Papers

Motivated by Mader's conjecture on connectivity keeping trees, we study the corresponding problem in triangle-free graphs. For positive integers $k,m$, we first prove that every $k$-connected triangle-free graph $G$ with $\delta(G)\geq k+\left \lceil \frac{m}{2} \right \rceil $ contains a path $P$ of order $m$ such that $G-V(P)$ remains $k$-connected. Moreover, if $\kappa(G)=k$, then for every end $F$ of $G$ and every vertex $v\in F$, the path $P$ can be chosen in $G[F]$ with $v$ as an endvertex. If $\kappa(G)\geq k+1$, then any vertex of $G$ can be chosen as an endvertex of $P$. This result confirms the conjecture of Luo, Tian and Wu on connectivity keeping trees in bipartite graphs for all paths, and it also sharpens Fujita's path theorem to the optimal minimum degree bound. For an integer $i$ with $1\leq i\leq m-1$, let $P_m^+(i)$ denote the tree obtained from a path of order $m-1$ by adding one pendant vertex adjacent to its $i$th vertex. Let $(X,Y)$ be the bipartition of $P_m^+(i)$. We further prove that every $k$-connected triangle-free graph $G$ with $\delta(G)\geq k+\max\{|X|,|Y|\}$ contains a subgraph $T\cong P_m^+(i)$ such that $G-V(T)$ remains $k$-connected. The minimum degree bound is sharp, and the result confirms the bipartite conjecture for all pendant extensions of paths.

Graphical user interface (GUI) agents now execute workflows across real applications, but when execution drifts, users must determine what changed, what should have remained untouched, and what can still be recovered. Plan-centric interfaces leave users supervising procedure, but users live with changes to application state. We introduce task-state governance, an interaction paradigm that represents a task as an editable contract linking desired outcomes, facts that must be preserved, and observed application state. We instantiate this paradigm in TaskVM, which projects live state into editable task controls, executes user edits as genuine interface actions, verifies outcomes through independent observation, and marks each action as reversible, compensatable, or irreversible. Across an automated contract benchmark, a controlled user study, and an open live-model exploration, the paradigm strengthened contract compliance and users' recovery control and trust, while execution outcomes were held constant. Task contracts open a design space for governable agent interfaces.

Large language model (LLM) agents are increasingly used for long-horizon research and engineering, yet evaluating these capabilities remains expensive, time-consuming, and heavily dependent on human expertise. This motivates a natural question: can LLM agents themselves construct efficient benchmarks that preserve the conclusions of costly reference evaluations? We study this capability by formulating automatic benchmark development as a meta-evaluation problem, where an agent is given a task and an expensive reference benchmark and requested to construct a lower-cost proxy benchmark that faithfully distinguishes among candidate models and solutions. Based on this formulation, we introduce EvalBuilder, a framework for evaluating such benchmark-generation capabilities along three key dimensions: fidelity, efficiency, and robustness. Specifically, we assess whether generated benchmarks preserve model rankings, generalize to held-out models and freshly collected responses, and provide well-calibrated and discriminative scores while substantially reducing evaluation cost. We further provide an iterative environment in which agents can refine their benchmarks under a fixed time budget. Our framework provides a systematic testbed and benchmark for understanding when current LLM agents can develop useful evaluators and how benchmark construction itself can be increasingly automated.

Technological progress can give rise to new loss exposures or reduce existing risks. In either case, it strongly affects insurance companies' existing lines of business. As the magnitude of such effects is often closely connected to the innovation's market penetration, reliably predicting its adoption process is vital in enabling insurers to adapt their business strategy accordingly. To tackle this challenge, we propose a novel combination of contributions from the domain of innovation diffusion. Our methodology generates adoption scenarios that holistically account for different sources of uncertainty, offers a structured way to incorporate expert judgment and insights from pre-existing technologies, and updates its predictions as new information on the technology's diffusion becomes available. Its modular nature ensures that components can be easily replaced by suitable alternatives. Using publicly accessible data on privately-owned battery electric vehicles in Germany, the application of our approach for predicting changes to insurance losses and for supporting insurers' sustainability strategies is visualized in a motor insurance case study.

We show that Payne's conjecture on the comparison between Dirichlet Laplacian eigenvalues and buckling eigenvalues does not hold on flat and hyperbolic cylindrical surfaces and on (round) hemispheres.

The single-mode approximation (SMA) has been widely employed in ultracold spinor gases, where all spin components share the same spatial mode. By adopting generalized Van Vleck (GVV) perturbation theory, we achieve a relative error of $10^{-6}$ in the ground-state energy with a reduced effective Hilbert space dimension of $\sim 10^3$ for two spin-1 bosons confined in a one-dimensional hard-wall trap. With the accurate GVV method, we explore the validity of the SMA across ground-state properties and quench spin dynamics for two $^{7}\text{Li}$, $^{87}\text{Rb}$, or $^{23}\text{Na}$ atoms. Numerical results show that the quadratic Zeeman energy $q$ provides a powerful control knob: by increasing $|q|$, the fidelity between the spin components in the ground state gradually decreases, leading eventually to the breakdown of the SMA (due to the competition between the kinetic energy and the quadratic Zeeman energy). Quench spin dynamics with abruptly increased $q$ further reveals multiple resonances, where the SMA-predicted micromotion and beyond-SMA macromotion appear simultaneously. These results point to a direction to investigate the quantum spin-mixing dynamics beyond the SMA, particularly in recent experiments of strongly interacting spin-1 atomic gases.

Many complex systems involve group interactions, which can readily be represented by higher-order structures such as hypergraphs. However, when observing a system's dynamical evolution, establishing whether that evolution actually results from higher-order interactions, or whether pairwise interactions suffice to explain the data, remains a challenge. Even in the simple case of a temporal sequence of nodes visited during a diffusion process, such a task is intricate. Indeed, group interactions leave their traces as memory on the observed nodes, while path dependence in a purely pairwise process can mimic that same footprint without any group structure. To resolve this, we propose an inference pipeline based on a hidden Markov model (HMM) that tests, directly from an observed sequence of nodes carrying no group labels, whether higher-order interactions are required to describe the dynamics. The HMM latent states represent higher-order interactions, seen as hyperedges of an unobserved hypergraph, so that their detection becomes a model selection problem between the HMM class and a class of null models without higher-order interactions. We first validate this approach on synthetic node sequences generated from random walks on graphs and hypergraphs, showing that it recovers both the number and the composition of the underlying hyperedges, while correctly rejecting them when the generating process is pairwise. As a second step, we consider a validation based on empirical data, namely empirical trajectories of ball possession in football matches. This application shows that the pipeline goes beyond providing statistical evidence of the presence of higher-order interactions, and yields interpretable underlying structures: the recovered hyperedges map directly onto recognizable tactical team formations.

Discrete directional data exhibiting p-fold rotational symmetry, where directions separated by integer multiples of 2{\pi}/p are equivalent, arise in various applications but are often modeled using continuous distributions. In this article, we develop two general methods for constructing distributions for such data: symmetrization and folding of discrete circular distributions, and wrapping of discrete linear distributions. Particular models arising from these constructions are studied, together with their properties and estimation methods. For axial sand-grain orientation data, the proposed models are compared with discretized continuous axial distributions, whose category probabilities require numerical integration. The proposed models attain smaller Akaike information criterion values among the models considered while allowing direct likelihood evaluation without numerical integration. The framework is also applied to binned Manhattan street-orientation data, demonstrating its applicability to higher-order rotational structures, specifically the 4-fold case.

Sensitive dependence on initial conditions limits long-horizon prediction of chaotic systems even for deterministic dynamics, yet some dynamical information may remain recoverable after precise state information is lost. Recursive multistep methods are fragile because they reuse each intermediate prediction as input, allowing local errors to propagate through the rollout. We investigate whether partial multistep prediction can recover predictive information beyond the predictability horizon by omitting intermediate positions instead of assigning them unreliable values. The method uses a lightweight pattern-based local predictor. We analyze partial trajectories generated by different omission patterns and quantify the trade-off between accuracy on retained positions and the fraction classified as non-predictable. Experiments on the Lorenz system show that admissible masks contain trajectories that remain accurate far beyond the horizon of predictability, and an agreement-based ensemble recovers part of this information without future observations at the cost of a growing rejected fraction. At short horizons a broad accepted subset retains accuracy at moderate rejection, whereas at long horizons positive geometric skill requires increasingly strong selection. In this regime retained predictions no longer localize the state within a Lorenz scroll but still identify the occupied scroll, so topological structure outlasts geometric accuracy. A noise-based control reproduces this survival only after tuning of its perturbation scale, unlike masking. Across a heterogeneous collection of chaotic systems the ensemble strictly extends the positive-$R^2$ horizon of the recursive baseline for every retained system.

Near-field beamfocusing confines radiated power into a localized three-dimensional focal spot, making the analytical characterization of radial and angular resolution critical for sixth-generation (6G) multi-user systems, yet existing models treat the focal resolution as a fixed geometric outcome rather than a tunable design variable. Based on the Angular Representation (ASR) approach, this paper presents a resolution framework to design contiguous focal regions across both the radial and angular domain for steered multi-user systems. By extending the definition of a tunable inter-beam overlap $\rho$, we derive closed-form expressions for the radial and angular focal boundaries and extents, alongside the steering-dependent minimum focal distance $d_{0,\text{min}}$ and maximum steering angle $\theta_{\text{max}}$. Using these boundaries, iterative synthesis algorithms are developed to construct uniform and non-uniform radial and angular beam arrangements. Finally, by analyzing both isolated and joint radial-angular configurations, we quantify the fundamental trade-offs between $\rho$, achievable user capacity, inter-user interference, and system sum-rate across varying steering angles.

Video scene graph generation (VidSGG) aims to capture objects and their evolving relationships in videos. This requires accounting for both the persistence of object identities and abrupt changes in relationships. Existing methods aggregate information across frames to exploit temporal context, but an emphasis on consistency can obscure these changes. As a result, a model may retain its previous prediction even after the underlying relation has changed. We refer to this failure mode as relational semantic inertia. To address this issue, we propose Relation-Transition-Aware Transformer (RTAformer), a one-stage framework that separately models entity persistence and relation changes. It injects calibrated differences between adjacent-frame relation queries to guide predicate updates, while cross-frame instance alignment during training helps reduce cross-frame representational drift. Experiments on Action Genome show improvements in recall and mean recall over existing methods, with ablation studies supporting the contributions of the proposed components and comparisons using matched backbones showing larger gains on relation-transition frames than on non-transition frames.

We study the estimation of the interaction parameter in singular interacting particle systems from continuous and discrete observations over a fixed time horizon. The singularity of the interaction drift prevents the direct application of standard likelihood and contrast-based methods, which rely on regularity assumptions that fail in this setting. Our approach exploits an exact reduction of the particle dynamics to a one-dimensional stochastic differential equation for a quadratic empirical moment. By the symmetry of the interaction kernel, the singular terms cancel, yielding an explicit estimator in which the unknown parameter enters linearly. We establish consistency and asymptotic normality as the number of particles, \(N\), tends to infinity. Letting \(\varepsilon_N\) denote the microscopic noise scaling of the system, we obtain asymptotic normality at the rate \(\sqrt{N/\varepsilon_N}\) for strictly positive interaction kernels, under an additional condition on the limiting empirical information. We further extend these results to degenerate interaction kernels, achieving consistency and asymptotic normality at rate \(N\) under suitable structural assumptions and the canonical scaling \(\varepsilon_N=N^{-1}\). In both regimes, we provide conditions on the observation mesh ensuring that the statistical limits remain valid under discrete sampling, in high frequency. Finally, we illustrate the applicability of our methodology through Dyson Brownian motion, the Dyson Ornstein–Uhlenbeck process, and Wishart–Laguerre particle systems, alongside a numerical investigation of the estimators' finite-sample performance.

Pairwise preference feedback has become a widely adopted supervision signal for reinforcement learning in video generation models, as pairwise comparisons provide a more reliable alternative than pointwise scalar ratings for evaluating the quality of generated videos. Specifically, we define a preference graph for each GRPO group under a pairwise evaluator, where nodes represent sampled rollouts and edges encode pairwise preferences. Auditing 6,976 on-policy comparison graphs, we find that cyclic preferences are prevalent and persist throughout training. Naive pairwise reward aggregation based on average win rates discards the underlying comparison structures and treats each rollout independently, which may introduce unreliable advantage estimates for certain rollouts and consequently affect reinforcement learning optimization. Therefore, we propose the Reliability-Anchored Preference Walk (\ours{}), a graph-aware advantage aggregation method that strengthens the global preference signal from win rates with reliable relational evidence from cyclic preference graphs through a reliability-guided preference walk. Under matched evaluator, comparison protocol, group size, prompt schedule, and query budget, \ours{} requires no additional evaluator queries beyond the observed comparisons within each rollout group and improves over Pairwise-GRPO across controlled comparisons, transfer settings, and blind human evaluations.

Let $\Gamma$ be a connected metric graph of first Betti number $b\ge 2$, and let $\Gamma_b$ be a trivalent graph of the same Betti number with all edges of unit length. We show that if $\text{length}(\Gamma) \le \lambda\, \text{length}(\Gamma_b)$, then the universal cover of $\Gamma$ contains a vertex around which, at every radius $R\ge 0$, the ball is at least as long as the ball of radius $R$ in the trivalent tree whose edges all have length $3\lambda$. In particular, for $\lambda\le\frac13$, this ball is at least as long as the ball of the same radius in the universal cover of $\Gamma_b$, with no multiplicative loss. This improves an earlier theorem of the author, which gives the weaker lower bound $(1-3\lambda)$ times the ball in the universal cover of $\Gamma_b$, and only for $\lambda\le\frac16$. The proof rests on an elementary comparison principle. Among trees whose vertices have degree at least three and whose edges have length at most $c$, the trivalent tree with all edges of length $c$ has the smallest balls at every radius. As an application, we double the exponential growth rate in the author's earlier uniform lower bound for the area of balls in the universal cover of small-area surfaces of hyperbolic type, from $\ln 2$ to $2\ln 2$, beyond the hyperbolic rate. We also obtain explicit constants in the positive answer to Guth's question for surfaces. Finally, we conjecture the sharp, all-scale version of the minimal volume entropy inequality of Kapovich–Nagnibeda and Lim, and show that it would be optimal.

We introduce binary cyclic gradient coding (BCGC), an exact gradient coding scheme for $n$ workers and up to $s$ stragglers. Its encoding matrix is binary, circulant when $(s+1)\mid n$ and nearly circulant otherwise, and the master decodes by a single summation. Like the fractional repetition coding scheme (FRC) and its generalized version (GFRC), BCGC splits the workers into $s+1$ classes that each cover the whole dataset, but it assigns the data through cyclic supports. Its encoding matrix has rank $n-s$, and $n-s-1$ workers keep the balanced load $s+1$, which is the largest possible number. We prove that encoding matrix of BCGC is not permutation-equivalent to those of FRC and GFRC schemes. Moreover, We also prove that a binary coded scheme with compression is equivalent to an uncoded compressed scheme on a coarser partition of the data. This explains why binary schemes remain stable under compression, whereas the large decoding coefficients of MDS codes amplify the compression error and lead to divergence in our experiments. For every contractive compressor, the standard convergence guarantee of compressed gradient descent holds on each coarse partition. FRC, GFRC and BCGC therefore share the same convergence guarantee and differ only in their partitions, with one partition for FRC, two for GFRC and $s+1$ distinct partitions for BCGC. Choosing among these partitions can recover the exact gradient in cases where FRC and GFRC cannot. Experiments on four datasets confirm the theory. BCGC matches GFRC, keeps its accuracy under top $\kappa$ sparsification while the MDS codes diverge, and on heterogeneous data its partition diversity reduces the compression error and improves the accuracy.

Synthetic data is increasingly used in language-model pretraining. Existing knowledge-corpus synthesis pipelines, including WRAP and Nemotron-CC, usually take a source passage or document segment as input and generate rewritten or QA-style samples from that text. This can improve surface form and prompt diversity, but it does not explicitly require fine-grained source facts – especially secondary entities, list/table entries, and precise temporal attributes – to appear in the synthesized corpus. We propose AFCS (Atomic-Fact-Conditioned Synthesis), a pipeline that first extracts source-supported atomic facts and then uses each retained fact to drive generation. AFCS uses structure-aware extraction over the document tree, source-grounded verification, local context expansion, and multi-format generation. In continued-pretraining experiments with OLMo-3-7B and a 32B base on the same FineWiki source corpus, AFCS outperforms WRAP and Nemotron-CC on SimpleQA, SimpleQA Verified, PopQA, and HotpotQA. Granularity ablations show that fact-level synthesis improves over chunk-level, paragraph-level, and entity-level synthesis; and a 100B-token mid-training integration improves factual benchmarks and raises the 12-task general benchmark average by +1.09.

Automatic prompt optimization (APO) has shown strong effectiveness for text-based LLMs and LLM systems, but its application to audio-visual understanding systems requires suitable textual interfaces through which multimodal reasoning can be exposed to text-based optimizers. We investigate how the design of textual interfaces affects prompt optimization for multimodal reasoning, on the audio-visual question answering task. We compare three interface designs, including a direct inference system consisting of a single omni-modal large language model (OmniLLM), a captioner-reasoner system, and an agentic architecture in which a primary agent orchestrates subagent OmniLLMs. Experiments with Qwen3-Omni and Gemini show that direct prompt optimization provides model-dependent gains; the captioner-reasoner system and the agentic system expose more interpretable optimization interfaces but are harder to optimize, where error analysis of cases affected by optimization is conducted. Our study highlights textual interface design as an important factor in making prompt optimization effective for omni-modal reasoning systems. Our implementation details are specified in GitHub repo.

Affective personal informatics (PI) involves capturing, tracking, analyzing, and reflecting on personal data to support emotional self-awareness and mental well-being. Recent advances in large language models (LLMs) are reshaping affective PI, yet a comprehensive survey of LLM-based affective PI systems is lacking. To bridge this gap, we systematically analyzed 45 papers published between January 2020 and June 2026 across four major computing and health databases, examining their macro trends, system taxonomies, and research methodologies. Our synthesis reveals an overreliance on multi-stage, text-centric pipelines, a predominance of active, screen-bound interactions, and a severe demographic skew toward young, university-campus-based cohorts in empirical evaluations. Based on these findings, we critically reflect on prevailing architectural and methodological shortcomings and outline actionable future directions for building end-to-end multimodal, low-burden, and inclusive affective PI systems.

Visual world knowledge is a core capability of multimodal large language models (MLLMs), underpinning knowledge-intensive visual question answering and fine-grained visual reasoning. However, existing benchmarks remain limited in two key respects. First, their category coverage is narrow: most benchmarks span only a small number of categories across a few domains, falling far short of the open-ended scale of real-world visual entities. Second, their task construction is often insufficiently rigorous: models can answer correctly using coarse-grained cues, vague associations, or elimination strategies without truly mastering precise concepts, making it difficult to accurately assess their knowledge of fine-grained entities. We introduce VisualWorldBench, a taxonomy-grounded multi-task benchmark built on a hierarchical taxonomy of 21,291 leaf-node classes across 8 visual domains, with 32,541 evaluation instances whose ground-truth labels cover 15,479 categories across four complementary tasks: closed-set recognition, contrastive selection, precise localization, and open-world naming, covering different directions of knowledge retrieval and varying degrees of answer openness to comprehensively evaluate visual world knowledge. Most questions are constructed from taxonomically proximate categories, forcing precise discrimination among fine-grained entities. Experiments reveal that the strongest closed-source model achieves only 80.4% average accuracy, exposing capability gaps hidden under conventional benchmarks. We further construct VisualWorldBench-50K, a training resource covering 50K+ categories. Fine-tuning on VisualWorldBench-50K yields over 21 percentage points improvement on VisualWorldBench, with consistent transfer to public fine-grained recognition and visual knowledge benchmarks.

Lowering the energy threshold of phonon-mediated kinetic inductance detectors is a key step toward next-generation cryogenic calorimeter arrays with large target mass and high sensitivity. In this work, we demonstrate the feasibility of integrating thin tungsten films, so far used for transition-edge sensors, into the fabrication of Kinetic Inductance Detectors (KIDs). Here we present the results from the characterization of a single KID prototype composed of a tungsten-aluminum bilayer of respectively 15 nm and 35 nm thicknesses. The detector was successfully calibrated, and the superconducting film characteristics were measured by operating the device at different temperatures. We show that, by exploiting the proximity effect of superconductors, the device combines the relatively high critical temperature of aluminum with the large kinetic inductance contribution of tungsten. The main feature is a high kinetic inductance, which accounts for 36% of the total inductance, combined with a superconducting critical temperature of around 630 mK.

We consider a reaction–diffusion equation with Kolmogorov–Petrovskii–Piskunov (KPP) nonlinearity and Neumann boundary conditions in a narrow tube $G^{\varepsilon,\delta}\subset\mathbb{R}\times\mathbb{R}^{n}$ of width of order $\varepsilon$. The tube is chosen from a family indexed by a second parameter $\delta>0$, whose boundary $\partial G^{\delta}$ is smooth for each $\delta>0$ but degenerates as $\delta\downarrow0$. In the iterated limit $\varepsilon\downarrow0$ followed by $\delta\downarrow0$ the problem becomes a Cauchy problem on the line whose spatial operator is a generalized second order differential operator $D_{v}D_{u}$ in the sense of Feller, rather than a classical second order elliptic operator. Solutions of the limiting problem need not be differentiable in $x$, so they must be understood in a generalized sense. Using the Feynman–Kac representation, we prove that the limiting problem has a unique generalized solution. When the cross sectional volume is bounded above and below, we also prove that this solution is Hölder continuous in $t$ with exponent $1/2$, locally uniformly in $x$, whenever it is Lipschitz continuous in $x$. Under the same volume bounds, this Lipschitz condition holds when the initial function and the nonlinearity are Lipschitz continuous in $x$. Finally we prove that the solutions in the narrow tubes converge to the generalized solution uniformly on compact time intervals in the same iterated limit if the tube, the initial function, and the nonlinearity are periodic in $x$.

This work focuses on planning daily routes for a group of employees of a condominium company. Given a set of employees and a set of customers with pre-scheduled visits, we want to build doubly-open routes to guarantee visits to all customers, ensuring that each customer is visited by an employee with the appropriate skills to carry out the required activity. The travel times between customers and the service time in each customer are known. The problem includes time windows for visiting customers, each employee has a maximum working time, and the daily working period is between 9 AM and 6:30 PM. The routes respect the lunch break period if they extend from morning to afternoon, which means that lunch break can be avoided if the route is fully completed in the morning or in the afternoon. The aim is to minimize the distance covered by all routes with a penalty for including lunch breaks. The distances and times between customers are collected via an API to Microsoft Azure; and the solutions are then displayed on Bing Maps. The results obtained show the operational advantages of an efficient and effective vehicle routing planning in a specific condominium management company. The model can be extended to other service provider companies.

Network coding allows intermediate nodes to combine messages, whereas routing only forwards them. The Li-Li conjecture asserts that network coding and fractional routing have the same capacity region in undirected multiple-unicast networks. We give a counterexample to this conjecture and apply it to external-memory integer sorting. Since Aggarwal and Vitter posed the question in 1988, whether integer sorting can beat the external-memory comparison bound has remained a central and extensively studied open problem. We give a deterministic sorting algorithm: for $N$ integers of $\Theta(\log N)$ bits, a memory holding $M$ integers, and block transfers of $B$ integers, where $2B\le M\le N$, the number of block transfers is $O\left(\frac{N}{B}\left[1+\frac{\log N}{(\log(M/B))^{1-\varepsilon}(\log M)^\varepsilon}\right]\right)$, where $\varepsilon>0$ is an absolute constant. In a range of parameter regimes, this bound is asymptotically smaller than the classical comparison-sorting bound. We also use Lean 4 to verify the sorting algorithm's correctness and complexity bounds, and the strict advantage of coding over routing.

We classify strong subadditivity for the canonical topological Rényi functional at finite positive orders on an unpunctured torus in the topological quantum field theory of any finite unitary modular tensor category. Universal validity means validity for all pure ground states and all regular region pairs with transverse or disjoint boundaries and compatible corner rounding. At von Neumann order one, the inequality holds universally. For each fixed order strictly between zero and one, universal validity is equivalent to pointedness, meaning that every simple anyon type has quantum dimension one. For every nonpointed category and each finite positive order other than one, we construct a violating pure state and an allowed pair. For a fixed pointed category and fixed order above one, universal validity is equivalent to a same-order modular Fourier entropy bound for every pure state. Global homological constraints on actual unions and intersections and established weighted modular uncertainty prove the order-one theorem. For parallel annuli at fixed flux distribution, the order-one functional is affine in their positive count. At other orders, unequal quantum dimensions on the occupied support induce strict curvature that suitable overlapping regions convert into negative deficits. Under the boundary-charge cutting prescription, the von Neumann theorem extends to arbitrary logical density matrices in the same ground space.

Let $G$ be a group of permutations of a set $\Omega$. The relational complexity $\mathrm{RC}(G)$ is the least integer $r\geq 2$ such that the $G$-orbit of every finite tuple is determined by the $G$-orbits of its $r$-subtuples; there is currently only a small collection of groups $G$ for which $\mathrm{RC}(G)$ is known precisely. In this paper we study the relational complexity of finite affine groups acting naturally on a $d$-dimensional vector space over $\mathbb{F}_q$. We prove that every such group has relational complexity at most $d+2$ when $q>2$ and at most $d+1$ when $q=2$; we produce a complete classification of the primitive such groups for which these bounds are attained.

Accurate bistatic radar cross-section (RCS) characterization requires near-field measurements over multiple dimensions, which, under typical near-field sampling requirements, can lead to long measurement durations for electrically large radar targets. This paper presents a near-field-to-far-field transformation based on an equivalent surface-current reconstruction using a-priori information about the target to reduce the number of newly acquired near-field samples. It is assumed that the prior target and the target under test (TUT) differ by localized geometrical modifications. Their complex differential near field is reconstructed using Tikhonov-regularized least squares QR factorization (LSQR) method. The reconstructed differential far- field contribution is coherently combined with the prior far-field contribution to estimate the bi-static RCS of the TUT. The method is preliminarily evaluated using simulations of a complex target at 6 GHz. The results indicate that, for the investigated simulation case, prior information can be used to thin out the sampling grid by 90% while maintaining close agreement with the simulation baseline.

Federated learning over decentralized networks inherently trades off the suppression of local finite-sample noise through collaboration against the bias that collaboration introduces between heterogeneous nodes. We study this tension by performing a large-dimensional analysis of Generalized Total Variation Minimization with least-squares models. Using tools from random matrix theory, we show that Lipschitz observations of the global GTVMin solution concentrate in large dimensions, universally for any underlying network structure. We provide exact analytic expressions for the asymptotically precise performance under both i.i.d. and non-i.i.d. Gaussian mixture distributions on a fixed network. For the latter, these expressions quantify how regularization balances local adaptation against collaboration. Our theoretical results are confirmed by experiments on synthetic and real-world data.

Catheter obstruction is the commonest cause of shunt failure; freehand insertion at Keen's point leaves the tip free in cerebrospinal fluid in only one case in ten. We built a digital twin that reconstructs skull, scalp, ear and ventricles from preoperative CT by deterministic geometry, searches every entry around Keen's point for the perpendicular trajectory with the longest intraventricular length under safety constraints, and returns the plan as two ruler measurements from the ear and two depths. Executed freehand in 11 consecutive adults (IDEAL Stage 2a), it achieved Hayhurst Grade 1 placement in 10 of 11 against 22 of 213 historically (p = 9 x 10^-9), median entry and angular deviations 2.5 mm and 5.9 degrees, 1.4 cm more intraventricular catheter than Keen's point, and no intraoperative complication. The technique was unchanged; the gain came from choosing entry and depth per patient. Whether it lowers revision is the next stage's hypothesis.

Accurate nuclei segmentation underpins quantitative computational pathology, yet remains challenging due to morphological variability, weak boundaries, nuclear crowding, and pronounced domain shifts arising from differences in tissue preparation, staining, and acquisition. While deep learning and recent foundation models have improved segmentation performance under matched distributions with the original training data, their generalization across heterogeneous histopathology domains remains limited. We introduce GDBA-Net, a parameter-efficient nuclei segmentation framework built around the proposed Gated Dual-Branch Adapter (GDBA). GDBA-Net adapts a frozen SAM2 encoder by integrating pretrained semantic representations with explicit frequency-derived structural priors. The complementary representations are independently transformed through Grid MLP branches and dynamically integrated using sample-adaptive channel-wise gating, selectively emphasizing structural cues relevant to nuclear delineation. Despite using only 4.3 million trainable parameters, GDBA-Net achieves state-of-the-art in-dataset performance and consistently superior cross-dataset generalization across six diverse nuclei segmentation benchmarks under fully supervised, cross-dataset, and five-shot adaptation protocols, outperforming competing CNN-, transformer-, and foundation model based methods. Comprehensive ablations confirm that these gains arise from the coordinated design of semantic-frequency complementarity and adaptive gating rather than increased model capacity. By uniting transferable semantic representations with explicit structural priors, GDBA-Net provides a robust, annotation-efficient solution to domain variability in nuclei segmentation. https://github.com/biplabpoudel25/GDBA_Net

We study short-range three-nucleon forces (3NFs) in nuclear lattice effective field theory with a chiral two-nucleon interaction at N${}^3$LO. The one-pion-exchange ($c_D$) and contact ($c_E$) terms of the leading 3NF are decomposed into locally and non-locally smeared components and supplemented by partial-wave-resolved pair contacts coupled to the density of a third nucleon. We determine their coefficients from nuclear binding energies for nuclei in the mass range from $A=3$ to $A=40$ and neutron–alpha finite-volume energies. This allows to work out the minimal three-nucleon force that can be used for future precision studies in NLEFT.