ASR performance varies across languages, speakers, and recording conditions, yet systematic analysis for Indic languages remain limited. We present a large-scale study of decoded outputs from multiple open-source ASR models evaluated on diverse Indian speech datasets in zero-shot settings. We analyze linguistic, speaker-level, and acoustic factors across Hindi, Bengali, Kannada, Telugu, and Marathi. We examine correlations between WER and speaker traits such as average word length, speaking rate, and utterance duration across multiple model dataset pairs. For Hindi, we further analyze audio factors including telephone codecs, bit depth, resampling, and background noise. Results reveal both cross lingual patterns and language-specific sensitivities, showing how speaker behavior and signal processing choices affect ASR robustness in real world Indic scenarios.

We discuss here two major issues related to the steady functioning of the pulsating (oscillating) heat pipe (PHP): the effect of the surface properties and stopovers. They are studied with the CASCO simulation software (Code Avanc{é} de Simulation du Caloduc Oscillant: Advanced PHP Simulation Code in French) version 4. Its experimental validation against two different prototypes is presented. The first is used also to study the effect of the nucleation barrier (the wall superheating necessary for the bubble nucleation) that reflects the wall wettability and roughness. An optimal value of the nucleation barrier is found where the thermal resistance achieves a minimum for a given evaporator power. The functioning regime is continuous showing pressure waves propagating along all the PHP channel. The stopover regime is observed both for small and large barriers. The second experimental setup (PHP Smart Loop) is used to study the stopover regime. It is found that it is characterized by a chaotically repeating sequence of fast pressure growth (corresponding to oscillations) followed by a slower pressure decay during a stopover. The decrease of the thermal resistance with heating load is explained by a decrease of the stopover time caused by a faster liquid film shrinking.

Structural heart disease (SHD) is a primary driver of heart failure and cardiovascular mortality, yet early detection remains constrained by the limited accessibility of echocardiography. While single-lead electrocardiogram (ECG) is ubiquitous through wearables, existing AI screening models often depend on 12-lead inputs, generalize poorly across institutions, or require massive, condition-specific labeled datasets. Recent work has demonstrated the feasibility of contrastive pre-training between single-lead ECGs and echocardiography reports within a single health system. Here, we present AnyECG-Echo, a framework that advance this paradigm toward clinical translation through three key developments: (1) evaluation in a geographically independent external cohort (n = 16,621); (2) diagnostic coverage of 13 fine-grained SHD subtypes spanning myocardial, chamber, valvular, and great-vessel pathologies; and (3) dual-axis mechanistic interpretability combining electrophysiology-grounded Shapley attribution with emergent correlations to quantitative measurements. Across validation cohorts totaling n = 25,222, the model demonstrated high AUROC for high-impact subtypes, including reduced left ventricular systolic function (AUROC 0.866-0.924), global heart enlargement (0.877-0.931), and mitral stenosis (0.836-0.906). Furthermore, we successfully validated the alignment of model outputs with established medical physiological traits, thereby enhancing interpretability. Notably, we discovered that AnyECG-Echo's outputs function as physiologically grounded digital biomarkers that accurately track objective metrics such as LVEF and myocardial wall thickness. These findings prove that wearable single-lead ECGs can effectively detect fine-grained structural heart disease, offering a practical solution for population-scale screening.

Extended Reality (XR) applications demand intensive computation and low latency, especially for real-time rendering tasks. In this letter, we present an edge-aided XR rendering testbed that dynamically offloads rendering workloads between the XR client and the edge server built upon network conditions and latency constraints. The testbed integrates a Microsoft HoloLens 2 headset, a GPU-enabled edge server, and a customized remote rendering toolkit based on the HOLO Stream SDK, enabling seamless switching between local and edge rendering modes in real time. To overcome the limitations of pixel-level quality metrics under head movements and asynchronous frame arrivals, we propose a perceptual evaluation metric based on deep feature embeddings and cosine similarity, which remains robust to spatial and temporal misalignments. Furthermore, we design a contextual bandit learning controller to adapt rendering placement decisions in real time by jointly optimizing perceptual quality and latency. Experimental results demonstrate the feasibility and performance of our testbed, validating its effectiveness in delivering high-quality and interactive XR experiences.

The superamalgamation property is a strengthening of the amalgamation property and has found many applications in algebraic logic, more recently, also in model theory. Here we introduce an even stronger notion we call the hyperamalgamation property. We show that lattices, semilattices, Boolean algebras and dual Heyting algebras have the hyperamalgamation property. As a first application, we obtain the amalgamation property for semilattices, Boolean algebras and Heyting algebras with further operators.

We investigate a generalized stochastic fractional neuronal model combining fractional dynamics with correlated stochastic inputs. The proposed framework is described by a fractional differential equation driven by a latent stochastic process with stationary increments and mean-reverting structure. This formulation allows the inclusion of both short-range and long-range dependence structures and naturally produces non-exponential relaxation phenomena. The main goal is the development of a feasible parameter estimation procedure based on discrete observations of the neuronal state process. We propose a two-step methodology. First, the parameters governing the fractional dynamics are estimated by exploiting the asymptotic behavior of Mittag-Leffler functions near the origin. Subsequently, the latent stochastic input is reconstructed through fractional differentiation techniques, allowing the estimation of the parameters governing the hidden noise dynamics. We derive quantitative error bounds for the estimators and analyze the reconstruction error of the latent process under suitable regularity assumptions on the driving noise. In particular, the interplay between the order of the fractional derivative and the Hölder regularity of the noise process naturally emerges in the stability analysis of the reconstruction procedure. Finally, simulation studies illustrate the applicability of the proposed methodology and highlight the influence of memory effects and noise regularity on the quality of statistical inference. The results support the relevance of fractional stochastic analysis for the modeling and inference of neuronal systems with memory and correlated inputs.

This letter presents a generalized technique for cancelling the parasitic inductance of capacitors using a lattice network. The Z-matrix-based equivalent transformation shows that the conventional vertically symmetric inductance condition is only a sufficient condition and can be relaxed. A vertically asymmetric lattice network is then proposed, enabling the parasitic inductance of capacitors to be cancelled by adjusting only one inductance. The method is further extended to common-mode noise reduction using a common-mode choke, and both concepts are experimentally verified.

Optical tidal disruption events (TDEs) exhibit extremely broad emission lines ($\approx 10^3$-$10^4~{\rm km~s^{-1}}$) and are observationally classified into four spectroscopic types: H-dominated, He-dominated, H+He, and featureless. The prevalent H+He class often displays Bowen fluorescence lines (notably \niii~and \oiii), features that are rarely observed in active galactic nuclei and whose origin has remained poorly understood. We present the first unified radiative transfer framework that reproduces all four TDE spectroscopic classes using simulations of optically thick, outflowing envelopes with solar composition. Our models successfully capture both the continuum properties and key spectral features, including strong \ha, \heii~and Bowen emissions. We demonstrate that the spectroscopic diversity of TDEs is primarily governed by the gas ionization state, controlled by the ratio of injected luminosity to envelope mass. As the ionization level decreases, the observed sequence of spectroscopic classes emerges naturally, transitioning from featureless to He-dominated, to Bowen-dominated, and finally to H-dominated spectra. We further show that electron scattering in the optically thick outflow is the dominant mechanism responsible for the extreme line widths, linking line profiles directly to the physical properties of the wind. The model also explains the observed correlations with luminosity, black hole mass, and the relative stability of spectral classifications during TDE evolution. This work establishes a unified physical framework for TDE spectroscopy, providing new insight into the emission mechanisms, energetics, and outflow structure of these transient events, and offering a practical pathway for interpreting and fitting observed spectra.

We present predictions for the elastic electromagnetic form factors of the $Ω$ baryon in both space-like and time-like regions, computed within a confining, symmetry-preserving framework based on a vector$\,\otimes\,$vector contact interaction. The calculation is performed in the rainbow-ladder truncation of QCD's Dyson-Schwinger equations, combined with a Poincaré-covariant Faddeev equation for the three-quark bound state. The $Ω$ baryon, composed solely of strange quarks, provides a particularly clean environment in which to investigate the role of quark mass and SU(3)-flavor symmetry in shaping baryon structure. Within this approach, the electromagnetic current is constructed consistently with the Ward-Takahashi identity, yielding four independent form factors associated with the electric monopole, magnetic dipole, electric quadrupole, and magnetic octupole moments. We compute these form factors over a broad kinematic domain and analyze their behavior in both space-like and time-like regions. The resulting static electromagnetic moments and multipole form factors of the $Ω$ baryon exhibit a visible sensitivity to the dressed-quark anomalous magnetic moment, particularly in the magnetic and higher-order multipole sectors. The time-like form factors are obtained through asymptotic analytic continuation of the corresponding space-like solutions, allowing the construction of the effective form factor and its comparison with available experimental data and recent phenomenological analyses.

The inverse spectral problem asks to what extent the Laplace--Beltrami spectrum determines the geometry of a Riemannian manifold. We study a natural weakening, called \emph{near isospectrality}, in which the spectra of two compact manifolds agree outside a finite set, counted with multiplicity. We prove that for compact quotients of a fixed simply connected symmetric space of nonpositive sectional curvature, near isospectrality already forces full isospectrality. We then extend this rigidity to a broad collection of compact quotients of irreducible symmetric spaces of noncompact type. In this larger setting, near isospectrality determines enough heat invariants to identify the universal cover within the class under consideration, and the fixed-cover rigidity result then implies full isospectrality. Thus, within the class studied here, eventual agreement of the Laplace spectrum already forces complete spectral agreement.

Accurate modelling of diffraction peak shapes is essential for extracting microstructural information from nanocrystalline materials. Common-volume functions are widely used to describe finite-size and shape broadening in powder diffraction, but analytical expressions are available only for a limited set of ideal geometries. Here, we introduce a generalized Fourier-based framework in which crystal-domain shape deformation, lattice deformation, and relative shape-lattice misorientation are treated as independently refinable tensor operations within a unified formalism. The approach enables continuous affine transformations of both crystal shape and lattice base while preserving analytical evaluation of directional Fourier coefficients. As a result, complex particle shapes, anisotropic deformations, and arbitrary relative orientations between shape and lattice can be modelled within a single reciprocal- and real-space framework, including coupled shape-lattice transformations not accessible using conventional powder diffraction line-profile methods. The formalism can be applied to individual diffraction peaks, full powder patterns, and total-scattering shape corrections. Validation against virtual scattering experiment data demonstrates that crystal size, shape, lattice deformation, and relative shape-lattice orientation can be simultaneously recovered with high accuracy.

The list ranking problem is one of the classical problems of parallel computing, with nontrivial algorithms and many applications as a subroutine for solving other problems. While it has been intensively studied in the early days of parallel computing, few things happened in the last 20 years. In particular, there is little work on scaling list ranking to large machines and input sizes. We reconsider list ranking starting from the ground-breaking results of Sibeyn a quarter century ago. We employ algorithm and performance engineering to improve his sparse ruling-set algorithm, making it capable of scaling to many processors, and provide a more detailed analysis of the impact of the algorithm's parameters, further guiding our practical implementation. We perform an extensive experimental study across a variety of input instances with different structural properties. We demonstrate that indirect communication, exploiting input locality, and message coalescing allows scaling to billions of elements on up to 24,576 cores.

Spoken language identification (LID) for Indian languages is a challenging problem due to the large number of languages, significant phonetic overlap among related varieties, and the scarcity of labeled data for many low-resource languages. In this work, we present a systematic comparative study of two pre-trained speech encoders -- Whisper and FastConformer -- combined with a linear classifier for large-scale Indic LID spanning 42 languages across four linguistic families. We evaluate both encoders in frozen (linear probing) and fine-tuned settings, and compare three training objectives: cross-entropy (CE), supervised contrastive loss with cross entropy (CE + supCon), and hierarchical softmax (HSM). Models are trained on the Vaani dataset and evaluated in a cross-corpus setting on Vaani-Test (held-out), FLEURS, and Kathbath, providing insights into domain generalization. The frozen FastConformer encoder achieves over 90\% macro accuracy on FLEURS and Kathbath without any task-specific adaptation, substantially outperforming Whisper on out-of-domain benchmarks, while fine-tuned Whisper yields stronger in-domain performance. HSM consistently outperforms CE and CE+SupCon for both encoders across all benchmarks, with the largest gains on out-of-domain test sets. CE+SupCon degrades FastConformer's cross-corpus generalization, suggesting that the contrastive objective over-specializes representations to in-domain conditions. Per-family analysis shows that Central Indo-Aryan varieties are the hardest to discriminate, with Hindi--Urdu and the Sadri--Chhattisgarhi--Surgujia cluster being the dominant confusion pairs.

We compute generalized susceptibilities of conserved charges in the Polyakov chiral SU(3) quark mean field (PCQMF) model with the fermion vacuum term. At $μ_B = 0$ MeV, the calculation covers the diagonal $χ_n^{B,Q,S}$ through eighth order and all twelve independent fourth-order off-diagonal correlators. Extending to finite $μ_B$ at $μ_Q = μ_S = 0$, we compute $χ_n^B$ through eighth order, $χ_n^{Q,S}$ through fourth order, the second-order off-diagonals, all twelve fourth-order off-diagonal correlators, and the odd-order baryon susceptibilities $χ_1^B$, $χ_3^B$, $χ_5^B$. The calculation includes the vacuum term (vac=1) and is repeated for an independently refitted no-sea variant (vac=0). At $μ_B = 0$ MeV, the chiral pseudocritical temperature is $T_{\mathrm{pc}} = 170.5$ MeV (vac=1) and $166.4$ MeV (vac=0), while the Polyakov-loop deconfinement temperature is $T_{\mathrm{dec}} = 144.4$ MeV (vac=1) and $146.6$ MeV (vac=0). In vac=1, the derivative $-dΔ_{l,s}/dT$ of the subtracted chiral condensate develops an inflection near $T_{\mathrm{dec}}$. Higher derivative orders resolve the chiral-deconfinement splitting as twin maxima in $χ_4^B$ and $χ_6^Q$, twin minima in $χ_8^B$ and $χ_8^Q$, and multiple zero crossings in $χ_6^B$. Among the fourth-order off-diagonal correlators, vac=1 amplitudes exceed vac=0 in the BQ channel across the chiral crossover. The BS, QS, and mixed BQS components peak near the strange-melting temperature, where vac=0 dominates. Along $T_{\mathrm{pc}}(μ_B)$, the kurtosis ratio $R_{42}^B \equiv χ_4^B/χ_2^B$ of vac=1 crosses zero at $μ_B/T_{\mathrm{pc}} \approx 2.15$, while vac=0 stays positive across the full range. The higher-order ratios $R_{51}^B \equiv χ_5^B/χ_1^B$ and $R_{62}^B \equiv χ_6^B/χ_2^B$ start negative in vac=1 and grow more negative as $μ_B$ increases.

Fast, highly sensitive, and broadband detectors operating in the mid-to-far-infrared (MIR-FIR) spectral region are essential for applications ranging from astrophysics to time-resolved spectroscopy using laboratory-based sources and beamlines at Infrared Free-Electron Laser (IR-FEL) facilities. Conventional Lumped Element Kinetic Inductance Detectors (LEKID) achieve high optical efficiency using resonant quarter wavelength (λ/4) backshort cavities. However, this cavity-based approach is inherently narrowband and becomes optomechanically challenging at the mid to far infrared (MIR-FIR) wavelengths. Here, we present a completely backshort-free LEKID absorber architecture that achieves broadband absorption exceeding 50%. The meander absorbers were fabricated from a superconducting Ti-V alloy and characterized using IR radiation from the IR-FEL at RRCAT, India. By illuminating through the silicon substrate and matching the meander's sheet resistance to the silicon substrate's wave impedance, the front-side reflection is strongly suppressed. Simultaneously, the sub-wavelength periodicity of the dense meander inhibits propagating transmission into free space via evanescent wave confinement. This combined mechanism drives efficient Ohmic dissipation within the metallic meander, yielding an experimental absorption efficiency ranging from 50% to 90% across the 12.5-30 micrometer wavelength range. The cavity-free design greatly simplifies the fabrication of the focal plane array while providing the broadband response required for next-generation detectors. To assess the suitability of the Ti40V60 alloy as an active superconducting detector material, a test LEKID resonator was also designed, fabricated, and experimentally characterized.

We study energy transport between two quantum systems coupled through a random interaction. The central feature of our approach is to model the coupling as a Gaussian random matrix, which enables a simple and systematic perturbative expansion. In the large-$N$ limit, we derive explicit expressions for the energy transfer rate and heat conductance up to second order in the coupling strength. Using spectral methods and diagrammatic expansions, we obtain the leading- and next-to-leading-order contributions to the energy transfer rate. We illustrate our results through explicit calculations for Gaussian, constant, semicircular, and Gamma densities of states.

Multivariate regression with many correlated responses and predictors commonly violates Gaussian error assumptions due to heavy tails, outliers, and asymmetry. Gaussian procedures then lose efficiency in coefficient estimation and produce biased estimates of conditional dependence graphs. We develop a robust Bayesian framework using a scale-location mixture error distribution and horseshoe+ global-local priors on both the regression coefficients and off-diagonals of the error precision matrix, coupling sparsity in the regression map with sparsity in the residual dependence structure. Theoretical contributions include joint posterior contraction, selection consistency for both supports, a Kullback-Leibler risk bound showing the dominance of horseshoe+ over horseshoe, and bounded sensitivity, ensuring that a single large outlier has vanishing influence under t errors. Simulations across four error regimes, contamination, and varying dimensions show that our estimator matches Gaussian procedures under normality and dominates them under heavy tails and skewness. Applications to FRED-MD macroeconomic data and S&P 500 daily returns recover interpretable sparse coefficient maps and residual dependence graphs while automatically down-weighting crisis-period observations.

Reservoir engineering can stabilize states inaccessible to unitary dynamics. Directed particle-conserving dissipation creates Lindbladian skin states, where Pauli exclusion turns edge accumulation into a many-body density imbalance. In a monitored fermion chain with tunable hopping range, we identify, within a Gaussian trajectory approximation, two finite-size scaling regimes: short-range hopping is consistent with complete skin accumulation and area-law entanglement, whereas sufficiently long-range hopping produces a finite bulk tail and effective algebraic sub-volume-law entanglement. Dissipation and coherent hopping thus jointly control skin localization and quantum entanglement, highlighting their close interconnection.

We construct a conformal product structure on $S^3$ using the Reeb foliation. This is the first example of a conformal product structure on a compact simply connected manifold which is not built on a global product manifold.

This paper investigates inverse problems for Linear-Quadratic-Gaussian (LQG) Mean Field Games (MFGs) based entirely on the observation of mean-covariance trajectories. We address three sequential challenges: identifying the optimal control for observed initializations, determining the control for arbitrary initializations, and recovering consistent cost parameters. After establishing the existence and uniqueness of the forward Nash equilibrium under mild hypotheses, we analyze the injectivity of the parameter-to-trajectory mapping, demonstrating that it is inherently non-injective and providing sufficient conditions for parameter equivalence. We prove that while the optimal control is locally identifiable for observed initializations under minimal assumptions, global identifiability requires a deeper structural recovery of the game's costs. To bridge this gap, we propose a constructive semidefinite programming method to infer cost parameters that are strictly consistent with the observed population dynamics. Numerical experiments illustrate this method.

We construct an explicit class of non-separable Gabor windows on $L^2(\R^d)$ by applying chirp deformations to tensor-product dual pairs on separable lattices. Starting from one-dimensional dual Gabor frames, we first obtain separable higher-dimensional dual pairs by tensorization. We then transport these systems through the unitary chirp operator $U_C f(x)=e^{πi x^T Cx}f(x)$ and the associated phase-space shear, obtaining Gabor systems on lower block-triangular lattices of the form $ Λ_{A,B,C}=\{(Ak,CAk+B\ell):k,\ell\in\Z^d\}. $ The construction preserves compact support, smoothness, frame bounds, exact duality, canonical duals, and approximate-duality errors. We also quantify chirp-induced coupling through a phase-space covariance defect and show that non-separability changes the geometry of the atoms without deteriorating deterministic or finite-section statistical robustness bounds.

We study a hyperbolic approximation ("hyperbolization") of the Cahn-Hilliard (CH) equation, originally proposed by Dhaouadi, Dumbser, and Gavrilyuk (2025, DOI: 10.1098/rspa.2024.0606) and study its convergence towards the CH model in a relaxation limit both via formal asymptotic expansions and, for a slightly modified approximation, via the relative energy framework. Moreover, we develop energy-stable semidiscretizations of the CH equation and of this hyperbolization using upwind summation-by-parts operators in space. Subsequently, we combine them with (additive) implicit-explicit (IMEX) Runge-Kutta methods based on a convex-concave splitting. We show that the resulting method is asymptotic preserving, i.e., it converges in the limit of the relaxation parameter to a stable discretization of the original CH equation. The choice of the necessary parameters is guided by the a priori error estimate based on the relative energy framework.

The Parker transport equation (TPE) has been the equation of choice for the past 60 years in studies of galactic cosmic ray (GCR) modulation. Conversely, the focused TPE describes the same processes on a more fundamental level than the Parker TPE by modelling an anisotropic distribution rather than an isotropic one. It is usually assumed that the Parker TPE is valid for modelling GCRs, but the two TPEs have not been tested against each other in this context. We conduct a first-of-its-kind comparison of these TPEs without particle drifts to test whether they produce the same results under identical diffusion conditions. A new model for protons during solar minimum conditions is developed to numerically solve the TPEs using stochastic differential equations. The TPEs are designed to be as consistent as possible for diffusion by normalising the pitch-angle-dependent diffusion coefficients (DCs) used in the focused TPE to the isotropic DCs used in the Parker TPE. The Parker TPE overestimates the GCR intensity at Earth's orbit for low energies by ~30%, and by ~40% over the poles. This stems from a small first-order anisotropy caused by particle fluxes over the poles. Particles gain easier access to the inner heliosphere by streaming in over the poles, where pitch-angle scattering is generally weaker, and the magnetic field is typically less wound. The focused TPE also yields nearly identical results for different pitch-angle dependencies of the DCs. The description of particle streaming and weak pitch-angle scattering as effective parallel diffusion in the Parker TPE makes it overly diffusive. This suggests that DCs derived from fitting the Parker TPE to observations are likely underestimated. Furthermore, GCR spectral and anisotropy data alone cannot distinguish between scattering theories with similar mean free paths but different pitch-angle dependencies.

We theoretically explore a phase transition between controlled and chaotic dynamics in a classical spin chain model subject to chaotic Hamiltonian dynamics and a contractive "control map", which alternate in time. The control map drives the system toward a target configuration that is an unstable fixed point under the chaotic dynamics. When the control is strong enough, the target configuration is the globally attracting stable fixed point of the dynamics; for weaker control, the many-body dynamics remains chaotic for almost all initial states. The phase transition between controlled and chaotic phases has a mixed character: As the transition is approached from the chaotic phase, the fraction of the spins that are far from the target configuration goes continuously to zero, and there are diverging spatial and temporal correlation lengths; however, the leading Lyapunov exponent is discontinuous across the transition, jumping from a positive value in the chaotic phase to a negative value in the controlled phase. We present evidence that this transition is in the same universality class as directed percolation in the presence of temporal randomness, a universality class for which we obtain results that are consistent with the dynamical Harris criterion but do not saturate the bound.

Constraining the physical properties of Earth's deep interior, particularly the viscosity of the solid inner core and the density structure of large low-velocity provinces (LLVPs), remains a major challenge in geophysics. Here we develop a unified dynamical framework that combines mantle-inner core gravitational coupling (MICG) with torsional oscillations in the fluid outer core and show that their interaction can produce a distinct and testable geodetic signature. Guided by this prediction, we analyze satellite gravity observations together with independent corrections for surface mass variability. We identify a robust approximately 6-year signal in the Stokes coefficient Delta S22, while no corresponding stationary signal is detected in Delta C22. A signal with the same periodicity is independently detected in length-of-day variations (Delta LOD), and the two signals exhibit a near anti-phase relationship. Interpreting this coupled signature within the proposed framework allows us to constrain the inner core viscosity to approximately 4.6 (+/- 1.8) x 10^16 Pa s and the equatorial relief of the inner core boundary to a semi-axis difference of about 200 +/- 70 m. The inversion further indicates mean density anomalies of +5.5 (+/- 0.6) per mil at the base of LLVPs. These results indicate that satellite gravimetry provides a direct observational window into deep-Earth dynamics and the physical properties of Earth's deep interior.

We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The algorithm uses adaptive multilevel Monte Carlo gradient estimates, provides parallel scalability as well as improved convergence rates and computational complexity compared to standard batched stochastic gradient descent methods. We study the method in computationally demanding settings using three-dimensional elliptic diffusion problems and large risk-aversion parameters.

We present global limits for Majorana neutrino masses by combining latest results from neutrinoless double-beta ($0νββ$) decay searches and ab initio nuclear theory. Limits are derived in a Bayesian framework utilizing likelihood functions from a suite of $0νββ$-decay experiments in conjunction with nuclear matrix elements calculated from nuclear and electroweak forces derived from chiral effective field theory and implemented in the in-medium similarity renormalization group many-body approach. In contrast to nuclear models, ab initio results indicate that the current generation of $0νββ$-decay experiments have likely \textit{not} yet reached sensitivities required to probe the mass regime allowed by neutrino-oscillation data, where the combined bounds are notably stronger than those given by individual experiments. Finally, from predicted sensitivities of next-generation searches, we show that, while no one individual experiment fully covers the inverted mass ordering, this can be achieved from combined contributions from the four key isotopes: $^{76}$Ge, $^{100}$Mo, $^{130}$Te, and $^{136}$Xe.

In this paper, a new notion, essential contractibility of Banach algebras, is introduced and some of its properties are examined. The main result is to investigate the essential contractibility of (symmetric abstract) Segal algebras.

Chemical abundances encode the fossil record of galaxy evolution in a complex and diverse way that requires innovative approaches to reconstruct galactic histories. We investigate the power of using phylogenetic methods to disentangle different evolutionary pathways in analytical chemical evolution models. We ran 1024 one-zone chemical evolution models using flexCE. The resulting chemical abundances are combined with those of two fiducial models, mw-fid and dw-fid, and then used both to determine which combinations produce two-branched phylogenetic trees, as well as how purely these trees split the two input models. We used random forests and Shapley analysis to predict which model combinations return well-separated trees and explain which input parameters are most important for this. We also studied the abundance patterns, as well as star formation rates, mass accumulation, and branch lengths. We found that η, the mass-loading outflow parameter in flexCE, had the largest impact in separating models into separate branches, due to its importance in driving the chemical enrichment rates and total abundances. Star formation rates and mass accumulation had some impact on η, but no direct relation between these quantities and the abundances was found. We also found that branches connected through the most metal rich tips in our trees, which is opposite to how phylogenetic trees connect in biological systems. Phylogenetic trees help to reconstruct histories when there is information that is inherited between generations, which is the case of the chemical elements in galaxy evolution. Branch topologies can provide information about the rates of evolutionary change of the various populations, and the connection between branches also contains information about their shared history. This work brings us a step further understanding galaxy evolution through cross-disciplinary research.

For approximately half of the individuals receiving mental health care, the results are suboptimal, even when treatments align with evidence-based guidelines. These limited effects may partly stem from how clinical decisions on treatment focus are made in mental health care. Typically, treatment strategy is guided by the diagnostic classification combined with the individualized case conceptualization. While standard, this approach may fall short for several reasons such as biases on the part of both the patient and therapist, and treatment guidelines being based on average effects that may not (exactly) suit the individual patient. To address these challenges, we propose a novel framework that reduces biases in clinical decision-making and makes it genuinely possible to tailor treatment focus to the individual patient. This framework involves (a) constructing causal graphs and estimating causal effects from intensively collected, longitudinal patient data, (b) simulating new time series based upon the causal relationships, and (c) using these simulations to identify the most effective treatment focus for the individual patient. By simulating and comparing different intervention strategies and examining both the estimated individual's responsiveness and its long-term effectiveness, this approach may generate useful insights to guide treatment focus and strategy, which can lead to a significant improvement of treatment outcomes in mental health care.