Standard Matrix Research Articles

Nuclear norm regularized loop optimization for tensor network

We propose a loop optimization algorithm based on nuclear norm regularization for the tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to the standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, ] for the critical two-dimensional Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion. Published by the American Physical Society 2024

Clusters of African countries based on the social contacts and associated socioeconomic indicators relevant to the spread of the epidemic

IntroductionIt is well known that social contact patterns differ from country to country. This variation coincides with significant socioeconomic heterogeneity that complicates the design of effective nonpharmaceutical interventions. This study examined how socioeconomic heterogeneity in selected African countries might be factored in to explain better patterns of social contact mix between countries.MethodsWe used a standardized contact matrix for 32 African countries, estimated in (Prem et al. in PLoS Comput Biol 17(7):e1009098, 2021). We scaled the matrices using an epidemic model from (Röst et al. in Viruses 12(7):708, 2020). We also analyzed aggregated data from the World Bank country website. The data includes 28 variables; social, economic, environmental, institutional, governance, health and well-being, education, gender inequality, and other development-related indicators that describe countries. Principal component analysis was used to visualize socioeconomic similarities between countries and identify the indicators for maximum variation. The (2D)2PCA\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$(2D)^{2} PCA$\\end{document} approach was used to reduce the dimension of synthetic contact matrices for each country to avoid the dimensionality curse. Then, hierarchical aggregate clustering was used to identify groups of countries with similar social patterns, taking into account the country’s socioeconomic performance.ResultsOur model yielded four meaningful clusters, each with a few distinguishing features. Social contacts varied between groups, but were generally similar within each set. The socioeconomic performance of the country influenced the clusters.ConclusionsOur results suggest that integrating socioeconomic factors into social contacts can better explain infectious disease transmission dynamics and that similar interventions can be implemented in countries within the cluster

Implementation of a Standardized Tool for Root Cause Analysis Selection.

This study sought to determine if a standardized root cause analysis (RCA2) selection algorithm, developed by the Veterans Affairs, would select high-risk events for RCA. Physician-entered incident reports for all surgical service admissions and perioperative visits were queried over 12 months in the DATIX Clinical Incident Management System. Independent reviewers assigned potential harm and event frequency scores using an institutional scoring system and then calculated and rounded average scores. These were classified using RCA2 terminology (catastrophic, major, moderate, minor for harm; frequent, occasional, uncommon, remote for frequency). The scores were then evaluated with the standardized Safety Assessment Code Matrix (SAC) algorithm from the National Patient Safety Foundation's RCA2 guidelines to determine Potential Harm Scores. The SAC combines severity and probability to determine the necessity of conducting an RCA. Catastrophic and major high-frequency events (matrix score = 3) were classified as "RCA recommended." The study then compared cases selected for RCAs using the updated RCA2 algorithm against cases selected using a current, institutional-specific RCA selection process. One hundred four cases were reviewed, comprising 20 catastrophic, 48 major harm, 26 moderate harm, and 10 minor harm events. After removing 9 high-variance cases, our institution's current selection process selected 18 cases for RCAs, including 6/20 catastrophic, 8/39 major harm, and 4/36 moderate/minor harm events. Only 17.3% of cases had an RCA completed, while the standardized RCA2 algorithm recommended investigation for 56.7% of patient safety events, based on SAC Matrix scoring. Current RCA selection processes rendered 4 RCAs on low potential harm or low-frequency events, while 45 potential high-frequency, high potential harm events did not complete RCAs. Standardizing the selection of patient safety incidents for RCA using the RCA2 algorithm improves case identification based on the event frequency and potential harm score. Thus, this algorithm has the potential to advance patient safety.

Constraining non-unitary neutrino mixing using matter effects in atmospheric neutrinos at INO-ICAL

The mass-induced neutrino oscillation is a well established phenomenon that is based on the unitary mixing among three light active neutrinos. Remarkable precision on neutrino mixing parameters over the last decade or so has opened up the prospects for testing the possible non-unitarity of the standard 3ν mixing matrix, which may arise in the seesaw extensions of the Standard Model due to the admixture of three light active neutrinos with heavy isosinglet neutrinos. Because of this non-unitary neutrino mixing (NUNM), the oscillation probabilities among the three active neutrinos would be altered as compared to the probabilities obtained assuming a unitary 3ν mixing matrix. In such a NUNM scenario, neutrinos can experience an additional matter effect due to the neutral current interactions with the ambient neutrons. Atmospheric neutrinos having access to a wide range of energies and baselines can experience a significant modifications in Earth’s matter effect due to NUNM. In this paper, we study in detail how the NUNM parameter α32 affects the muon neutrino and antineutrino survival probabilities in a different way. Then, we place a comparable and complementary constraint on α32 in a model independent fashion using the proposed 50 kt magnetized Iron Calorimeter (ICAL) detector under the India-based Neutrino Observatory (INO) project, which can efficiently detect the atmospheric νμ and ν¯μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\overline{\ u}}_{\\mu } $$\\end{document} separately in the multi-GeV energy range. Further, we discuss the advantage of charge identification capability of ICAL and the impact of uncertainties in oscillation parameters while constraining α32. We also compare the α32 sensitivity of ICAL with that of future long-baseline experiments DUNE and T2HK in isolation and combination.

Controller switching with the anti-bump adapter

Switching on a new or retuned controller while keeping the control loop engaged tends to generate transient “bumps” in the commands and plant outputs. For a linear time-invariant (LTI) controller in state–space form, these bumps can be mitigated or even suppressed by resetting the controller state to an appropriate non-zero value adapted to the pre-switching trajectories of the feedback loop signals. This paper proposes a simple way to compute this adapted controller state by minimizing the difference between the commands actually applied immediately before switching and the virtual command trajectory which the new controller would have generated if it had been activated in parallel. This adapted state can be recursively computed as the output of an LTI system in standard state–space form, the anti-bump adapter. Computing the anti-bump adapter involves only standard matrix algebra and control concepts (e.g., observability and controllability matrices/Gramians). Calculations are very simple and can be translated into compact computer code. This bump suppression procedure is applicable to any discrete-time or continuous-time LTI SISO or MIMO controller, without any assumption on or knowledge of either the previously active controller or the plant. Illustrative applications to continuous-time and discrete-time switching problems and a Matlab® code for computing the anti-bump adapter are presented.

Quantification of mycolic acids in different mycobacterial species by standard addition method through liquid chromatography mass spectrometry

Mycobacteria possess unique and robust lipid profile responsible for their pathogenesis and drug resistance. Mycolic acid (MA) represents an attractive diagnostic biomarker being absent in humans, inert and known to modulate host-pathogen interaction. Accurate measurement of MA is significant to design efficient therapeutics. Despite considerable advances in Liquid chromatography coupled with tandem mass spectrometry (LC–MS/MS) based approaches, quantification of mycobacterial lipids including MA is still challenging mainly because of ion suppression effects due to complex matrix and non-availability of suitable internal standards for MA. The current study demonstrates the use of standard addition method (SAM) to circumvent this problem and provides a reliable and exhaustive analytical method to quantify mycobacterial MA based on reversed-phase ultra-high-performance liquid chromatography- mass spectrometry data acquisition. In this method, multiple reaction monitoring (MRM) has been applied, wherein 16 MRM channels or transitions have been chosen for quantification of alpha-, methoxy- and keto-MAs with C-24 and C-26 hydrocarbon chains that are actually best suited for TB diagnostics. We found that the overall methodological limit of detection and limit of quantification were in the range 0.05–0.71 ng/µl and 0.16–2.16 ng/µl. Taken together, SAM quantitative technique could serve as promising alternative for relative concentration determination of MA to aid medical research.

Enabling 3D bioprinting of cell-laden pure collagen scaffolds via tannic acid supporting bath.

The fabrication of cell-laden biomimetic scaffolds represents a pillar of tissue engineering and regenerative medicine (TERM) strategies, and collagen is the gold standard matrix for cells to be. In the recent years, extrusion 3D bioprinting introduced new possibilities to increase collagen scaffold performances thanks to the precision, reproducibility, and spatial control. However, the design of pure collagen bioinks represents a challenge, due to the low storage modulus and the long gelation time, which strongly impede the extrusion of a collagen filament and the retention of the desired shape post-printing. In this study, the tannic acid-mediated crosslinking of the outer layer of collagen is proposed as strategy to enable collagen filament extrusion. For this purpose, a tannic acid solution has been used as supporting bath to act exclusively as external crosslinker during the printing process, while allowing the pH- and temperature-driven formation of collagen fibers within the core. Collagen hydrogels (concentration 2-6mg/mL) were extruded in tannic acid solutions (concentration 5-20mg/mL). Results proved that external interaction of collagen with tannic acid during 3D printing enables filament extrusion without affecting the bulk properties of the scaffold. The temporary collagen-tannic acid interaction resulted in the formation of a membrane-like external layer that protected the core, where collagen could freely arrange in fibers. The precision of the printed shapes was affected by both tannic acid concentration and needle diameter and can thus be tuned. Altogether, results shown in this study proved that tannic acid bath enables collagen bioprinting, preserves collagen morphology, and allows the manufacture of a cell-laden pure collagen scaffold.

A rapid and reliable targeted LC-MS/MS method for quantitative analysis of the Tryptophan-NAD metabolic network disturbances in tissues and blood of sleep deprivation mice

BackgroundTRY-NAD metabolic network includes TRY (tryptophan), 5-HT (5-hydroxytryptamine), KYN (kynurenine), and NAD (nicotinamide adenine dinucleotide) pathway, which plays a significant role in neurological diseases and ageing. It is important to monitor these metabolites for studying the pathological anatomy of disease and treatment of responses evaluation. Although previous studies have reported quantitative methods for several metabolites in the network, the bottlenecks of simultaneously quantifying the whole metabolic network are their similar structures, diverse physico-chemical properties, and instability. Standardized protocols for the whole metabolic network are still missing, which hinders the in-depth study of TRY-NAD metabolic network in laboratory research and clinical screening. ResultsWe developed a LC-MS/MS method for quantifying 28 metabolites in the TRY-NAD network simultaneously. Optimization was done for the mass spectral parameters, chromatographic conditions and sample pretreatment process. The developed method was fully validated in terms of standard curves, sensitivity, carryover, recovery, matrix effect, accuracy, precision, and stability. The pretreatment of 30 samples only takes 90 min, and the LC-MS/MS running time of one sample is only 13 min. With this method, we bring to light the chaos of global TRY-NAD metabolic network in sleep deprivation mice for the first time, including serum, clotted blood cells, hippocampus, cerebral cortex, and liver. NAD pathway levels in brain and blood decreased, whereas the opposite happened in the liver. The 5-HT pathway decreased and the concentration of KYN increased significantly in the brain. The concentration of many metabolites in KYN pathway (NAD+ de novo synthesis pathway) increased in the liver. SignificanceThis method is the first time to determine the metabolites of KYN, 5-HT and NAD pathway at the same time, and it is found that TRY-NAD metabolic network will be disordered after sleep deprivation. This work clarifies the importance of the pH of the extraction solution, the time and temperature control in pretreatment in standardized protocols building, and overcoming the problems of inconsistent sample pretreatment, separation, matrix effect interference and potential metabolite degradation. This method exhibits great prospects in providing more information on metabolic disturbances caused by sleep deprivation as well as neurological diseases and ageing.

Microscopic instabilities in single crystal matrix composites

A finite strain micromechanical analysis is presented for the prediction of the loss of microscopic stability of a class of metal matrix composites that are subjected to axial compressive loading and undergoing large deformations. The metallic constituent behavior is modeled by the single crystal anisotropic plasticity theory in which, due to the resolved shear stresses, plastic deformations occur along certain pre-defined slip planes. Thus, this incremental plasticity theory is capable of providing the effect of the applied axial loading on the induced shear stresses which dominate the microbuckling. The composites are assumed to possess slight imperfections at the interfaces, and in order to satisfy the interfacial conditions, a perturbation expansion is employed which yields zero and first order micromechanical analysis problems. The zero order problem corresponds to the micromechanical modeling of the composite with no imperfections, whereas the solution of the first order problem is utilized to obtain the critical stresses and deformations at which bifurcation buckling occurs. Both problems are solved by employing the finite strain high-fidelity generalized method of cells (HFGMC) micromechanics. Applications are given for various types of single crystal matrix composites including layered, particulate, continuous and short fiber composites. Finally, a comparison between the compressive strengths of a standard metal matrix boron/aluminum and SiC/single crystal composites is presented and discussed.

Emotion recognition of EEG signals based on contrastive learning graph convolutional model.

Electroencephalogram (EEG) signals offer invaluable insights into the complexities of emotion generation within the brain. Yet, the variability in EEG signals across individuals presents a formidable obstacle for empirical implementations. Our research addresses these challenges innovatively, focusing on the commonalities within distinct subjects' EEG data.We introduce a novel approach named Contrastive Learning Graph Convolutional Network (CLGCN). This method captures the distinctive features and crucial channel nodes related to individuals' emotional states. Specifically, CLGCN merges the dual benefits of Contrastive Learning's synchronous multisubject data learning and the Graph Convolutional Network's proficiency in deciphering brain connectivity matrices.Understanding multifaceted brain functions and their information interchange processes is realized as CLGCN generates a standardized brain network learning matrix during a dataset's learning process. Our model significantly streamlines the retraining process for new subjects, requiring only 5% of the initial sample size for fine-tuning to attain a remarkable 92.8% accuracy rate. Additionally, our model has undergone extensive testing on the DEAP and SEED datasets, demonstrating the effectiveness of our model.&#xD.

Efficient Mixed-Precision Matrix Factorization of the Inverse Overlap Matrix in Electronic Structure Calculations with AI-Hardware and GPUs.

In recent years, a new kind of accelerated hardware has gained popularity in the artificial intelligence (AI) community which enables extremely high-performance tensor contractions in reduced precision for deep neural network calculations. In this article, we exploit Nvidia Tensor cores, a prototypical example of such AI-hardware, to develop a mixed precision approach for computing a dense matrix factorization of the inverse overlap matrix in electronic structure theory, S-1. This factorization of S-1, written as ZZT = S-1, is used to transform the general matrix eigenvalue problem into a standard matrix eigenvalue problem. Here we present a mixed precision iterative refinement algorithm where Z is given recursively using matrix-matrix multiplications and can be computed with high performance on Tensor cores. To understand the performance and accuracy of Tensor cores, comparisons are made to GPU-only implementations in single and double precision. Additionally, we propose a nonparametric stopping criteria which is robust in the face of lower precision floating point operations. The algorithm is particularly useful when we have a good initial guess to Z, for example, from previous time steps in quantum-mechanical molecular dynamics simulations or from a previous iteration in a geometry optimization.

Infrared finite scattering theory: scattering states and representations of the BMS group

Any non-trivial scattering with massless fields in four spacetime dimensions will generically produce an “out” state with memory which gives rise to infrared divergences in the standard S-matrix. To obtain an infrared-finite scattering theory, one must suitably include states with memory. However, except in the case of QED with massive charged particles, asymptotic states with memory that have finite energy and angular momentum have not been constructed for more general theories (e.g. massless QED, Yang-Mills and quantum gravity). To this end, we construct direct-integral representations over the “Lorentz orbit” of a given memory and classify all “orbit space representations” that have well-defined energy and angular momentum. We thereby provide an explicit construction of a large supply of physical states with memory as well as the explicit action of the BMS charges all states. The construction of such states is a key step toward the formulation of an infrared-finite scattering theory. While we primarily focus on the quantum gravitational case, we outline how the methods presented in this paper can be applied to obtain representations of the Poincaré group with memory for more general quantum field theories.

Kaon mixing beyond the standard model with physical masses

We present nonperturbative results for beyond the standard model kaon mixing matrix elements in the isospin symmetric limit (mu=md) of QCD, including a complete estimate of all dominant sources of systematic error. Our results are obtained from numerical simulations of lattice QCD with Nf=2+1 flavors of dynamical domain wall fermions. For the first time, these quantities are simulated directly at the physical pion mass mπ∼139 MeV for two different lattice spacings. We include data at three lattice spacings in the range a=0.11–0.07 fm and with pion masses ranging from the physical value up to 450 MeV. Compared to our earlier work, we have added both direct calculations at physical quark masses and a third lattice spacing making the removal of discretization effects significantly more precise and eliminating the need for any significant mass extrapolation beyond the range of simulated data. We renormalize the lattice operators nonperturbatively using RI-SMOM off-shell schemes. These schemes eliminate the need to model and subtract nonperturbative pion poles that arises in the RI-MOM scheme and, since the calculations are performed with domain wall fermions, the unphysical mixing between chirality sectors is suppressed. Our results for the bag parameters in the MS¯ scheme at 3 GeV are BK≡B1=0.5240(17)(54), B2=0.4794(25)(35), B3=0.746(13)(17), B4=0.897(02)(10) and B5=0.6882(78)(94), where the first error is from lattice uncertainties and the second is the uncertainty due to the perturbative matching to MS¯. Published by the American Physical Society 2024

Reaching the precision limit with tensor-based wavefront shaping

Perturbations in complex media, due to their own dynamical evolution or to external effects, are often seen as detrimental. Therefore, a common strategy, especially for telecommunication and imaging applications, is to limit the sensitivity to those perturbations in order to avoid them. Here, instead, we consider enhancing the interaction between light and perturbations to produce the largest change in the output intensity distribution. Our work hinges on the use of tensor-based techniques, presently at the forefront of machine learning explorations, to study intensity-based measurements where its quadratic relationship to the field prevents the use of standard matrix methods. With this tensor-based framework, we can identify the maximum-information intensity channel which maximizes the change in its output intensity distribution and the Fisher information encoded in it about a given perturbation. We further demonstrate experimentally its superiority for robust and precise sensing applications. Additionally, we derive the appropriate strategy to reach the precision limit for intensity-based measurements, leading to an increase in Fisher information by more than four orders of magnitude compared to the mean for random wavefronts when measured with the pixels of a camera.

Gauged permutation invariant matrix quantum mechanics: partition functions

The Hilbert spaces of matrix quantum mechanical systems with N × N matrix degrees of freedom X have been analysed recently in terms of SN symmetric group elements U acting as X → UXUT. Solvable models have been constructed uncovering partition algebras as hidden symmetries of these systems. The solvable models include an 11-dimensional space of matrix harmonic oscillators, the simplest of which is the standard matrix harmonic oscillator with U(N) symmetry. The permutation symmetry is realised as gauge symmetry in a path integral formulation in a companion paper. With the simplest matrix oscillator Hamiltonian subject to gauge permutation symmetry, we use the known result for the micro-canonical partition function to derive the canonical partition function. It is expressed as a sum over partitions of N of products of factors which depend on elementary number-theoretic properties of the partitions, notably the least common multiples and greatest common divisors of pairs of parts appearing in the partition. This formula is recovered using the Molien-Weyl formula, which we review for convenience. The Molien-Weyl formula is then used to generalise the formula for the canonical partition function to the 11-parameter permutation invariant matrix harmonic oscillator.

Glass fibre hybridization to improve the durability of circular flax fibre reinforced composites with off-the-shelf recyclable polymer matrix systems for large scale structural applications

Natural fibre composites (NFCs) are not durable in the long run because of the susceptibility of natural fibres to environmental conditions and specifically moisture. Hybridizing NFC laminates externally, with synthetic fibre reinforcements, may improve durability, due to their inherent environmental resistance. This work aims to investigate the effects of glass hybridization, on flax fibre composites, studied via accelerated ageing. In specific, the durability of hybrid flax/glass fibre reinforced polymer composites, with two recyclable polymer matrices was investigated. Unidirectional (UD) flax and UD glass fibre reinforcements were employed to fabricate laminates, with two fully-recyclable off-the-shelf resin systems, as matrix: (i) a bio-based epoxy resin and (ii) an acrylic liquid thermoplastic (Elium®). In addition, a standard petroleum-based epoxy polymer matrix was for reference purposes. Weathering and hygrothermal ageing were used to test the durability of coupons, exposed to UV radiation/condensation/water spray environment (weathering ageing), and full-immersion in distilled water at 23, 40, and 60°C (hygrothermal ageing). In all cases, ageing was performed for a total duration of 56 days. The performance of the unaged and aged composite coupons was assessed and compared in terms of flexural and viscoelastic performance as well as SEM (Scanning Electron Microscopy) analysis. It was revealed that the addition of glass fibres with flax fibres in the hybrid composites improves the performance and better resistance against ageing environments than their neat flax fibre composites.

Deep Learning-Driven Compiler Enhancements for Efficient Matrix Multiplication

Matrix multiplication is a fundamental operation in many computational fields, requiring optimization to handle increasing data sizes efficiently. In this paper, the implementation of Deep Learning in Matrix multiplication is reviewed, which is considered important nowadays due to the growing complexity of matrix multiplication for gaming and complex programs. The current standard matrix multiplication and the time taken by it on different matrix sizes are described. The Tiled Matrix multiplication, which trims the matrix into various pieces and calculates the product for each piece, and thereafter combines the result, is also described. The times taken by both methods for different matrix sizes were compared. The main idea was to use Deep Neural Networks (DNN) to compare and rank code variants that are obtained in pieces and determine their relative performance. A tournament-based ranking system is used for assigning ranks to the code versions. The effectiveness of these techniques was evaluated on various matrix multiplication operations commonly found in deep learning workloads. Up to 8.844x speedup over the naive implementation for a matrix size of 1024 is achieved by this approach. The results demonstrate the effectiveness of combining compiler optimization techniques and deep learning models in optimizing matrix multiplication.

Mutual incidence matrix of two balanced incomplete block designs

AbstractWe propose to consider a mutual incidence matrix of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all eigenvalues of the matrices and and their eigenspaces.

An effective Hamiltonian for the simulation of open quantum molecular systems

We discuss the derivation of an effective Hamiltonian for open quantum many-particle systems. The aim is to define an operator that can be used for (molecular) simulations where, through the exchange of energy and matter with the surrounding environment (reservoir), the number of particles, n, becomes a variable of the problem. The Hamiltonian is formally derived from the Von Neumann equation; specifically, we derive an n-hierarchy of equations for the density matrix, ρ^n , for near equilibrium situations. Such a hierarchy, in case of stationary equilibrium, delivers the standard grand canonical density matrix as it would be expected. We report that a similar Hamiltonian was conjectured, from empirical considerations, in the field of superconductivity. Thus our result also provide a formal basis for this long-standing hypothesis. Finally, an application is discussed for Path Integral simulations of molecular systems.

Dissipativity-based robust filter design for singular fuzzy systems with dynamic quantization and event-triggered mechanism

This paper focus on the design issue of event-based dissipative filter for quantized nonlinear singular systems. To save the communication resource, we employ a dynamic quantizer to quantized the measurement output signal prior to transmitting it to the filter via digital communication. Furthermore, the paper also presents an event-triggered mechanism for determining the transmission of the quantized signal. The intention of this paper is to try to propose an event-triggered filter to ensure that the filtering error system (FES) is admissible and satisfies strictly dissipativity performance, in the presence of dynamic quantization and occurring uncertainties. The Lyapunov function is utilized to establish a sufficient condition for the FES to meet the strictly dissipative performance. Depending on the obtained conditions, the required filter parameters are proposed using the standard linear matrix inequality (LMI) technique. Ultimately, the effectiveness of the developed method is verified by an actual circuit simulation.