Matrix Model Research Articles

Baby universe operators in the ETH matrix model of double-scaled SYK

We consider the baby universe operator Ba\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{B}}_a $$\\end{document} in the double-scaled SYK (DSSYK) model, which creates a baby universe of size a. We find that Ba\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{B}}_a $$\\end{document} is written in terms of the transfer matrix T, and vice versa. In particular, the identity operator on the chord Hilbert space is expanded as a linear combination of Ba\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{B}}_a $$\\end{document}, which implies that the disk partition function of DSSYK is written as a linear combination of trumpets. We also find that the thermofield double state of DSSYK is generated by a pair of baby universe operators, which corresponds to a double trumpet. This can be thought of as a concrete realization of the idea of ER=EPR.

On the ratio of extremal eigenvalues of 𝛽-Laguerre ensembles

Classical β \beta -Laguerre ensembles consist of three special matrix models taking the form X X T \mathbf {X}\mathbf {X}^T with X \mathbf {X} denoting a random matrix having i.i.d. entries being real ( β = 1 \beta =1 ), complex ( β = 2 \beta =2 ) or quaternion ( β = 4 \beta =4 ) normal distribution. It had been actually believed that no other choice of β > 0 \beta >0 (besides 1 , 2 1,2 and 4 4 ) would correspond to a matrix model X β X β T \mathbf {X}_\beta \mathbf {X}_\beta ^T which can be constructed with entries from a classical distribution until the work done by Dumitriu and Edelman in 2002. Since then the spectral properties of general β \beta -Laguerre ensembles have been extensively studied dealing with both the bulk case (involving all the eigenvalues) and the extremal case (addressing the (first few) largest and smallest eigenvalues). However, the ratio of the extremal eigenvalues (equivalently the condition number of X β \mathbf {X}_\beta ) has not been well explored in the literature. In this paper, we study such ratio in terms of large deviations.

First Principles Numerical Demonstration of Emergent Decoherent Histories

Within the histories formalism the decoherence functional is a formal tool to investigate the emergence of classicality in isolated quantum systems, yet an explicit evaluation of it from first principles has not been reported. We provide such an evaluation for up to five-time histories based on exact numerical diagonalization of the Schrödinger equation. We find a robust emergence of decoherence for slow and coarse observables of a generic random matrix model and extract a finite-size scaling law by varying the Hilbert space dimension over 4 orders of magnitude. Specifically, we conjecture and observe an exponential suppression of coherent effects as a function of the particle number of the system. This suggests a solution to the preferred basis problem of the many-worlds interpretation (or the set selection problem of the histories formalism) within a minimal theoretical framework without relying on environmentally induced decoherence, quantum Darwinism, Markov approximations, low-entropy initial states, or ensemble averages. Published by the American Physical Society 2024

Formulation of perfect-crystal diffraction from Takagi-Taupin equations: numerical implementation in the crystalpy library.

The Takagi-Taupin equations are solved in their simplest form (zero deformation) to obtain the Bragg-diffracted and transmitted complex amplitudes. The case of plane-parallel crystal plates is discussed using a matrix model. The equations are implemented in an open-source Python library crystalpy adapted for numerical applications such as crystal reflectivity calculations and ray tracing.

The hazard analysis of passenger-cargo ferries: a revised risk matrix model based on fuzzy best-worst method.

Improving hazards in maritime transport is essential to maintain the reliability and sustainability of the industry, ensure safety and security, and support global trade and economic growth. This paper is aimed at analyzing the hazards of passenger-cargo ferries (PCFs). The novelty of this paper is fourfold: (1) developing a revised risk matrix (RRM) model with considering the adaptability-based resilience of organization to assess PCFs' hazards, (2) identifying risk factors (RFs) in ferry navigation and developing adaptive strategies to mitigate hazards, (3) applying the fuzzy best-worst method (BWM) to determine the RFs' weight, and (4) employing the leading Taiwanese passenger-cargo ferry operator (the Taiwan-ferries case) as an empirical study to verify the proposed model. The empirical result can provide pragmatic information for ferry operators to improve the safety of their ferry navigations. Additionally, the proposed RRM model can provide a methodological reference for related research in hazard management.

Comparative Analysis of the Markowitz Model and the Kraljic Matrix Model in Portfolio Optimization and Procurement Management

This research studied two important models of portfolio management: the Markowitz model and the Kraljic Matrix Model. The Markowitz model is the basis of modern portfolio theory and is designed to optimise asset allocation by minimising risk while maximising returns. This paper provides a system to build a balanced portfolio by utilising diversity. On the other hand, the Kraljic Matrix Model classifies products based on supply risk and profit impact and provides a strategic tool for purchasing management. This model categorises products into four categories: noncritical, leverage, strategy, and bottleneck to support informed purchasing decisions. Despite its usefulness, the Kraljic matrix has been criticised for not taking into account the supplier’s perspective and for not providing guidelines for managing the movement of goods within the matrix. This paper studies the application and limitation of the two models, emphasises the need to adapt to the strategy in the portfolio and procurement management, and adjust according to the market dynamics.

Organizational health literacy in hospitals and primary health care - developing innovative tools

Abstract Background Organizational health literacy (OHL), particularly in health systems, is vital for supporting public health. Self-assessment tools (SAT), critical for quality assessment/improvement and for empowering relevant stakeholders, could support hospitals and primary healthcare services to promote their role in health literacy responsiveness, and support organizations in identifying strengths and areas of improvement. Methods The SAT for OHL in hospitals (OHL-Hos) and in primary healthcare (OHL-PHC) were developed via a participatory process, based on the “Vienna Concept of a Health Literate Healthcare Organization”. Piloting of the tools in European countries shed light on the tools’ depth and the need for revision. The development of short versions followed a Delphi process with experts from ten to thirteen European countries, respectively, from December 2023 - April 2024. Healthcare service diversity within and between countries was taken into consideration as well as cultural/language adaptation. Shortening OHL-Hos followed four steps: 1) prioritization of the most relevant indicators, 2) considering additional resources, 3) consensus process, 4) refinement of the tool and wording. Results The SATs for both healthcare settings are now established. The SAT for OHL-Hos includes a matrix model of eight standards, 21 sub-standards and 75 indicators. The SAT for OHL-PHC includes seven standards, 19 sub-standards and 69 indicators, covering OHL in organizational structures and processes for staff, patients and the community served with specific focus on navigation, communication, and participation. Both SATs are accompanied by a guide to direct organizations through in the self-assessment process. Conclusions The process of identifying OHL needs and opportunities in the health system, facilitated by participatory methods for tool development, led to innovative SATs for OHL which are currently ready for piloting and implementation in European countries.

Achieving bifacial photovoltaic performance in PTB7-based organic solar cell by integrating transparent contact for emerging semi-transparent applications

In this study, the design, fabrication and detailed analysis of semi-transparent bifacial organic solar cells (ST-OSC) based on MoO3/Ag/WO3 (10/dm/dod nm) dielectric/metal/dielectric (DMD) transparent contact system integrated with PTB7 polymer were investigated. The study emphasizes the importance of designing transparent contact systems to optimize the solar cells’ transparency (average visible transmittance, AVT), color rendering (color rendering index, CRI), efficiency (power conversion efficiency, PCE), and bifaciality. The performance of three distinct configurations was examined in the AVTmax (47.14% AVT, 3.93% PCE), (CRIext)max (23.82% AVT, 6.21% PCE), and Extreme Color (26.34% AVT, 5.81% PCE). The theoretically predicted AVTs for these configurations were 48.75%, 22.29%, and 25.15%, respectively. The strong agreement between theoretical and observed outcomes confirmed the accuracy of the Transfer Matrix Model (TMM). Furthermore, the assessment of bifaciality performance exhibited that the AVTmax had a bifaciality factor of 0.94, with a PCE of 3.67% under top illumination and 3.93% under bottom illumination. The high bifaciality of the structure designed with TMM to maximize the AVT demonstrates the value of calculations prior to solar cell structure fabricating and the possibility of constructing high bifaciality structures using this technique.

Wear studies on friction stir processed surface modified AZ61 magnesium alloy with nano titanium oxide

ABSTRACT Surface modification of magnesium alloy enables the improvement of wear characteristics for use in sliding applications and places where surface hardness improvement is essential without affecting the microstructure of the underneath material. In this study, a pin-on disc wear test was used to examine the dry sliding wear behaviour of AZ61 Mg alloy reinforced with nTiO2 by a recursive friction stir processing technique. The trio-behavior of the surface-modified Mg alloy was detailed by the response surface methodology-central composite design matrix with the use of design experiments, considering three levels of reinforcement (%), sliding speed, and axial load parameters. In order to achieve the desired results of minimal wear loss, lower friction coefficient (COF), and lower friction force between surfaces (FF), this present work employed design expert software to develop a generative mathematical model to optimize the process parameters. Wear mechanisms were investigated using images captured by scanning electron microscope.

Jackiw-Teitelboim gravity as a noncritical string

Jackiw Teitelboim (JT) gravity has proven to be an excellent tool for investigating aspects of quantum gravity and black hole physics. In recent years, the study of JT gravity and its deformations has helped us learn about the different contributions of geometries in the gravitational path integral, the quantum gravity Hilbert space, the space-time factorization problem, the role of averaging in holography, the black hole information paradox, and the matrix models. All this motivates the exploration of the JT gravity in different setups, with and without matter. Here, we consider JT gravity conformally coupled to Liouville field theory and matter fields. This model admits to be interpreted as a noncritical string theory on a linear dilaton background with a tachyonic Liouville potential along a null direction. The constant curvature constraint of JT gravity results in a neutralization of the Liouville mode, which makes it possible to compute the four-point correlation function of the theory analytically. Here we give the explicit derivation of the four-point function and briefly comment on its properties, such as monodromy invariance, crossing symmetry, factorization, and limits. Published by the American Physical Society 2024

Towards bootstrapping F-theory

We consider type IIB string theory with N D3 branes and various configurations of sevenbranes, such that the string coupling gs is fixed to a constant finite value. These are the simplest realizations of F-theory, and are holographically dual to rank N Argyres-Douglas conformal field theories (CFTs) with SU(2) and SU(3) flavor groups, and Minahan-Nemeschansky CFTs with E6, E7 and E8 flavor groups. We use the Seiberg-Witten curves of these theories to compute the mass deformed sphere free energy F (m) at large N in terms of novel matrix models with non-polynomial potentials. We show how F (m) can be used along with the analytic bootstrap to fix the large N expansion of flavor multiplet correlators in these CFTs, which are dual to scattering of gluons on AdS5 × S3, and in the flat space limit determine the effective theory of sevenbranes in F-theory. As a first step in this program, we use the matrix models to compute the log N term in F (m) and thereby fix the logarithmic threshold in the AdS5 × S3 holographic correlator, which matches the flat space prediction.

Efficient algorithm for thermal nondestructive testing and evaluation by considering the heteroscedastic nature of noise sources in infrared thermography

Abstract Thermal Imaging is a promising Non Destructive Testing & Evaluation (NDT & E) approach to monitor the health
of composite materials. Among various post processing approaches adopted in thermal imaging for NDT & E, statistical
analysis schemes gained importance due to their reliability and data reduction capabilities. This paper provides an insight
to a factor analysis-based statistical approach to detect the hidden defects in the Glass Fiber Reinforced Polymer (GFRP)
sample. The proposed approach models the observed data covariance into combination of temporal signal covariance
and noise covariance matrices. The modeling of the diagonal covariance matrix (with different elements) is motivated by
the presence of heterogeneity in the experimental data obtained from GFRP sample. This novel method is based on the
coordinate descent technique, which estimates the covariance matrix of the noise variances iteratively by minimizing the
negative log likelihood function. The obtained results from the chosen GFRP samples compared with the widely used
statistical Principal Component Thermography (PCT) technique illustrate the improved performance in terms of defect
detection with the proposed technique.

Spatiotemporal patterns and factors influencing metro ridership of people with disabilities

Rail transit’s safety and convenience have made it a preferred option for people with disabilities. In this study, utilizing the geographically weighted regression based on the network weight matrix (NWM GWR) model, we investigated the spatiotemporal patterns and influencing factors of metro ridership among this group in Nanjing, China. Our findings revealed significant fluctuations in metro ridership across seasons, with a decrease observed during summer. We also discovered that people with disabilities had evening peak hours one hour earlier than regular peak hours on weekdays, while weekends did not exhibit a significant peak. Geographically, metro trips of individuals with disabilities were concentrated in Old City and Main City. Furthermore, the results revealed that except distance to CBD and access to barrier-free facilities, the other factors positively influenced weekday and weekend ridership of people with disabilities. These insights provide valuable guidance for enhancing the mobility and accessibility of people with disabilities.

Optimal TIG Welding Parameters of Dissimilar Aluminum Alloys 7075 and Al 6061 Using Ultrasonic Vibration and Nanocomposite Filler (Al 5356/ZrB2) to Alleviate Hot Cracking Phenomenon

Abstract In this study, the welding of dissimilar aluminum alloys, Al 7075 and Al 6061, was investigated using Al 5356 filler rods reinforced with ZrB2 particles. The welding process was conducted using TIG welding, with and without ultrasonic vibration, to enhance weld quality and reduce hot cracking. Optimization of process parameters for dissimilar TIG welding was performed through Response Surface Methodology (RSM), which generated a design matrix to analyze the influence of process parameters on response variables. Numerical and graphical optimization were applied to minimize hot cracking sensitivity and maximize microhardness. The RSM-based models suggested an optimal welding current of 93A, the use of Al 5356/ZrB2 nanocomposite filler, and the application of ultrasonic vibrations. Experimental validation of the identified solution demonstrated improvements in weld quality, including increased yield strength and ductility. The combination of nano-reinforced fillers and ultrasonic vibrations was found to enhance weldability and mitigate hot cracking in dissimilar aluminum joints. The mechanism of hot cracking reduction involved grain refinement, degassing, and homogenization due to ultrasonic vibrations, as well as the modification of weld pool chemistry and control of dilution by the nanocomposite filler, which collectively minimized solidification shrinkage and stress. Under these optimized conditions, no hot cracking was observed experimentally.

Identification and Analysis of Potential Biomarkers Associated with Neutrophil Extracellular Traps in Cervicitis.

Early diagnosis of cervicitis is important. Previous studies have found that neutrophil extracellular traps (NETs) play pro-inflammatory and anti-inflammatory roles in many diseases, suggesting that they may be involved in the inflammation of the uterine cervix and NETs-related genes may serve as biomarkers of cervicitis. However, what NETs-related genes are associated with cervicitis remains to be determined. Transcriptome analysis was performed using samples of exfoliated cervical cells from 15 patients with cervicitis and 15 patients without cervicitis as the control group. First, the intersection of differentially expressed genes (DEGs) and neutrophil extracellular trap-related genes (NETRGs) were taken to obtain genes, followed by functional enrichment analysis. We obtained hub genes through two machine learning algorithms. We then performed Artificial Neural Network (ANN) and nomogram construction, confusion matrix, receiver operating characteristic (ROC), gene set enrichment analysis (GSEA), and immune cell infiltration analysis. Moreover, we constructed ceRNA network, mRNA-transcription factor (TF) network, and hub genes-drug network. We obtained 19 intersecting genes by intersecting 1398 DEGs and 136 NETRGs. 5 hub genes were obtained through 2 machine learning algorithms, namely PKM, ATG7, CTSG, RIPK3, and ENO1. Confusion matrix and ROC curve evaluation ANN model showed high accuracy and stability. A nomogram containing the 5 hub genes was established to assess the disease rate in patients. The correlation analysis revealed that the expression of ATG7 was synergistic with RIPK3. The GSEA showed that most of the hub genes were related to ECM receptor interactions. It was predicted that the ceRNA network contained 2 hub genes, 3 targeted miRNAs, and 27 targeted lnRNAs, and that 5 mRNAs were regulated by 28 TFs. In addition, 36 small molecule drugs that target hub genes may improve the treatment of cervicitis. In this study, five hub genes (PKM, ATG7, CTSG, RIPK3, ENO1) provided new directions for the diagnosis and treatment of patients with cervicitis.

Remarks on Limit Theorems for the Free Quadratic Forms.

In 2021, Ejsmont and Biernacki showed that the free tangent distribution can be used to measure household satisfaction with durable consumer goods. This distribution arises as the limit of free random variables. This, new article serves as the theoretical introduction to the continuation of the research presented in the paper from 2021. We continue the study of the limit of specific quadratic forms in free probability, which is the first step towards constructing a new distribution for the evaluation of satisfaction with material affluence among household. We formulate a non-central limit theorem for weighted sums of commutators and square of the sums for free random variable. In addition we give the random matrix models for these limits.

Sample efficient nonparametric regression via low-rank regularization

Nonparametric regression suffers from curse of dimensionality, requiring a relatively large sample size for accurate estimation beyond the univariate case. In this paper, we consider a simple method of dimension reduction in nonparametric regression via series estimation, based on the concept of low-rankness which was previously studied in parametric multivariate reduced-rank regression and matrix regression. For d > 2 , the low-rank assumption is realized via tensor regression. We establish a faster convergence rate of the estimator in the (approximate) low-rank case. Limitations of the model are also discussed. Through simulation studies and real data analysis, we compare the estimation accuracy of the proposed method with that of existing approaches. The results demonstrate that the proposed method yields estimates with lower RMSE compared to existing methods.

Formulation, Optimization, and Evaluation of Solid-lipid Formulation for Bioavailability Enhancement Utilizing Diltiazem Hydrochloride

Background: Cardiac arrhythmia is a health concern, requiring effective medication for proper treatment. Diltiazem hydrochloride (DTZ.HCL), a class IV anti-arrhythmic calcium channel blocker, was used as a model drug due to its ability to block Ca++ channels in the SA and AV nodes, reducing calcium entry into cardiac cells and subsequently decreasing the force of contraction and oxygen consumption by the heart. Despite its good oral absorption, DTZ.HCL bioavailability is reduced to approximately 40% due to extensive first-pass metabolism. A nano-enabled drug delivery system has the advantage of incorporating both lipophilic and hydrophilic drugs with improved physical stability and enhanced bioavailability. Objective: The objective of this study was to develop a solid-lipid formulation utilizing diltiazem hydrochloride and evaluate it for its bioavailability enhancement. Method: In the experimental study, SLNs were prepared using the microemulsion technique. A blend ratio (1:1) of lipid (stearic acid: compritol 888 ATO), span 80, PEG 200, and water was selected based on the microemulsion region obtained from the Triplot (4.1) ternary phase diagram. The hydrophilic drug diltiazem hydrochloride was incorporated into the lipid blend, and a preheated Smix was maintained at 80°C to obtain a transparent microemulsion, which then crystallized to form SLNs upon subsequent dispersion in cold water (1:25). Critical process parameters, including magnetic stirring speed, homogenizer speed, and probe sonication cycle, were optimized using Design Expert 10 software to achieve the desired particle size diameter, PDI, and entrapment efficiency. Results: The results revealed that the particle size and PDI were significantly influenced by the span 80 and PEG 200. An increase in the concentration of the lipid blend resulted in large particle sizes. The optimized formulation showed a particle size of 415.4±0.2 nm, PDI of 0.184±0.01, and zeta potential of -24.19±0.12 mV. These results were corroborated by DSC thermograms, which indicated reduced enthalpy associated with the reduced particle size of SLNs. Given that diltiazem hydrochloride is a hydrophilic drug with high water solubility, the entrapment efficiency was relatively 30.6% ±0.45. In vitro release studies demonstrated an initial burst release, followed by a sustained release of 85% over 24 hours. The optimized SLNs followed the Higuchi matrix model, with a coefficient of correlation (R²) value of 0.9369. Conclusion: Results concluded successful development of SLNs with improved bioavailability when compared by way of in-vitro method with marketed preparations.

Estimation of demographics of self-sustaining groups of pied flycatcher <i>Ficedula hypoleuca</i> (Passeriformes: Muscipapidae) taking into account the long-term dynamics of the population breeding in the Tomsk oblast (Western Siberia)

We present the main demographic parameters of the Western Siberian pied flycatcher population, nesting in natural habitats, at different stages of population dynamics. The average values, range, boundaries, and direction of changes in the survival of sexually mature individuals, fecundity, and the encounter probability at different ages were analyzed. Using matrix models of population structure and population dynamics, an estimate of the true survival rate of fledglings is given. The range of values of demographic parameters that characterize viable groups of the studied bird species is indicated.

Quantisation of type IIB superstring theory and the matrix model

We discuss the path-integral quantisation of perturbative string theory and show equivalence between the Polyakov-type, Schild-type and Nambu-Goto-type formulations of critical type II superstring theory. Remarkably, we also find that the Minkowskian path integral realises causality in the sense that a string does not propagate between points at space-like separation, by giving careful consideration to the measure of the world-sheet metric. We also discuss matrix regularisation of the path integral for type IIB perturbative superstring theory. The obtained matrix models are the Euclidean IKKT matrix model and a modified Minkowskian IKKT model, depending on how the matrix regularisation is applied.