We study variable-length feedback (VLF) codes over binary-input memoryless symmetric (BMS) channels using posterior matching with small-enough-difference (SED) partitioning. Prior analyses of SED-based schemes rely on bounded log-likelihood ratio (LLR) increments, restricting their scope to discrete-output channels such as the binary symmetric channel (BSC). We remove this restriction and provide an analysis of posterior matching that covers a broad class of BMS channels, including continuous-output channels such as the binary-input AWGN channel. We derive a novel non-asymptotic achievability bound on the expected decoding time that decomposes into communication, confirmation, and recovery terms with explicit dependence on the channel capacity~$C$, the KL divergence~$C_1$, and the Bhattacharyya parameter of the channel. The proof develops new stopping-time and overshoot bounds for submartingales and random walks with unbounded increments, drawing on tools from renewal theory. On the algorithmic side, we propose a low-complexity encoder that enforces the exact SED partition at every step by grouping messages according to their log-likelihood ratios that are assumed to land on a lattice, and applying a batched correction step that restores the partition balance. The resulting encoder complexity is polynomial in the number of transmitted bits. For continuous-output channels, the lattice structure is enforced through output quantization satisfying an exact induced-lattice constraint; the associated capacity loss is $O(\log B / B^2)$ for a $B$-level quantizer. These results yield a VLF coding scheme for BMS channels that simultaneously achieves strong non-asymptotic performance and practical encoder complexity.

We derive quantum gravity contributions to the beta functions of the gauge and Yukawa couplings of a matter theory using the Schwinger proper-time flow equation. Working in the Einstein-Hilbert truncation, we investigate the gauge-fixing and regulator dependence of the corresponding renormalization group equations. We quantify the sensitivity of our results on unphysical parameters by evaluating the gravitational correction to the running matter couplings at the interactive fixed point of gravity and we compare our findings with existing determinations in alternative schemes. We finally confront the derived contributions with the typical size they should assume to generate observable low-scale predictions in the Standard Model and in several scenarios of new physics.

We aim to understand the progenitor channels of CCSNe via a statistical study of the ages of their environments. We compiled a large and minimally biased sample of 129 CCSNe discovered by untargeted wide-field transient surveys and with archival VLT/MUSE integral-field-unit spectroscopy. We measured the local Hα luminosity within a 300-pc aperture centered on the SN explosion site as an empirical proxy for the environmental age. We find that the environments of Type II(P), IIb and Ib SNe do not show a significant age difference while Type Ic SNe are located in systematically younger environments than the other types (i.e. II $\approx$ IIb $\approx$ Ib > Ic). This is inconsistent with some previous reports of monotonically younger CCSNe environments with increasing envelope stripping (II > IIb > Ib > Ic). Our result suggests that Type Ic SNe have much younger and more massive progenitors than the other CCSN types and they likely originate from a distinct progenitor channel. The distinction between Types II(P), IIb and Ib SNe is insensitive to progenitor mass and mainly due to the different binary separation; in contrast, Type Ic SNe predominantly require much higher-mass progenitors accompanied by close companions with large mass ratios and/or much stronger stellar wind that depends sensitively on progenitor mass.

Vegetation in semi-arid environments self-organizes into striking spatial patterns -- bands, spots, labyrinths, and gaps -- with characteristic wavelengths on the order of tens to hundreds of meters. Existing reaction-diffusion models postulate nonlinearities and transport laws from qualitative physical reasoning, making it hard to distinguish essential structural features from artifacts of the chosen forms. Here we show how energy-balance and water-conservation principles can constrain the admissible model class before a specific closure is chosen. These constraints motivate a family of semilinear closures; an Euler--Lagrange representative yields a fourth-order vegetation equation coupled to quasi-steady water transport on a one-dimensional hillslope. Linear stability analysis identifies three instability mechanisms: classical water-mediated feedback, energy-balance spatial coupling, and water deflection by vegetation gradients. Their balance depends on terrain geometry. On slopes, the water-mediated coupling dominates and the model reproduces two empirical observations: pattern wavelength increases with aridity, and vegetation bands migrate uphill. On flat terrain, the energy-balance spatial coupling can drive instability independently. Numerical simulations confirm the linear predictions, and exploratory continuation reveals a narrow hysteresis region consistent with subcritical bifurcation.

We introduce a class of continuous-state branching processes with immigration, predation and competition, which can be viewed as a combination of the classical Lotka-Volterra model and continuous-state branching processes with competition that were introduced by Berestycki, Fittipaldi, and Fontbona (Probab. Theory Relat. Fields, 2018). This model can be constructed as a unique strong solution to a class of two-dimensional stochastic differential equations with jumps. We establish sharp conditions for the uniform ergodicity in the total variation of this model. Our proof relies on a novel, localized Markovian coupling approach, which is of its own interest in the ergodicity theory of Markov processes with interactions.

Boolean networks are widely used to model biological regulatory networks and study their dynamics. Classical semantics, such as the asynchronous semantics, do not always accurately capture transient or asymptotic behaviors observed in quantitative models. To address this limitation, the Most Permissive semantics was introduced by Paulevé et al., extending Boolean dynamics with intermediate activity levels that allow components to transiently activate or inhibit their targets during transitions. In this work, we provide a Boolean encoding of the Most Permissive semantics: each component of the original network is represented by a triplet of Boolean variables, and we derive the extended logical function governing the resulting network. We prove that the asynchronous dynamics of the encoded network exactly reproduces the attainability properties of the original network under Most Permissive semantics. This encoding is implemented as a modifier within the bioLQM framework, making it directly compatible with existing tools such as GINsim. To address scalability limitations, we further extend the tool to support partial unfolding, restricted to a user-defined subset of components.

Convergent evolution provides powerful evidence for natural selection, yet its molecular basis is typically sought in protein-coding amino acid substitutions. Whether adaptive pressures can drive the convergent evolution of synonymous codon usage bias (CUB) to override phylogenetic history remains a fundamental question. Here, we investigate this within the rapidly radiating fern family Thelypteridaceae by establishing a comparative framework that integrates chloroplast phylogenomics with dimensionality reduction of codon usage, morphological data, and divergence time estimation. Our results reveal that chloroplast CUB patterns are strikingly incongruent with the phylogeny of this family. Instead, they partition species into distinct clusters that strongly correlate with a convergently evolved morphological trait, lamina base architecture, a key adaptation whose radiation we date to the early Neogene. This convergent molecular signal is driven by a specific subset of photosynthesis-related genes (ndhJ, psaA, and psbD), which exhibit a high density of type-specific, third-position codon substitutions. These findings demonstrate that CUB can serve as a powerful, quantifiable indicator of adaptive history, revealing a cryptic layer of molecular convergence linked to the regulation of protein synthesis. Our work providing a new framework for uncovering adaptive histories obscured by complex evolutionary processes.

Machine learning force field (MLFF) has emerged as a powerful data-driven tool for atomistic simulations, enabling large-scale and complex atomic systems to be simulated with accuracy comparable to \textit{ab initio} methods. However, MLFFs often suffer from low training efficiency in the phase transition regime, where structural fluctuations are significantly elevated. To address this challenge, we propose a Central-Peripheral Distillation (CPD) algorithm for training dataset distillation. By strategically integrating representative samples with critical corner cases, the CPD algorithm ensures that the distilled dataset retains maximum structural diversity. We validated the efficacy of the CPD method on the liquid-liquid phase transition of dense hydrogen. Results show that, with the CPD approach, only 200 configurations are sufficient to train a MLFF that can fully reproduce the structural and dynamical properties of liquid hydrogen in the vicinity of its phase transition regime. This work paves the way for high-fidelity labeling of the MLFF training datasets, for instance by adopting high-level \textit{ab initio} calculations beyond the standard density functional theory, thereby enhancing the predictive accuracy of MLFFs.

We study Hilbert space fragmentation and quantum scars in quantum spin systems with Ising interactions. The system consists of two sets of quantum spins, A and B. As the parent system, set A is an Ising model on arbitrary lattices with a transverse field, while set B comprises free spins that are coupled to set A. We show that the Hilbert space is fragmented into exponentially many decoupled sectors when the transverse field and the side coupling strength are at resonance. As examples, several typical systems with quantum scars are studied analytically. Numerical simulations of probability distribution of entanglement entropy for finite-size chains, square and triangular lattices are performed using the Monte Carlo method. The results show that Hilbert space fragmentation and the corresponding quantum scars become pronounced when the system approaches resonance.

We analyse the UK income distribution from 2000 to 2023 using HMRC annual percentile data for both pre-tax and post-tax income. We fit a prefactor-adjusted $κ$-generalised specification to the data by weighted non-linear least squares and use inverse transform sampling to generate simulated income populations. The results suggest a redistribution of income shares over the period: the bottom 40\% appears to have increased its share, the middle-upper part of the distribution (50th--90th percentiles) lost share, the top 10\% remained broadly stable, and the top 1\% increased its share of pre-tax income. Because the modified specification is defined only above a positive threshold, conclusions concerning the lower tail should be interpreted with some caution. Using simulated 2023 pre-tax incomes to examine tax reform scenarios, we find that revenue-equivalent tax increases on high-income earners must be more than four times as large as comparable increases on lower-income earners. This suggests that, despite increased concentration at the top, the UK tax base remains driven primarily by the large number of taxpayers outside the very top of the distribution.

DBMSs are complex systems prone to bugs that may lead to system failures or compromise data integrity. Establishing unified DBMS bug repositories is crucial for systematically organizing bug-related data, enabling code improvement, and supporting automated testing. In particular, bug reports often contain valuable test inputs and bug-triggering clues that help explore rare execution paths and expose critical buggy behavior, thereby guiding automated DBMS testing. However, the heterogeneity of bug reports, along with their incomplete or inaccurate content, makes it challenging to build unified repositories and convert them into high-quality test cases. In this paper, we propose BugForge, a framework that constructs standardized DBMS bug repositories and leverages them to generate high-quality test cases to enhance DBMS testing. Specifically, BugForge progressively collects bug reports, then employs syntax-aware processing and input-adaptive raw PoC extraction to construct a DBMS bug repository. The repository stores structured bug-related data, including bug metadata and raw PoCs that entail potential bug-triggering semantics. These data are further refined into high-quality test cases through semantic-guided adaptation, thereby enabling enhanced DBMS testing methods, including DBMS fuzzing, regression testing, and cross-DBMS bug discovery. We implemented BugForge for PostgreSQL, MySQL, MariaDB, and MonetDB, totally integrated 37,632 bug reports spanning up to 28 years. Based on the repository, BugForge uncovered 35 previously unknown bugs with 22 confirmed by developers, demonstrating the value of constructing and utilizing bug repositories for DBMS testing.

Speech production requires the rapid coordination of a complex hierarchy of linguistic units, transforming a semantic representation into a precise sequence of articulatory movements. To unravel the neural mechanisms underlying this feat, we leverage recordings from eight 3.2 x 3.2 mm 64-microelectrode arrays implanted in the motor cortex and inferior frontal gyrus of two patients tasked to produce twenty thousand sentences. We show that a hierarchy of linguistic features are robustly encoded in most of these small cortical patches. Contrary to our expectations, instead of a clear macroscopic organization between patches, we observe a multiplexing of phonetic, syllabic and lexical representations within each cortical patch. Critically, this coding scheme dynamically changes over time to allow successive phonemes, syllables and words to be simultaneously represented without interference. Overall, these results, reminiscent of position encoding in transformers, show how small cortical patches organize the unfolding of the speech hierarchy during language production.

Deep learning has emerged as a compelling framework for scientific and engineering computing, motivating growing interest in neural network-based solvers for partial differential equations (PDEs). Within this landscape, network architectures with deterministic feature construction have become an appealing approach, offering both high accuracy and computational efficiency in practice. Among them, the transferable neural network (TransNet) is a special class of shallow neural networks (i.e., single-hidden-layer architectures), whose hidden-layer parameters are predetermined according to the principle of uniformly distributed partition hyperplanes. Although TransNet has demonstrated strong performance in solving PDEs with relatively smooth solutions, its accuracy and stability may deteriorate in the presence of highly oscillatory solution structures, where activation saturation and system conditioning issues become limiting factors. In this paper, we propose a generalized transferable neural network (GTransNet) for solving steady-state PDEs, which augments the original TransNet design with additional hidden layers while preserving its interpretable feature-generation mechanism. In particular, the first hidden layer of GTransNet retains TransNet's parameter sampling strategy but incorporates an additional symmetry constraint on the neuron biases, while the subsequent hidden layers omit bias terms and employ a variance-controlled sampling strategy for selecting neuron weights.

The design of the coordination environment of magnetic ions is key to achieving properties such as large magnetic anisotropy and slow magnetic relaxation, but a systematic exploration of the relevant chemical space for these compounds is missing. Here, we automatically extract all entries of mononuclear Dy coordination complexes from crystallographic databases and use multireference ab initio methods to compute their magnetic anisotropy. In addition, we generate and simulate magnetic anisotropy for 25k new molecules with the general formula [Dy(H$_2$O)$_5$L$_2$]$^{n-}$ and pentagonal bipyramidal coordination geometry, a motif selected as very promising. While no molecule with record magnetic anisotropy is serendipitously identified in crystallography databases, molecules with crystal field splittings over 1600 cm$^{-1}$ are identified by systematically exploring new organic ligands. This corresponds to a ~100% increase of magnetic anisotropy over the reference compound, ~30% over any known pentagonal bipyramidal Dy complex, and approaching record values of pseudo bi-coordinated Dy ions. This study demonstrates that the fine-tuning of Dy's second coordination sphere by organic ligands design can significantly improve magnetic anisotropy and that automated computational screening is key to accelerating this chemically non-intuitive process.

To the best of the authors' knowledge, all previously known examples of $μ$-, $μ^*$-, link-, or ordinary Zariski pairs of surface singularities in $\mathbb{C}^3$ consist of (possibly weighted) Lê-Yomdin singularities. In this paper, we present an example of a $μ$-Zariski pair involving surface singularities that are not of Lê-Yomdin type.

Assume-guarantee reasoning is a technique for compositional model checking in which system specifications are checked under certain assumptions on system parameters or inputs, and provide guarantees on observations of system state. We present a categorical framework for assume-guarantee reasoning for safety problems by viewing systems as lenses, following our earlier work on the compositionality of generalized Moore machines. Generalized Moore machines include ordinary Moore machines, partially observable Markov (decision) processes, and systems of parameterized ODEs (control systems); our framework gives assume-guarantee reasoning specially adapted to each of these cases. In particular, we give a novel formulation of assume-guarantee reasoning for (local) input-to-state stability ((L)ISS) Lyapunov functions on systems of parameterized ODEs. Our framework is categorically natural and straightforwardly compositional. A flavor of generalized Moore machine is determined by a tangency: a fibration with a section. We show that symmetric monoidal loose right modules of assume-guarantee certified generalized Moore machines over symmetric monoidal double categories of certified wiring diagrams can be constructed 2-functorially from fibrations internal to the 2-category of tangencies.

We interpret a wide range of flavors of Spectral Deferred Corrections (SDC) as Runge-Kutta methods (RKM). Using Butcher series, we show that the considered class of SDC methods achieve at least order p after p iterations compared to the underlying RKM, independently of the error discretisation chosen and the choice of nodes. For all collocation RKM, we analyse the phenomenon of order jumps in SDC iterations, where the order is increased by two at each iteration. We prove that it can be obtained by using appropriate inconsistent, implicit, parallelisable error discretisations. We also investigate the stability properties of the new SDC methods which can in general reduce to that of explicit RKM, but it can be improved by suitable combinations of error discretisations. We confirm the convergence analysis with numerical experiments and we apply relaxation RKM to derive SDC variants that conserve quadratic invariants.

An infinite family of integrable vortex equations is studied and related to the Cartan geometry of the underlying Riemann surfaces. This Cartan picture gives an interpretation of the vortex equations as the flatness of a non-Abelian connection. Solutions of the vortex equations also give rise to magnetic zero-modes for a certain Dirac operator on the lifted geometry. The family of integrable vortex equations is parametrised by a positive number $n$, that is equal to unity in the standard case and an integer in the case of polynomial vortex equations; finally, it may be extended to any positive real number.

Aza-BODIPY dimers represent promising molecular systems for efficient triplet-state generation through either intramolecular-singlet fission (iSF) or spin-orbit charge transfer intersystem crossing (SOCT-ISC). In this work, we investigate the role of molecular geometry in governing these mechanisms across four regioisomeric aza-BODIPY dimers (D[1,1], D[1,3], D[3,3], and D[2,2]) using multireference quantum-chemical calculations. Ground- and excited-state properties were analyzed at the MP2 and SA-XMCQDPT levels of theory, while diabatic couplings and spin-orbit matrix elements were evaluated to estimate iSF and SOCT-ISC rate constants, respectively. Our results reveal that triplet formation is strongly governed by the torsional angle (Φ) between monomer units, with regio-connectivity exerting a secondary influence. Dimers D[1,1] and D[1,3] exhibit favorable iSF energetics and coupling magnitudes, whereas D[2,2] displays low iSF rate constant (kSF ) but enhanced SOCT-ISC activity. The D[3,3] dimer shows exothermic multiexciton formation but reduced iSF efficiency due to destructive coupling interactions. The dominant ISC channel proceeds through the S1-T3 transition with large spin-orbit coupling and a small energy gap. These findings provide critical mechanistic insights into geometry-dependent triplet generation in aza-BODIPY dimers.

Ionization is a major driver of both physical and chemical evolution in protostellar systems. Recent observations reveal substantial chemical processing in protoplanetary disks by the time the surrounding envelope has cleared. Thus, physical conditions during the preceeding phase, when an infalling envelope of material is still present, are crucial for determining the extent of chemical processing at early stages. We used observations of H13CO+ and C18O from the Northern Extended Millimeter Array (NOEMA) and IRAM 30m telescope to constrain the ionization rate in the envelopes of three Class 0 protostars: NGC-1333 IRAS4A, L1448-C, and L1157. We find ionization rates in the range zeta = 1e-16 - 1e-13 s$^{-1}$ , several orders of magnitude above the ionization rate of zeta = 6e-17 s$^{-1}$ in the diffuse interstellar medium. This supports the idea that ionization driven chemistry is more efficient at earlier stages (< 1e5 years) of protostellar evolution.

Memory-disaggregated key-value (KV) stores suffer from a severe performance bottleneck due to their I/O redundancy issues. A huge amount of redundant I/Os are generated when synchronizing concurrent data accesses, making the limited network between the compute and memory pools of DM a performance bottleneck. We identify the root cause for the redundant I/O lies in the mismatch between the optimistic synchronization of existing memory-disaggregated KV stores and the highly concurrent workloads on DM. In this paper, we propose to boost memory-disaggregated KV stores with pessimistic synchronization. We propose CIDER, a compute-side I/O optimization framework, to verify our idea. CIDER adopts a global write-combining technique to further reduce cross-node redundant I/Os. A contention-aware synchronization scheme is designed to improve the performance of pessimistic synchronization under low contention scenarios. Experimental results show that CIDER effectively improves the throughput of state-of-the-art memory-disaggregated KV stores by up to $6.6\times$ under the YCSB benchmark.

Planar AdS black branes have a scaling symmetry that maps a brane solution at one temperature to a solution at another. It is natural to expect that boundary representations of bulk field modes should inherit this symmetry i.e. their correlators should transform covariantly under boundary dilatations. We derive a covariance condition that any boundary representation of interior modes in a planar AdS black brane should satisfy. We then show that Papadodimas-Raju mirror operators satisfy this condition. Thus the Papadodimas-Raju reconstruction of the bulk interior, although state-dependent, inherits the scaling symmetry of planar AdS black holes.

The variational formulation of nonlinear filtering due to Mitter and Newton characterizes the filtering distribution as the unique minimizer of a free energy functional involving the relative entropy with respect to the prior and an expected energy. This formulation rests on an absolute continuity condition between the joint path measure and a product reference measure. We prove that this condition necessarily fails whenever the signal and observation diffusions share a common noise source. Specifically we show that the joint and product measures are mutually singular, so no choice of reference measure can salvage the formulation. We then introduce a conditional variational principle that replaces the prior with a reference measure that preserves the noise correlation structure. This generalization recovers the Mitter--Newton formulation as a special case when the noises are independent, and yields an explicit free energy characterization of the filter in the linear correlated-noise setting.

We present a detailed proof of Wolstenholme's theorem using an Egorychev-type contour integral and an exponential change of variables. All formal series manipulations are justified, and the connection with harmonic sums and Bernoulli numbers is made completely explicit. We further derive the classical refinement modulo $p^4$ and provide a precise extraction of the $B_{p-3}$ term. Our purpose is not to provide the most concise proofs, but rather to demonstrate, by showing how established results can be recovered, a general method based on complex analysis for deriving congruence properties in number theory.

We are a group of over two dozen astronomers, computer scientists, data scientists and digital Big Data research platform experts at 11 universities and research institutes in South Africa and Europe. We study Near-Earth Objects (NEOs) for Planetary Defence and scientific purposes. We present our research and development programme for algorithms and digital data analysis platforms for machine learning-assisted NEO discovery and polarimetric characterisation in astronomical surveys. Typically, this is serendipitous because these surveys are designed for galactic and extragalactic science.

This paper studies a two-player nonzero-sum stochastic differential game governed by a controlled convection-diffusion stochastic partial differential equation (SPDE) with spatially heterogeneous coefficients. The diffusion and transport operators depend on the players' controls, allowing each agent to influence the system dynamics. We prove the existence and uniqueness of solutions to both the forward uncontrolled SPDE and the associated adjoint backward SPDE (BSPDE) in a Hilbert space framework. Using a Hamiltonian approach, we derive sufficient and necessary maximum principles characterizing Nash equilibria. Special attention is given to operators with piecewise constant coefficients, where interface transmission conditions arise naturally. As an illustration, we provide two examples from composite materials where the game structure models the interaction between different material phases in a diffusion process.

We construct an sl(2)-action on the equivariant skein lasagna module.

We study relationships between worst-case and random-noise properties of error correcting codes. More concretely, we consider connections between minimum distance, list decoding radius, and block error probability on noisy channels. A recent result of Pernice, Sprumont, and Wootters established the tight connection between list decoding radius and symmetric channel performance for linear codes. We extend this result to general codes. The proof proceeds by directly bounding the weight distribution rather than by sharp threshold techniques. We then turn to the relation between minimum distance and symmetric channel performance. The results we just described imply that a $q$-ary code of relative distance $δ$ has vanishing error probability on the symmetric channel up to the Johnson radius $J_q(δ)$. We improve upon this bound in the case of linear codes, for a range $δ$, for $q\ge 4$. In our proof we consider the \emph{erasure} properties of codes, and bound their weight distribution through inequalities introduced by Samorodnitsky. The latter part of the proof gives a more general technique that bounds the symmetric channel performance of a linear code with constant relative distance and good erasure channel performance.

We investigate the synthetic model of globular cluster (GC) systems of 17 compact massive galaxies (CMGs) from the Illustris TNG100 simulation to explore their connection with massive relic galaxies, systems that have undergone little structural evolution across cosmic time. The co-evolution of the GC systems and their host galaxies is based on a GC formation and evolution model that assigns clusters to stellar particles according to age and local conditions, providing positional, kinematic, and chemical information for individual GCs. By combining stellar assembly histories, effective radius evolution, and GC properties such as in-situ vs. ex-situ origin, metallicity, and spatial distribution, we identify consistent signatures of early formation and late-time accretion. We find that the GC mass fraction traces the host assembly history more robustly than the GC number fraction, as massive clusters better preserve the imprint of the early accretion history. Three CMGs from TNG100 emerge as strong massive relic analogs, exhibiting high in-situ GC fractions, narrow metallicity distributions, and compact spatial distributions. A tight correlation between the host stripped fraction and the extent of the ex-situ GC population further reveals the possibility to consider GC spatial profiles as a signature to identify tidal stripping processes. These results indicate that the combined analysis of GC populations and host stellar assembly offers a robust diagnostic for identifying massive relic galaxies and constraining their evolutionary histories.

Statistical practice does not automatically follow methodological innovation. Regularization methods, widely advocated to reduce overfitting and stabilize inference, are readily available in modern software, but are not consistently used by data analysts. We investigate this implementation gap in a large-scale empirical study of trust in, and acceptance of, regularization techniques, based on $N = 606$ data analysts. Drawing on measurement frameworks from technology acceptance research, we survey practitioners and embed a randomized experiment to test whether written recommendation of regularization methods increases trust or intended use. We find no evidence of such an effect. Instead, adoption intentions are strongly associated with analysts' perceptions of ease of implementation and practical benefit, such as improved bias control or interpretability. Perceived social norms also emerge as a central driver. These results indicate that uptake of statistical methodology depends less on formal recommendations than on usability, perceived utility, and community practice.