The inverse Kohn-Sham (KS) problem seeks a local effective potential whose noninteracting ground state reproduces a prescribed electron density. Although many inversion formulations and schemes have been developed, they are often formulated in disparate languages, including reduced variational optimization, penalty regularization, response-based iteration, and PDE-constrained optimization. In this work, we develop a unified framework for inverse KS theory in two steps. First, we identify the fixed-density noninteracting constrained search and its density-potential duality as the natural variational anchor of the inverse KS problem. In this setting, the KS potential appears as the variational dual object associated with density reproduction, reducing to the familiar multiplier picture in regular regimes. Second, building on this anchor, we classify major inversion formulations according to how the KS state equations and density-reproduction condition are treated within the optimization architecture, with orbital orthonormality retained as an additional structural constraint. Within this framework, the Wu-Yang formulation appears as a potential-space reduced multiplier formulation, the Zhao-Morrison-Parr construction as a quadratic-penalty relaxation, and PDE-constrained approaches as explicit state-constraint formulations at the orbital level. Rather than comparing inversion formulations primarily at the level of implemented algorithms, the present work develops an optimization-theoretic formulation map. This viewpoint identifies where additive-constant ambiguity, asymptotic normalization, nonsmooth variational structure, metric choice, and weak-gap instability enter different inversion architectures, and it makes explicit how major inversion approaches are connected and where algorithmic design choices arise.

Accurately reconstructing and forecasting ocean fields from sparse observations is critical for both operational and scientific purposes. Optimizing sensor placement to maximize reconstruction skill remains challenging due to evolving ocean dynamics and practical deployment constraints. Traditional approaches, such as Empirical Orthogonal Functions, greedy search, or Gaussian processes, either assume static observation networks or scale poorly in high-resolution and non-stationary regimes. We introduce a differentiable adaptive sensor placement framework based on a Gumbel-Softmax sampling operator. Given an ensemble of forecasts or simulations, the method jointly optimizes a probabilistic sampling mask and the reconstruction mapping (e.g., Optimal Interpolation correlation lengths) under strict observation budgets. Numerical experiments are conducted for Sea Surface Height reconstruction in a Gulf Stream region through Observing-System Simulation Experiments using a state-of-the-art high-resolution ocean simulation. With a sensor budget of only 0.1% (fewer than 100 point-wise observations on a 14°x14° domain) the optimized sampling reduces the reconstruction RMSE by more than half (0.0908 m versus 0.1750 m) and increases explained variance by about 20% (93.1% versus 74.4%) compared with a uniform random strategy. The method remains robust when trained on noisy ensembles with significant spatial displacement (up to 1°), demonstrating practical applicability under forecast uncertainty. Overall, the framework provides a scalable, budget-aware approach to designing observation networks. Beyond improved skill, it yields interpretable sampling patterns that consistently target energetic regions such as eddies and fronts, offering a transferable tool for adaptive sensing in geophysical systems.

Scattering black holes spin up and gain mass through the re-absorption of orbital angular momentum and energy radiated in gravitational waves during their encounter. In this work, we perform a series of numerical relativity simulations to investigate the spin-up and mass-gain for equal-mass black holes with a wide range of equal initial spins, $χ_{\rm i}\in[-0.7,0.7]$, aligned (or anti-aligned) to the orbital angular momentum. We also consider a variety of initial momenta. Furthermore, we explore a range of incident angles and identify the threshold between scattering and merging configurations. The spin-up and mass-gain are typically largest in systems with incident angles close to the threshold value, large momenta, and negative (i.e. anti-aligned) initial spins. When evaluated at the threshold angle, we find that the spin-up decreases linearly with initial spin. Intriguingly, systems with initial spin $χ_{\rm i}=0.7$ sometimes experience a spin-down, in spite of an increase in the black-hole angular momentum, due to a corresponding gain in the black-hole mass. Across the simulation suite, we find a maximum spin-up of $0.3$ and a maximum increase in the black-hole mass of $15\%$.

Motivation: Protein function prediction is a challenging task and an open problem in computational biology. The Critical Assessment of protein Function Annotation (CAFA) is a triennial, community-driven initiative that provides an independent, large-scale evaluation of computational methods for protein function prediction through time-delayed benchmarking experiments. CAFA has played a key role in highlighting high-performing methodologies and fostering detailed analysis and exchange of ideas. However, outside the periodic CAFA challenges, there is no platform for the continuous evaluation of newly developed methods and tracking performance as function annotations accumulate. Results: Here we introduce the Longitudinal Assessment of Protein Function Annotation Models server (LAFA) as a persistent benchmarking system for protein function prediction methods. LAFA provides a continuous evaluation of containerized function prediction methods, enabling up-to-date and robust comparative assessment of method performance under evolving ground truth. LAFA accelerates methodological iteration, supports reproducibility, and offers a more dynamic and fine-grained view of progress in protein function prediction. Code and Data Availability: LAFA is available at https://functionbench.net/. Detailed evaluation results can be found at https://github.com/anphan0828/CAFA_forever

We present high-angular-resolution ($\sim0.05^{\prime\prime}$, $\sim 60-250$ au) ALMA Band~6 observations from the HOTDISK project (Hot-Origin Tracer survey of DISKs of massive protostars) aimed at investigating the "hot-disk" chemical pattern traced by vibrationally excited water, NaCl, SiS, and SiO in the innermost regions around massive protostars. Ten targets were selected based on strong CH$_3$CN emission exhibiting clear rotational signatures and centrally concentrated SiO emission from lower-resolution observations. We detect vibrationally excited water emission toward 7 of the 10 sources. In all detections, the blueshifted and redshifted components are compact and located on opposite sides of the 1.3 mm continuum peak, with velocity gradients approximately perpendicular to the outflow axes, consistent with rotation on disk scales. Emission from NaCl and SiS is detected toward 5 of these 7 sources and exhibits similar kinematics, further supporting the presence of compact rotating structures. In contrast, commonly used hot-core tracers (e.g., CH$_3$CN and SO$_2$) primarily probe larger-scale envelope gas. These results demonstrate that vibrationally excited water, NaCl, and SiS are powerful tracers of disk structures on $\sim$100 au scales, when observed at sufficient angular resolution and sensitivity. The high detection rate suggests that hot-disk chemical patterns -- and thus compact rotating disks -- are common in massive star-forming regions, at least among sources with well-developed rotating envelopes.

We examine the role of anisotropic subgrid-scale (SGS) stress in wall-modeled large-eddy simulation (WMLES) of flow over a spanwise-uniform Gaussian-shaped bump, with emphasis on predicting flow separation. The simulations show that eddy-viscosity-based SGS models often yield non-monotonic predictions of the mean separation bubble size on the leeward side under grid refinement, whereas models incorporating anisotropic SGS stress produce more consistent results. To identify where SGS anisotropy is most critical, we introduce anisotropic SGS stress in selected regions of the domain. The results reveal that the windward side, where a strong favorable pressure gradient (FPG) occurs, is crucial in determining downstream separation. Analysis of the Reynolds stress transport equation shows that fluctuations of anisotropic SGS stress modify SGS dissipation and diffusion in this region, thereby altering the Reynolds stress and the onset of separation. Examination of the mean streamwise momentum equation indicates that at coarse resolutions, the mean SGS shear stress dominates, and the differences between the eddy-viscosity-based and anisotropic models remain minor. With grid refinement, resolved Reynolds stresses increasingly govern the near-wall momentum transport, and the influence of SGS stress fluctuations grows as they determine the SGS dissipation and diffusion of Reynolds stresses. Component-wise analysis of the SGS stress tensor further shows that the improvement arises mainly from including significant normal stress contributions. An a priori study using filtered direct numerical simulation of turbulent Couette-Poiseuille flow confirms that wall-bounded turbulence under FPG is highly anisotropic and that anisotropic SGS models provide a more realistic SGS stress representation than eddy-viscosity-based models.

We show that a three-dimensional superconductor with a non-Abelian SU(2) order parameter can support an extended resistive regime a Bose metal, in which transport is carried by bosonic electron-Majorana bound states - separating a uniform superconductor from a pair-density-wave (PDW) phase. The setting is a solvable Kondo lattice model introduced previously by the present authors, in which Kondo screening of a Yao-Lee $\mathbb{Z}_2$ spin liquid generates an order parameter with SU(2), rather than conventional U(1), symmetry, containing both superconducting and spin-density-wave components. Two effects cooperate to make fluctuations anomalously strong in three dimensions: the vanishing of the quadratic superconducting stiffness near the Lifshitz point where the optimal pairing momentum shifts from zero to finite $Q$, and the enlarged SU(2) order-parameter manifold. Building on our prior result that doping away from half-filling drives amplitude-modulated PDW order via finite-momentum electron-Majorana condensation, we analyze the fluctuation-dominated regime above that phase using a nonlinear sigma model. We find that the order-parameter propagator develops a ring of soft modes throughout the disordered phase, and that the resulting resistivity scales approximately as $R \sim T^3$ in three dimensions.

Raw datasets are often too large and unstructured to work with directly, and require a data preparation phase. The domain of industrial Cyber-Physical Systems (CPSs) is no exception, as raw data typically consists of large time-series data collections that log the system's status at regular time intervals. The processing of such raw data is often carried out using ad hoc, case-specific, one-off Python scripts, often neglecting aspects of readability, reusability, and maintainability. In practice, this can cause professionals such as data scientists to write similar data preparation scripts for each case, requiring them to do much repetitive work. We introduce CPSLint, a Domain-Specific Language (DSL) designed to support the data preparation process for industrial CPS. CPSLint raises the level of abstraction to the point where both data scientists and domain experts can perform the data preparation task. We leverage the fact that many raw data collections in the industrial CPS domain require similar actions to render them suitable for data-centric workflows. In our DSL one can express the data preparation process in just a few lines of code. CPSLint is a publicly available tool applicable for any case involving time-series data collections in need of sanitisation.

beta-Ga2O3 is a promising material for next-generation power electronics; however, its performance is strongly affected by lattice defects such as dislocations. In this study, we demonstrate three-dimensional (3D) visualization of dislocations in \b{eta}-Ga2O3 using synchrotron-radiation X-ray topo-tomography under a two-beam Borrmann-effect condition in transmission X-ray topography. By rotating the sample about the diffraction vector and acquiring a series of topo-tomographic images at different rotation angles, the evolution of dislocation contrast is captured, providing intuitive, depth-resolved visualization of dislocations. This method enables clear separation of dislocations in the epilayer and substrate in Schottky barrier diode structures, offering insight into dislocation propagation and their impact on epitaxial growth and device performance. This study represents the first demonstration of 3D dislocation reconstruction in beta-Ga2O3.

In this work, we revisit the one- and two-sample testing problems: binary hypothesis testing in which one or both distributions are unknown. For the one-sample test, we provide a more streamlined proof of the asymptotic optimality of Hoeffding's likelihood ratio test, which is equivalent to the threshold test of the relative entropy between the empirical distribution and the nominal distribution. The new proof offers an intuitive interpretation and naturally extends to the two-sample test where we show that a similar form of Hoeffding's test, namely a threshold test of the relative entropy between the two empirical distributions is also asymptotically optimal. A strong converse for the two-sample test is also obtained.

This paper presents a novel nonlinear backstepping control law for continuous, low-thrust station-keeping in the Earth-Moon system. Quasi-periodic libration point orbits are targeted under a high-fidelity model of the dynamics. Almost global uniform exponential stability guarantees are attained, as shown through Lyapunov's stability theory. Saturation of the actuators is formally included in the controller design, such that these guarantees hold even in the event of saturation. The relationship between saturation threshold, control gains, and deviation is studied and an optimal procedure for gain selection is discussed. The control solution is tested numerically through a Monte Carlo analysis over representative application cases, subject to operational errors, constraints, and external perturbations. Station-keeping under actuation saturation is validated considering a conservative threshold for typical electric propulsion systems.

Given the $r$-distance graph on the hypercube $\mathbb{F}_2^n$, where two vertices are adjacent if their Hamming distance is exactly $r$, we study the maximum size $T(n,r)$ of a triangle-free set of vertices. For even $r\le n/2$, we prove \[ T(n,r)=O\!\left(\frac{r2^n}{n+1}\right). \] In particular, $T(n,r)=o(2^n)$ whenever $r=o(n)$. For fixed $0<α<2/3$, we also prove that if $r=αn$, then \[ T(n,r)\le 2^{(1-\varepsilon_α)n} \] for some $\varepsilon_α>0$. We also obtain lower bounds in various regimes of $r$ as a function of $n$.

The era of large-scale, high-cadence astronomical surveys demands efficient and robust methods for time-series analysis. ARIMA models provide a versatile parametric description of stochastic variability in this context. However, their practical use is limited by the challenge of selecting optimal model orders while avoiding overfitting. We present a novel solution this problem by combining Autoregressive Integrated Moving Average (ARIMA) models with the Nested Sampling algorithm. Our method yields Bayesian evidences for model comparison and also incorporates an intrinsic Occam's penalty for unnecessary model complexity. Using JAX and Blackjax, a vectorized ARIMA-Nested Sampling framework with GPU-acceleration support is implemented, allowing us to perform model selection across grids of Autoregressive (AR) and Moving Average (MA) orders, with efficient inference of selected model parameters. We validate the approach using simulated time series with known ground-truth parameters and demonstrate accurate recovery of both model order and parameters. We then apply the method to several astronomical datasets, including the historical sunspot number record, stellar light curves of KIC 12008916 and Kepler 17 from the Kepler mission, and quasar light curves of 3C 273 and S4 0954+65 from the TESS mission. For all cases, except Kepler 17, the ARIMA models selected by this method were able to accurately model the stochastic variability in the time series data as well as produce accurate multi-step ahead forecasts for the sunspot number time series. Our results demonstrate that nested sampling offers a rigorous and computationally tractable alternative to autoregressive model selection in astronomical time-series analysis.

We study the optical depth to reionization in a cosmological setting that includes backreaction from matter inhomogeneities, using the Buchert averaging formalism. We construct a spacetime model consisting of multiple inhomogeneous domains, hereafter referred to as the backreaction model, characterized by a set of parameters. We first examine how these parameters influence the computation of the optical depth to reionization, $τ_{reion}$. Next, we carry out a Markov Chain Monte Carlo (MCMC) analysis based on the PantheonPlus+SH0ES Type Ia supernova sample to infer the best-fit values of the model parameters, and then use these to evaluate $τ_{reion}$. We obtain $τ_{reion} = 0.0581^{+0.0105}_{-0.0096}$ (68$\%$ confidence limits). This result indicates that, when PantheonPlus+SH0ES data are used to constrain the model parameters, our backreaction model yields a value of $τ_{reion}$ that aligns more closely with observational estimates than the value predicted by the standard cosmological model. We further demonstrate that the backreaction model leads to a modest reduction of the Hubble tension, while avoiding the need for exotic or non-standard physics.

A simple method is presented for deriving universal formulae for the correlators, frequently denoted $W_{g,n}(\{z_i\}), i=1,..n$, of a wide range of models of physical and mathematical interest. While many alternative methods exist for constructing such correlators, these formulae can be simply written in terms of one defining function and its derivatives. The method has been applied to the Airy and Bessel models, various minimal string and superstring theories, and their associated intersection theory settings, ordinary and various kinds of supersymmetric Weil-Petersson volumes, and more besides. For all these cases, their $W_{g,n}(\{z_i\})$ are just all specializations of the same universal formulae. A special variant of the method useful for ${N}{=}1$ supersymmetric cases is also presented. It allows for swift derivations of Norbury's three closed-form formulae for the volumes $V_{g,n}$ ($g{=}1,2,3$) of ${ N}{=}1$ supersymmetric Weil-Petersson volumes, and generalizations of them to a wider set of models. Moreover a new closed-form formula for the genus 4 case $V_{4,n}$ is derived. The straightforward method for how to derive such formulae for $g{>}4$ cases is described. Throughout, crucial roles are played by the underlying integrable KdV flows, as well as the Gel'fand-Dikii equation.

Type IIB string theory on AdS$_3 \times S^3\times T^4$ with RR flux as the near-horizon limit of the D1-D5 solution is expected to be dual to a (4,4) supersymmetric 2d CFT parametrized by the integers $Q_1,Q_5$ and other moduli. It is related by T-duality to type IIA string theory in the near-horizon limit of the D2-D4 solution which admits an uplift to the 11d AdS$_3 \times S^3\times T^5$ background which is the near-horizon limit of the M2-M5 solution. We point out that this relation allows one to use the quantum M2-brane description to probe ``non-planar'' corrections in the dual 2d CFT, in close analogy with the ABJM theory case (described by M-theory on AdS$_4 \times S^7/\mathbb{Z}_k$). We consider an analog of a supersymmetric Wilson loop (line defect) expectation value represented by type IIA string partition function expanded around AdS$_2\subset $AdS$_3$ minimal surface. Its M-theory analog is the M2 brane partition function expanded near AdS$_2\times S^1$. We compute the 1-loop contribution $Z_1$ to the M2 brane partition function and find that in contrast to the ABJM case in arXiv:2303.15207 (where $Z_1= (2\sin{\frac{2π}{ k}})^{-1} = \frac{k}{ 4 π} +\fracπ{ 6k} +...$ contains an infinite series of higher genera string corrections, $k^{-1} \sim \frac{g_s}{ \sqrt {\rm T}}$), here it is given solely by the leading string-theory contribution $Z_1= \fracκ{ \sqrt{2π}}$ where $κ\sim \sqrt{Q_5}$ plays a role analogous to $k$. We also discuss a generalization to the mixed flux case which is straightforward from the 11d perspective.

Runtime introspection of dependencies, i.e., the ability to observe which dependencies are currently used during program execution, is fundamental for Software Supply Chain security. Yet, Java has no support for it. We solve this problem with Classport, a blueprint and system that embeds dependency information into Java class files, enabling the retrieval of dependency information at runtime. We evaluate Classport on six real-world projects, demonstrating the feasibility in identifying dependencies at runtime.

Although AI assistance can improve writing quality, it can also decrease feelings of ownership. Ownership in writing has important implications for attribution, rights, norms, and cognitive engagement, and designers of AI support systems may want to consider how system features may impact ownership. We investigate how the stage at which AI support for writing is provided (planning, drafting, or revising) changes ownership. In a study of short essay writing (between subjects, n = 253) we find that while any AI assistance decreased ownership, planning support only minimally decreased ownership, while drafting support saw the largest decrease. This variation maps onto the amount of text and ideas contributed by AI, where more text and ideas from AI decreased ownership. Notably, an AI-generated draft based on participants' own outline resulted in significantly more AI-contributed ideas than AI support for planning. At the same time, more AI contributions improved essay quality. We propose that writers, educators, and designers consider writing stage when introducing AI assistance.

Global pandemics, such as the recent COVID-19 crisis, highlight the need for stochastic epidemic models that can capture the randomness inherent in the spread of disease. Such models must be accompanied by methods for estimating parameters in order to generate fast nowcasts and short-term forecasts that can inform public health decisions. This paper presents a comparison of two advanced Bayesian inference methods: 1) pseudo-marginal particle Markov chain Monte Carlo, using an unbiased likelihood estimate obtained by Particle Filter (PF), and 2) Conditional Normalizing Flows (CNF). We investigate their performance on three commonly used compartmental models: A classical Susceptible-Infected-Susceptible (SIS), a Susceptible-Infected-Recovered (SIR) model and a two-variant Susceptible-Exposed-Infected-Recovered (SEIR) model, complemented by an observation model that maps latent trajectories to empirical data. Addressing the challenges of intractable likelihoods for parameter inference in stochastic settings, our analysis highlights how these likelihood-free methods provide accurate and robust inference capabilities. The results of our simulation study further underscore the effectiveness of these approaches in capturing the stochastic dynamics of epidemics, providing prediction capabilities for the control of epidemic outbreaks. Results on an Ethiopian cohort study demonstrate operational robustness under real-world noise and irregular data sampling. To facilitate reuse and to enable building pipelines that ultimately contribute to better informed decision making in public health, we make code and synthetic datasets publicly available.

We establish Harnack inequalities for viscosity solutions of a class of degenerate fully nonlinear anisotropic elliptic equations exhibiting non-standard growth conditions. A primary example of such operators is the degenerate anisotropic $(p_i)$-Laplacian. Our approach relies on the sliding paraboloid method, adapted with suitably chosen anisotropic functions to derive the basic measure estimates. A central contribution of this work is the development of a doubling property, achieved through the explicit construction of a novel barrier function. By combining these tools with the intrinsic geometry techniques introduced in [DGV08, VV25], we prove the intrinsic Harnack inequality for this class of operators under appropriate conditions on the exponents $(p_i)$.

We study a minimal $\mathbb{Z}_2$-symmetric extension of the Standard Model containing two singlet fermions and a singlet scalar that interact with the SM particles through the Higgs-portal. We identify regions of parameter space in which all three new particles are kinematically stable, giving rise to a multi component dark matter (DM) scenario. The parameter space consistent with the observed dark matter relic abundance are determined, and the contribution of each component to the total relic density is evaluated. While the DM-nucleon elastic scattering cross sections of the two fermionic dark matter components are loop-suppressed, the corresponding cross section of the scalar dark matter particle arises at tree level and is therefore expected to dominate. We find a viable region of the parameter space in which the scalar dark matter candidate with mass range of approximately $125-400$ GeV, evades current direct detection (DD) bounds while contributing only a small fraction of the observed relic density. In contrast, the fermionic dark matter possesses a loop-suppressed DD cross section that lies below the neutrino floor and can constitute a substantial fraction of the total relic density.

Amidst the exoplanet revolution in which multiple techniques have successfully found planets, the Doppler (Radial Velocity, or "RV") technique is unique in its sensitivity to giant planets at long orbital periods around Sun-like stars. The upcoming retirement of Keck-HIRES will incur irreversible changes in the continuation of HIRES's decades-long stable RV baseline and with it, the exoplanet community's ability to detect giant exoplanets with periods longer than Jupiter. With the time elapsed from the last HIRES RV for many stars of interest at ~3 years and growing, we tested the impact of a "critical RV", one that would bridge this gap between past HIRES RVs and future stable Keck-KPF RVs, on the recovery of long-period giant exoplanets. We generated 2000 1-planet systems with RVs sampled at a representative timeseries and used the planet-finding code Octofitter to perform injection-recovery experiments including and omitting this critical RV for each system. For the injected long-period super-Jupiters (~8-55 years, 1-13 $M_J$), including the critical RV induced a $1.5\times$ enhancement in overall planet recovery and a more specific $3.5\times$ enhancement in the recovery of super-Jupiters with Saturn-like periods. These experiments show that gathering a critical RV for stars of interest can help ensure that HIRES's decades-long stable RV baseline in conjunction with future KPF RVs, or indeed that the observationally-gapped RV baselines of any instruments that will undergo an RV zeropoint offset, will continue to be foundational to the discovery of long-period giant exoplanets in years to come.

We introduce persistence with an emphasis on its algebraic foundations, using the representation theory of posets. Linear representations of posets arise in several areas of mathematics, including the representation theory of quivers and finite dimensional algebras, Morse theory and other areas of geometry, as well as topological inference and topological data analysis -- often via persistent homology. In some of these contexts, the category of poset representations of interest admits a metric structure given by the so-called interleaving distance. Persistence studies the algebraic properties of these poset representations and their behavior under perturbations in the interleaving distance. We survey fundamental results in the area, applications to pure and applied mathematics, advanced topics such as multiparameter persistence, as well as theoretical challenges and open questions.

Singular knot theory extends classical knot theory by allowing transverse double points without over/under information, together with singular Reidemeister moves of types IV and V. A central open problem in this theory is to determine the minimal generating sets of oriented singular Reidemeister moves. In this paper, we completely solve this problem. In addition, we establish independence results for singular Reidemeister moves by introducing an invariant that provides obstructions and lower bounds for generating sets, including the independence of type III from types I, II, IV, and V. More precisely, starting from a minimal generating set of ordinary Reidemeister moves of types I--III, we prove that the singular moves admit exactly $96$ distinct inclusion-minimal generating sets, and that these exhaust all possibilities. Our proof introduces a new invariant for singular links, constructed via a projection to self-singular links, which detects the distinction between the two families of type IV moves and provides an obstruction for generating type V moves from types I--IV. We also determine the unoriented case, where the classification collapses to exactly $8$ minimal generating sets.

The strongly correlated fermions play a vital role in modern physics. For a given fermionic Hamiltonian system, the most widely used approach to explore the underlying physics is to study the wave function that incorporates Fermi-Dirac statistics, which can be obtained variationally by energy minimization or by imaginary-time evolution. In this work, we develop an accurate tensor network method for one-dimensional interacting fermionic models based on the coherent-state path-integral representation of the fermionic partition function. Employing the coherent-state representation, the partition function is effectively represented as a (1+1)-dimensional anisotropic Grassmann-valued tensor network, and the Grassmann version of the corner transfer-matrix renormalization group algorithm is developed to contract the tensor network and evaluate physical quantities. We validate our method in the one-dimensional fermionic Hubbard model with a magnetic field, where the essential features of the phase diagram in the $(μ, B)$ plane are quantitatively captured. Our work offers a promising approach to interacting fermionic models within the framework of tensor networks.

Extremely high-peaked BL Lac objects - also named extreme blazars - are among the most energetic and persistent extragalactic accelerators in the Universe, defined by a synchrotron emission peaking above $10^{17}$ Hz in X-rays. Such emission is then reprocessed and produces radiation extending deeply into very-high-energy (VHE, energy E>100 GeV) gamma rays. Observations in this energy band - optimally investigated by the Imaging Air-Shower Cherenkov telescopes - are crucial for probing the physical processes that drive their extreme behavior. This study extends our investigation of extreme blazars in the VHE gamma-ray range, providing a second new mini-catalog of sources observed by the MAGIC telescopes. We report on the monitoring of seven targets between 2017 and 2025, including four newly observed sources and three that have been part of long-term observation campaigns, for a total of approximately 338 hours of observations. The analysis of MAGIC data reveals two new VHE detections of extreme blazars, along with three additional sources showing hints of VHE emission. Joint observations of MAGIC and the first Large-Sized Telescope (LST-1) also confirmed a new VHE extreme blazar. Our results are complemented by simultaneous multiwavelength observations in other energy bands, including optical-UV, X-rays, and high-energy gamma rays (100 MeV<E<100 GeV). We confirm typical behavior of extreme blazars, such as a modest variability and a ``harder-when-brighter'' trend in X-rays across the sample. This new set increases the population of extreme blazars and their broadband analysis confirms the physical properties of these extreme sources.

Quantum loop algebras generalize $U_q(\widehat{\mathfrak{g}})$ for simple Lie algebras $\mathfrak{g}$, and they include examples such as quantum affinizations of Kac-Moody Lie algebras, K-theoretic Hall algebras of quivers, and BPS algebras for toric Calabi-Yau threefolds. In the present paper, we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of $U_q(\widehat{\mathfrak{g}})$. We use our construction to prove fundamental facts about representations of quantum loop algebras, such as the rationality of $R$-matrices, multiplicativity of $q$-characters, and polynomiality of theta series.

Efficient mixed-precision MMA operations are critical for accelerating deep learning workloads on GPGPUs. However, existing open-source Tensor Core implementations rely on discrete arithmetic unit designs, leading to high latency, accumulated rounding errors, and poor resource utilization. To address these challenges, we propose Ten-Four, a configurable mixed-precision fused dot product unit integrating both floating-point and integer arithmetic pipelines within a unified architecture, implemented as part of the open-source RISC-V-based Vortex GPGPU's Tensor Core Unit extension. It supports low-precision multiplication in TF32/FP16/BF16/FP8/BF8/INT8/INT4 with higher-precision FP32/INT32 accumulation, native Microscaling (MX) support, and sparse lane clock-gating for dynamic power reduction, while matching NVIDIA Tensor Core numerical accuracy. Ten-Four achieves 4-cycle latency at 300 MHz Fmax on the Xilinx U55C FPGA, delivering 130.368 GFLOPS peak throughput per Tensor Core and 2.7x-7.9x speedup over equivalent Berkeley HardFloat and FPnew based implementations at less than 60% the area cost. ASIC synthesis in 7nm FinFET achieves 2.771 TFLOPS/W peak efficiency at 1.58 GHz Fmax.

Matrix multiplication is a fundamental operation in both training of neural networks and inference. To accelerate matrix multiplication, Graphical Processing Units (GPUs) provide it implemented in hardware. Due to the increased throughput over the software-based matrix multiplication, the multipliers are increasingly used outside of AI, to accelerate various applications in scientific computing. However, matrix multipliers targeted at AI are at present not compliant with IEEE 754 floating-point arithmetic behaviour, with different vendors offering different numerical features. This leads to non-reproducible results across different generations of GPU architectures, at the matrix multiply-accumulate instruction level. To study numerical characteristics of matrix multipliers - such as rounding behaviour, accumulator width, normalization points, extra carry bits, and others - test vectors are typically constructed. Yet, these vectors may or may not distinguish between different hardware models, and due to limited hardware availability, their reliability across many different platforms remains largely untested. We present software models for emulating the inner product behavior of low- and mixed-precision matrix multipliers in the V100, A100, H100 and B200 data center GPUs in most supported input formats of interest to mixed-precision algorithm developers: 8-, 16-, and 19-bit floating point. These matrix multiplier models are first approximated by determining the numerical features via test vectors designed to trigger outputs sensitive to bit level differences in the implementation, followed by semi-exhaustive comparison (randomised input vectors of $10^7$ values) between the models and the actual GPU matrix multipliers - this process is repeated until the model is bit accurate.

We study the photon bulk-to-bulk propagator in AdS in various gauges, including axial, Coulomb, and the standard covariant gauge. We compute the propagator using both momentum and position space techniques. We ensure the propagators obtained obey the right subsidiary conditions arising from gauge invariance. In particular, BRST invariance implies a relation between the longitudinal components of the gauge field propagator and the ghost bulk-to-bulk propagator. Our method relies on decomposing the components of the propagator in terms of independent tensor structures and solving for the form factors. We recover some previously existing results and obtain new expressions for the propagator in other gauges. The propagator in axial and Coulomb gauge is simpler in momentum space, as momentum space makes manisfest the translational invariance in the boundary directions, while the position space expression is the simplest in the covariant Fried-Yennie gauge. In this gauge the propagator has an improved IR behavior, somewhat analogous to the UV improved behavior associated with the Landau gauge in flat space. The results readily extend to Yang-Mills fields.