal-ratio (AASR). The processing results of simulated data and real raw data verify the effectiveness of the proposed algorithm.

Spectral Analysis of Translation-Invariant Mechanical Systems with Application to Structural Vibrations and Stability

The paper considers the problems and the methods of spectral analysis of elastic structural systems. The presented consideration focuses on the translation-invariant spectral formulations. Some periodic representations and the spectral decomposition are derived. In the context of general analysis of translation-invariant systems, the particular problems of structural vibration and stability are solved in analytical form.

Emergent fractal phase in energy stratified random models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between fully-localized Richardson’s model and the celebrated Rosenzweig-Porter model (with implemented translation-invariant symmetry). In order to do this, we propose the energy-stratified spectral structure of the hopping term allowing one to decrease the range of correlations gradually. We show both analytically and numerically that any deviation from the completely correlated case leads to the emergent non-ergodic delocalization in the system unlike the predictions of localization of cooperative shielding. In order to describe the models with correlated kinetic terms, we develop the generalization of the Dyson Brownian motion and cavity approaches basing on stochastic matrix process with independent rank-one matrix increments and examine its applicability to the above set of models.

On two reversible cellular automata with two particle species

We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P), and time-reversal (T) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the hydrodynamic prediction for the model with exactly three local charges. Surprisingly, the numerically observed 'sound velocity' does not match the hydrodynamic value. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.

Entanglement marginal problems

We consider the entanglement marginal problem, which consists of deciding whether a number of reduced density matrices are compatible with an overall separable quantum state. To tackle this problem, we propose hierarchies of semidefinite programming relaxations of the set of quantum state marginals admitting a fully separable extension. We connect the completeness of each hierarchy to the resolution of an analog classical marginal problem and thus identify relevant experimental situations where the hierarchies are complete. For finitely many parties on a star configuration or a chain, we find that we can achieve an arbitrarily good approximation to the set of nearest-neighbour marginals of separable states with a time (space) complexity polynomial (linear) on the system size. Our results even extend to infinite systems, such as translation-invariant systems in 1D, as well as higher spatial dimensions with extra symmetries.

Non-Hermitian Skin Custers from Strong Interactions

Strong, non-perturbative interactions often lead to new exciting physics, as epitomized by emergent anyons from the Fractional Quantum hall effect. Within the actively investigated domain of non-Hermitian physics, we discover a new family of states known as non-Hermitian skin clusters. Taking distinct forms as Vertex, Topological, Interface, Extended and Localized skin clusters, they generically originate from asymmetric correlated hoppings on a lattice, in the strongly interacting limit with quenched single-body energetics. Distinct from non-Hermitian skin modes which accumulate at boundaries, our skin clusters are predominantly translation invariant particle clusters. As purely interacting phenomena, they fall outside the purview of generalized Brillouin zone analysis, although our effective lattice formulation provides alternative analytic and topological characterization. Non-Hermitian skin clusters fundamentally originate from the fragmentation structure of the Hilbert space, and may thus be of significant interest in modern many-body contexts like the ETH and quantum scars.

Translation-Invariant Bipolarons and Charge Density Waves in High-Temperature Superconductors

A correlation is established between the theories of superconductivity based on the concept of charge density waves (CDWs) and the translation invariant (TI) bipolaron theory. It is shown that CDWs are originated from TI-bipolaron states in the pseudogap phase due to the Kohn anomaly and form a pair density wave (PDW) for wave vectors corresponding to nesting. Emerging in the pseudogap phase, CDWs coexist with superconductivity at temperatures below those of superconducting transition, while their wave amplitudes decrease as a Bose condensate is formed from TI bipolarons, vanishing at zero temperature.