Correlated equilibria arise naturally when agents communicate or rely on intermediaries such as recommendation systems. We study when a given Nash equilibrium can be improved within the set of correlated equilibria for general objectives. Our key insight is a detail-free criterion: any Nash equilibrium with three or more randomizing agents is generically improvable. We refine this insight to specific classes of games and objectives, including Pareto and utilitarian welfare, and provide constructive methods to obtain improvements. Our findings underscore the ubiquity of improvable Nash equilibria and the crucial role of correlation in enhancing strategic outcomes.

The death of massive stars produces central accreting compact objects and sometimes relativistic jets. Not all jets escape the stellar envelope: unsuccessful, or choked, jets dissipate their energy into a pressurized cocoon, which expands and may break out as a mildly relativistic outflow. We investigate the plasma physics of collapsing massive stars hosting choked jets through relativistic, non-resistive magnetohydrodynamical simulations. We delineate the parameter space for jet choking and quantify the acceleration rate and efficiency of charged particles at strong shocks, which are potential sources of high-energy neutrinos and electromagnetic transients. Our study focuses on blue and red supergiant progenitors, both promising candidates for jet choking.

If sufficient training data are available, neural networks are attractive for representing missing physics in simulations, such as sub-grid scales in the coarse-mesh particle-turbulence system we consider. Physical constraints are known to both increase performance and reduce the need for data; we use the complete physics represented in the discretized governing equations as a constraint. Two-way coupled particles in two-dimensional turbulence provide a sufficiently complex system to assess effectiveness for various training data, all constructed from well-resolved simulations, in cases intentionally degraded to assess robustness. Surprisingly, using the full space-time data actually hinders model effectiveness. Instead, training that targets only spectra -- hence, neglecting phase information -- provides better closures, which is related to the well-known success of non-dissipative discretizations for simulating turbulence. It is found that some of the missing physics that lead to preferential particle concentration errors are fundamentally stochastic on the coarse mesh and therefore uncorrectable by the basic approach; a learning formulation is introduced for a Langevin-type closure to correct this. Most importantly, training just for particle kinetic energy -- without any direct input from the flow field -- also yields effective sub-grid-scale stress models. This holds true even if noise is added to the particle data, if only a sub-sample of particles are used, or if only one component of the particle velocity is used. In sum, these results show a path for inferring sub-grid-scale physics based just on particle data from experiments.

Species-resolved azimuthal anisotropy scaling functions are constructed from identified particle $v_2$ and $v_3$ obtained from event-by-event iEBE-VISHNU simulations for Pb+Pb collisions at $\sqrt{s_{NN}}=2.76$ and $5.02$~TeV. The scaling functions exhibit a robust collapse across transverse momentum, centrality, particle species, and beam energy, indicating a common and tightly constrained scaling structure. High scaling fidelity yields quantitative agreement with the data-defined reference through an energy-dependent attenuation baseline $β_0$ in central to mid-central collisions and a centrality-dependent modification of the effective attenuation in more peripheral collisions, with only a weak dependence on $\sqrt{s_{NN}}$. The multiplicity dependence of the extracted scaling parameters reflects the interplay of EOS-driven collective expansion, finite system lifetime, and hadronic re-scattering. These results demonstrate that the scaling framework provides a quantitative, constraint-driven probe of the hydrodynamic response, enabling the disentanglement and constraint of the coupled contributions to azimuthal anisotropy.

Data discovery - retrieving relevant tables from a data lake in response to user queries - is a fundamental building block for downstream analytics. In practice, data discovery must support different query modalities, including natural language (NL) statements and tables, and accommodate diverse user intents, ranging from open-ended enrichment to task-driven inference for applications such as table question answering and fact verification. However, most existing methods are designed for a single query modality or a specific user intent, limiting their generalizability. We propose UniDisc, a unified data discovery framework that supports both NL statements and tables as queries and generalizes across diverse user intents without intent-specific representations or relevance modeling. UniDisc learns a common cross-modal representation model that produces unified representations for queries of different modalities and candidate tables, enabling uniform relevance assessment across discovery scenarios. Since learning such a model typically requires large labeled collections of query-table pairs, which are expensive to obtain, UniDisc instead exploits contextual signals naturally available in data lakes. Specifically, it models NL statements and tables as nodes in a heterogeneous graph with multiple edge types, and applies dual-view neighbor aggregation and joint optimization to learn robust, context-aware representations under limited supervision. These representations support flexible relevance estimation during retrieval. Experiments on seven datasets show that UniDisc consistently outperforms strong baselines on both NL- and table-based discovery.

We study prethermal time quasicrystalline (TQC) order in a quasiperiodically driven chain of non-interacting spin-1/2 particles. The drive consists of two parts, switched on and off periodically with frequency $ω_d$: (i) disordered Ising interactions, with exchange couplings chosen from a symmetric interval $[-J/2, J/2]$, allowing random antiferromagnetic or ferromagnetic nearest-neighbor couplings, together with a random transverse field; and (ii) a rotating transverse magnetic field with frequency $Ω$. The ratio $ω_d/Ω$ is chosen to be irrational, producing multiple incommensurate frequencies and yielding quasiperiodic dynamics beyond Floquet theory. Using exact diagonalization, we analyze the time autocorrelation function, dynamical structure factor, and entanglement entropy (EE). In the high-frequency regime, robust spectral peaks at incommensurate frequencies (not integer multiples of the fundamental drives) signal quasiperiodic time-translation symmetry breaking (QTTSB). The EE exhibits sublinear power-law growth followed by a prethermal plateau, indicating suppressed resonant heating due to an energy scale mismatch. The nonequilibrium lifetime increases rapidly with driving frequency. Unlike symmetric disorder sampling, an asymmetric distribution of the Ising exchange couplings induces collective spin rigidity, enhancing the system's resistance to heating. The TQC phase remains stable against next-nearest-neighbor (NNN) exchange perturbations and rotational imperfections, with robustness comparable to discrete time crystals (TCs) under periodic driving. Our results establish this quasiperiodically driven system as a platform for long-lived nonequilibrium temporal order, revealing the interplay of disorder, collective rigidity, and quasiperiodic driving.

Even simplified models of quantum many-body systems can be difficult to analyse. However, taking inspiration from the foundations of physics, one may wonder whether there are practical advantages to constructing alternative beyond-quantum descriptions of many-body systems. We explore this question in the context of quantum interactions that are diagonal in the computational basis. We construct a hypothetical model of a continuous time dynamical many-body system that is based upon lattices of interacting particles called "cylindrical bits", a concept first introduced in [6]. In the language of [5] our toy model is {\it non-free}, as we need spatial constraints on how the particles interact to ensure valid probabilities. We investigate these constraints and explore the resulting `entangled' states that can exist. Certain pure {\it quantum} entangled systems can be faithfully mimicked by our cylindrical worlds. This allows us to simulate efficiently classically, in the sense of sampling measurement outcomes, a variety of previously unknown quantum systems. Examples include some states created by pure Ising interactions algebraically decaying faster than $\sim 1/r^{3D/2}$, with spatial dimension $D$, under measurements in the $Z$ eigenbasis or eigenbases of $aX+bY$ for $a,b \in \mathbb{R}$. We also explore whether another choice of non-quantum `particle' could expand the applicability of the classical simulation by defining and partially optimising a figure-of-merit that attempts to capture how useful various possibilities may be.

We study the set of image tuples arising from fixed cameras observing varying planar 3-dimensional point configurations. We derive a formula for the number of complex critical points of the triangulation problem, which seeks to reconstruct such configurations from noisy image data. Valid for an arbitrary number of views, this formula quantifies the intrinsic algebraic complexity of planar triangulation. We validate our theoretical findings through numerical experiments on both synthetic and real data, demonstrating that incorporating the planar incidence constraints leads to faster point reconstruction and improved accuracy compared to unconstrained triangulation.

Query Performance Prediction (QPP) estimates the retrieval quality of ranking models without the use of any human-assessed relevance judgements, and finds applications in query-specific selective decision making to improve overall retrieval effectiveness. Although unsupervised QPP approaches are effective for lexical retrieval models, they usually perform weaker for neural rankers. Recent work shows that leveraging query variants (QVs), i.e., queries with potentially similar information needs to a given query, can enhance unsupervised QPP accuracy. However, existing QV-based prediction methods rely on query variants generated by term expansion of the input query, which is likely to yield incoherent, hallucinatory and off-topic QVs. In this paper, we propose to make use of queries retrieved from a log of past queries as QVs to be subsequently used for QPP. In addition to directly applying retrieved QVs in QPP, we further propose to leverage large language models (LLMs) to generate QVs conditioned on the retrieved QVs, thus mitigating the limitation of relying only on existing queries in a log. Experiments on TREC DL'19 and DL'20 show that QPP enhanced with RAQG outperform the best-performing existing QV-based prediction approach by as much as 30% on neural ranking models such as MonoT5.

Engineering design problems are often modeled as multi-objective optimization tasks in which a scalarized utility function selects an optimal design from the Pareto set. In practice, preferences are imperfectly known, so uncertainty in the preference model leads to uncertainty in the resulting optimal design. This paper proposes a probabilistic framework that treats preference parameters as random variables and examines how preference uncertainty propagates to decision uncertainty. A random preference vector induces a probability distribution over optimal designs, allowing us to identify which regions of the Pareto front are most likely to be selected and to assess recommendation stability under preference variability. To explain the sources of this variability, we apply variance-based global sensitivity analysis to the induced optimal solutions, using Sobol' indices and Shapley values to quantify the contributions of individual design variables and their dependencies. We further summarize the overall dispersion of the optimal-design distribution using the Fréchet variance, which provides a scalar measure of decision stability under a given preference model. Two vehicle design case studies demonstrate how problem structure can lead to discrete versus continuous decision distributions and show how the proposed quantities support preference-aware design analysis.

We study the effective estimation of the diffusivity and Hurst parameter for the homogenized limit of a class of slow/fast systems. Depending on the system parameters, this limit solves a stochastic differential equation driven by either a Wiener process or a Hermite process. In the class of models we consider, the fast variable is a fractional Ornstein--Uhlenbeck process. We show that estimators constructed from the homogenized limit remain consistent when applied to appropriately subsampled data generated by the original slow/fast system. A key tool in our analysis is the consistency of renormalized quadratic variations for a family of additive functionals of the fast process. Using Wiener chaos expansions, we obtain an \(L^2\)-orthogonal decomposition of these renormalized quadratic variations. This allows us to show that, under appropriate subsampling conditions, the consistency properties of the estimators are preserved even when the data is generated by the slow/fast system rather than the homogenized limit. We also show that, under stricter subsampling conditions, a non-central limit theorem is preserved in the case where the fluctuations of the estimator around the true value are non-Gaussian. As a direct consequence of convergence in \(L^2\), we obtain consistency of an estimator for the limiting self-similarity that does not require knowledge of the limiting diffusivity. Finally, we show that our results apply to a class of one-dimensional fluctuation models.

We introduce root-to-leaf path random walks on double covers of graded signed graphs and analyze their behavior in a general setting. Viewing simplicial complexes within this framework, we show that these walks induce the natural normalization of the coboundary operator and of the Hodge Laplacians while preserving the basic structural features of combinatorial Hodge theory. We then derive Cheeger inequalities for the upper side of the normalized Hodge spectrum, identify the coherent structures governing these bounds, and combine the up- and down-cases into sharper estimates.

Piezoionic hydrogels offer a route to mechanically driven bioelectronic interfaces, but their output is limited by rapid, symmetric ion redistribution that dissipates charge gradients. In biological electrocytes, efficient signal generation arises from the coupling of ion selectivity with spatial confinement that regulates transport. Here, we introduce a confinement-connectivity design strategy for piezoionic hydrogels, implemented through a supramolecular poly(vinyl alcohol)-glycerol-cucurbit[5]uril (PVA-glycerol-CB[5]) mesoporous network with a layered Negative-Neutral-Positive architecture that simultaneously increases pore fraction while reducing characteristic pore size. This architecture constrains ionic redistribution while maintaining a large mobile-ion reservoir, enabling deformation-driven charge separation. Compression generates peak outputs of ~180 mV and ~9 mA and elicits synchronized electromyographic responses in the mouse sciatic nerve without external power. These results establish confinement-connectivity coupling, rather than bulk conductivity, as a materials design framework in which coupling pore connectivity and confinement governs piezoionic transduction.

As large language models (LLMs) are increasingly fine-tuned for hardware tasks like RTL code generation, the scarcity of high-quality datasets often leads to the use of rapidly assembled or generated training data. These datasets frequently lack security verification and are highly susceptible to data poisoning attacks. Such poisoning can cause models to generate syntactically valid but insecure hardware modules that bypass standard functionality checks. To address this, we present SafeTune, a framework designed to harden LLM-based RTL generation against poisoning, specifically focusing on hardware Trojan (HT) insertion. SafeTune integrates two core components: (i) a Graph Neural Network (GNN) that models structural properties to identify anomalous circuitry patterns during fine-tuning, and (ii) a semantic verification module using text embeddings and an XGBoost classifier to assess prompt security. By coupling structural and semantic knowledge, SafeTune effectively filters poisoned inputs without sacrificing legitimate data. Experimental results demonstrate that SafeTune significantly enhances the robustness and reliability of LLM fine-tuning without requiring modifications to the underlying model architecture.

X-ray Thomson scattering (XRTS) is a common diagnostic used in the warm dense matter (WDM) regime to estimate plasma parameters like density, temperature and charge state. Experimental analysis typically relies on a forward model to obtain estimates for these parameters, as the measured spectrum is a convolution of the dynamic structure factor (DSF) and the source-instrument function. The Chihara decomposition, where the spectrum is separated into contributions from bound and free electrons, is commonly used to estimate DSFs in the WDM regime, as it allows for the fast calculation of DSFs and therefore can easily be applied in a large-scale parameter optimization. Due to the limited availability of XRTS codes, in this work we present the ``\textbf{X}-ray \textbf{D}iagnostics, \textbf{A}nalysis, \textbf{V}erification and \textbf{E}xploration`` (\texttt{xDAVE}) code, designed to quickly estimate DSFs using the Chihara decomposition and analyse experimental spectra. The code is validated by re-analysing an experiment with isochorically heated beryllium at the OMEGA Laser Facility. In addition, we demonstrate the applicability of the code to plan experiments and predict scattering spectra through the coupling to a ray-tracing code. Lastly, the importance of accounting for the energy-dependence of spectrometer instrument functions is demonstrated by comparing ray-tracing simulations to the standard convolution for strongly compressed Beryllium shots at the National Ignition Facility similar to previously published results.

Non-equilibrium energy dissipation in multi-shell swift-ion/matter systems remains a fundamental yet incompletely understood problem, with electronic stopping power $\mathcal{S}_\text{e}$ as a relevant observable for electronic friction. Using real-time time-dependent density functional theory, we perform first-principles calculations of $\mathcal{S}_\text{e}$ for beryllium self-irradiation with explicit treatment of all electrons. Our results reveal a Bragg peak exhibiting a distinct structure which lies beyond the reach of standard semi-empirical models. We attribute its appearance to a dual effect of the presence of core electrons, by which their excitation provides an additional dissipation channel while simultaneously suppressing valence electron excitations. An electron capture process by the projectile's core from the host cores is behind such suppression, rather than Pauli blocking. This dual mechanism contrasts with the shake-up effect reported for water, whereby the inclusion of core electrons enhances valence excitation. Our work provides a new perspective on the effect and importance of core electrons in projectile energy dissipation in matter.

Computer science (CS) education needs to evolve to support software and artificial intelligence (AI) systems engineering, and it needs to happen now -- precisely because the core intellectual contributions of CS have never been more important. We argue that traditional curricula, built around programming, data structures, and algorithms as ends in themselves, must be reframed so that these topics become foundational building blocks within a systems- and engineering-centered education. Graduates should be prepared not to compete with AI on routine coding tasks, but to design, orchestrate, verify, and own complex AI-enabled systems operating under real-world constraints. More importantly, computer science education should be geared toward preparing students for future disruptions. The broad history of computing is marked by one disruptive technology after another, requiring us to rise to the moment instead of merely acquiescing to it.

We study some interesting hypersurfaces that naturally arise when studying the period map on the moduli space of hypersurfaces, in the context of Sung Gi Park's recent work on studying the GIT moduli space of hypersurfaces via the minimal exponent. We compute the Hodge structure on the singular cohomology and the intersection cohomology of these hypersurfaces, and also show the $K$-polystability of certain mildly singular degenerate hypersurfaces among them. In particular, the following hypersurface is $K$-polystable for $l \geq 2$: $$ \{ x_{11}\cdots x_{1d} + \ldots + x_{ld} \cdots x_{ld} = 0\} \subset \PP^{ld-1}.$$

Connectivity of temporal graphs has been widely studied both as graph theory and as gossip theory. In particular, it is well known that in order to connect every vertex to every other, a temporal graph needs to have at least $2n-4$ edges where $n$ is the number of vertices. This paper investigates the optimal number of edges required to satisfy partial connectivity requirements. We introduce the problem of Connectivity Request Satisfaction where we are given a directed graph that we call the request graph, where an arc from $u$ to $v$ means that we need to be able to go from $u$ to $v$. Our goal is to build a temporal graph on the same vertex set with as few temporal edges as possible that would satisfy all the requests. When the graph we build is directed, we prove that the number of temporal arcs required is $n-\mathrm{cc}+\mathrm{dfvs}$ where $\mathrm{cc}$ is the number of connected component of the request graph and $\mathrm{dfvs}$ is the size of its smallest directed feedback vertex set. It follows that the problem is NP-complete but inherits fixed parameter tractability properties of Directed Feedback Vertex Set. When the graph we build is undirected, we establish a characterization of strongly connected request graphs that admit a solution with $n-1$ edges: it is possible if and only if any set of pairwise non-vertex-disjoint closed walks all share a common vertex. We prove that this criteria can be tested in polynomial time.

I study the impact of mixed contrarians on the opinion dynamics of an heterogenous population with conformists using Galam Majority Model. Activation of contrarians is a function of the ratio majority/minority in the local groups of discussion. Restricting the group size to 3, two types of contrarians are included in respective proportions $c_{3,0}$ for configurations with ratio 3 to 0 and $c_{2,1}$ for ratio 2 to 1. I then derive the explicit update Equation and obtained analytically the fixed points, their stability, and the resulting full two-dimensional landscape of the dynamics of opinion. Setting $c_{3,0} =c_{2,1} = c$ recovers the original results obtained with uniform contrarians. The findings allow for considering a wide spectrum of new disruptive strategies to secure either a majority/minority ending ensuring the opinion having the larger initial support to win, or a single attractor dynamics at fifty/fifty, which implies a random winner regardless of initial supports.

The rapid integration of generative AI into academic workflows demands curricula that equip students not only with tool proficiency but with the critical judgment to use those tools responsibly in scholarly work. Existing offerings cluster around two inadequate poles: technical AI development courses serving narrow specialist audiences, and brief general-literacy interventions that cannot develop the sustained, practice-based competencies rigorous research requires. This paper reports the design, theoretical rationale, and implementation of BSTA 495/395: Getting Started with AI-Assisted Research, developed and delivered at Lehigh University (Spring 2026). The course addresses an underserved gap: the competencies required for rigorous AI-assisted literature review. Its architecture organizes instruction into four sequential modules aligned with the cognitive demands of that task: comprehension of individual papers, construction and validation of knowledge taxonomies, identification of research gaps, and synthesis and production of complete literature reviews. Each module embeds an explicit verification discipline and standardized AI attribution practice. Prerequisite-free and discipline-agnostic, the course enrolls upper-level undergraduates and graduate students across all fields with differentiated assessment expectations. Pre- and post-course survey data from the inaugural offering indicate substantial self-reported confidence gains, with the largest in hallucination detection (d = +1.45), responsible AI use (d = +1.33), and AI attribution practice (d = +2.40), consistent with the course's design emphasis. The course constitutes a replicable model for the emerging genre of AI research literacy curricula.

Graph databases offer unparalleled flexibility for managing interconnected data, yet the lack of strict schema enforcement often leads to runtime uncertainties and complex query development. This paper introduces Graphify, an end-to-end framework that enables developers to visually model graph data schemas and automatically synthesize a fully functional, type-safe backend. This paper proposes a formal mapping of GraphQL artifacts to the Gremlin traversal machine, supporting complete CRUD operations and arbitrarily nested queries. The system generates a transpiler capable of converting complex GraphQL requests into a single, optimized Gremlin query, including advanced features such as nested logical predicates, multi-key sorting, and pagination. At the core of the framework is a recursive state machine algorithm that processes GraphQL Abstract Syntax Trees (ASTs) with linear time complexity $O(S)$ relative to the number of selected fields. This paper demonstrates the practical efficiency and theoretical robustness of the approach through formal complexity analysis and empirical evaluation using the MovieLens 100k dataset. The result is a system that enables the generation of graph interfaces in minutes, bridging the gap between flexible graph storage and type-safe API consumption.

The chemical bond is a central organizing concept in chemistry, yet it is absent from the molecular Hamiltonian and no "bond operator" exists. Bonding is therefore not a primitive physical entity but a derived descriptor emerging from the quantum state. The logical consequences of this observation are revisited. Statements such as "bonding stabilizes structure" when taken literally risk circular reasoning (petitio principii), whereby bonding is inferred from a stationary structure and then invoked as its cause. The same caution applies to concepts such as steric repulsion, which is also a derived descriptor. Bonding accompanies stable or metastable states and correlates with their properties without constituting their cause. Illustrative examples are drawn from QTAIM, non-covalent interaction (NCI) approach, protein structure, and hydrogen-hydrogen bonding. Causation, language, and the autonomy of chemistry are also briefly discussed. The aim is not at all to diminish the role of bonding, but to place it at the correct logical level, that is, as a powerful, state-dependent descriptor that organizes, classifies, and predicts chemical behavior without serving as its fundamental cause.

Multirate characterization of spin responses in nuclear magnetic resonance (NMR) is a promising approach to fingerprinting complex molecules in the presence of multiple relaxation mechanisms. Here we present experimental and theoretical investigations simultaneously accessing 8 relaxation rates describing the density matrix of two adjacent non-equivalent nuclear spins 1/2 ($^1$H and $^{\ 13}$C) belonging to a molecule in a liquid. The selected nuclear pair is stable with respect to chemical exchange. Some of the rates are obtained from conventional measurements of inversion recovery and nuclear Overhauser effect, while other, less conventional ones, are extracted from the relaxation initialized by the maximally entangled pseudo-pure Bell states (Bell PPSs) of the spin pair. The Bell PPSs are created using a hereby introduced method based on a detuned Hartmann-Hahn double resonance condition. Microscopic theory behind the measured relaxation rates is presented, and its consistency is demonstrated by several parameter-free tests. In particular, it is shown both theoretically and experimentally, that the eigenmodes of the off-diagonal relaxation of the two-spin density matrix can be selectively initialized using Bell PPSs. Our multirate analysis suggests that the measured off-diagonal relaxation is partly due to an unconventional mechanism arising from very weak $J$-couplings of the spin pair with fluctuating distant nuclear spins. Furthermore, we identify a dimensionless ratio of diagonal relaxation rates, which is determined exclusively by intra-pair magnetic dipolar interaction and hence possesses a universal value for a broad class of nuclear spin pairs. This value is consistent with both our experiments and other experiments reported in the literature.

The Immersed Boundary Method has long served as a robust computational framework for fluid-structure interactions, yet the rigorous analysis of 1D Peskin filaments anchored to rigid boundaries remains sparse. In this paper, we generalize the classical Peskin problem to the half-plane by considering an elastic filament whose endpoints are anchored to a no-slip wall. Moving beyond the algebraic complexity of the traditional Blake image system, we utilize the boundary-symmetric formulation of Gimbutas, Greengard, and Veerapaneni. This representation allows for a transparent decomposition of the hydrodynamic interactions into a free space principal part and a regularizing reflected component without resorting to hypersingular integral operators. Through this framework, we prove that the leading-order evolution of the anchored filament is governed by a fractional Laplacian equipped with homogeneous Dirichlet boundary conditions. We characterize the stationary states of the system, proving that all equilibria are circular arcs connecting the anchor points, a result that holds for a broad class of elastic energy densities. By framing the non-local dynamics in weighted little Hölder spaces, we establish local well posedness and prove that the filament exhibits instantaneous $C^\infty$ regularization in both space and time. This work provides a rigorous analytical foundation for anchored filaments in bounded domains and suggests a spectrally accurate numerical path for simulating tethered biological structures.

Nanoscaled friction is a fundamental tribological phenomenon with complex behavior of its dynamical force. Here, we utilize the Prandtl-Tomlinson framework to investigate systematically the different means of control of the frictional force at the quantum and classical levels. It is found that the frictional dynamics can be controlled by the corrugation and characteristic length ratio parameters dependent upon properties of the nanoparticle-chain system. In addition to the stick-slip regime, other types of motion are uncovered, highlighting the richness of the frictional dynamics. The importance of Landau-Zener tunneling for the quantum motion is also analyzed. These findings provide valuable insights for interpreting experimental observations and controlling quantum frictional behavior in nanoscale systems.

We prove the validity of using subsampling method for inference under a two-way clustered panel in which the time effects are serially correlated. Subsamples should be drawn without replacement from randomly partitioned individual index set and consecutive blocks of time effects. We present two subsampling inference methods: estimating the quantiles directly and constructing the confidence interval by first estimating the asymptotic variance. The quantile method is very adaptive, allowing for non-Gaussian limit which invalidates all existing methods in two-way clustering with serial correlation. Although the variance method only works under Gaussian limit, it comes with a data-driven bandwidth selection algorithm and a bias-correction under suitable estimators. Monte Carlo simulations demonstrate our methods exhibiting the desired coverage level in the finite sample except when the serial correlation is extremely strong. This paper is the first one that allows for inference on non-Gaussian asymptotics under two-way clustering with serial correlation.

On-chip silicon photonic coupled cavity arrays (CCA) are a promising platform for quantum simulators, with access to high Quality (Q) factor resonators, tunability, and foundry compatibility. Furthermore, scalable two-dimensional (2D) silicon photonic CCAs allow for simulation of rich physical phenomena via Hamiltonian engineering. However, complete reconstruction of the Hamiltonian is limited by access to cavities in the bulk, with current approaches relying on imaging scattered light from bulk resonators. These approaches often require additional scatterers to be built in, limiting scalability, while also being hampered by imaging technology in the near-infrared range. Instead of these approaches, Hamiltonian tomography algorithms that require homodyne boundary measurements have been demonstrated in literature, however measurements of complex scattering measurements along a CCA boundary have not been shown. Here, we experimentally demonstrate an on-chip homodyne measurement setup along a single boundary of a $3\times 3$ silicon photonic racetrack resonator array and reconstruct the system's edge scattering matrix.

We initiate the study of Reidemeister hardness of Legendrian unknot front projections. Using normal rulings, we obstruct several infinite families of hard unknot diagrams from being drawn with max-tb unknot fronts, along with 1.7 million of the 2.6 million hard unknot diagrams studied in \cite{applebaum2024unknottingnumberhardunknot}. We construct infinitely many smoothly hard max-tb unknot diagrams, and bound their minimum possible writhe. With respect to these bounds, our constructions are conjecturally sharp.

We study fair allocation of indivisible goods among strategic agents with additive valuations. Motivated by impossibility results for deterministic truthful mechanisms, we focus on randomized mechanisms that are \emph{Truthful-in-Expectation (TIE)}. From a fairness perspective, we seek to guarantee every agent a large fraction of their \emph{Maximin Share (MMS)} ex-post. Among other results, Bu~and~Tao~[FOCS 2025] presented a TIE mechanism that guarantees $\frac{1}{n}$-MMS ex-post. First, we present an ordinal TIE mechanism that guarantees $\frac{1}{H_n + 2}$-MMS ex-post, where $H_n$ is the $n$-th harmonic number ($H_n \simeq \ln n$). This is nearly best possible for ordinal mechanisms, as even non-truthful ordinal allocation algorithms cannot obtain an approximation better than $\frac{1}{H_n}$. We then show that with just a small amount of additional cardinal information, the ex-post guarantee can be improved to $Ω(\frac{1}{\log\log n})$-MMS, at the cost of relaxing the incentive requirement to $(1-\varepsilon(n))$-TIE for negligible $\varepsilon(n)$. Finally, for two agents, we present a TIE mechanism that is $\frac{2}{3}$-MMS ex-post. All our mechanisms are ex-ante proportional (thus also providing ``Best-of-Both-Worlds'' results) and run in polynomial time. Moreover, all our results extend to the truncated proportional share (TPS), which is at least as large as the MMS. Our two-agent $\frac{2}{3}$-TPS result is best possible for the TPS.