Papers

Neutron stars (NSs) receive natal kicks during supernovae that affect their survival in binaries and motion through the Galaxy. The global distribution of these kick velocities across the NS population remains uncertain. Here, we combine the orbital properties and birth rates of Gaia NS and Be+NS binaries with velocity constraints from young isolated pulsars to construct a concordance model of NS natal kicks. We find that all three populations can be jointly described by a shared bimodal kick distribution. The low-velocity component follows a lognormal distribution with $\mu_{\ln v}=1.87^{+0.65}_{-0.53}$ and $\sigma_{\ln v}=0.55^{+0.85}_{-0.44}$, corresponding to a median speed of $6.5^{+5.9}_{-2.7}~{\rm km~s^{-1}}$. The high-velocity component is consistent with the distribution inferred from young pulsars, which peaks near $200~{\rm km~s^{-1}}$. The low-velocity component contributes only $\sim10\%$ of all NS births, but produces most Gaia NS binaries and roughly half of Be+NS binaries. The same model predicts systemic recoil velocities consistent with the observed kinematics of Gaia NSs, Be+NS binaries, and NS low-mass X-ray binaries. For Gaia NSs, whose formation history remains unknown, we use this kick distribution to constrain their progenitors. We favor pre-supernova binaries containing intermediate-mass stripped stars with $\sim1~{\rm M_\odot}$ companions in au-scale orbits, and predict $\sim300$ such binaries in the Milky Way today, $\sim40$ in the LMC, and $\sim30$ in the SMC. Finally, we consider the implications of these kicks for NSs in hierarchical triples. We find that 2-10$\%$ of Gaia NS triples and 3-23$\%$ of Be+NS triples retain their tertiary after the supernova. Overall, our results suggest that a shared natal kick law can account for isolated pulsars and surviving NS binaries, where most NSs receive large kicks and low kicks are common among surviving binaries.

Large Audio Language Models (LALMs) are prone to hallucinating and over-relying on text priors when simultaneously presented with audio and text inputs. To mitigate these hallucinations, we propose utilizing the multimodal Direct Preference Optimization (mDPO) objective, which forces the model to ground its generation in the acoustic input by contrasting intact and distorted audio counterparts. We extend this preference learning framework to the audio domain by applying a variety of acoustic perturbations. Evaluating the Qwen2-Audio backbone across the DCASE 2025 Challenge and AH Existence datasets, we demonstrate that extending mDPO to LALMs significantly enhances temporal reasoning in the complex DCASE dataset, and improves performance on basic existence verification in the AH benchmark. We identify temporal reversal, frequency masking, and random noise as the most effective perturbations. Ultimately, our approach achieves an absolute accuracy improvement of 14.0% on the DCASE 2025 dataset and 27.4% on AH Existence.

Few-Shot Class-Incremental Learning (FSCIL) requires models to continuously learn new classes from limited samples while retaining prior knowledge, under strict constraints on compute and memory. Existing approaches lie along a difficult trade-off: simple fine-tuning is computationally efficient but suffers from catastrophic forgetting, replay-based methods mitigate forgetting at the cost of substantial compute and memory, and exemplar-free methods often reduce forgetting by freezing most of the backbone, improving efficiency at the expense of adaptability. We propose Selective Backpropagation (SBP), a deterministic parameter budgeting framework that bridges this gap. SBP restricts gradient updates to a pre-allocated subset of network parameters, freezing past knowledge and preserving unbiased capacity for future learning, enabling rapid adaptation without costly mask optimization. We show that SBP achieves strong performance across standard FSCIL benchmarks while requiring training time close to that of naive fine-tuning and substantially lower training time than prior SOTA methods. Crucially, our experiments expose a limitation of standard FSCIL evaluation: performance on short, distribution-consistent benchmarks does not necessarily predict behavior under distribution shift or over substantially longer learning horizons. We therefore evaluate FSCIL methods in cross-domain settings and over an 80-session ImageNet-1K stream. SBP remains strong across these regimes while maintaining low training cost, providing a favorable stability-plasticity-efficiency trade-off. Our code is available at https://github.com/PaInt-Lab/sbp-main-public.

A trainable input embedding table assigns each vocabulary item an independently adjustable vector. We investigate whether this token-specific parameterization is required for substantial language-modeling capability, or whether a shared Transformer can learn from fixed token identities. We compare three decoder-only language models trained from scratch with the same tokenizer, contextual backbone, untied output-head architecture, and training recipe, with a target budget of 100 billion prediction tokens per model. Their input interfaces are a learned table, canonical 16-bit token-ID codes, and one fixed invertible recoding over GF(2). The fixed codes are repeated to model width without an additional trainable input projection. Both fixed-code models acquire substantial capabilities: canonical codes achieve 52.40% HellaSwag normalized accuracy, 70.51% PIQA accuracy, and 42.75% LAMBADA accuracy. The learned-input control performs better on several evaluations, including HellaSwag and LAMBADA, so these results establish viability rather than performance parity. The fixed interfaces remove 100.7 million trainable parameters, yielding 1.711B-parameter models, but parameter reduction is not the central result. These single-run experiments distinguish architectural necessity from empirical utility: independently trainable token-specific input vectors are not required for the observed capabilities. A fixed identity interface also provides a controlled setting for studying representation learning downstream of an immutable input, without establishing where particular capabilities are localized.

In this work we provide the complete classification of all non-zero finite-dimensional complex Lie subalgebras of the universal enveloping algebra of the special linear Lie algebra $\mathfrak{sl}(2,\mathbb{C})$. That is, we show that every such nilpotent Lie subalgebra is abelian and every non-solvable Lie subalgebra is reductive, with semisimple component isomorphic to $\mathfrak{sl}(2,\mathbb{C})$ itself. Every non-nilpotent solvable Lie subalgebra is the direct sum of an abelian center and a member of the family of solvable Lie algebras $\mathfrak{r}(\boldsymbol{d},\boldsymbol{m})$, parameterized by a vector $\boldsymbol{d}$ whose entries are strictly increasing positive integers that have greatest common divisor one together with a positive integer vector $\boldsymbol{m}$ of the same length recording their multiplicities. Moreover, we discuss the corresponding classification in a real skew-hermitian setting and its relation to the realizations in the single- and two-mode Weyl algebras.

We study finite and countable point configurations in the trace of Brownian motion in $\mathbb{R}^d$, $d\geq2$. In the plane, the set of translations placing a prescribed finite configuration on the trace has Hausdorff dimension two in every nonempty open set; we prove analogous dimension-preservation results for radial and bilipschitz patterns, and every prescribed countable configuration has a dense translation set. For $d\geq3$ we prove a sharp occurrence criterion for regular scale-invariant families of configurations, in terms of the ranks of all labelled subconfigurations. It gives exact thresholds for arithmetic progressions and for homothetic and similar copies of finite sets. In particular we recover and extend a result of Benjamini and Kozma: almost surely the longest arithmetic progression in the trace has length five in $\mathbb{R}^3$, three in $\mathbb{R}^4$ and $\mathbb{R}^5$, and two in $\mathbb{R}^d$ for $d\geq6$.

Large language models (LLMs) offer a flexible approach to network intrusion detection, but direct classification of numerical flow records can be unreliable without traffic- specific decision boundaries. Retrieval-augmented generation (RAG) enables LLMs to leverage external experience; however, free-form textual experience requires the model to infer the numerical conditions that distinguish traffic classes. We propose SERA-IDS, a Structured Experience Retrieval-Augmented Intru- sion Detection framework that learns decision knowledge from classification errors. A Small Language Model (SLM) analyzes misclassified flows and generates structured rules containing behavioral descriptions, feature conditions, class-confusion infor- mation, tool-derived confidence, and provenance. A confidence gate admits supported rules into the Experience Library. During testing, the library is frozen, and retrieved class-diverse rules are condition-matched to the query flow and provided as evidence to the decision SLM. The same library is evaluated with three small, locally deployable SLMs, namely Llama 3.1, Phi-4:14B, and Qwen2.5:7B, without fine-tuning or paid hosted inference. On the test sets, SERA-IDS improves macro F1 on NF-BoT- IoT from 11.66%, 9.26%, and 7.83% to 86.46%, 69.50%, and 83.51%, respectively, and on NF-ToN-IoT from 3.82%, 6.17%, and 1.94% to 84.16%, 87.66%, and 83.37%. These results show that structured experience retrieval enables small, free, and locally deployable SLMs to achieve strong intrusion-detection performance, including performance exceeding that of the re- ported existing work used in our comparison.

Large language models (LLMs) are increasingly used as synthetic personas representing survey respondents. Their validity as substitutes for particular respondents depends on whether they reproduce individuals' decisions. We examine what information helps synthetic respondents predict each individual's later choices, using five conditions that add progressively richer information: no personal information, demographics, personality traits, cognitive scores, and finally the respondent's earlier survey choices as behavioral history. We use a two-wave panel of 845 US adults who completed measures of 14 behavioral biases (spanning risk, time preferences, overconfidence, and reasoning), so each respondent's earlier answers provide a human test-retest benchmark; in the behavioral-history condition, all items that score the target bias are withheld. At the population level, the average number of biases per respondent in every condition is close to the human average (7.1-8.1 biases, against 7.1 for humans). This aggregate similarity masks differences in variance: persona descriptions recover only 53-67% of human between-person variation, whereas adding behavioral history restores it to approximately the human level. At the individual level, description-based personas achieve only 7-12% of the informedness observed in human test-retest responses, while adding behavioral history raises this to 28%. The condition including behavioral history has the highest estimated informedness in all 17 demographic groups, whereas description-based conditions provide little or no information for some groups. Synthetic responses also exhibit stronger education- and income-related differences than human responses. For LLM synthetic personas, a respondent's past answers add more to individual-level prediction than a description of who they are.

Robots can acquire bad habits from a few defective moments in otherwise useful teleoperation. In mixed-quality robot data, normal and problematic demonstrations share most task behavior and differ only at a local action continuation. Full retraining is costly, while fine-tuning on clean data alone offers limited recovery under a small update budget. We ask whether the local difference can instead be fixed with only 1% of the full-training sample-backward budget. Using only episode-level retained/problematic labels, REDIRECT localizes the branch, assigns a coherent retained continuation to the original observations around it, and anchors shared behavior, without frame-level annotations or additional interaction. Across three randomized ManiSkill tasks and three seeds, REDIRECT raises the mean success rate from 68.2% to 90.3%, recovering 88.8% of the clean-retraining gap versus 22.1% for matched-compute fine-tuning. On a PiPER arm, it recovers 86.7-92.9% of the clean-only gap across cup insertion and towel folding. Local robot habits can therefore be repaired by spending the update budget on the behavioral difference rather than relearning shared behavior.

The millisecond pulsar PSR J0435+3233, discovered by FAST, exhibits an unusually large apparent spin-down rate, potentially reflecting line-of-sight acceleration from a distant companion. Recent investigations reveal a hierarchical triple consisting of an inner pulsar-helium white dwarf binary with an orbital period of ~8 days, orbited by a G-type subgiant tertiary on an eccentric ~74 yr orbit. The current timing description admits two distinct geometrical solutions. We develop a singly averaged (SA) formulation that averages over the inner orbit while retaining the instantaneous phase of the eccentric outer orbit, thereby capturing the time-dependent quadrupolar perturbations induced by the tertiary. We show how this physical three-body description can be incorporated naturally into pulsar-timing analyses and use it to forward-propagate the two currently viable configurations, Tv1 and Tv2, to forecast when their timing signatures become distinguishable with FAST. The SA evolution predicts that the two configurations will become distinguishable in the coming years, with the effective projected semi-major axis, $x_{1,\mathrm{eff}}$, providing the earliest discriminating observable. We further extend the framework to predict the tertiary's spectroscopic radial-velocity and astrometric evolution, linking FAST timing with LAMOST time-domain spectroscopy and Gaia astrometry. This multi-band framework has the potential to establish PSR J0435+3233 as an exceptionally well-constrained laboratory for three-body dynamics, compact-binary and stellar evolution, and gravitational physics.

Crossing-based selection is well-studied, yet past research has overlooked multi-object and attribute selection with crossing gestures. We present viaCross, a pen-based technique in which crossing strokes define attribute constraints, paired with attribute widgets that visualize and allow subsequent edits to these constraints. A controlled study compared viaCross with traditional WIMP filter panels. Results show that viaCross was more efficient for complex object-level selections, requiring fewer strokes and maintaining efficiency as task difficulty increased. WIMP panels were faster and more intuitive for simple attribute-based selections, but participants encountered repeated deselections and occasional misclicks. viaCross matched panel performance for creating attribute selections but was slower during refinement, as widgets had to be recreated, indicating the need for persistent widgets or hybrid support with a WIMP-style interface. Overall, viaCross demonstrates that crossing-based gestures can provide an efficient and scalable approach to multi-object and attribute selection.

VeriContest is a benchmark of 1007 competitive-programming problems in Rust, each with a Verus specification, a judge-accepted solution, and a Verus proof. Its authors report that proof generation is the bottleneck for frontier models: given the specification and the code, the best model produces an accepted Verus proof for 13.95% of the problems on the first attempt. We report on solving the same proof-generation task with Rust-Prover, a verifier for Rust backed by Lean 4. The Verus specification and the Rust code are restated and translated into Lean, each specification becomes a theorem, and agents prove the theorems with Lean's kernel as the final check. All 1325 theorems of all 1007 problems were proved. 1259 of them were proved in one run of under 32 hours on Claude Opus 5.5, at a median of 3.2 minutes and $1.17 per proof, and 70% of them on the first iteration. The restated specifications were checked against the benchmark's test suites, and reviewed where no suite applies. None was wrong or weakened. The translated Lean programs were run on 21,413 of the benchmark's test cases and produced the same output as the Rust programs on every one. Across four Claude and four GPT models at five reasoning-effort settings, every current frontier model proves nearly all of a ten-theorem sample at every setting, and more effort raises the cost without raising the number of proofs. The cheapest Claude setting, Sonnet 5.5 at low effort, proves all of the 50 hardest theorems. We also rerun the benchmark's own Verus protocol with Claude Opus 5.5 on the 50 problems with the longest reference proofs. Opus 5.5 alone fails to prove one of them.

We present ToF-PAX-RIXS, a compact instrument that combines time-of-flight momentum-microscopy angle-resolved photoemission spectroscopy (ARPES) with resonant inelastic X-ray scattering (RIXS). The latter is based on photoelectron spectrometry for analysis of X-rays (PAX). The two techniques are implemented with a single multimode electron-optical column, allowing measurements to be performed sequentially on the same sample under identical experimental conditions. In ARPES mode, the instrument records the photoemission intensity as a function of kinetic energy and two in-plane momentum components. In PAX-RIXS mode, scattered soft X-ray photons are absorbed in a thin metallic converter, and the generated photoelectrons are analyzed in energy and position of emission on the converter. The electron kinetic energy retains the spectral information of the scattered photons, while the position is related to the scattering angle and therefore to the momentum transfer, enabling simultaneous access to a finite momentum-transfer interval. We describe the mechanical design, converter assembly, scattering geometry, and multimode electron optics of the instrument. Its PAX-RIXS performance is benchmarked at the Cu $L_3$ edge using CaCuO$_2$, with Au, Ag, and Pt converters. The measured spectra reproduce the principal features obtained with a conventional grating RIXS spectrometer, and deconvolution yields an effective reconstructed energy resolution better than $120$~meV under the present conditions. Finally, combined ARPES and PAX-RIXS measurements on the same Ca-doped YBa$_2$Cu$_3$O$_{6.45}$ sample demonstrate the capability of the instrument to correlate electronic structure and collective excitations within a common compact platform.

Mathematical invariants provide complementary representations of molecular structure, but their predictive utility can vary across datasets and prediction tasks. For a new dataset, appropriate construction of invariant representations from algebraic topology, differential geometry, topological spectral theory, and commutative algebra is a challenging task, particularly when evaluating multiple representations is computationally expensive. We develop a Mathematical Agentic Model (MathAgent) to automatically optimize invariant representations in molecular property prediction. The framework combines dataset-aware representation design, low-cost candidate screening, and progressive evaluation. Language-model reasoning supports task interpretation, strategy proposal, and workflow coordination, while scientific computations and numerical decisions are carried out by deterministic tools. We evaluate MathAgent on protein–ligand binding-affinity and quantitative toxicity prediction tasks. Different datasets favor different combinations of mathematical invariants, demonstrating the need for dataset-adaptive representation selection rather than a fixed universal representation. Objective-conditioned executions further show that the framework can adjust its evaluation strategy according to user-specified goals. MathAgent therefore provides a systematic, evidence-driven, and traceable approach for optimizing mathematical invariant representations and reducing reliance on manual configuration and/or experimentation in molecular property prediction.

Multimodal skin lesion classification combines clinical images with patient metadata to improve diagnostic accuracy. However, complete metadata available during training may be only partially accessible at deployment, and resource-constrained settings additionally require computational efficiency. We address these challenges with a privileged-information distillation framework in which a multimodal teacher trained on complete metadata supervises a 9.2x smaller student trained with randomly masked clinical fields. Clinical fields are masked as whole groups at a per-sample rate drawn from U(0,1), so one training run covers the full metadata availability range. Fusion is residual, with metadata added as a gated correction to an unconditional image base. On the PAD-UFES-20 dataset, distillation under masked training improves balanced accuracy over cross-entropy training at every availability level, by an average of +4.7 points versus +1.8 points without masking. The masked student loses only 7.8 balanced-accuracy points as metadata decreases from complete to absent, compared with 36.6 points for the same student trained on complete metadata, highlighting the role of masked training in graceful degradation beyond distillation alone. Grad-CAM visualizations further show that the masked student's attention generally remains lesion-centered as metadata is withdrawn. The resulting compact model targets point-of-care settings, where clinical metadata is often incomplete.

The LSJM R package provides a series of functions to estimate models based on location-scale linear mixed model and location-scale joint model theory. For longitudinal data, it includes the estimation of location-scale mixed models with subject-specific residual variance that can be time-dependent or distinguish within-visit and between-visits variability. When survival data is considered, implemented joint models handle competing risks as well as semi-competing risks possibly with interval-censored data through the use of a illness-death sub-model. They incorporate flexible dependence structure between the longitudinal marker and the times-to-events through the current value, the slope and/or the residual variability of the marker. Maximum likelihood estimators are obtained using the Marquardt-Levenberg algorithm with stringent convergence criteria. The package also provides several post-fit functions including goodness-of-fit analyses and individual dynamic predictions. Some examples on real data allows to illustrates the use of this package.

Algorithms which prepare states via the variational principle assume that closeness in energy implies closeness in state; we formalise how this assumption can fail by showing that a ground-state energy estimate converged to within $\epsilon$ of the true value is compatible with observable expectation values in error by up to $\sqrt{2\epsilon\chi_O}$ at leading order, where $\chi_O$ is the static susceptibility of the observable. As a result, the observable error can be orders of magnitude larger than the energy error, a mechanism we call non-linear error amplification, and because a variational algorithm cannot guarantee the correctness of these properties from energy alone, energy does not necessarily certify an observable. In light of our findings, we examine three algorithms: the variational quantum eigensolver on the transverse-field Ising chain, the density-matrix renormalisation group on a pair of weakly coupled hydrogen chains, and Krylov quantum diagonalisation on lithium fluoride. In each case we demonstrate that a well-converged energy can leave observables uncertified.

In 1906, Maillet proved that every nonconstant rational function over $\mathbb{Q}$ maps Liouville numbers to Liouville numbers. Let $R$ be a nonconstant rational function with real algebraic coefficients, of degree $d$, and let $e$ be the degree of its minimal field of definition over $\mathbb{Q}$. We prove that, for every $m\geq 1$, the possible types of $R(\xi)$, as $\xi$ ranges over $U$-numbers of type $m$, are exactly the integers $r$ with $\lceil m/(ed)\rceil\leq r\leq em$. Moreover, every such type occurs for some $\xi$ of type $m$ in every nonempty open interval. Consequently, for $m\geq2$, the only rational functions with real algebraic coefficients preserving the class of $U$-numbers of type $m$ are the Möbius transformations over $\mathbb{Q}$.

Motivated by a real-life problem, namely, inferring genomic regions affected by selection, we studied some properties of a two-step method that performs this task based on the FST. This approach exhibits computational simplicity as an appealing feature. Step one involves fitting a conjugate Bayesian model to find point estimates of FST and selecting the markers to be considered in step two, where they are grouped using such estimates. Subjective priors are frequently used in this problem and large hyperparameters may be encountered; hence, there is interest in addressing their impact. Preliminary analyses suggested that, the number of markers selected in step one tends to zero when the hyperparameters have the same value and tend to infinity, or are different but tend to infinity and their difference tends to zero. Thus, we studied how hyperparameters affect the posterior mean, variance, and predictive density of allele frequencies, and the posterior distribution of FST, formally. Moreover, an empirical approach based on simulated and real data was performed. Our main findings are summarized in two theorems that set the asymptotic behavior of the method, providing a foundation to understand the aforementioned phenomena. As to the empirical studies, the groups created in the second step, the estimated posterior means and the number of selected markers showed high sensitivity to hyperparameters. Albeit the mathematical intractability of the posterior distribution of FST, our results revealed asymptotic properties explaining two features of the method that lacked a formal elucidation.

Let X and Y be finite ordered sets and let $X^Y$ denote the ordered set of order-preserving maps from $Y$ to $X$. Let $t$ be a~term formed from a~single variable by exponentiation. We prove that, for every term $t$ with at most twelve variable occurrences and arbitrary finite ordered sets $A,B$, $t(A)\cong t(B)$ implies that $A\cong B$. General constructions and reconstruction principles are developed first; the second part gives the occurrence-by-occurrence proofs. At twelve occurrences the proof covers 4,766 interchange normal forms, representing all 58,786 binary parenthesizations, including 40 exceptional forms. Two additional unbounded reconstruction families, complete finite audit data, and 457 exact height-comparison certificates are included.

In wireless sensor and mesh networks, modular robots, and shape-adaptive computers, computing modules attach, detach, or are replaced while the others keep running with their local state. A value computed under the old arrangement, such as a cached next hop, stays in memory but may no longer describe the current one, so a program can send to a neighbor that has left without any runtime errors. We present morph-aware computing, a programming model in which the application specifies a corrective update of such state, called a repair, and the compiler decides when it runs. In MorphLang, the repair is a Reconfigure branch next to the ordinary branches that handle sends, receives, and sensor samples. MorphC compiles MorphLang to bare-metal RISC-V and inserts a guard before every ordinary branch, so that each module repairs its state before any other branch sees a new topology. Relying on this order, MorphC also rejects sends whose target may be a literal or a value the repair does not always refresh. For a model of the code MorphC generates, we prove in Rocq that the repair precedes every later ordinary branch for any number of roles and topology changes. This shows that send-target checking is sound for a core language. On 19 MorphLang programs derived from seven network stacks, removing the repair worsens destination validity in ten of the 13 programs that declare one and never improves it. In a reduced reproduction of a released Contiki-NG defect, a callback-based version sends to a departed parent after 60 of 384 changes and the MorphLang version after none. The guards cost 12 cycles per loop in a microbenchmark, and on an FPGA the delay from each commit to the first send to the new neighbor matches RTL simulation.

Autonomous coding agents solve repository issues by reading code, running commands, editing files, and submitting patches. Extra inference-time compute yields gains only when it produces a useful repair and supplies reliable evidence for choosing one. Three behaviors decide both, and we argue they are teachable rather than byproducts of scale, so a policy can carry them instead of a scaffold. Location diversity remains narrow, since attempts return to the same site and extra samples add no coverage. Edit diversity is left unexploited, since methodologies that differ resolve complementary issues no single run reaches. Verification misleads, since a test the agent writes for its own patch accepts many incorrect ones. Directing search by execution feedback and scoring each patch against its own reverted tree resolves 52.8% of SWE-bench Verified using 48.1% of the agent-steps an eight-sample baseline spends. Training moves these behaviors into the policy. On the 270 issues held out from SFT and RL training, weighted supervised fine-tuning raises pass@1 from 31.9% to 35.2% and pass@8 from 46.7% to 51.1%. A reinforcement objective then trains the verifier against gold-labeled repairs and incorrect variants, crediting the assertions that detect them. It raises pass@1 to 43.0% and pass@8 to 60.7%, lifts verifier precision from 26.8% to 41.7%, and more than halves false acceptance. Resolution improves on two of three out-of-distribution suites and verifier precision on all three, and the gains hold at 7B, 14B, and 30B against published coder baselines.

We study constrained online convex optimization with adversarial convex costs and constraints ($\mathsf{COCO}$). At each round $t\in[T]$, a learner selects $x_t$ from a $d$-dimensional convex decision set $X$, after which an adaptive adversary reveals a convex cost function $f_t$ and constraint function $g_t$. Consequently, the learner incurs a cost of $f_t(x_t)$ and a constraint violation of $\max\{0,g_t(x_t)\}$, and aims to simultaneously minimize regret and cumulative constraint violation ($\mathsf{CCV}$) over the entire horizon. Existing algorithms achieve $O(\sqrt{T})$ regret and $\widetilde O(\sqrt{T})$ $\mathsf{CCV}$. We show that an online policy can achieve $O(\sqrt{T\log T})$ regret and $O(\log^2 T)$ $\mathsf{CCV}$, reducing the $\mathsf{CCV}$ from polynomial to polylogarithmic while retaining near-optimal regret. When all cost functions are either $\alpha$-exp-concave or $\beta$-strongly convex, the algorithm achieves $O(\log T)$ regret with the same $\mathsf{CCV}$ bound as above. Our approach combines continuous Hedge with elimination on shrinking feasible sets. The key observation is that whenever the mean of the Hedge distribution violates a constraint, Grünbaum's inequality guarantees that a constant fraction of the Hedge probability mass is eliminated. We use an adaptive learning-rate schedule and a potential function coupling the surviving volume with the learning rate to convert this probability-mass reduction into a bound of $O(\log^2 T)$ on the $\mathsf{CCV}$.

We study constant-delay enumeration for conjunctive queries with negation ($\texttt{CQ}^{\neg}$). It is known that $\textit{signed-acyclic}$ queries can be enumerated with constant delay after linear preprocessing time, using linked lists with skip links. We use a hypergraph width measure for $\texttt{CQ}^{\neg}$, the $\textit{fractional signed hyperorder width}$ ($\textsf{sfhow}$), which requires a single variable order to simultaneously handle every subset of the negative atoms, which Capelli et al. introduced to characterize the preprocessing time of direct access. $\textsf{sfhow}$ strictly generalizes signed-acyclicity (recovered when $\textsf{sfhow} = 1$) and fractional hypertree width (recovered on queries without negation). Our main algorithmic result is a variable-elimination algorithm that achieves constant-delay enumeration on input $I$ for any full $\texttt{CQ}^{\neg}$ query with preprocessing time $O(|I|^{\textsf{sfhow}})$. Furthermore, we show that using multiple variable orders can improve this bound, exhibiting an $O(|I|^{3/2})$ algorithm for $k$-cycle queries with at least one negative edge.

Satellite populations provide sensitive tests of the galaxy-halo connection, but studies have largely focused on Milky Way (MW)-mass host galaxies or a small number of nearby dwarf galaxy hosts. Here we present a statistical census of bright, star-forming satellite galaxies around sub-MW-mass hosts using the first data release of the Merian Survey. Our sample consists of 357 hosts with stellar mass $10^{9.5}<M_{\star,\text{host}}<10^{10.5} \ \text{M}_\odot$ at redshifts $0.07<z<0.09$, all selected to be central galaxies. Merian's medium-band imaging isolates H$\alpha$ and [O iii] emission lines for galaxies in this redshift range, enabling efficient selection of star-forming satellites down to $M_{\star,\text{sat}}\gtrsim 10^{7.5} \,\text{M}_\odot$. We identify 471 satellite candidates within the projected virial radii of these hosts. After statistically subtracting the contribution from foreground and background galaxies, we find $148\pm 7$ satellite candidates associated with the host sample. We find that $\mathord{\sim} 60\%$ of hosts have $N_{\rm sat}< 1$ massive satellites within their virial radii, $\mathord{\sim} 22\%$ have $1\leq N_{\rm sat}< 2$, $\mathord{\sim} 10\%$ have $2\leq N_{\rm sat}< 3$, and $\mathord{\sim} 8\%$ have $N_{\rm sat} > 3$. Satellite abundance increases with host stellar mass across the sub-MW regime, extending the observed trend from dwarf to MW-mass galaxies and broadly agreeing with predictions from the TNG50 simulation. The radial distribution of satellites around sub-MW-mass hosts is similar to that around MW-mass hosts and broadly consistent with TNG50. Together, these results extend our empirical view of satellite populations across the previously sparsely sampled transition between dwarf and MW-mass hosts.

Text-to-video (T2V) diffusion models can reproduce copyrighted, violent, or explicit content, which motivates concept erasure: removing designated concepts from a pretrained model while preserving its behavior on everything else. Existing T2V erasure methods leave two problems open. Their frame-agnostic suppression can leave isolated frames in which an erased concept resurfaces, a frame-reactivation gap that clip-level averages obscure; and they are usually evaluated with one target concept or category at a time. We propose Frame-Aware Diffusion Erasure (FADE), a multi-concept video unlearning framework. FADE first applies a joint closed-form key/value edit that suppresses all target concepts, then trains per-concept frame-aware low-rank adapters whose strength is gated by the frame index and the denoising timestep to remove residual per-frame leakage. Each adapter is trained with the other targets' prompts as hard negatives, which keeps the concept-specific components of different adapters well separated, and a similarity-based soft router combines the adapters according to the prompt. With 16 concepts (objects, artistic styles, and nudity) erased from a single Wan2.1-T2V-1.3B backbone, FADE reduces the residual accuracy on the object benchmark to 4.9%, against 15.5% for the strongest of eight baselines, while keeping the VBench average within 0.9% of the unedited model. The ranking is unchanged under a VLM judge and a blinded human study, and the advantage over the strongest baseline carries over to prompts that combine several erased concepts, to 30 simultaneously erased celebrity identities, and to Wan2.1-T2V-14B, CogVideoX-2B, and HunyuanVideo-1.5.

Despite its remarkable empirical success and predictive power, quantum theory is riddled with mysteries. One such conceptual puzzle is the measurement problem: why do quantum systems in superposition collapse to a single-valued outcome upon being measured? The scenario of Wigner's friend illustrates this tension, with recent extensions deriving strong no-go results for the nature of reality. Another fundamental puzzle arises at the interface of quantum theory and general relativity—the black hole information paradox. This thesis further explores these two foundational paradoxes. Part I of this thesis focuses on extensions of the Wigner's friend scenario. We introduce several novel extended Wigner's friend arguments, and establish connections with notions of nonclassicality, i.e. the study of quantum phenomena that evade classical explanation. Key results are a refined version of the Frauchiger–Renner paradox, new extended Wigner's friend scenarios based on contextuality, and an argument against the absoluteness of free choices based on the Pusey–Barrett–Rudolph theorem. The latter result complements the Local Friendliness no-go theorem, which challenged the absoluteness of experimentally obtained measurement outcomes. In Part II of this thesis, we turn to black hole puzzles and the interplay of quantum theory and gravity. We present a paradox that unifies extended Wigner's friend arguments with black hole puzzles, strengthening the cloning and firewall paradoxes. After discussing subtleties in these paradoxes, we next present an analysis combining elements of quantum theory with gravity, analyzing the detector response near a superposed black hole using elements of quantum reference frames.

Autoregressive transformers remain comparatively weak for protein sequence and structure generation. We study the role of target representation: amino acid tokens encode residue identities without explicit contextual semantics, while backbone coordinates require a discrete representation in our framework. We introduce two learned latent protein languages. Protein Latent Language (PLL) maps sequences to a 4,096-state contextual alphabet built on a frozen ESM-2 encoder, with one token per residue. Structure Latent Language (SLL) adapts GCP-VQVAE Lite with auxiliary sequence and confidence supervision while retaining decoding to backbone coordinates. We separately pretrain autoregressive transformer models on PLL and SLL tokens using next-token prediction, yielding PLLM and SLLM. Under matched downstream sequence training, PLLM has a fitted compute-scaling exponent of 0.038 versus 0.020 for the amino acid autoregressive model. In unconditional sequence generation, PLLM reduces the fraction of samples below a heuristic 1.5-bit residue-composition entropy threshold by 54% relative to the amino acid model across sampling temperatures. For sequence-to-structure prediction, replacing the original GCP-VQVAE Lite tokenizer with SLL reduces best validation perplexity by 34% under matched training. For long proteins, latent-token sampling is approximately 1,000 times faster than MSA-based AlphaFold2 in our measurements. In backbone generation, SLLM compares favorably with other generative models on diversity and novelty. We also observe early signs that using SLLM's internal token confidence for inference-time sampling can improve sequence-to-structure prediction quality beyond a single decoded sample. These results position learned latent protein languages as a promising substrate for autoregressive transformer scaling and inference-time sampling in protein generation.

We examine the dc driven transport of particles with Yukawa interactions through an assembly of chiral active particles undergoing circular motion. The driven particles exhibit a jammed phase, a nonlinear disordered or plastic regime where there is a finite Hall effect produced by interactions with the active chiral particles, and a high drive linear regime where the driven and nondriven particles phase separate and the Hall effect nearly disappears. The chiral particles experience strong drag and Hall effects from the driven particles, and these effects vary monotonically with changing thermal fluctuations or chiral motion parameters. The different dynamical phases are correlated with features in the longitudinal and transverse transport curves, and we map out the phases as a function of active orbit size, thermal fluctuations, and particle density.

Let $F$ be a number field and $f$ a normalized cuspidal Hecke eigenform on $\mathrm{GL}(2)$ over $F$, with $k/2$ as the central critical point of its $L$-function $L(f,s)$. Let $\mathfrak{p}$ be a totally split prime ideal of $F$ lying above an odd prime $p$ and coprime to the level ideal of $f$. In this article, we show that $L(f\otimes\phi, k/2)$ does not vanish for sufficiently ramified Hecke characters of $F$ of $p$-power order and $\mathfrak{p}$-power conductor. Our result improves previous works of Jaesung Kwon and Hae-Sang Sun, in which the additional hypothesis that $p$ does not divide the class number of $F$ is required.