Papers

We prove a positive mass theorem for one-ended asymptotically flat spin initial data with multiple time directions and a smooth compact boundary. Assuming the trace-norm dominant energy condition and pairwise commutativity of the second fundamental forms, a fixed auxiliary time direction on each boundary component determines a local chirality condition. We identify the surviving mixed boundary term and obtain the inequality $E\geq\|\mathcal P\|_{\mathrm{tr}}$ under the boundary condition $H+\operatorname{tr}_\Sigma k^T+\|\mathcal Q_T\|_{\mathrm{tr}}\leq0$. The proof constructs a Dirac–Witten harmonic spinor in an affine energy space and evaluates the mass identity by approximation. We also establish the pointwise sharpness of this boundary condition for the fixed projector and give two-time data with a nonzero mixed boundary term.

Software systems increasingly embed a large language model in features that must satisfy a numeric output constraint, that is, a requirement expressible as a number or an interval and checkable by code, such as a target word count or a target readability grade band. Because such a model is non-deterministic, is configured through natural-language instructions rather than a typed interface, and satisfies a stated requirement only approximately, a single prompt neither reliably meets the target nor preserves the source content. This paper presents and evaluates a closed-loop control architecture for this problem. It has five stages: generate, evaluate, adjust, archive, and analyze. The model is called only to write and to edit text, while deterministic code compares a composite readability value against a target band, rejects any edit that drops source entities, numbers, or keywords, and makes every accept decision. Over 114 single-shot generation jobs and 240 closed-loop runs on four commercial models, single-shot prompting met the target in 21.1 to 31.6 percent of cases and the closed loop in 92.5 to 98.8 percent, within two edit rounds on average and at a recall-based fidelity of 0.92 to 0.93; the two models common to both settings show the same effect. Because the controller optimizes the value on which success is scored, the result establishes reproducible control over a declared, computable metric and not validated human difficulty. The transferable practice is to declare the acceptance condition as code, bound the model to local edits, and gate every edit on a content check.

Batched multi-armed bandits update on a service's own schedule, and the usual implementation carries each arm's absolute reward rate from one update to the next. When the shared level moves between batches, that memory goes stale even though the comparisons between arms may not have. Odds-Ratio Thompson Sampling (OR-TS) instead carries the joint posterior over log-odds contrasts and fits the common level afresh in every batch, marginalizing it out. This paper specifies that update, places it inside a Bayesian bandit agent with two controls, decay for how much past evidence survives an update and aggressiveness for how sharply belief becomes allocation, and evaluates it against absolute-rate memory. Across 86 public A/B series the level varies about twenty-five times more than the contrast. In prespecified synthetic environments a moving level costs absolute-rate memory five times the regret and leaves the best arm below a majority of traffic in 7 of 20 runs, against none for OR-TS. In a policy simulation built from 71 real experiments, where the contrasts are too small to resolve, expected-click differences stay within 0.1% for 58 of them, yet contrast memory still ends on the better arm more than twice as often. Where the contrasts themselves move, the bet fails, and that case is reported too.

Several institutions test one family of hypotheses under family-wise error control but cannot pool their data, so each site releases only a quantized report of its p-value for each hypothesis, such as whether the p-value is significant. The report's resolution is the number of values it can take. We quantify the power lost to such reports relative to the most powerful centralized procedure given all p-values (the oracle), with reports and combining rule chosen optimally. A report from which the p-value can be recovered loses no power, so the loss is due to compression, not decentralization. Under the stated regularity and power-objective conditions, every finite resolution loses power, and the optimal loss decays as the inverse square of the resolution: equal-width intervals attain this order, and no partition into as many cells improves it. In two-site Beta examples, optimized one-bit reports are nearly lossless for a single hypothesis but lose several times as much power for two. At level 0.05 with two Beta(1,2) hypotheses, optimally combined three-bit equal-width reports retain 99.2% of oracle power. We give the power-optimal combining rule for given reports, and a rule using only their exactly known null distribution, valid under arbitrary dependence across hypotheses.

Probabilistic models are often constructed separately for different test suites and then expected to share a single latent dynamical system. We study bounded-state shared realization for probabilistic automata from finite partial trace specifications. A shared realization uses one normalized automaton with named initial distributions, a common family of row-stochastic letter-transition matrices, and one final output vector. We compare it with separate local realizations and a labelled query-specific static relaxation. Local and labelled query-specific static optima need not compose. For every $k,L\ge1$, we construct finite partial specifications for which each individual specification and the labelled query-specific static relaxation have minimum state count $k$, whereas every exact shared realization requires exactly $k(L+1)$ states. The factor $L+1$ reflects the prefix progress that must be tracked by a single shared transition family. In the linear-rank-tight calibrated regime, the existence of an exact $k$-state shared realization is equivalent to finding a $(k-1)$-simplex containing the root responses, contained in the response polytope, and forward-invariant under every single-letter affine update. For finite rational specifications, exact shared realization with at most $K$ states is $\exists\mathbb{R}$-complete, while distinguishing zero minimax defect from inverse-polynomial defect is $\mathsf{PromiseNP}$-complete. Both classifications hold over a fixed five-letter alphabet when the local and labelled query-specific static optima already equal $K$. They remain valid with Boolean final output vectors, and the robust gap persists over the full cube $[0,1]^d$. Thus the hardness arises from shared word composition.

We study a Stackelberg model where two players compete in a sequential contest, and the player that successfully invests the most effort wins. Our formulation considers a probability that each player fails to invest their chosen level of effort, as captured by a failure function that increases with the amount of effort. The players each have their own cost of failure, as well as a maximum level of effort (capturing different abilities of the players). We prove three key results. First, we provide the optimal strategy for Player 1 (the follower), to maximize their utility given an observed effort exerted by Player 2 (the leader). Next, we characterize the optimal strategy to maximize the expected utility of Player 2, anticipating the optimal response by Player 1. Finally, we analyze the expected utilities of each player when both play their optimal strategy, and provide key insights into how heterogeneous player abilities and failure costs affect the outcomes of the game.

Large language model (LLM) agents already trade real capital, and builders copy a few published designs that share models and news feeds, so one shock reaches many agents at once. We present FARSIGHT (Financial Agent Robustness and Security Investigation and Global Holistic Taxonomy), a systematization that rates trading agents on robustness to market stress and on security against source manipulation, agent compromise, and agents acting as attackers, and checks the ratings against released code. Across 15 academic schemes, no paper describes a halt that skips LLM inference or combines source provenance with cross-source corroboration, and the 7 code releases enforce no stop-loss or position limit outside the LLM. Three LLMs sell whole positions on a fake headline and on real hoaxes, including the fake press release behind the 2000 Emulex crash. In a simulated market driven by these decisions, one fake headline crashes the market in all runs with 400 agents, and 400 agents that sell when prices fall nearly double a 2010-sized crash. The pause that U.S. exchanges apply to large stocks starts in no headline run, whereas automatic halts and hard loss limits outside the model remove both effects. Restated as a domain-independent threat model, FARSIGHT maps the same gaps onto agents in healthcare, law, software, and crypto, where compromised agents spread harm as worms and as cascades. We derive 14 open problems and urge deployers to corroborate sources, keep interrupts that bypass the model, and enforce loss limits outside it.

In this paper, we establish existence and pointwise Wolff potential bounds for nonnegative solutions of $-\Delta_{\mathbb{G},p}u=H_l(\alpha u^\beta)+\mu$ on Carnot groups, where $H_l(t)=e^t-\sum_{j=0}^{l-1}t^j/j!$ and $\mu$ is a nonnegative Radon measure. Under suitable conditions on the reaction parameters, we treat arbitrary open sets in the subcritical range $1<p<Q$ under a maximal potential condition, and bounded domains in the critical case $p=Q$ under a small total mass condition.

In this paper, we study polyhedral aspects on commutative and noncommutative Edmonds' problems for computing the rank of linear symbolic matrix $A = \sum_{k=1}^m A_k x_k$. We regard them as linear optimization over integral polytopes ${\cal P}(A)$ and ${\cal Q}(A)$, respectively, which are obtained by the convex hulls of exponent vectors of subdeterminants of~$A$ and its blow-ups $A^{\{d\}} = \sum_{k=1}^m A_k \otimes X_k$ $(d=1,2,\ldots)$. By extending previously known results on nc-rank, we establish a hierarchy of integral polytopes ${\cal P}(A) \subseteq {\cal P}^{\leq 2}(A) \subseteq {\cal P}^{\leq 3}(A) \subseteq \cdots = {\cal Q}(A)$ and show that the integrality gap of ${\cal Q}(A)$ relative to ${\cal P}(A)$ is at least $1/2$. Further, we show that if each $A_k$ is rank-2 skew-symmetric, then the above hierarchy terminates at the second level and the integrality gap is improved to $2/3$.

Autoregressive image generation has emerged as a paradigm for multimodal AI systems due to its compatibility with transformer-based LLM serving infrastructures. However, generating thousands of visual tokens per request makes decoding increasingly bottlenecked by KV cache accesses during attention computation. Sparse attention is particularly attractive for this workload because many visual generation applications tolerate moderate quality degradation in exchange for improved performance and efficiency. While sparse attention has been extensively explored for text-based LLM inference, it remains unclear whether its sparsity assumptions generalize effectively to autoregressive image generation. We present the first systematic characterization of attention sparsity in autoregressive image generation across diverse workloads and representative open-source models. Our analysis reveals several distinguishing properties, including a pronounced prefill-decode asymmetry, strong attention concentration on prompt and local tokens, and a unique diagonal attention sparsity pattern arising from the spatial locality of visual tokens. Motivated by these observations, we propose a diagonal-aware sparse attention mechanism that selectively skips KV entries along the diagonal attention direction within a recent window. Implemented on top of a GPU-based serving system using FlexGen, FlashAttention-2, and custom kernels, our approach achieves up to 3.1x throughput and 1.19x latency improvements with less than 2% quality degradation compared to dense inference.

We study sparse composite quantile regression (CQR) for distributed data with heterogeneous honest sites and Byzantine workers. Honest sites share a common slope but may differ in their covariate distributions, error laws, and quantile intercepts. The proposed heterogeneity-calibrated robust CQR (HC-RCQR) profiles local intercepts and calibrates scores using an approximate inverse profile Hessian. Honest workers transmit the resulting vectors, whereas Byzantine workers may send arbitrary vectors. The server updates the estimate by coordinatewise trimming and soft thresholding. A scalar example shows how unequal honest-site curvatures allow intermediate Byzantine reports to survive trimming and how ideal calibration reduces their possible effect. We also establish nonidentification of the mean of unrestricted honest-site slopes when fault identities are unknown. Under suitable conditions, we establish conditional contraction and support-recovery guarantees. The bound separates score offset, sampling fluctuation, contamination, calibration error, and the Newton remainder. Simulations and a bike-demand study examine performance under heterogeneous data and adversarial messages.

Long-distance transport of magnon spin currents in antiferromagnetic (AFM) insulators has attracted tremendous attention recently, however, the AFM magnon spin relaxation mechanisms remain elusive. Here, we report that the Dyakonov-Perel-type magnon spin relaxation mechanism governs the spin current transport along the easy axis in two prototypical uniaxial AFM insulators, Cr2O3 and alpha-Fe2O3. First, an over 450% enhancement of the first-harmonic nonlocal signal induced by a magnetic field is observed prior to the spin-flop transition, which can be well-interpreted by our model incorporating Dyakonov-Perel-type magnon spin relaxation. Secondly, we find that the magnon spin diffusion length in both crystals increases with magnetic field and saturates at fields above 0.8 T, consistent with our model. Finally, the temperature dependence of the zero-field magnon spin diffusion length in both AFM insulators can be qualitatively explained through our model. These findings are valuable for the development of low-dissipation antiferromagnetic spintronic devices.

Modern vehicular embedded systems increasingly combine ROS 2-based autonomous-driving stacks with AUTOSAR Adaptive Platform (AUTOSAR AP). Such mixed stacks make scenario-based evaluation hard to interpret because execution paths cross DDS-SOME/IP middleware boundaries between ROS 2 and AUTOSAR AP. Existing simulators and tracing tools execute scenarios or collect platform-local traces but cannot reconstruct cross-domain data flows. This paper presents BA-TRACE, a boundary-aware trace reconstruction framework for scenario-based evaluation of mixed AUTOSAR AP and ROS 2 vehicular embedded systems. BA-TRACE combines ROS 2 trace events, AUTOSAR ara::log events, ARXML-derived structural dependencies, and bridge-level instrumentation to reconstruct an end-to-end execution graph across the DDS-SOME/IP boundary. A case study with an AWSIM/OpenSCENARIO-based object-detection and braking scenario shows that BA-TRACE reconstructs the expected cross-platform path and exposes boundary-specific latency such as point-cloud transfer overhead. The reconstructed topology is used as evidence of traceability, not as proof of behavioral correctness or safety.

In this paper, we study the fixed angle scattering problems raised by Rakesh and Salo. We show that a compactly supported potential is uniquely determined by the far field pattern at a fixed angle, which is an open problem. Our method is based on a novel Carleman estimate and the ideas introduced by Bukhgeim and Klibanov on the use of Carleman estimates for inverse problems.

In our previous work we introduced the Reconstruction Dimension, an upper bound on the reconstructable degrees of freedom determined solely by the symmetry. In actual physical systems, however, the state quantities are generated through physical processes $P_o$ induced by the cause $O$. The state space is therefore often degenerate, and the upper bound determined by the representation-theoretic structure is not reached. This calls for a distinction between the upper bound determined solely by symmetry and the one realized after the physical process. We therefore introduce a three-level structure of upper bounds: the Structural, Effective, and Physical Reconstruction Dimensions (SRD, ERD, PRD), determined respectively by the representation-theoretic structure of the intermediate space, by the concrete design of the reconstruction map, and by the degeneracy of the state space under the physical process $P_o$. For each irreducible component they form the hierarchy $\mathrm{SRD}\ge\mathrm{ERD}\ge\mathrm{PRD}$, so that the two gaps identify at which level reconstructability is lost. The framework is illustrated through two contrasting systems: the orientation dynamics of flake-like particles, where the cause is a velocity gradinet, and the two-body problem, where the cause itself is defined through the symmetry. This paper provides a concrete framework for reconstruction in physical inverse problems.

In the present paper, we study finite subgroups of the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields from the point of view of mono-anabelian geometry. We shall refer to a finite subgroup of the outer automorphism group of the absolute Galois group of a mixed-characteristic local field as quasi-geometric if its inverse image in the automorphism group of the corresponding absolute Galois group is isomorphic to the absolute Galois group of some mixed-characteristic local field. It is well-known that the image of the natural injective homomorphism from the automorphism group of a mixed-characteristic local field to the outer automorphism group of the associated absolute Galois group yields a typical example of a quasi-geometric subgroup. The main result of the present paper asserts the existence of non-quasi-geometric finite subgroups of the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields. This result shows that the set of quasi-geometric subgroups of the outer automorphism group of the absolute Galois group of a mixed-characteristic local field cannot be characterized, in general, as the set of all finite subgroups of the outer automorphism group.

Federated learning (FL) enables privacy-preserving, on-device training across heterogeneous Internet-of-Things (IoT) deployments such as smart-city water-metering networks, where each smart meter observes a household-specific consumption time series. Under such statistical heterogeneity, the standard Federated Averaging (FedAvg) aggregation averages dissimilar local models into a single global model that may fail to capture client-specific patterns. We address this by forming client coalitions directly in the local-weight space and aggregating at the coalition level. Extending a prior weight-driven coalition-formation scheme, we model coalition formation as a Hegselmann-Krause (HK) bounded-confidence opinion-dynamics process acting on the local weights, and develop variants of the HK interaction based on Euclidean-distance and cosine-similarity confidence criteria. The framework is applied to short-term water-consumption forecasting with local Long Short-Term Memory (LSTM) models and evaluated against FedAvg, Per-FedAvg, FedProx, and FedAvg with Euclidean-distance or cosine-similarity coalition formation. Experiments on a real smart-metering dataset of water consumption show that the proposed HK-based coalition formation produces stable, endogenous coalition structures within at most ten inner iterations, incurs no additional client-side computation or communication compared to FedAvg, and reduces the average MAE by up to 54% relative to FedAvg, 39% relative to FedProx, and 24% relative to Per-FedAvg, while achieving the highest global accuracy (83-85%).

Interstellar comet 3I/ATLAS shows unusual volatile activity, including strong H$_2$O, CO, and CO$_2$ production and a delayed post-perihelion detection of CH$_4$. In this work, we investigate the delayed CH$_4$ detection in an H$_2$O, CO$_2$, and CO ice matrix using a shape model coupled with a thermophysical nucleus model that incorporates interstellar processing by Galactic Cosmic Rays. We track the sublimation, trapping, depletion, and release of these volatiles as a function of heliocentric distance and explore the relevant parameter space through 12000 model runs to identify viable combinations of primordial volatile inventory and effective GCR exposure age that reproduce the observed production rates of these volatiles. The viable models favour a volatile-rich primordial inventory consistent with formation in an ultra-cold ($T < 20$ K) region beyond the CO snowline, followed by an effective GCR processing exposure of 0.87–3.1 Gyr during interstellar passage. GCR processing produces a continuous compositional gradient and converts part of the CO reservoir into secondary CO$_2$ and depletes near-surface CH$_4$ through radiolytic conversion. The delayed CH$_4$ detection can be explained by the survival of CH$_4$ trapped within the deeper H$_2$O matrix and its subsequent release as subsurface heating progresses after perihelion. The timing of CH$_4$ sublimation can be used to estimate the effective GCR processing age of 3I/ATLAS. The posterior distributions also reveal a degeneracy between primordial dust content and GCR exposure, where dust-rich, weakly processed and ice-rich, strongly irradiated evolutionary pathways produce processed subsurface layers with similar thermophysical properties.

The rapid increase of deepfakes has raised significant concerns due to their spread on social media. Traditional multi-face forgery detectors crop and verify each face independently, ignoring background context and inter-face relationships, which often yields suboptimal performance. To overcome these limitations, we leverage instruction-based Large Vision-Language Models (LVLMs), which can interpret entire images and follow complex textual instructions. We propose a simple yet effective single-stage multi-face forgery detector, called IMFD (Instruction-based Multi-face Forgery Detector), which is trained end-to-end to jointly localize faces and predict per-face forgery labels. Rather than treating face box prediction only as a joint objective, IMFD explicitly integrates predicted face bounding boxes into the instruction as visual cues that enhance instruction grounding and forgery detection. To support the training and evaluation of IMFD, we convert existing multi-face forgery datasets into an instruction-based format. Experimental results and analyses show that IMFD improves multi-face forgery detection by integrating face bounding boxes into the instruction, and consistently outperforms various state-of-the-art methods.

Perverse schobers are a categorification of perverse sheaves, originally proposed by Kapranov and Schechtman. The purpose of this paper is to initiate a microlocal study of perverse schobers. We first categorify $\operatorname{Perv}(\mathbb{C},R)/\operatorname{Loc}(\mathbb{C})$, the category of perverse sheaves on a complex line with singular points at $R$, modulo local systems. We use this to propose a general definition for microlocal perverse schobers supported on the open conormal to a germ of a hypersurface, and we conjecture that this is invariant under Radon transform. Here we make the key observation that while the analogous quotient of perverse schobers $\mathsf{2Perv}(\mathbb{C},R)/\mathsf{2Loc}(\mathbb{C})$ is a reasonable categorification, the resulting theory fails to be invariant under Radon transform. In fact, our proposed categorification can be recovered by correcting an instance of this failure in a universal manner. We prove Radon invariance when our hypersurface is the curve $y^m=x^n$ in $\mathbb{C}^2_{x,y}$. Along the way, we explain how our theory relates to Fourier transforms of perverse schobers, periodic SODs, and spherical monads.

It is shown that if $u$ solves the wave equation in $\mathbb{R}^{4+1}$ with initial data $u(\cdot,0) = u_0(\cdot) \in H^s$ and $\partial_tu(\cdot,0) = u_1(\cdot ) \in H^{s-1}$, where $0.5 < s \leq 0.55$, then $u(x,t) \to u_0(x)$ and $\partial_tu(x,t) \to u_1(x)$ pointwise as $t \to 0$, for all $x$ outside an exceptional set of Hausdorff dimension at most $6-4s$. In a very small range of $s$, this verifies a conjecture of Barceló, Bennett, Carbery, and Rogers. More generally, a partial improvement to the exceptional set bound in $\mathbb{R}^{n+1}$ is obtained for $n \geq 4$ and $1/2 < s < n/4$.

Daily locomotion encompasses diverse activities and frequent transitions between them, yet most exoskeleton controllers are designed for a single activity or a narrow set of related movements. Changes in activity therefore typically require explicit mode switching and separately tuned or retrained controllers. Simulation-based learning reduces the need for hardware-based tuning but generally retains this limitation. Here we present UniExo, a framework that first constructs a multi-skill musculoskeletal human policy and then jointly trains an exoskeleton control policy with it. Four single-skill imitation experts for walking, turning, running and backward walking are distilled into a single network structured by a skill latent and subsequently fine-tuned through reinforcement learning on transition sequences. The resultant unified human policy achieves a mean tracking success rate of 94.7% on unseen clips of the four skills and exhibits greater robustness to perturbations than its constituent experts. A single hip exoskeleton controller (UniExo) is initialized from hip moment prediction of the human policy and co-adapted with it through multi-agent reinforcement learning across the four skills. This co-adaptation shifts the timing of the assistance torque and raises the fraction of positive work delivered to the hip. When deployed on a custom hip exoskeleton, the controller generalizes across four treadmill speeds in six participants and assists one participant through a continuous route of all four skills and their transitions, without skill labels or explicit mode switching. UniExo thus provides a step towards replacing activity-specific controllers with unified, user-specific controllers that support diverse locomotor activities and the transitions between them.

The shape of the submillimeter galaxy number counts below the confusion limit is a key record of cosmic star formation but is accessible only statistically, through the one-point distribution of map surface brightness, $P(D)$. Classical $P(D)$ analysis compresses the counts into flux-integrated constraints and requires a full instrument forward model. We introduce an extreme-value-theory analysis of the confusion $P(D)$ tail: the peaks-over-threshold formalism, in which exceedances above a threshold $u$ follow a generalized Pareto distribution (GPD). The GPD shape parameter $\xi(u)$ is a flux-resolved, normalization-free readout of the local logarithmic slope of the counts, and its gravitational-lensing modulation $\Delta\xi(u)$ probes their local curvature. We derive analytic relations for both, validate them with end-to-end simulations, and apply the method to Planck 857 GHz maps and the Herschel/SPIRE 350 $\mu$m map of GAMA-09. At Planck's 5' resolution the tail reflects the bright, clustered sky rather than the faint counts, though the background alone excludes the single power-law count model. At SPIRE resolution $\xi$ rises markedly with threshold, consistent with the strongly lensed bright population (a first detection of lensing in a $P(D)$ tail), and the bright-masked map favors the Schechter model. Behind galaxy clusters we set the first calibrated upper limits on $\Delta\xi(u)$. CCAT/FYST should separate the count models directly, but a cluster-lensing detection needs more $10^{15}\,M_\odot$ clusters than the sky contains. The GPD tail statistic thus discriminates the functional form of the counts at fluxes of order the threshold, below the detection limit, invariant to map mean, gain and count normalization, and robust to clustering; lensing supplies a calibrated ruler for count features, whose detection awaits deep, high-resolution surveys of massive clusters.

We present LYRIC, a generative flow-matching controller for language-driven physics-based contact-rich interaction control, that enables simulated characters to perform contact-rich whole-body object interactions from a free-form language instruction and a sparse terminal object goal. To obtain reliable expert trajectories from imperfect motion-capture references, a single tracking policy is trained using geometry-conditioned interaction rewards and relaxed reference tracking near hand-object contact. To guide interaction progress without prescribing a full-body kinematic reference, we factorize the controller into a task-level planner that predicts short-horizon object and humanoid-root trajectories, and an action generator that resolves whole-body motion and contacts in closed loop. After behavior cloning, we freeze the planner and post-tune the action generator on policy using the planner's predictions as stable supervision for intermediate task progression. In a controlled OMOMO evaluation, our tracker achieves 64.3% success compared with 53.2% for an InterMimic reimplementation, while a unified policy achieves 76.5% on the full OMOMO dataset. On the held-out split, LYRIC achieves 90.3% task success, compared with 74.2% for the strongest matched kinematic-planner baseline, with better semantic alignment and motion quality. Without retraining, the controller also supports test-time object-waypoint guidance. Qualitative results further demonstrate robust, natural contact-rich interactions and zero-shot transfer to novel object shapes. The webpage is available at https://neu-vi.github.io/LYRIC/

We report JWST observations of a $z_{\rm spec}=5.196$ compact group of three strongly lensed low-mass galaxies ($M_\star \sim 10^{6-7} M_\odot$ each) whose small line-of-sight velocity offsets (from $-120\pm100$ to $+160\pm110$ km s$^{-1}$) and projected separations ($\sim2$ kpc) suggest that they are undergoing merging. On the basis of abundance-matching arguments, the trio appear to be destined to evolve into a Milky Way-mass galaxy by the present day. Our spectrophotometric analysis suggests that the stellar mass growth of this system is not simply just due to the merging of its components; rather, it is being dramatically enhanced by intense bursts of star formation. Presumably initiated by tidally-induced gas inflows, these star-forming bursts boost the mass growth $2.6\pm0.5$ times that expected in straightforward merging of the existing stellar masses. These spectroscopic observations thus not only demonstrate that hierarchical assembly remains a viable formation channel in the early assembly phases of present-day massive galaxy, but also that interaction-induced bursts of star formation are a major accelerator of this assembly process.

The discovery of superconductivity in nickelates has seeded a new field for exploring unconventional superconductivity in transition metal oxides. However, to date superconductivity has only been realized in thin films or under extreme pressure in the bulk. Here we report signatures of superconductivity at ambient pressure in bulk nickelate single crystals of (La1-xPrx)4Ni3O8 and (La1-xYx)4Ni3O8, whose crystal structure comprises interleaving trilayers of square-planar nickel oxide and fluorite-like spacer layers. The parent compound La4Ni3O8 exhibits an insulating ground state, where electrons order into intertwined, insulating charge/spin stripes. Substitution of smaller lanthanide ions disrupts this order, eventually leading to a metallic ground-state. We find that superconductivity emerges in a narrow window proximate to the insulator-metal phase boundary, where both metallic and charge-stripe phases co-exist. The observed low volume-fraction superconductivity is non-percolative, suggesting the prospect of filamentary superconductivity nucleated at the boundary between these phases. However, intergrowth defects that approximate the known infinite layer nickelates are observed in TEM, leaving open the possibility that superconductivity resides here rather than in the trilayer matrix. Remarkably, the electronic phase diagrams of both the Y and Pr series coincide when parameterized by the volume of the fluorite like spacer layers, revealing that this steric parameter profoundly modifies the nickel oxide trilayer electronic structure. Our results identify better understanding of the co-existence region between metallic and charge-ordered phases as a priority for expanding the range of bulk, ambient-pressure nickelate superconductivity and establish spacer-layer engineering as a design tool for exploring this regime of phase competition.

We show that $\bigl(\frac{\log n}{\log\log n}\bigr)$-approximate parameterized $k$-SetCover is W[1]-hard, and has no $n^{o(k/\log k)}$-time algorithms under ETH. This improves upon the previous best factors $\bigl(\frac{\log n}{\log\log n}\bigr)^{1/k}$ in (Lin, 2019) and $(\log n)^{1/\operatorname{poly}(k)}$ in (Karthik, Laekhanukit, and Manurangsi, 2019). Here $k$ is the yes-case guarantee and $n$ is the number of candidate sets. While the best approximation ratio is still $O(\log n)$ via the greedy algorithm, closing this $1/k$ gap in the exponent has been a longstanding open problem; we remove this loss via a simple direct reduction. The construction is self-contained and does not rely on the parameterized inapproximability hypothesis (PIH). Starting with sparse parameterized 2-CSP instances (Karthik, Marx, Pilipczuk, and Souza, 2024), we build a monotone CNF formula, which is equivalent to a SetCover instance. To obtain a $k$-versus-$h$ gap, the reduction enumerates all hash functions from $\Sigma$ to $[2h]$ and all unsatisfiable 2-CSP instances on the same constraint graph with alphabet $[2h]$. For each such instance, it asks for a certificate that the hashed label pairs are not all contained in that instance. Perfect hashing makes this enumeration efficient for $h=\log n/\log\log n$.

Three-dimensional fine-grained plastic scintillator detectors are extensively used in high-energy physics experiments where particle tracking, identification, calorimetry and sub-nanosecond timing information are required. Moreover, the low cost of plastic scintillator makes, in principle, the scalability to multi-tonne detectors possible. In order to circumvent the difficulties related to the long production time and the challenging assembly of millions of tiny independent scintillating voxels, a new technology consisting of gluing a few thousand $9 \times 9 \times 9$ mm$^3$ plastic scintillator cubes in a single large monolithic layer with machining precision, while ensuring an efficient optical separation, was developed and demonstrated. In this work we demonstrate that such technology can be reliably extended to a monolithic layer of $48 \times 48$ optically-isolated scintillating cubes, the size required for future ton-scale detectors, fulfilling the requirements of future neutrino detectors and sampling calorimeters.

The deployment of Vision-Language Models (VLMs) on edge devices is severely bottlenecked by memory bandwidth, necessitating aggressive sub-8-bit quantization. Since edge accelerators are strictly constrained by area and power, they require end-to-end quantized models. However, the extreme dynamic range gap between multi-modal tokens causes standard block formats to suffer "microscaling collapse," where a single massive outlier hijacks the shared exponent, underflowing surrounding elements and destroying attention maps. To break this bottleneck, we propose Micro-Inverted-Scaling (MiX), a novel format that mathematically inverts the microscaling paradigm: rather than grouping multiple mantissas under one shared exponent, MiX groups private, per-element exponents under a single shared mantissa. To handle asymmetric VLM outlier topologies, we introduce an adaptive dual-format (MiX-MX) inference framework. By algebraically factoring out the shared MiX mantissa, this framework maps to a custom accelerator, replacing multipliers with efficient shifters. Evaluated end-to-end on multiple VLMs, our 4.5-bit MiX formulation exhibits equivalent or superior accuracy on multi-modal benchmarks compared to NVFP4. Simultaneously, the MiX accelerator delivers a 25% improvement in area efficiency over the NVFP4 baseline and a 2.3-4.5x speedup with 1.4-2.9x energy reduction across models compared to the state-of-the-art accelerator Focus, proving the inverted-scaling datapath is physically superior for efficient VLM deployment.

For second-order systems under continuous sliding mode control (SMC), the literature has long relied, largely through phase-portrait illustrations, on the implicit convention that the phase-plane trajectory approaches the equilibrium along a direction tangential to the designed sliding surface. This paper investigates this tangential convergence assumption through a rigorous phase-plane analysis of the double-integrator system subject to standard linear SMC. We reveal that the asymptotic state ratio is not unique but instead exhibits a bifurcation that depends on the control gains, the sliding surface parameter, and the initial conditions. The key finding is that the system may converge along an implicit secondary manifold rather than aligning with the designed sliding surface, implying that smooth entry is not globally guaranteed. We derive closed-form expressions for the convergence ratios and establish a classification framework that precisely characterizes when the smooth-entry assumption holds and when it fails. The analysis is further extended to classical PD control, and we show that the bifurcation threshold coincides with the critical damping boundary that separates the two convergence regimes. These findings bridge terminal geometry and convergence smoothness, providing a predictive framework for high-performance motion control design. Simulation results validate the proposed classification of convergence regimes.