Papers

Vision-language models (VLMs) achieve strong visual reasoning performance, yet subtle changes from routine image capture and processing can alter their reasoning trajectories even when images appear nearly identical. In long-horizon generation, the resulting activation shifts may accumulate across decoding steps, progressively altering reasoning tokens and ultimately changing the final answer, a phenomenon referred to as answer flips. To address this instability, we propose FlipDir (Flip-Direction Steering), a training-free inference-time method that estimates a low-rank flip-inducing activation subspace from contrastive pairs of original and answer-flipping inputs and selectively steers hidden states during decoding. A margin-based gate limits subspace attenuation to uncertain decoding steps, recovering original predictions while preserving stable ones. To evaluate robustness beyond accuracy or consistency on fixed test sets, we introduce VisFlip, a benchmark framework that constructs evaluation groups for a target model and visual variation setting to separately assess recovery of original predictions and preservation of stable ones. VisFlip spans nine dataset-variation combinations across scientific reasoning, robot-scene understanding, and medical VQA, covering subtle visual variations common in each domain. Experiments across 18 settings demonstrate that FlipDir consistently outperforms existing methods on the combined recovery and preservation metric. We will make our code publicly available.

Reproducing a machine learning paper involves most research steps, from installing software and debugging to running experiments, work that AI agents increasingly do. We introduce RECLAIM, a benchmark of 100 NeurIPS 2025 papers that can be rebuilt yearly from new conferences. For each paper we fix in advance the result to reproduce, what counts as a successful reproduction, and a GPU-hour budget. An agent must reproduce that result using the paper and whatever its authors released. What the authors released decides the difficulty tier. Run-tier releases include code, data, and weights; Retrain-tier releases lack weights, so the agent trains the model; Reimplement-tier releases lack code, so the agent writes it. A separate language model grades runs from logs and outputs rather than agents' reports. We run four agents once per paper; the best agent in each tier reproduces only 41% of Run-tier papers, 27% at Retrain, and 15% at Reimplement, where every agent does worst. Failed attempts use on average 29% of their budget, so most stop with budget left. The most common agent error is writing the method without checking any part against the paper's numbers, in 63 of 400 runs.

Self-similar dynamics are often described in terms of a single asymptotic scaling regime. Here we experimentally investigate the post-breakup recovery of a hydrodynamic interface over substantially wider temporal and spatial ranges than previously accessible. Beyond the previously identified scaling behavior, we find four successive self-similar regimes characterized by the $R_{\beta}$-scaling with $\beta=1/6$, 1/2, 1, and 2, connected by three distinct crossovers. All four regimes exhibit robust collapse near the interface tip, while geometrical dependence becomes detectable farther from the singular region. This systematic variation across space and scaling regimes is consistent with scale separation and enhanced universality closer to the breakup singularity. The characteristic scales associated with the different $R_{\beta}$-scalings become comparable at the common geometric scale $z_m \simeq R$. These findings demonstrate that self-similar dynamics can undergo multiple successive crossovers among distinct scaling regimes rather than directly approaching a single asymptotic self-similar state.

Let $(c_t)_{t\geq 0}$ be a deterministic family of edge conductances on a countable vertex set, monotone in $t$, and let $(X_t)$ be the random walk that takes its $t$-th step using the conductances $c_t$. We prove that if $c_t\uparrow c_\infty$ and $c_\infty$ is recurrent (respectively, $c_0$ is transient), then $(X_t)$ is almost surely recurrent (respectively, transient), i.e., visits every vertex infinitely (respectively, finitely) often. We also establish the analogous results in continuous time. This proves conjectures of Amir, Benjamini, Gurel-Gurevich, and Kozma, and the special case of $\{ 0, 1 \}$-valued conductances corresponds to simple random walk on a growing graph, and in this special case our results prove a conjecture of Dembo, Huang, and Sidoravicius. In addition, we provide counterexamples to the corresponding conjectures when $(c_t)$ is monotone non-increasing: if $c_t\downarrow c_\infty$ and $c_\infty$ is transient, $(X_t)$ need not be transient, and similarly if $c_0$ is recurrent, $(X_t)$ need not be recurrent, even if $c_\infty\geq\alpha c_0$ for some $\alpha>0$.

The Hildas are objects trapped in 3:2 mean-motion resonance (MMR) with Jupiter, and are a fascinating window into the Solar system's formation and evolution. We present the results of detailed dynamical integrations of 2,699 numbered asteroids in the Hilda region, following 243 clones of each Hilda for 1 Gyr under the influence of the giant planets and the Sun; 54.7% of our sample exhibit extreme dynamical stability, with all clones of 1,475 Hildas remaining trapped in the 3:2 MMR for the full 1 Gyr of our integrations. A further 408 Hildas (15.1% of the sample) see more than 50% of their clones surviving within the MMR at the end of the simulations. Of the remaining 30.2% of the population, 327 objects (12.1%) lose 50% of their clones at some point between the 100 Myr and 1 Gyr point, leading to dynamical half-lives measured in hundreds of millions of years – a result compatible with those objects being members of a once larger population of Hildas trapped since the Solar system's youth. The final 489 objects (18.12%) prove highly unstable – and may well be interlopers, captured to the Hilda population in the relatively recent past. Overall, our results suggest that the Hilda population was larger in the past, while its remarkably high stability over Gyr timescales is consistent with a primordial origin.

We study how discrete parameters which enumerate non-crossing permutations become geometric quantities in JT gravity. Analyzing non-crossing permutations on the disk together with two classes of annular non-crossing permutations, we find that under suitable continuum scaling limits the number of marked boundary points becomes the thermal boundary length, while the number of through-connections becomes a geodesic length. In this limit, the enumerations reproduce the universal low-temperature behavior of the Schwarzian theory on the disk and the orientable and orientation-reversing double-trumpet geometries. We then relate these constructions to higher-boundary non-crossing diagrams, whose continuum enumeration reproduces the JT result obtained by attaching trumpets to the top-degree part of genus-zero Weil-Petersson volumes, suggesting that the same trumpet–enumeration parameter mapping extends beyond the planar case. Together, these results establish a direct connection between non-crossing permutation enumerations and Weil-Petersson volumes with trumpets attached, a construction that plays a central role in the gravitational path integral in JT gravity, and suggest that non-crossing diagrams provide a combinatorial route to computing multi-boundary partition functions.

On-policy distillation (OPD) corrects a student on the responses it writes, but its signal is the teacher's next-token distribution: it tells the student what the teacher says but misses how it thinks. Latent supervision promises the missing part by aligning the student's latent states to the teacher's. Recent methods such as OPRD bring this signal into on-policy distillation. However, we observe two failures of this recipe when distilling Qwen3-4B and Qwen3-8B into Qwen3-1.7B-Base. Early gain, late collapse: latent supervision alone lifts MATH-500 accuracy from 25 to 46 in 10 steps, but subsequent training degrades performance down to 11 with no recovery. Better alignment, worse behavior: although the alignment metric steadily improves throughout this collapse, the most aligned model turns out to be the worst performing. Further analysis suggests a mismatch in how the latent signal is applied: layers paired by depth play different roles in the two models, so continued alignment may pull the student toward teacher states it cannot understand. To address this, we propose LastOPD, which applies the latent signal only at the last-layer state, the common interface both LM heads read, and only during a 10-step crossfade into token-level OPD. This keeps the useful part of the latent signal and hands the student to token-level supervision before the collapse sets in. Extensive experiments show that LastOPD improves MATH-500 over token-only OPD by 5.55 and 4.02 points with the 4B and 8B teachers, leads on most held-out datasets, and reaches the final score of token-only OPD in about half the steps. Code is available at https://github.com/Muyiiiii/LastOPD.

Sagittarius A* (Sgr A*) exhibits intermittent flaring behavior, characterized by strong enhancements in high-energy emission (infrared and X-ray). These events have been interpreted as related to the coherent orbital motion of localized regions of energized plasma - hotspots. While this framework has been quite fruitful in constraining properties of Sgr A*, it is subject to important challenges and limitations. In this brief review we discuss the recent observational and theoretical developments related to this line of research, commenting on the concerns regarding the hotspot model validity and the future perspectives.

Blockchain and artificial intelligence (AI) are converging into a single infrastructural layer for securing data sharing, model integrity, and autonomous decision-making across distributed systems. This paper presents a meta-synthesis that draws together four constituent studies covering adversarial machine learning, AI-powered anomaly detection in cloud environments, automated vulnerability patching by multi-agent large language model (LLM) pipelines, and the broader landscape of securing AI systems across their lifecycle and situates their findings within the emerging literature on blockchain-enabled AI and autonomous AI agents. Each constituent study addresses a distinct point of failure in modern AI-driven security operations: the integrity of training data and model behavior, the reliability of real-time monitoring, and the trustworthiness of automated code remediation. We argue that blockchain's properties of immutability, decentralized consensus, and verifiable provenance directly address a gap common to all three: the difficulty of establishing trust in data, models, and autonomous agents that operate without a central authority. Building on real-world research on blockchain-secured data sharing, federated learning, and multi-agent coordination, we propose a layered reference architecture that couples adversarially hardened models, blockchain-anchored data provenance, AI-driven anomaly detection, and smart-contract-governed multi-agent remediation. We conclude by identifying open problems in scalability, privacy-transparency trade-offs, and the governance of autonomous agents that must be resolved before such integrated systems can be trusted in production-critical environments.

We show that for every $n\in \mathbb{N}$, the Lipschitz-free space $\mathcal{F}(\mathbb{R}^n)$ has the Dunford-Pettis property. As a consequence, for every $n\in \mathbb{N}$ and every nonempty $M\subset \mathbb{R}^n$, the space $\mathcal{F}(M)$ has the Dunford-Pettis property. This implies that $\mathcal{F}(M)$ is not isomorphic to $\mathcal{F}(X)$ for any separable Banach space $X$ that fails the Dunford-Pettis property. In particular, this applies to $X=\ell_2$, and more generally to every infinite-dimensional separable reflexive space. We also deduce that if $1<p<\infty$, then $\mathcal{F}(\ell_p)$ is not isomorphic to $\left(\bigoplus\limits_{n=1}^\infty \mathcal{F}(\ell_p^n) \right)_{\ell_1}$.

Matrix time series is a series of matrix data observed over time. Analytical tools for such time series is needed in many applications in finance, economics, engineering and many other fields. To avoid the use of vectorization of the matrices which loses the column and row information, and the vector autoregression framework in traditional time series analysis, \cite{chen2021autoregressive} proposed the Matrix Autoregressive (MAR) Model. The model maintains and utilizes the matrix structure, leading to a substantial dimensional reduction and admitting explicit interpretations, comparing with the vector autoregressive model on the vectorized data. However, the MAR model still encounters difficulties in dealing with large dimensional matrix time series as the coefficient matrices in MAR models are also large. In this paper we propose to achieve further dimension reduction through reduced-rank constraints of the coefficient matrices in the MAR model. Estimation and rank determination procedures are studied. Theoretical investigation and empirical examples show that the reduced-rank constraint can achieve higher statistical efficiency than the MAR model.

We propose a ”stepping stone” realization of the varying Peccei Quinn (PQ) scale solution to the QCD axion isocurvature problem. In conventional implementations, suppressing isocurvature during high scale inflation requires a large inflationary PQ scale, while the subsequent evolution toward the much smaller late time vacuum can induce parametric resonance and nonthermal restoration of the PQ symmetry. We ameliorate this tension by introducing an intermediate PQ-breaking vacuum that is reached before the end of inflation, so that the later evolution to the present day PQ scale spans only a moderate hierarchy. The vacuum structure arises radiatively: a Yukawa coupling between the PQ scalar and PQ-charged fermions drives the quartic coupling negative at high scales while keeping it positive at lower scales. A positive dimension six operator then stabilizes a large field minimum, while the positive low energy quartic together with the quadratic terms generates the intermediate vacuum. We study two mechanisms in which the rolling inflaton removes the large field minimum, either by scanning a hidden non-Abelian gauge coupling or by directly scanning the Yukawa coupling. In both cases the PQ field is released toward the intermediate vacuum during inflation, after CMB modes have exited the horizon. We exhibit benchmark regions with subdominant backreaction on the inflationary sector and suppressed vacuum tunneling, and show that the construction permits substantially less hierarchical quartic and higher-dimensional couplings than conventional realizations that depend on a varying PQ scale. The underlying logic may have analogues for extra-dimensional or string axions, where the effective axion decay constant is controlled by geometric moduli, although realizing the required intermediate vacuum in a controlled modulus potential is nontrivial.

We prove that the XOR of $k$ majorities on disjoint blocks of $\ell$ bits has correlation at most $(4d/\sqrt{\ell})^k$ with every Boolean-valued degree-$d$ polynomial over an arbitrary field. By known techniques, we obtain explicit pseudorandom generators that fool such polynomials on $n$ Boolean inputs with seed length $d^2\cdot\polylog(n/\varepsilon)$. The correlation and the generator extend to small $\mathsf{AC}^0[q]$ circuits, for every fixed prime power $q$. These results resolve several long-standing questions in circuit complexity and pseudorandomness.

Online reinforcement learning fine-tuning of pretrained flow-matching vision-language-action (VLA) policies promises robots that keep learning after deployment, but continued updates often destroy competence on individual tasks while the aggregate still looks healthy. We study this failure mode, which we call task collapse, under a matched small-compute budget on LIBERO-10 with a 450M-parameter SmolVLA policy trained by PPO with stochastic (SDE) sampling. Three exploration-noise policies differ in one live variable: a fixed noise scale, a ReinFlow-style learned noise network, and an uncertainty-gated controller that redistributes exploration across task streams from task-agnostic novelty and competence signals, without task labels or episode boundaries. Under the pooled definition, fixed noise collapses tasks in two of three seeds and learned noise in every seed measured to iteration 200, while the controller collapses none in any of its three seeds. Measured parameter displacement shows the controller's action expert keeps changing, while its mean applied noise is close to the fixed scale in the available logs. The matched comparison supports the controller's effect on task preservation; the separate contributions of its adaptation across states and over time are not disentangled. A lower fixed scale slows the decline but does not stop it. No arm improves on the behavior-cloning baseline in this budget. Two properties of that regime are measured beside this result, not offered as its cause: following the reference recipe, training runs in bfloat16 with no fp32 master copy, under which 96.02% of the action expert's elements stay bit-identical across three consecutive iterations, and an fp32 master copy at the reference learning rate collapses both arms in a single-seed observation. We release tools measuring per-task collapse under four definitions, rescoring noise and instrument tares.

Two-dimensional superconductors test our understanding of quantum phases. Low-temperature "anomalous metal" states are widely observed where conventional theories predict only superconducting or insulating ground states. In model systems based on proximity-coupled Josephson junction arrays, the critical temperature falls far faster with decreasing normal-state conductance than predicted by existing models. Whether these observations indicate a new quantum phase, a need to refine models of disorder and fluctuations, or both remains unresolved. Using scanning magnetic susceptometry, we image the local superfluid phase stiffness $\rho_s$ in gate-tunable Josephson junction arrays consisting of epitaxial Al islands on an InAs quantum well. Across six arrays and more than two orders of magnitude in the zero-temperature phase stiffness $\rho_{s0}$, the diamagnetic critical temperature $T_{c,\varphi}$ is suppressed more strongly than can be explained solely by thermal phase fluctuations, scaling approximately as $T_{c,\varphi}\propto\rho_{s0}^{0.3}$. While $\rho_s$ is remarkably uniform at high carrier densities, at low carrier densities we find that anomalous metal transport emerges together with large-scale inhomogeneity that transport alone cannot directly detect. These results are inconsistent with a classical XY description within standard junction models, instead pointing to quantum fluctuations that suppress superconductivity throughout the superconducting phase and amplify inhomogeneity near the superconductor-insulator transition, producing anomalous metal behavior.

While various multimodal methods combining imaging and tabular data for Alzheimer's disease (AD) diagnosis were proposed, they are often limited in generalization across cohorts. In-context learning (ICL) has demonstrated excellent generalization performances and high flexibility in foundational tabular models such as TabPFN. To extend TabPFN's ICL to multimodal AD analysis, the main obstacle is that TabPFN is meta-trained on synthetic tabular priors that do not naturally match the statistical structure of image-derived features. We propose M$^2$PFN, an end-to-end framework that turns this tabular foundation model into a multimodal AD predictor. M$^2$PFN (i) performs differentiable inference through TabPFN's transformer, back-propagating task gradients into 3D-MRI and tabular encoders; (ii) aligns the two modalities into a shared subspace, via disentanglement and a contrastive objective, matched to the ICL engine's prior; and (iii) folds in a frozen tabular-only prediction through a learnable gated shortcut. Because the ICL engine stays frozen, its in-context mechanism is preserved for test-time generalization, while end-to-end training shapes the encoders into features it can exploit. On ADNI ($n=2240$, three-class CN/MCI/AD), M$^2$PFN attains $65.55\%$ macro-F1 and $82.21\%$ macro-AUC, surpassing a comprehensive set of unimodal and multimodal baselines. By swapping only the head for a TabPFN regressor, the same architecture regresses baseline MMSE on a $1250$-subject sub-cohort to test MAE $1.743$, outperforming every multimodal baseline. On two external cohorts (OASIS-3 and SCAN) with no retraining, M$^2$PFN achieves the best AUC and the lowest MMSE MAE across all baselines, and transfers even when the cognitive instrument changes.

These notes are aimed at providing a relatively concise and self-contained introduction to anomalies in quantum field theory. A first part reviews the necessary notions of quantum field theory, in particular its functional integral formulation which we use throughout. Then we discuss in some detail how and why anomalies arise as non-invariance of the functional integral measure or through the absence of a regulator preserving all symmetries, and how they manifest themselves as current non-conservation in anomalous loop diagrams and anomalous Ward identities, or equivalently as a non-invariance of the effective action. Specifically, we deal with the so-called abelian anomaly under chiral transformations, and the so-called chiral anomaly which is a violation of non-abelian gauge invariance in the presence of chiral fermions. We perform a detailed triangle Feynman diagram computation for both cases. Then we move on to provide a brief overview of some important properties of anomalies (locality, finiteness, one-loop exactness), and how they are characterized in general by the Wess-Zumino consistency condition. We show how this condition can be reformulated in terms of BRST cohomology and how it can be solved, for arbitrary (even) space-time dimensions, by the descent equations. Finally, we briefly discuss the general relation between anomalies in arbitrary even dimensions 2n and index theorems in 2n+2 dimensions, generalizing also to gravitational anomalies. We conclude with the exhibition of the highly non-trivial anomaly cancellation in ten-dimensional IIB supergravity.

Fluctuation–response relations (FRRs) provide a fundamental relation between spontaneous fluctuations and the linear response to external perturbations, yet their validity in non-equilibrium systems remains an open problem. In a general class of noisy, finite-size, mean-field models of coupled phase oscillators, we reveal two types of FRRs in the incoherent phase below the synchronization transition. The first, corresponding to the infinite-size limit (I-FRR), involves the convolution between the external force and the correlation function in the time domain. The second, the finite-size counterpart (F-FRR), is governed by finite-size fluctuations and carries a correction factor: a spectrum function whose roots correspond to eigenvalues, or Landau poles, of the linear operator. The finite-size fluctuations are suppressed in the weak-coupling or strong-noise limits, and F-FRR reduces to I-FRR. Our analytical findings are verified by extensive numerical simulations.

Communities exhibiting cyclic (i.e., “winnerless”) competition occur throughout nature. These systems can exhibit qualitatively different long-term behavior depending on the strength of inter-species competition and a specific property of the number of interacting species: parity. We consider how ecological communities can adapt to and transition between an odd and an even number of cyclically competing species. Previous studies have shown that, for strong inter-species competition, odd parity communities are dynamically unstable, while species in even parity communities form stable alliances of maximal noncompeting sets. We trace a homotopy between two May-Leonard type models: the odd parity N=3 model and the even parity N=4 system. We identify all physical steady states and analyze their stabilities. We show the existence of stable transitional states that are unique to our symmetric model. We then use a piecewise linear approximation technique to characterize the stability of heteroclinic cycles. We use numerical simulations to map distinct regimes in parameter space. Our computations confirm our analytical results and also reveal a window in parameter space where limit cycles occur. We illustrate that parity transitions can be complex and characterized by diverse parameter-dependent pathways.

Reconstruction-based unsupervised learning can fail in two opposing ways: a model may reconstruct anomalies too accurately or discard valid nominal variation. Using the Pursuit of Subspaces hypothesis, we characterize these failures through the meet, union, and join geometries induced by the nominal components. Excess learned range produces join blindness, while insufficient capacity produces meet preference and loss of nominal fidelity. We show that the compact nominal union is optimal among nominal faithful ranges and generally requires a nonlinear reconstruction map. Based on this geometry, we introduce Dynamic Push and Pull, which learns from controlled perturbations without anomaly labels, and nested manifold carving, which applies the same principle recursively in latent space. Experiments confirm the predicted changes in latent geometry across every tested Push and Pull configuration. The proposed methods improve reconstruction-based anomaly detection across standard benchmarks and unseen image degradations, while also improving pretrained ECG representations for downstream classification. These results connect reconstruction failures to identifiable geometric conditions and provide practical mechanisms for learning compact representations.

We introduce GRACE (the General Regime-Aware Changepoint Estimator), a general, globally exact multiple-changepoint detection and estimation framework in which arbitrary numbers of model parameters may change at or persist across estimated changepoint locations, and all permissible changepoint types and patterns of parameter sharing compete within a single $\ell_0$-penalized optimization. The analyst specifies which types of changepoints are permitted and which parameters each type must preserve, without specifying which changes actually occur, where they occur, or in what order. GRACE jointly estimates the number and locations of changepoints, the type of change at each location, the model fitted between changepoints, and all continuous parameters. As a direct consequence, GRACE can estimate models in which the slope persists across a mean shift. The generality of the framework is achieved through an exact dynamic-programming recursion that retains the accumulated fitting cost conditional on whichever parameters a subsequent change may preserve, tracking multiple parameters jointly when necessary. We establish the global exactness of the recursion and develop functional, penalty-based, and objective-bound pruning rules that eliminate candidates without sacrificing optimality. Ordinary optimal partitioning, FPOP, and CPOP are recovered as special cases, while piecewise-polynomial and seasonal models illustrate the broader range of permissible segment structures and transitions. The resulting framework supports heterogeneous changepoint types, parameter sharing across segments, and substantial parallel computation within a unified approach to exact changepoint estimation.

The rapid integration of distributed energy resources is fundamentally altering power flow patterns in primary distribution networks and intensifying operational uncertainty. These problems are further compounded by lack of real-time situational awareness and frequent topology changes. To address these problems, this paper proposes an integrated deep learning framework for simultaneous topology identification (TI) and distribution system state estimation (DSSE) in real-time unobservable primary distribution networks instrumented by a minimal set of synchronized measurement devices (SMDs). A correlation-driven SMD placement algorithm is introduced first that jointly satisfies TI accuracy and DSSE performance requirements by exploiting temporal and spatial correlations in nodal voltage measurements. A dual deep neural network (DNN)-based DSSE model is developed next to estimate three-phase voltage magnitudes and angles across diverse operating conditions. To extend the framework beyond the base topology, fine-tuning-based transfer learning is employed to adapt the DSSE model to reconfigured topologies using limited retraining data. The framework is validated under both Gaussian and non-Gaussian measurement noise and benchmarked against a conventional estimation approach and a single DNN model.

We present molecular dynamics simulation results for an ultracold $^{40}$Ca plasma in a constant, homogeneous magnetic field. The magnetic field induces a significant spatial separation of charges. Furthermore, a significant fraction of the electrons escapes from the region bounded by the ions, in contrast to the case of plasma expansion into a vacuum. This leads to the formation of a quasineutral plasma core containing the remaining electrons and surrounded by an outer, thick ion shell, where the ion density drops sharply. Anisotropy in the ion kinetic energy is also observed, depending on the direction of ion motion relative to the magnetic field lines. The simulation results are in agreement with experimental data on ion dynamics.

Parity violation in the early Universe may lead to a chiral gravitational wave background. We show that, for finite-time parity-violating sources, the low-frequency tail of the generated chiral gravitational wave background is universally unpolarized, and that the chirality fraction decreases linearly with frequency. Our result generally applies to any parity-violating gravitational-wave source that appears quadratically in the wave equation. We consider both Gaussian sources and explicit trispectrum templates. We attribute the lack of chirality of the low-frequency tail to the fact that, on large scales, gravitational wave generation is almost equally inefficient for both helicities.

Two phase-optimized multisine peak factor minimization algorithms are presented and evaluated. The first algorithm minimizes peak factor by iteratively clipping the peaks of generated multisine signals. The second algorithm optimizes peak factor indirectly through minimization of an approximation of the infinity norm of the multisine. Algorithm performance was evaluated as a function of different signal properties, including the number of harmonics, harmonic spacing, and number of snow harmonics (extra harmonics included for further reduction of the peak factor). The two algorithms are compared against results obtained by minimizing peak factor directly using a simplex algorithm, which has been a common approach when designing phase-optimized multisines for system identification flight tests. Sample results show that the clipping and infinity norm algorithms produced multisine signals with comparable peak factors that were lower than that of the simplex algorithm. However, the clipping algorithm runs an order of magnitude faster than the other two algorithms, which also makes it practical to repeat the algorithm multiple times to achieve even lower peak factors.

Machine translation (MT) for Indian languages remains constrained by the limited availability of high-quality, Indic-centric parallel corpora and evaluation benchmarks. Existing multilingual resources are largely constructed from English-pivot content and often fail to capture the linguistic diversity, cultural complexity, and domain-specific characteristics of Indian languages. We present COILD, an Indic-centric parallel corpus comprising over 1.16 million human-translated and human-verified sentence pairs, covering 20 Indian language pairs across the Indo-Aryan, Dravidian, Tibeto-Burman, and Austro-Asiatic language families. The corpus is built entirely from original Indian language sources collected from licensed repositories spanning eight domains with direct real-world applicability. Furthermore, we introduce a domain-centric benchmark comprising 2,000 expert-verified sentences to enable consistent multilingual and cross-lingual evaluation across Indian language pairs. To validate the effectiveness of COILD, we fine-tune two representative multilingual neural machine translation models, IndicTrans2-Distilled and NLLB-200. Experimental results demonstrate consistent improvements across language pairs, domains, automatic evaluation metrics, and human evaluation, highlighting the effectiveness of high-quality Indic-centric supervision. COILD provides a valuable training and evaluation resource for advancing multilingual machine translation and future multilingual language models for Indian languages.

Quantum computing offers a new, orthogonal direction for investigating fundamental physics, extending beyond classical numerical methods and conventional observables. Realizing this potential requires directly confronting the noise limiting currently available quantum computers. Progress rests on advancing algorithms, interpreting their results, and managing their errors together. This thesis presents several advancements in the use of quantum simulation and quantum information to probe fundamental physics. The first is in the use of quantum computers to simulate collisions in quantum field theories. Central to these simulations are new wavepacket preparation, time evolution, and error mitigation techniques, which allow for simulations with some of the largest effective circuit volumes to date. These methods enable the first quantum simulation providing numerical evidence for inelastic particle production, a key process in fundamental physics. The second advancement centers on the role quantum-information-theoretic quantities play in physical processes. Beyond mere correlations with the physics of the process, entanglement and magic are shown to probe the interactions present in scattering and hadronization dynamics. A precision study requires a complete quantification of algorithmic and hardware uncertainties, an outstanding goal as quantum simulations mature. The third advancement in this thesis addresses error management. A framework minimizing the effect of algorithmic errors in analog quantum simulations is presented. In a step toward fault tolerance, error detection in encoded quantum simulations is shown to improve estimation of local observables relative to unencoded runs. Together, the developments in this thesis mark practical progress toward fault-tolerant quantum simulations of fundamental physics capable of scientific discovery.

In this article, we extend the classical relationship between ADE singularities and their maximal Cohen-Macaulay modules to quotient singularities of types A and D. We identify projected hypersurfaces which allow us to construct explicit matrix factorizations, and in return, families of maximal Cohen-Macaulay modules. These hypersurfaces also yield the dual resolution graphs of the corresponding quotient singularities via Oka's method. Finally, we show that all special Cohen-Macaulay modules over the original quotient singularity can be recovered from those over the projected hypersurfaces.

This paper studies the bullwhip effect, the amplification of demand fluctuations into larger order fluctuations upstream, in supply chain networks where each firm orders from several suppliers over routes with different lead times. We show that on a directed acyclic network every response from demand to orders is a sum over paths of products of nodal responses, so that the stability and stability margins of the network are determined by those of its individual nodes, and that a node which splits its orders across routes of different lengths gains margin it can spend on a higher gain and a faster response. We then minimize the worst-case amplification of the network by choosing how each firm splits its orders among its suppliers, which route lead times to shorten, and each firm's ordering gain, with gradients from one adjoint pass per demand node and frequency. On a 14-city network the optimized design amplifies 20~dB less than cost-minimal routing and 17~dB less than a design that shortens the longest routes with the same budget, and is better connected than either. Amplification is therefore a property of routing and delay, not only of the ordering policy, and designing against it also makes the network more robust to a lost route.

Variadic generics are a powerful tool for type-safe meta-programming. Yet in most widely used languages, they remain an "expert-only" feature due to their reliance on complex patterns such as recursive decomposition or expansion expressions that do not compose naturally with ordinary control flow. In C++, for example, accessing elements of parameter packs has traditionally relied on unintuitive recursive patterns that "peel off" elements. This paper presents Pack Iteration, a feature introduced in Swift 6.0 that allows developers to iterate over parameter packs using a familiar, imperative for-in loop. By treating pack expansion as a first-class source for iteration, Swift bridges the gap between high-level expressiveness and advanced generic programming. We detail the design and implementation of this feature within the Swift compiler, focusing on the challenges of bridging static type-checking in the constraint system with dynamic execution in the Swift Intermediate Language. Unlike traditional models that expand packs at compile time, Swift's implementation supports on-demand evaluation, enabling efficient dynamic iteration and short-circuiting control flow. Our empirical evaluation confirms that pack iteration provides performance comparable to - and sometimes significantly better than - the complex workarounds previously required.