We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category, and show that it is invariant under suitable Morita equivalences of the second kind. A bimodule version of Koszul duality is constructed and used to show that Hochschild cohomology of the second kind is preserved under (nonconilpotent) Koszul duality. We show that Hochschild cohomology of the second kind of an algebra often computes the ordinary Hochschild cohomology of geometrically meaningful dg categories. Examples include the category of infinity local systems on a topological space, the bounded derived category of a complex algebraic manifold and the category of matrix factorizations.

We study capillary-gravity surface waves for fluid flows governed by Darcy's law. This includes flows in vertical Hele-Shaw cells and in porous media (the one-phase Muskat problem) with finite or infinite depth. The free boundary is acted upon by an external pressure posited to be in traveling wave form with an arbitrary periodic profile and an amplitude parameter. For any given wave speed, we first prove that there exists a unique local curve of small periodic traveling waves corresponding to small values of the parameter. Then we prove that as the parameter increases but could possibly be bounded, the curve belongs to a connected set $\mathcal{C}$ of traveling waves. The set $\mathcal{C}$ contains traveling waves that either have arbitrarily large gradients or are arbitrarily close to the rigid bottom in the finite depth case. To the best of our knowledge, this is the first construction of large traveling surface waves for a viscous free boundary problem.

Many small to large organizations have adopted the Microservices Architecture (MSA) style to develop and deliver their core businesses. Despite the popularity of MSA in the software industry, there is a limited evidence-based and thorough understanding of the types of issues (e.g., errors, faults, failures, and bugs) that microservices system developers experience, the causes of the issues, and the solutions as potential fixing strategies to address the issues. To ameliorate this gap, we conducted a mixed-methods empirical study that collected data from 2,641 issues from the issue tracking systems of 15 open-source microservices systems on GitHub, 15 interviews, and an online survey completed by 150 practitioners from 42 countries across 6 continents. Our analysis led to comprehensive taxonomies for the issues, causes, and solutions. The findings of this study informthat Technical Debt, Continuous Integration and Delivery, Exception Handling, Service Execution and Communication, and Security are the most dominant issues in microservices systems. Furthermore, General Programming Errors, Missing Features and Artifacts, and Invalid Configuration and Communication are the main causes behind the issues. Finally, we found 177 types of solutions that can be applied to fix the identified issues. Based on our study results, we propose a future research framework that outlines key problem dimensions and actionable study strategies to support the engineering of emergent and next-generation microservices systems.

For a Keller-Segel model for chemotaxis in two spatial dimensions we consider a modification of a positivity preserving fully discrete scheme using a local extremum diminishing flux limiter. We discretize space using piecewise linear finite elements on an quasiuniform triangulation of acute type and time by the backward Euler method. We assume that initial data are sufficiently small in order not to have a blow-up of the solution. Under appropriate assumptions on the regularity of the exact solution and the time step parameter we show existence of the fully discrete approximation and derive error bounds in $L^{2}$ for the cell density and $H^{1}$ for the chemical concentration. We also present numerical experiments to illustrate the theoretical results.

Using the method of paracontrolled distributions, we show the local well-posedness of an additive noise approximation to the fluctuating hydrodynamics of the Keller-Segel model on the two-dimensional torus. Our approximation is a non-linear, non-local, parabolic-elliptic stochastic PDE with an irregular, heterogeneous space-time noise. As a consequence of the irregularity and heterogeneity, solutions to this equation must be renormalised by a sequence of diverging fields. Using the symmetry of the elliptic Green's function, which appears in our non-local term, we establish that the renormalisation diverges at most logarithmically, an improvement over the linear divergence one would expect by power counting. Similar cancellations also serve to reduce the number of diverging counterterms.

We revisit Wagoner et al. (1967), a classic contribution in the development of Big Bang Nucleosynthesis. We demonstrate that it presents an incorrect expression for the temperature of the early universe as a function of time in the high temperature limit, $T \gtrsim 10^{10}$K. As this incorrect expression has been reproduced elsewhere, we present a corrected form for the initial conditions required for calculating the formation of the primordial elements in the Big Bang.

We study track categories (i.e., groupoid-enriched categories) endowed with additive structure similar to that of a 1-truncated DG-category, except that composition is not assumed right linear. We show that if such a track category is right linear up to suitably coherent correction tracks, then it is weakly equivalent to a 1-truncated DG-category. This generalizes work of the first author on the strictification of secondary cohomology operations. As an application, we show that the secondary integral Steenrod algebra is strictifiable.

The dual motivic Steenrod algebra with mod $\ell$ coefficients was computed by Voevodsky over a base field of characteristic zero, and by Hoyois, Kelly, and Østvær over a base field of characteristic $p \neq \ell$. In the case $p = \ell$, we show that the conjectured answer is a retract of the actual answer. We also describe the slices of the algebraic cobordism spectrum $MGL$: we show that the conjectured form of $s_n MGL$ is a retract of the actual answer.

In previous work of the first author and Jibladze, the $E_3$-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the $E_3$-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms $E_m$. In this paper, we introduce $2$-track algebras and tertiary chain complexes, and we show that the $E_4$-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.

RF cavities loaded with magnetic alloy (MA) or ferrite ring cores are used in synchrotrons and storage rings if the maximum RF frequency is in the order of a few MHz. A simple model for the description of cavities of this type is derived. The most important parameters are defined, and some properties of the material and of the cavity are summarized. Different cavity configurations, development aspects, and several practical topics are covered. A few specific ferrite- and MA-loaded cavity systems are discussed as examples.

We analyse our recently-published velocity measurements of alpha Cen A (Butler et al. 2004). After adjusting the weights on a night-by-night basis in order to optimize the window function to minimize sidelobes, we extract 42 oscillation frequencies with l=0 to 3 and measure the large and small frequency separations. We give fitted relations to these frequencies that can be compared with theoretical models and conclude that the observed scatter about these fits is due to the finite lifetimes of the oscillation modes. We estimate the mode lifetimes to be 1-2 d, substantially shorter than in the Sun.

We investigate the multiband photometric properties of seven supernovae (SNe) showing double-peaked light-curve evolution and prominent shock-cooling emission, observed by the Wide Field Survey Telescope (WFST) during its first year of operation. By jointly employing an analytic early shock-cooling model and the Arnett radioactive-diffusion model, we fit the bolometric light curves and infer ejecta masses in the range $1.1$-$2.6 M_\odot$, consistent with a transitional population between ultra-stripped supernovae (USSNe) and normal stripped-envelope supernovae (SESNe). The envelope masses are estimated to be $M_{\rm env}=0.1$-$0.4 M_\odot$, while the progenitors are constrained to be yellow or blue supergiants (YSGs/BSGs) with radii of $R=120$-$300 R_\odot$. Using empirical relations, we estimate progenitor luminosities of $L=10^{4.6}$-$10^{4.9} L_\odot$, corresponding to zero-age main-sequence (ZAMS) masses of $8$-$20 M_\odot$. Theoretical models suggest that such progenitors are more naturally produced through binary evolution channels, as single-star evolutionary pathways are unable to yield ejecta masses this low.

Statistical boosting algorithms are renowned for their intrinsic variable selection and enhanced predictive performance compared to classical statistical methods, making them especially useful for complex models such as generalized additive models for location scale and shape (GAMLSS). Boosting this model class can suffer from imbalanced updates across the distribution parameters as well as long computation times. Shrunk optimal step lengths have been shown to address these issues. To examine the influence of socio-economic factors on the distribution of the number of antenatal care visits in Nigeria, we generalize boosting of GAMLSS with shrunk optimal step lengths to base-learners beyond simple linear models and to a more complex response variable distribution. In an extensive simulation study and in the application we demonstrate that shrunk optimal step lengths yield a more balanced regularization of the overall model and enhance computational efficiency across diverse settings, in particular in the presence of base-learners penalizing the size of the fit.

We present comprehensive photometric and spectroscopic observations of a transitional type Ia SN 2024aedt, discovered by the 2.5-meter Wide Field Survey Telescope (WFST) within one day of the explosion. Its light curve is characterized by a peak absolute magnitude of $M_B = -18.49 \pm 0.03$ mag and a decline rate of $Δm_{15}(B) = 1.53 \pm 0.36$ mag, placing the object on the $Δm_{15}(B)$--$M_B$ diagram in the transition region between normal and subluminous SNe Ia. Furthermore, the early-color evolution and host galaxy environment of SN 2024aedt underscore its transitional nature, sharing properties with both normal and 91bg-like SNe Ia. Light-curve modeling with MOSFiT yields a synthesized $^{56}\mathrm{Ni}$ mass of $0.414 \pm 0.042\,M_{\odot}$ and a total ejecta mass of $0.548 \pm 0.108\,M_{\odot}$. A comparison with theoretical models suggests that the evolutionary trend can be broadly explained by both delayed-detonation (DDT) and double-detonation (DDet) scenarios while possible early-excess emissions predicted by DDet cannot be identified given the limited detections soon after the SN explosion. Although the overall spectral evolution of SN 2024aedt is similar to that of other transitional SNe Ia, the spectroscopic comparison reveals diversity in the early-phase blue-end features, which becomes more homogeneous at later phases. The result indicates the importance of early-time observations in understanding the origin of SN Ia diversity.

In this paper we present 16 early-phase type Ia supernovae (SNe Ia) discovered during the pilot survey of the 2.5-meter Wide Field Survey Telescope (WFST-PS) from March 4 to July 10, 2024, including three SNe Ia with early-excess emission features (EExSNe Ia). The discovery magnitude of the 16 WFST-PS early-phase SNe is at least 3 mag fainter than their peak brightness. A large scatter of color indices is found in approximately the first 10 days of supernova explosions, indicating diverse photometric behaviors in the early phase. Three EExSNe Ia show relatively brighter peak luminosities and longer rise time compared to those of non-EExSNe Ia. The results indicate that current theoretical models require further refinement to fully capture the early photometric evolution of SNe Ia. Based on the initial high-cadence ugr-band data from the WFST-PS survey, we emphasize that early near-ultraviolet (NUV) observations are indispensable for placing tight constraints on the explosion mechanisms and progenitor systems of SNe Ia.

Conventionally, dc fields are used for switching dipole orientations in ferroelectrics. Such fields tilt the potential surface experienced by domain walls and thereby lower activation energies for their movement: escape from tilted potential wells is then realised by thermal excitation, allowing a "creep" process of pinning and depinning to develop. Borrowing ideas of domain wall resonance from the magnetic racetrack community, we show that ac fields, applied at the right frequency, can cause switching at much lower field magnitudes than dc ones (by factors of 4-5). Ferroelectric wall motion appears to be overdamped in the system studied (relaxor strontium barium niobate) and so the maximum in switching efficacy observed, at ~100 kHz, cannot be associated with resonant amplification, which needs an underdamped environment. Instead, in this high viscosity system, the frequency at which the maximum switching efficacy occurs seems to represent a compromise between the attempt frequency for wall depinning (which increases with frequency) and the extent to which energy is transferred to the wall within each field cycle (which decreases with frequency). Notwithstanding the absence of true resonance, the observation that ac excitation can dramatically reduce the bias levels needed for ferroelectric switching could still have significant ramifications for low energy memory technology.

User-centric evaluation has become a key paradigm for assessing Conversational Recommender Systems (CRS), aiming to capture subjective qualities such as satisfaction, trust, and rapport. To enable scalable evaluation, recent work increasingly relies on third-party annotations of static dialogue logs by crowd workers or large language models. However, the reliability of this practice remains largely unexamined. In this paper, we present a large-scale empirical study investigating the reliability and structure of user-centric CRS evaluation on static dialogue transcripts. We collected 1,053 annotations from 124 crowd workers on 200 ReDial dialogues using the 18-dimensional CRS-Que framework. Using random-effects reliability models and correlation analysis, we quantify the stability of individual dimensions and their interdependencies. Our results show that utilitarian and outcome-oriented dimensions such as accuracy, usefulness, and satisfaction achieve moderate reliability under aggregation, whereas socially grounded constructs such as humanness and rapport are substantially less reliable. Furthermore, many dimensions collapse into a single global quality signal, revealing a strong halo effect in third-party judgments. These findings challenge the validity of single-annotator and LLM-based evaluation protocols and motivate the need for multi-rater aggregation and dimension reduction in offline CRS evaluation.

We seek to narrow the gap between parametric and nonparametric modelling of stationary time series processes. The approach is inspired by recent advances in focused inference and model selection techniques. The paper generalises and extends recent work by developing a new version of the focused information criterion (FIC), directly comparing the performance of parametric time series models with a nonparametric alternative. For a pre-specified focused parameter, for which scrutiny is considered valuable, this is achieved by comparing the mean squared error of the model-based estimators of this quantity. In particular, this yields FIC formulae for covariances or correlations at specified lags, for the probability of reaching a threshold, etc. Suitable weighted average versions, the AFIC, also lead to model selection strategies for finding the best model for the purpose of estimating e.g.~a sequence of correlations.

These lecture notes are based on lectures given by the author at the Les Houches 2025 summer school on "Exact Solvability and Quantum Information". The central theme of these notes is to apply the philosophy of statistical mechanics to study the dynamics of quantum information in ideal and monitored random quantum circuits -- for which an exact description of individual realizations is expected to be generically intractable.

A signal processing-based framework is proposed for detecting random segment failures in segmented waveguide-enabled pinching-antenna systems. To decouple the passively combined uplink signal and to provide per-segment observability, tagged pilots are employed. A simple tag is attached to each segment and is used to apply a known low-rate modulation at the segment feed, which assigns a unique signature to each segment. Based on the tagged-pilot model, a low-complexity per-segment maximum-likelihood (ML) detector is developed for the case in which the pilot length is no smaller than the number of segments. For the case in which the pilot length is smaller than the number of segments, sparsity in the failure-indicator vector is exploited and a compressive sensing-based detector is adopted. Numerical results show that the per-segment detector approaches joint ML performance, while the compressive sensing-based detector achieves reliable detection with a short pilot and can outperform baselines that require much longer pilots.

Background: What counts as violence is neither self-evident nor universally agreed upon. While physical aggression is prototypical, contemporary societies increasingly debate whether exclusion, humiliation, online harassment or symbolic acts should be classified within the same moral category. At the same time, Large Language Models (LLMs) are being consulted in everyday contexts to interpret and label complex social behaviors. Whether these systems reproduce, reshape or simplify human conceptions of violence remains an open question. Methods: Here we present a systematic comparison between human judgements and LLM classifications across 22 scenarios carefully designed to be morally dividing, spanning from physical and verbally aggressive behavior, relational dynamics, marginalization, symbolic actions and verbal expressions. Human responses were compared with outputs from multiple instruction-tuned models of varying sizes and architectures. We conducted global, sentence-level and thematic-domain analyses, and examined variability across models to assess patterns of convergence and divergence. Findings: This study treats violence as a strategically chosen proxy through which broader belief formation dynamics can be observed. Violence is not the focus of the study, but it serves as a tool to investigate broader analysis. It enables a structured investigation of how LLMs operationalize ambiguous moral constructs, negotiate conceptual boundaries, and transform plural human interpretations into singular outputs. More broadly, the findings contribute to ongoing debates about the epistemic role of conversational AI in shaping everyday interpretations of harm, responsibility and social norms, highlighting the importance of transparency and critical engagement as these systems increasingly mediate public reasoning.

This methodological note investigates and discuss possible selection and collider restriction bias due to predictor availability in prognostic models.

AllReduce is a fundamental collective operation in distributed computing and a key performance bottleneck for large-scale training and inference. Its completion time is determined by the number of communication steps, which dominates latency-sensitive workloads, and the communication distance affecting both latency- and bandwidth-bound regimes. Direct-connect topologies, such as torus networks used in Google's TPUv4, are particularly prone to large communication distances due to limited bisection bandwidth. Latency-optimal algorithms such as Bruck's complete AllReduce in $\log_3 n$ steps on a bidirectional ring, but incur large communication distances that result in substantial congestion. In contrast, recent approaches such as Swing reduce communication distance and congestion, but are inherently required to perform $\log_2 n$ steps to complete AllReduce, sacrificing latency-optimality. In this paper, we present Trivance, a novel AllReduce algorithm that completes within $\log_3 n$ steps, while reducing congestion compared to Bruck's algorithm by a factor of three and preserving bandwidth-optimality. Trivance exploits both transmission ports of a bidirectional ring within each step to triple the communication distance along both directions simultaneously. Furthermore, by performing joint reductions, Trivance improves both the number of steps and network congestion. We further show that Trivance extends naturally to multidimensional torus networks, retaining its latency advantage while achieving performance comparable to bandwidth-optimal algorithms for large messages. Our empirical evaluation shows that Trivance improves state-of-the-art approaches by 5-30% for message sizes up to 8\,MiB, in high-bandwidth settings up to 32MiB and for 3D tori up to 128MiB. Throughout the evaluation, Trivance remains the best-performing latency-optimal algorithm.

Symmetric edge polytopes are a recent and well-studied family of centrally symmetric polytopes arising from graphs. In this paper, we introduce a generalization of this family to arbitrary simplicial complexes. We show how topological properties of a simplicial complex can be translated into geometric properties of such polytopes, and vice versa. We study the integer decomposition property, facets and reflexivity of these polytopes. Using Gröbner basis techniques, we obtain a (not necessarily unimodular) triangulation of these polytopes. Due to the tools we use, most of our results hold in the more general setting of arbitrary centrally symmetric polytopes.

We have reproducibly grown near-single-domain superconducting aluminum (Al) films on GaAs(111)A wafers using molecular beam epitaxy. Synchrotron X-ray diffraction revealed twin-domain ratios of 0.00005 and 0.0003 for 19.4-nm- and 9.6-nm-thick films, respectively-the lowest reported for Al on any substrate and long considered unattainable for practical device platforms. Azimuthal scans across off-normal Al{$11\bar{1}$} reflections exhibit narrow full width at half maximum (FWHM) values down to $0.55^\circ$, unmatched by epi-Al grown by any other method. Normal scans showed a well-defined (111) orientation with pronounced Pendellösung fringes, and $θ$-rocking-curve FWHM values down to $0.018^\circ$; the former indicates abrupt film-substrate and oxide-film interfaces. Electron backscatter diffraction mapping confirms macroscopic in-plane uniformity and the absence of $Σ$3 twin domains. Atomic force microscopy and scanning transmission electron microscopy confirmed atomically smooth surfaces and abrupt heterointerfaces. The films exhibit critical temperatures approaching bulk values, establishing a materials platform for scalable, high-coherence superconducting qubits.

This paper investigates goal-oriented remote monitoring of an unobservable Markov source using energy-harvesting sensors that communicate with a mobile receiver, such as a Low Earth Orbit (LEO) satellite or Unmanned Aerial Vehicle (UAV). Unlike conventional systems that assume stationary base stations, the proposed framework explicitly accounts for receiver mobility, which induces time-varying channel characteristics modeled as a finite-state Markov process. The remote monitoring problem is formulated as a partially observable Markov decision process (POMDP), which is transformed into a tractable belief-state MDP and solved using relative value iteration to obtain optimal sampling and transmission policies. Two estimation strategies are considered: Maximum Likelihood (ML) and Minimum Mean Distortion (MMD). Numerical results demonstrate that incorporating receiver mobility and channel state information into the optimization reduces the average distortion by 10% to 42% compared to baseline policies and constant-channel assumptions, highlighting the importance of base station motion knowledge for effective goal-oriented communication.

We investigate low-scale baryogenesis \textit{via} tri-resonant leptogenesis within the scotogenic model with a scalar dark matter embedded in non-holomorphic modular $A_4$ symmetry framework. The model naturally accommodates three nearly degenerate right-handed (RH) neutrinos when they are assigned to the triplet representation of $A_4$. The near degeneracy originates from treating the symmetric contribution to the Majorana mass matrix, arising from the $\mathbf{3}\otimes\mathbf{3}$ decomposition of $A_4$, as a small perturbation to the dominant singlet contribution. Generalized CP (gCP) symmetry is imposed in the model, rendering the complex modulus $τ$ as the sole source of CP violation. In particular, for the inverted hierarchy (IH), the predicted $3σ$ range of $θ_{23}$ lies in the lower octant close to maximal value while CP phase $δ_{\mathrm{CP}}$ and the Majorana phase $α_{21}$ are predicted to lie close to $0^\circ$ or $360^\circ$. Also, in this case, predicted values of $m_{ee}$ and $\sum_i m_i$ can be tested and constrained by future neutrinoless double beta decay $(0νββ)$ experiments, as well as by cosmological observations, particularly DESI+BAO and Planck data. In fact DESI+BAO disallows IH in the model. We further show that successful baryogenesis can be achieved for both normal hierarchy (NH) and inverted hierarchy (IH) of light neutrino masses with RH neutrino masses as low as $537~\mathrm{GeV}$ rendering this scenario experimentally testable. For NH, RH neutrino mass degeneracy of $\mathcal{O}(10^{-7}\!-\!10^{-6})$ is required, while for IH a stronger degeneracy of $\mathcal{O}(10^{-8})$ is needed. Remarkably, in the NH case, successful baryogenesis can occur even in the deep washout regime with decay parameters of $\mathcal{O}(10^{5})$ owing to the tri-resonant enhancement of the CP asymmetry and the inclusion of flavor effects.

Electrified heating systems with thermal storage, such as electric boilers and heat pumps, represent a major source of demand-side flexibility. Under current electricity market designs, balance responsible parties (BRPs) operating such assets are required to submit binding day-ahead electricity consumption schedules, and they typically do it based on forecasts of heat demand and electricity prices. Common scheduling approaches implicitly assume that forecast uncertainty can be well characterized using historical forecast errors. In practice, however, the cumulative effect of uncertainty creates significant exposure to imbalance-price risk when the committed schedule cannot be followed. To address this, we propose a distributionally robust chance-constrained optimization framework for the day-ahead scheduling of a multi-MW electric boiler using only limited residual forecast samples. We derive a tractable convex reformulation of the problem and calibrate the ambiguity set directly from historical forecast-error data through an a priori tunable risk parameter. Numerical results show that enforcing performance guarantees on the heat-demand balance constraint reduces demand violations by 40% compared to a deterministic forecast-based scheduler and up to 10% relative to a nominal chance-constrained model with a fixed error distribution. Further, we show that modeling the real-time rebound cost of demand violations as a second-stage term can reduce the overall daily operating cost by up to 34% by hedging against highly volatile day-ahead electricity prices.

We investigate superconductivity emerging in the photodoped Mott insulating Hubbard model using steady-state dynamical mean-field theory implemented on the real-frequency axis. By employing high-order strong-coupling impurity solvers, we obtain the nonequilibrium phase diagram for photoinduced $η$-pairing superconductivity with a remarkably high effective critical temperature. We further identify a superconducting gap in the momentum-resolved spectral function and optical conductivity, providing spectroscopic signatures accessible to experiments. Our results highlight a route to a controllable form of high-temperature superconductivity in nonequilibrium strongly correlated systems, fundamentally distinct from the equilibrium $s$-wave pairing state in the attractive Hubbard model or cuprate-like $d$-wave superconductors.

We introduce a compositional approach to model-based test generation in Behavior-Driven Development (BDD). BDD is an agile methodology in which system behavior is specified through textual scenarios that, in our approach, are translated into transition systems used for model-based testing. This paper formally defines disjunction composition, to combine BDD transition systems that represent alternative system behaviors. Disjunction composition allows for modeling and testing the integrated behavior while ensuring that the testing power of the original set of scenarios is preserved. This is proved using a symbolic semantics for BDD transition systems, with the property that the symbolic equivalence of two BDD transition systems guarantees that they fail the same test cases. Also, we demonstrate the potential of disjunction composition by applying the composition in an industrial case study.