A useful formula for periodic Jacobi matrices on trees.

We introduce a function of the density of states for periodic Jacobi matrices on trees and prove a useful formula for it in terms of entries of the resolvent of the matrix and its "half-tree" restrictions. This formula is closely related to the one-dimensional Thouless formula and associates a natural phase with points in the bands. This allows streamlined proofs of the gap labeling and Aomoto index theorems. We give a complete proof of gap labeling and sketch the proof of the Aomoto index theorem. We also prove a version of this formula for the Anderson model on trees.

Scoring alignments by embedding vector similarity.

Sequence similarity is of paramount importance in biology, as similar sequences tend to have similar function and share common ancestry. Scoring matrices, such as PAM or BLOSUM, play a crucial role in all bioinformatics algorithms for identifying similarities, but have the drawback that they are fixed, independent of context. We propose a new scoring method for amino acid similarity that remedies this weakness, being contextually dependent. It relies on recent advances in deep learning architectures that employ self-supervised learning in order to leverage the power of enormous amounts of unlabelled data to generate contextual embeddings, which are vector representations for words. These ideas have been applied to protein sequences, producing embedding vectors for protein residues. We propose the E-score between two residues as the cosine similarity between their embedding vector representations. Thorough testing on a wide variety of reference multiple sequence alignments indicate that the alignments produced using the new $E$-score method, especially ProtT5-score, are significantly better than those obtained using BLOSUM matrices. The new method proposes to change the way alignments are computed, with far-reaching implications in all areas of textual data that use sequence similarity. The program to compute alignments based on various $E$-scores is available as a web server at e-score.csd.uwo.ca. The source code is freely available for download from github.com/lucian-ilie/E-score.

Unveiling order from chaos by approximate 2-localization of random matrices.

Quantum many-body systems are typically endowed with a tensor product structure. A structure they inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. It is interesting to understand whether a given Hamiltonian is compatible with some particular tensor product structure. In particular, we ask, is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e., it contains only pairwise interactions? Here we show, using analytical and numerical calculations, that a generic Hamiltonian (e.g., a large random matrix) can be approximately written as a linear combination of two-body interaction terms with high precision; that is, the Hamiltonian is 2-local in a carefully chosen basis. Moreover, we show that these Hamiltonians are not fine-tuned, meaning that the spectrum is robust against perturbations of the coupling constants. Finally, by analyzing the adjacency structure of the couplings [Formula: see text], we suggest a possible mechanism for the emergence of geometric locality from quantum chaos.

PIEZO1-mediated mechanosensing governs NK-cell killing efficiency and infiltration in three-dimensional matrices.

Natural killer (NK) cells play a vital role in eliminating tumorigenic cells. Efficient locating and killing of target cells in complex three-dimensional (3D) environments are critical for their functions under physiological conditions. However, the role of mechanosensing in regulating NK-cell killing efficiency in physiologically relevant scenarios is poorly understood. Here, we report that the responsiveness of NK cells is regulated by tumor cell stiffness. NK-cell killing efficiency in 3D is impaired against softened tumor cells, whereas it is enhanced against stiffened tumor cells. Notably, the durations required for NK-cell killing and detachment are significantly shortened for stiffened tumor cells. Furthermore, we have identified PIEZO1 as the predominantly expressed mechanosensitive ion channel among the examined candidates in NK cells. Perturbation of PIEZO1 abolishes stiffness-dependent NK-cell responsiveness, significantly impairs the killing efficiency of NK cells in 3D, and substantially reduces NK-cell infiltration into 3D collagen matrices. Conversely, PIEZO1 activation enhances NK killing efficiency as well as infiltration. In conclusion, our findings demonstrate that PIEZO1-mediated mechanosensing is crucial for NK killing functions, highlighting the role of mechanosensing in NK-cell killing efficiency under 3D physiological conditions and the influence of environmental physical cues on NK-cell functions.

A modeling framework for detecting and leveraging node-level information in Bayesian network inference.

Bayesian graphical models are powerful tools to infer complex relationships in high dimension, yet are often fraught with computational and statistical challenges. If exploited in a principled way, the increasing information collected alongside the data of primary interest constitutes an opportunity to mitigate these difficulties by guiding the detection of dependence structures. For instance, gene network inference may be informed by the use of publicly available summary statistics on the regulation of genes by genetic variants. Here we present a novel Gaussian graphical modeling framework to identify and leverage information on the centrality of nodes in conditional independence graphs. Specifically, we consider a fully joint hierarchical model to simultaneously infer (i) sparse precision matrices and (ii) the relevance of node-level information for uncovering the sought-after network structure. We encode such information as candidate auxiliary variables using a spike-and-slab submodel on the propensity of nodes to be hubs, which allows hypothesis-free selection and interpretation of a sparse subset of relevant variables. As efficient exploration of large posterior spaces is needed for real-world applications, we develop a variational expectation conditional maximization algorithm that scales inference to hundreds of samples, nodes and auxiliary variables. We illustrate and exploit the advantages of our approach in simulations and in a gene network study which identifies hub genes involved in biological pathways relevant to immune-mediated diseases.

Time-efficient filtering of imaging polarimetric data by checking physical realizability of experimental mueller matrices.

MOTIVATION: Imaging Mueller polarimetry has already proved its potential for biomedicine, remote sensing and metrology. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms. First, one must check the physical realizability of the experimental Mueller matrices in order to filter out non-physical data, ie to test the positive semi-definiteness of the 4 × 4 Hermitian coherency matrix calculated from the elements of corresponding Mueller matrix pixel-wise. For this purpose, we compared the execution time for the calculations of i) eigenvalues, ii) Cholesky decomposition, iii) Sylvester's criterion, and iv) coefficients of the characteristic polynomial (two different approaches) of the Hermitian coherency matrix, all calculated for the experimental Mueller matrix images (600 pixels × 700 pixels) of mouse uterine cervix. The calculations were performed using C ++ and Julia programming languages. RESULTS: Our results showed the superiority of the algorithm iv) based on the simplification via Pauli matrices over other algorithms for our dataset. The sequential implementation of latter algorithm on a single core already satisfies the requirements of real-time polarimetric imaging. This can be further amplified by the proposed parallelization (e.g., we achieve a 5-fold speed up on 6 cores). AVAILABILITY AND IMPLEMENTATION: The source codes of the algorithms and experimental data are available at https://github.com/pogudingleb/mueller_matrices.

Negative Capacitance and Dielectric Constant of Nanocomposite SiAlzOxNy(Si) Films with Semiconductor Nanoparticles.

The electrical properties of nanocomposite SiAlzOxNy(Si) films containing Si nanoclusters embedded into amorphous SiAlzOxNy matrix have been studied by measurements of DC current-voltage and AC capacitance-voltage characteristics. Analysis of the results allowed us to conclude the existence of a negative dielectric constant. The temperature dependence of the negative dielectric constant has been obtained and analyzed. The negative capacitance has been revealed during measurements of capacitance-voltage characteristics at testing signal frequency of 2 kHz. The negative capacitance also points out the appearance of a negative dielectric constant effect. The qualitative model for explanation of negative dielectric constant based on peculiarities of SiAlzOxNy(Si) films polarization due to electron capture at Si nanoparticles-amorphous SiAlzOxNy matrix interface traps near cathode region has been proposed. In the case of AC C-U measurements, a negative capacitance is observed if conductivity current through the nanocomposite film is relatively high.

miRNA-124 loaded extracellular vesicles encapsulated within hydrogel matrices for combating chemotherapy-induced neurodegeneration.

Chemotherapy-induced neurodegeneration represents a significant challenge in cancer survivorship, manifesting in cognitive impairments that severely affect patients' quality of life. Emerging neuroregenerative therapies offer promise in mitigating these adverse effects, with miRNA-124 playing a pivotal role due to its critical functions in neural differentiation, neurogenesis, and neuroprotection. This review article delves into the innovative approach of using miRNA-124-loaded extracellular vesicles (EVs) encapsulated within hydrogel matrices as a targeted strategy for combating chemotherapy-induced neurodegeneration. We explore the biological underpinnings of miR-124 in neuroregeneration, detailing its mechanisms of action and therapeutic potential. The article further examines the roles and advantages of EVs as natural delivery systems for miRNAs and the application of hydrogel matrices in creating a sustained release environment conducive to neural tissue regeneration. By integrating these advanced materials and biological agents, we highlight a synergistic therapeutic strategy that leverages the bioactive properties of miR-124, the targeting capabilities of EVs, and the supportive framework of hydrogels. Preclinical studies and potential pathways to clinical translation are discussed, alongside the challenges, ethical considerations, and future directions in the field. This comprehensive review underscores the transformative potential of miR-124-loaded EVs in hydrogel matrices, offering insights into their development as a novel and integrative approach for addressing the complexities of chemotherapy-induced neurodegeneration.

An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess.

The minimization of the commutator of the Fock and density matrices as the error matrix in the direct inversion of the iterative subspace (CDIIS) developed by Pulay is a powerful self-consistent field (SCF) acceleration technique for the construction of optimum Fock matrix, if initiated with a fair initial guess. In this work, we present an alternative minimized error matrix to the commutator in the CDIIS, namely the residual or the gradient of the energy-functional for a Slater determinant subject to the orthonormality constraints among orbitals, representing the search for a newly improved Fock matrix in the direction of the residual in the direct inversion of the iterative subspace (RDIIS). Implemented in the computational chemistry package GAMESS, the RDIIS is compared with the standard CDIIS and the second order SCF orbital optimization (SOSCF) for tested molecules started with a crude guess. As a result, the RDIIS stably and efficiently performs the SCF convergence acceleration. Furthermore, the RDIIS is considerably independent on the subspace size with the concentrated linear coefficients accounting proportionally for the Fock matrices close to the current iteration.

Multiphase electroextraction of malachite green from surface water and its determination using digital imaging and chemometric tools.

This study introduces a novel method for the quantification of malachite green (MG), a pervasive cationic dye, in surface water by synergizing multiphase electroextraction (MPEE) with digital image analysis (DIA) and partial least square discriminant analysis. Aimed at addressing the limitations of conventional DIA methods in terms of quantitation limits and selectivity, this study achieves a significant breakthrough in the preconcentration of MG using magnesium silicate as a novel sorbent. Demonstrating exceptional processing efficiency, the method allows for the analysis of 10 samples within 20 min, exhibiting remarkable sensitivity and specificity (over 0.95 and 0.90, respectively) across 156 samples in both training and test sets. Notably, the method detects MG at low concentrations (0.2 µg L-1) in complex matrices, highlighting its potential for broader application in environmental monitoring. This approach not only underscores the method's cost-effectiveness and simplicity but also its precision, making it a valuable tool for the preliminary testing of MG in surface waters. This study underscores the synergy among MPEE, DIA, and chemometric tools, presenting a cost-efficient and reliable alternative for the sensitive detection of water contaminants.

Boosting the Efficiency of Red Thermally Activated Delayed Fluorescence via Conjugation Enhancement in Push-Pull Naphthalimide Derivatives.

In this work, we synthesize a series of push-pull compounds bearing naphthalimide as the electron acceptor and tetraphenylethylene (TPE)/triphenylamine (TPA)/phenothiazine (PTZ) as the electron rich/electron donor units. These moieties are arranged in highly conjugated quadrupolar structures. The structure-property relationships are investigated through a joint experimental time-resolved spectroscopic and computational TD-DFT study. The femtosecond transient absorption and fluorescence up-conversion experiments reveal ultrafast photoinduced intramolecular charge transfer. This is likely the key factor leading to efficient spin-orbit CT-induced intersystem crossing for the TPA- and PTZ-derivatives as well as to small singlet-to-triplet energy gap. Consequently, evidence for a delayed fluorescence component is found together with the main prompt emission in the fluorescence kinetics both in solution and in thin film. The weight of the Thermally Activated Delayed Fluorescence (TADF) is greatly enhanced when these fluorophores are used as guests in solid-state host matrices. TADF is interestingly revealed in the orange-red region of the visible. Such long wavelength emission is here observed with surprisingly large fluorescence quantum yields, thanks to the conjugation enhancement achieved in these newly synthesized structures relative to previous studies. Our findings may be thus promising for the future development of efficient third generation TADF-based OLEDs.

Does the use of Acellular Dermal Matrices (ADM) in women undergoing pre-pectoral implant-based breast reconstruction increase operative success versus non-use of ADM in the same setting? A systematic review.

BACKGROUND: Breast cancer is the most common malignancy among women in the UK. Reconstruction - of which implant-based breast reconstruction (IBBR) is the most common - forms a core part of surgical management of breast cancer. More recently, pre-pectoral IBBR has become common as technology and operative techniques have evolved. Many surgeons use acellular dermal matrix (ADM) in reconstruction however there is little evidence in literature that this improves surgical outcomes. This review will assess available evidence for surgical outcomes for breast reconstructions using ADM versus non-use of ADM. METHODS: A database search was performed of Ovid Medline, Embase, Cochrane Central Register of Controlled Trials and Cochrane Database of Systematic Reviews (2012-2022). Studies were screened using inclusion and exclusion criteria. Risk of Bias was assessed using the Newcastle Ottawa scale and ROBIS tools. Analysis and meta-analysis were performed. RESULTS: This review included 22 studies (3822 breast reconstructions). No significant difference between overall complications and failure rates between ADM and non-ADM use was demonstrated. Capsular contracture, wound dehiscence and implant rippling had significant differences however these results demonstrated high heterogeneity thus wider generalisation may be inaccurate. Patient quality of life scores were not recorded consistently or comparably between papers. CONCLUSIONS: This review suggests a lack of significant differences in most complications between ADM use and non-use for pre-pectoral IBBR. If no increase in complications exists between groups, this has significant implications for surgical and legislative decision-making. There is, however, inadequate evidence available on the topic and further research is required.

Empirical evidence of resource dependent evolution of payoff matrices in Saccharomyces cerevisiae populations.

In evolutionary game theory, a relative comparison of the cost and benefit associated with obtaining a resource, called payoff, is used as an indicator of fitness of an organism. Payoffs of different strategies, quantitatively represented as payoff matrices, are used to understand complex inter-species and intra-species interactions like cooperation, mutualism, and altruism. Payoff matrices, however, are usually treated as invariant with time - largely due to the absence of any empirical data quantifying their evolution. In this paper, we present empirical evidence of three types of resource-dependent changes in the payoff matrices of evolving Saccharomyces cerevisiae populations. We show that depending on the carbon source and participating genotypes, N-player games could collapse, be born, or be maintained. Our results highlight the need to consider the dynamic nature of payoff matrices while making even short-term predictions about population interactions and dynamics.

Negative variance components and intercept-slope correlations greater than one in magnitude: How do such "non-regular" random intercept and slope models arise, and what should be done when they do?

Statistical models with random intercepts and slopes (RIAS models) are commonly used to analyze longitudinal data. Fitting such models sometimes results in negative estimates of variance components or estimates on parameter space boundaries. This can be an unlucky chance occurrence, but can also occur because certain marginal distributions are mathematically identical to those from RIAS models with negative intercept and/or slope variance components and/or intercept-slope correlations greater than one in magnitude. We term such parameters "pseudo-variances" and "pseudo-correlations," and the models "non-regular." We use eigenvalue theory to explore how and when such non-regular RIAS models arise, showing: (i) A small number of measurements, short follow-up, and large residual variance increase the parameter space for which data (with a positive semidefinite marginal variance-covariance matrix) are compatible with non-regular RIAS models. (ii) Non-regular RIAS models can arise from model misspecification, when non-linearity in fixed effects is ignored or when random effects are omitted. (iii) A non-regular RIAS model can sometimes be interpreted as a regular linear mixed model with one or more additional random effects, which may not be identifiable from the data. (iv) Particular parameterizations of non-regular RIAS models have no generality for all possible numbers of measurements over time. Because of this lack of generality, we conclude that non-regular RIAS models can only be regarded as plausible data-generating mechanisms in some situations. Nevertheless, fitting a non-regular RIAS model can be acceptable, allowing unbiased inference on fixed effects where commonly recommended alternatives such as dropping the random slope result in bias.

Age-related differences of the time-varying features in the brain functional connectivity and cognitive aging.

Brain functional modular organization changes with age. Considering the brain as a dynamic system, recent studies have suggested that time-varying connectivity provides more information on brain functions. However, the spontaneous reconfiguration of modular brain structures over time during aging remains poorly understood. In this study, we investigated the age-related dynamic modular reconfiguration using resting-state functional MRI data (615 participants, aged 18-88 years) from Cam-CAN. We employed a graph-based modularity analysis to investigate modular variability and the transition of nodes from one module to another in modular brain networks across the adult lifespan. Results showed that modular structure exhibits both linear and nonlinear age-related trends. The modular variability is higher in early and late adulthood, with higher modular variability in the association networks and lower modular variability in the primary networks. In addition, the whole-brain transition matrix showed that the times of transition from other networks to the dorsal attention network were the largest. Furthermore, the modular structure was closely related to the number of cognitive components and memory-related cognitive performance, suggesting a potential contribution to flexibility cognitive function. Our findings highlighted the notable dynamic characteristics in large-scale brain networks across the adult lifespan, which enhanced our understanding of the neural substrate in various cognitions during aging. These findings also provided further evidence that dedifferentiation and compensation are the outcomes of functional brain interactions.

Multi-Emission Carbon Dots Combining Turn-On Sensing and Fluorescence Quenching Exhibit Ultrahigh Selectivity for Mercury in Real Water Samples.

Mercury is a ubiquitous heavy-metal pollutant and poses serious ecological and human-health risks. There is an ever-growing demand for rapid, sensitive, and selective detection of mercury in natural waters, particularly for regions lacking infrastructure specialized for mercury analysis. Here, we show that a sensor based on multi-emission carbon dots (M-CDs) exhibits ultrahigh sensing selectivity toward Hg(II) in complex environmental matrices, tested in the presence of a range of environmentally relevant metal/metalloid ions as well as natural and artificial ligands, using various real water samples. By incorporating structural features of calcein and folic acid that enable tunable emissions, the M-CDs couple an emission enhancement at 432 nm and a simultaneous reduction at 521 nm, with the intensity ratio linearly related to the Hg(II) concentration up to 1200 µg/L, independent of matrix compositions. The M-CDs have a detection limit of 5.6 µg/L, a response time of 1 min, and a spike recovery of 94 ± 3.7%. The intensified emission is attributed to proton transfer and aggregation-induced emission enhancement, whereas the quenching is due to proton and electron transfer. These findings also have important implications for mercury identification in other complex matrices for routine, screening-level food safety and health management practices.

Animal Feedlots and Domestic Wastewater Discharges are Likely Sources of N-Nitrosodimethylamine (NDMA) Precursors in Midwestern Watersheds.

N-nitrosodimethylamine (NDMA) precursor concentrations along four major rivers in Minnesota, USA were quantified and correlated with watershed land cover types, anthropogenic activity, and organic matter characteristics. River water samples (36 in total) were chloraminated under uniform formation conditions (UFC) before and after lime-softening treatment, and the resulting NDMA concentrations were quantified (NDMAUFC). Regarding land cover, NDMAUFC in raw river water exhibited weak positive correlations with urban land (ρ = 0.33, p = 0.05) and cropland coverage (ρ = 0.35, p = 0.04). For anthropogenic activity, NDMAUFC in raw river water positively correlated with the number of feedlots (ρ = 0.57), total weight of animals (ρ = 0.68), and total number of domestic wastewater treatment plants (WWTPs; ρ = 0.63) with p < 0.01. NDMAUFC positively correlated with region IV fluorescence intensity from fluorescence excitation-emission spectra (ρ = 0.70, p < 0.01). Lime softening of river water typically increased NDMAUFC and preferentially removed organic matter that fluoresces in region V, suggesting that the organic matter in this region decreases NDMAUFC by competing for available chloramines. Overall, animal feedlots, along with domestic WWTPs, are predominant sources of NDMA precursors in the studied watersheds, while croplands and urban runoff are of lesser importance.

Towards clinical adherence monitoring of oral endocrine breast cancer therapies by LC-HRMS-method development, validation, comparison of four sample matrices, and proof of concept.

Oral endocrine therapies (OET) for breast cancer treatment need to be taken over a long period of time and are associated with considerable side effects. Therefore, adherence to OET is an important issue and of high clinical significance for breast cancer patients' caregivers. We hypothesized that a new bioanalytical strategy based on liquid chromatography and high-resolution mass spectrometry might be suitable for unbiased adherence monitoring (AM) of OET. Four different biomatrices (plasma, urine, finger prick blood by volumetric absorptive microsampling (VAMS), oral fluid (OF)) were evaluated regarding their suitability for AM of the OET abemaciclib, anastrozole, exemestane, letrozole, palbociclib, ribociclib, tamoxifen, and endoxifen. An analytical method was developed and validated according to international recommendations. The analytical procedures were successfully validated in all sample matrices for most analytes, even meeting requirements for therapeutic drug monitoring. Chromatographic separation of analytes was achieved in less than 10 min and limits of quantification ranged from 1 to 1000 ng/mL. The analysis of 25 matching patient samples showed that AM of OET is possible using all four matrices with the exception of, e.g., letrozole and exemestane in OF. We were able to show that unbiased bioanalytical AM of OET was possible using different biomatrices with distinct restrictions. Sample collection of VAMS was difficult in most cases due to circulatory restraints and peripheral neuropathy in fingers and OF sampling was hampered by dry mouth syndrome in some cases. Although parent compounds could be detected in most of the urine samples, metabolites should be included when analyzing urine or OF. Plasma is currently the most suitable matrix due to available reference concentrations.

Towards green extraction of bioactive natural compounds.

The increasing interest in natural bioactive compounds is pushing the development of new extraction processes that may allow their recovery from a variety of different natural matrices and biomasses. These processes are clearly sought to be more environmentally friendly than the conventional alternatives that have traditionally been used and are closely related to the 6 principles of green extraction of natural products. In this trend article, the most critical aspects regarding the current state of this topic are described, showing the different lines followed to make extraction processes greener, illustrated by relevant examples. These include the implementation of new extraction technologies, the research on new bio-based solvents, and the development of new sequential process and biorefinery approaches to produce a full valorization of the natural sources. Moreover, the future outlook in the field is presented, in which the main areas of evolution are identified and discussed.

Harnessing potential of avian eggshell membrane derived collagen hydrolysate for bone tissue regeneration.

BACKGROUND: Natural bone grafts are the highly preferred materials for restoring the lost bone, while being constrained of donor availability and risk of disease transmission. As a result, tissue engineering is emerging as an efficacious and competitive technique for bone repair. Bone tissue engineering (TE) scaffolds to support bone regeneration and devoid of aforesaid limitations are being vastly explored and among these the avian eggshell membrane has drawn attention for TE owing to its low immunogenicity, similarity with the extracellular matrix, and easy availability. METHODOLOGY AND RESULTS: In this study, the development of bone ingrowth support system from avian eggshell membrane derived collagen hydrolysates (Col-h) is reported. The hydrolysate, cross-linked with glutaraldehyde, was developed into hydrogels with poly-(vinyl alcohol) (PVA) by freeze-thawing and further characterized with ATR-FTIR, XRD, FESEM. The biodegradability, swelling, mechanical, anti-microbial, and biocompatibility evaluation were performed further for the suitability in bone regeneration. The presence of amide I, amide III, and -OH functional groups at 1639 cm- 1,1264 cm- 1, and 3308 cm- 1 respectively and broad peak between 16°-21° (2θ) in XRD data reinstated the composition and form. CONCLUSIONS: The maximum ratio of Col-h/PVA that produced well defined hydrogels was 50:50. Though all the hydrogel matrices alluded towards their competitive attributes and applicability towards restorative bone repair, the hydrogel with 40:60 ratios showed better mechanical strength and cell proliferation than its counterparts. The prominent E. coli growth inhibition by the hydrogel matrices was also observed, along with excellent biocompatibility with MG-63 osteoblasts. The findings indicate strongly the promising application of avian eggshell-derived Col-h in supporting bone regeneration.