Refractory body-centered cubic (BCC) metals and alloys are of extraordinary importance in modern technological and structural applications. However, their wider adoption in science and technology is severely restricted by low-temperature brittleness, quantified by an unacceptably high value of the brittle-to ductile transition temperature (DBTT). The DBTT of these alloys is known to depend strongly on the particular microstructure of the material following mechanisms that are not well understood. Here we apply cross-scale molecular dynamics (MD), a simulation approach that preserves full atomic resolution while capturing the collective evolution of dislocations, twins, and cracks in near-micron-scale volumes, to investigate ductility and fracture in single-crystal tungsten pillars as a function of initial defect microstructure, deformation conditions, and temperature. The simulations reveal a sequence of microscopic processes conducive to failure: dislocation starvation, nucleation and growth of twins, pinning of the twin boundaries at surface asperities, resulting in disconnection pile-ups that trigger crack nucleation and propagation at low macroscopic stresses along incoherent boundary segments. By resolving these processes within a single atomistic framework, our simulations connect defect-level dynamics to macroscopic fracture behavior and identify microstructural pathways capable of shifting the DBTT through targeted promotion or suppression of the underlying deformation mechanisms.

We determine the phase diagram of the Anderson tight-binding model on random regular graphs with Gaussian disorder and sufficiently large degree. In particular, we prove that if the degree is fixed and the number of vertices goes to infinity, the spectrum asymptotically consists of a finite delocalized interval surrounded by two unbounded localized components. Our argument uses a recent description of the spectrum of the tight-binding model on the Bethe lattice (Aggarwal--Lopatto, 2025). By viewing the Bethe lattice as the local limit of a random regular graph, and establishing suitable concentration, eigenvalue-counting, and resolvent estimates, we transfer this characterization of the spectrum of the limiting model to the finite-volume setting.

We study a heavily overloaded single-server queue with abandonment and derive bounds on stationary tail probabilities of the queue length. As the abandonment rate $γ\downarrow 0$, the centered-scaled queue length $\tilde{q}$ is known to converge in distribution to a Gaussian. However, such asymptotic limits do not quantify the pre-limit tail $\mathbb{P}(\tilde{q}>a)$ for fixed $γ>0$. Our goal is to obtain pre-limit bounds that are \emph{efficient} across different deviation regimes. For constant deviations, efficiency means Gaussian-type decay in $a$ together with a pre-limit error that vanishes as $γ\downarrow 0$, yielding the correct Gaussian tail in the limit. We establish such an efficient bound that is best-of-both-worlds. For larger deviations when $a$ is a function of $γ$, efficiency translates into exponentially tight, matching upper and lower bounds. For moderate deviation, we obtain sub-Gaussian tails, while in the large deviation regime the decay becomes sub-Poisson. Our bounds are obtained using a combination of Stein's method for Wasserstein-$p$ distance and the transform method. We then consider a load-balancing system of abandonment queues with heterogeneous servers, operating under the join-the-shortest-queue (JSQ) policy in the heavily overloaded regime. As in the case of single-server queue, we again obtain Wasserstein-$p$ bounds w.r.t.\ a Gaussian, and efficient concentration for constant and moderate deviations. For larger deviations, our JSQ upper bounds exhibit a transition from Gaussian-type decay to sub-Weibull decay. All these results are obtained using Stein's method. In addition, a key ingredient here is establishing a state space collapse (SSC) where all queues become equal. We establish a $p$-th moment bound on the orthogonal component of the queue length vector that is essential for our Wasserstein-$p$ bound.

We prove that free fermions in the spin (tensor product) factorization violate monogamy of mutual information: $I_3^{\mathrm{spin}} > 0$ for adjacent strips of width $w \le 6$ at all Fermi momenta, and for all $w$ at $z = k_F w < z^* \approx 1.329$. Many-body computation at $w=6$ via the $G$-matrix formula maps the scaling-limit function $I_3^{\mathrm{spin}}(z)$: it has a minimum of $0.100$ at $z \approx 1.5$, numerically establishing the conjecture $I_3^{\mathrm{spin}} > 0$ for all $z$ and $w$. The proof rests on an exact identity: the fermionic and spin reduced density matrices of disjoint regions $A$, $D$ separated by $B$ differ by the parity insertion $(-1)^{N_B}$ in the partial trace. A Perron--Frobenius argument proves element-wise coherence damping; for free fermions, an independent Gaussian bound gives the entropy ordering $ΔS_{AD} \ge 0$. Exact diagonalization confirms this for interacting fermions. DMRG on the $t$-$V$ chain shows that the factorization contribution exceeds the genuine interaction contribution to $I_3$ by a factor of 8, accounting for $\sim 80\%$ of the deviation in spin-basis numerics. Strong repulsion ($K \lesssim 0.7$) restores monogamy. Conversely, $Z_2$ parity superselection enforces $I_3 \le 0$ at all fillings (proved for $w \le 3$), with the ratio of parity entropy to quantum excess approaching $2\ln 2/(3\ln(4/3)) = 1.606$. Any use of $I_3$ as a diagnostic for holographic duality, quantum chaos, or Fermi surface topology must specify the operator algebra; without this, the sign of $I_3$ is ambiguous.

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for a particular derivation to ''correspond'' to a particular proof. Mere existence of a formalization is not enough, and a substantive account of the required correspondence resolves into two criteria -- adequate representation (of the original theorem) and tracking (of the steps in the original proof). An examination of the actually-existing formalization systems we have today shows the variety of quasi-empirical ways we establish these criteria, and points towards new burdens that may be placed on the future evolution of mathematics itself.

We investigate magnetotransport in a time-reversal symmetry-broken, untilted Weyl semimetal in the simultaneous presence of momentum-space Berry curvature and real-space topology arising from a skyrmion-induced emergent magnetic field $\mathbf{B}_{\mathrm{emer}}$. Using a semiclassical Boltzmann approach incorporating Berry-curvature corrections and intervalley scattering, we analyze the longitudinal magnetoconductivity and planar Hall conductivity in this mixed-topology regime. In the absence of $B_{\mathrm{emer}}$, increasing intervalley scattering drives a strong sign reversal of the longitudinal magnetoconductivity. A finite $\mathbf{B}_{\mathrm{emer}}$ introduces an additional shift of the parabolic magnetic-field dependence, leading to a weak sign-reversal regime without altering the curvature. The coexistence of these effects naturally produces a strong-and-weak sign-reversal regime, demonstrating that intervalley scattering and real-space topology control distinct geometric features of the response. The emergent field further induces asymmetry in the angular dependence of both longitudinal and planar Hall conductivities. We show that a finite planar Hall response can arise solely from $\mathbf{B}_{\mathrm{emer}}$ when its direction is varied, providing a transport signature of real-space topology. Our results establish that the skyrmion-induced emergent field acts as an independent topological tuning parameter, revealing measurable consequences of the interplay between real- and momentum-space Berry curvature in Weyl systems.

In recent years, large language models (LLMs) have driven substantial intelligent transformation across diverse industries. Commercial LLM training is typically performed over data center networks (DCNs) comprising hundreds to thousands of GPUs, with multiple devices collocated per node. As network scale expands, inter-node communication becomes a primary bottleneck to training efficiency. Network-state simulators therefore play a crucial role by enabling cost-effective evaluation of network configurations and parallelization strategies through faithful emulation of DCN dynamics during LLM training. However, existing simulators are constrained by a efficiency-fidelity tradeoff, as packet-level simulators (PLSs) incur prohibitive runtime overhead, whereas flow-level simulators (FLSs) compromise essential modeling accuracy. In this paper, we develop \texttt{HyGra}, a hybrid-granularity network-state simulator that exploits intrinsic network dynamics in LLM training to adaptively switch simulation granularity. Specifically, \texttt{HyGra} employs packet-level simulation during non-steady phases with transient fluctuations and flow-level simulation during steady phases with periodic patterns, thereby accelerating execution while preserving high fidelity. Moreover, it requires no specialized hardware, supports single-machine deployment, and is compatible with existing simulators. Experiments based representative commercial LLM workloads, including ChatGPT, DeepSeek, and Qwen, show that \texttt{HyGra} achieves up to 15.4$\times$ speedup under single parallelization strategy and 7.8$\times$ under hybrid parallelization strategies while maintaining high accuracy.

The performance of shallow-depth quantum optimization algorithms is known to depend strongly on problem structure, yet the role of real-world network topology remains poorly understood. In this work, we study how urban graph structure influences the behaviour of the Quantum Approximate Optimization Algorithm (QAOA) at depth p=1. Using street-network subgraphs extracted from two cities in Pakistan with contrasting urban designs-a planned city (Islamabad) and an organically grown city (Lyari)-we analyze probability concentration, approximation quality, and performance variability on the minimum vertex cover problem. By comparing classical brute-force solutions with QAOA outcomes, we show that planned topologies yield more reliable convergence, while organic networks exhibit higher variance and a greater tendency toward trivial solutions. Our results suggest that urban structure primarily affects the robustness rather than the average quality of shallow QAOA solutions, highlighting the importance of higher-order structural heterogeneity in shaping low-depth quantum optimization landscapes. This research is vital because it bridges the gap between abstract quantum theory and the chaotic reality of our physical world, proving that the way we build our cities directly impacts our ability to optimize them. By identifying how "topological DNA" influences algorithmic success, this work enables the development of more resilient quantum solutions for critical infrastructure, such as smart power grids and emergency response routing. Ultimately, these insights benefit society by paving the way for more efficient, data-driven urban management that can reduce resource waste and improve the quality of life in both planned and organically growing metropolitan areas.

We present a scalable formal verification methodology for Quantum Phase Estimation (QPE) circuits. Our approach uses a symbolic qubit abstraction based on quantifier-free bit-vector logic, capturing key quantum phenomena, including superposition, rotation, and measurement. The proposed methodology maps quantum circuit functional behaviour from Hilbert space to a bit-vector domain. We develop formal properties aligned with this abstraction to ensure functional correctness of QPE circuits. The method scales efficiently, verifying QPE circuits with up to 6 precision qubits and 1,024 phase qubits using under 7.5~GB of memory.

Understanding how structured sequence information can be represented and generalized in neural systems is key to modeling the transition from acoustic input to emergent structure. In this study, we propose a rank-order based neural network inspired by the STG-LIFG-PMC pathway, modeling the bottom-up transition from acoustic input to abstract rank representation and the top-down generation from that representation to motor execution. Building on previous work in rank coding, we first demonstrate that this model efficiently compresses input while retaining the capacity to reconstruct full utterances from partial cues, revealing emergent structure-sensitive generation process that reflects context-general representations of sensorimotor states, which are later shaped into context-specific motor plans during speech planning. We then show that the network exhibits global-level novelty detection similar to the P3B novelty wave, replicating the global-sequence-sensitive mechanism. As a supplement, we also compare the model's behavior under local (index-level) and global (rank-level) perturbations, revealing robustness to superficial variation and sensitivity to abstract structural violation, key features associated with hierarchical generalization. These results suggest that rank-order coding not only serves as a compact encoding scheme but also captures hierarchical structure in acoustic sequences.

We study the gap between the minimum size of a Boolean circuit (DAG) and the minimum size of a formula (tree circuit) over the And-Inverter Graph (AIG) basis {AND, NOT} with free inversions. We prove that this gap is always 0 or 1 (Unit Gap Theorem), that sharing requires opt(f) >= n essential variables (Threshold Theorem), and that no sharing is needed when opt(f) <= 3 (Tree Theorem). Gate counts in optimal circuits satisfy an exact decomposition formula with a binary sharing term. When the gap equals 1, it arises from exactly one gate with fan-out 2, employing either dual-polarity or same-polarity reuse; we prove that no other sharing structure can produce a unit gap.

Let $G$ be a graph of order $n$ and $P(G,x)$ be the chromatic polynomial of $G$. Dong, Ge, Gong, Ning, Ouyang, and Tay (J. Graph Theory 96(2021) 343) conjectured that $\frac{d^k}{dx^k} \bigl( \ln[(-1)^n P(G, x)] \bigr) < 0$ holds for all $k \geq 2$ and $x \in (-\infty, 0)$. We prove this conjecture for all $k \geq 2 $ and $ x\leq -6.66Δk $, in which $Δ$ is the maximum degree of $G$.

We study energy extraction and particle acceleration in the rotating Einstein-Maxwell-Dilaton-Axion (EMDA) black hole, focusing on the impact of dilaton hair $b\le 0$ on near-horizon energetics relative to Kerr. For the Penrose process we derive analytic expressions for the maximum efficiency and show that negative $b$ can strongly enhance the ideal gain in the extremal regime (e.g., reaching $\sim 91\%$ for $b=-0.3$). We then compute the irreducible mass $M_{\rm irr}$ and the corresponding rotationally extractable energy $\mathcal{E}_{\rm rot}\equiv M-M_{\rm irr}$, finding that $M_{\rm irr}$ decreases monotonically as $b$ becomes more negative while $\mathcal{E}_{\rm rot}$ increases, indicating a larger spin-energy reservoir; at extremality the extracted share from rotation is $\mathcal{E}_{\rm rot}/M\simeq 0.63$ for EMDA, reducing to the Kerr value $\simeq 0.29$ at $b=0$. Kinematic constraints relevant to fragment production are quantified via the Wald and Bardeen--Press--Teukolsky bounds, which are progressively relaxed for more negative $b$. For wave superradiance we obtain the flux balance and the amplification window $0<β<kΩ_H$, with $Ω_H$ expressed through $Ξ=r_H^{2}+2br_H+a^{2}$; negative $b$ modifies $Ω_H$ and enlarges the parameter region exhibiting negative horizon flux. Finally, we analyse two-particle collisions and derive $E_{\rm cm}$, showing that the Bañados--Silk--West divergence persists at the horizon when one particle is tuned to the critical angular momentum $L_c=E/Ω_H$, while $E_{\rm cm}$ remains finite for generic angular momenta. Overall, dilaton hair in EMDA simultaneously amplifies energy-extraction channels and reshapes the near-horizon thresholds governing high-energy collisions.

We propose a new decoder for "matchable'' qLDPC codes that uses a Markov Chain Monte Carlo algorithm - called the worm algorithm - to approximately compute the probabilities of logical error classes given a syndrome. The algorithm hence performs (approximate) optimal decoding, and we expect it to be computationally efficient in certain settings. The algorithm is applicable to decoding random errors for the surface code, the honeycomb Floquet code, and hyperbolic surface codes with constant rate, in all cases with and without measurement errors. The efficiency of the decoder hinges on the mixing time of the underlying Markov chain. We give a rigorous mixing time guarantee in terms of a quantity that we call the defect susceptibility. We connect this quantity to the notion of disorder operators in statistical mechanics and use this to argue (non-rigorously) that the algorithm is efficient for typical errors in the entire decodable phase. We also demonstrate the effectiveness of the worm decoder numerically by applying it to the surface code with measurement errors as well as a family of hyperbolic surface codes. For most codes, the matchability condition restricts direct application of our decoder to noise models with independent bit-flip, phase-flip, and measurement errors. However, our decoder returns soft information which makes it useful also in heuristic "correlated decoding'' schemes which work beyond this simple setting. We demonstrate this by simulating decoding of the surface code under depolarizing noise, and we find that the threshold for "correlated worm decoding'' is substantially higher than for both minimum-weight perfect matching and for correlated matching.

Magnitude is an isometric invariant of metric spaces introduced by Leinster. Although magnitude is nowhere continuous on the Gromov-Hausdorff space of finite metric spaces, continuity results are possible if we restrict the ambient space. In this paper, we focus on $\ell_1^N$ and prove that magnitude is continuous at every skew finite subset of $\ell_1^N$, that is, at every finite set whose coordinate projections are injective. For such sets, we analyze cubical thickenings and derive an explicit formula for their weight measures. This yields a formula for the magnitude of these thickenings, which we use to prove that their magnitude converges to that of the underlying finite set. Since skew finite subsets of $\ell_1^N$ form an open and dense subset of the space of all finite subsets, magnitude is continuous on an open dense subset of the space of finite subsets of $\ell_1^N$.

Analyses of baryon acoustic oscillations (BAO) commonly employ template-based methods to extract compressed parameters from the clustering of dark-matter tracers, which are then interpreted in terms of ratios of the sound-horizon scale and cosmological distances relative to a fiducial cosmology. A small mismatch between the sound-horizon scale derived from the standard analytic formulation (integral over the sound speed) and the effective scale imprinted in clustered matter can, however, introduce a systematic bias in cosmological inference. We extend previous work to a broader class of cosmological models, quantify this bias for surveys with DESI-like precision, and propose strategies to correct for the effect. We find that the induced bias becomes a significant fraction of the statistical uncertainty for deviations from the fiducial cosmology, at the level of $|ΔΩ_m| = 0.03$ and $|ΔN_\mathrm{eff}| = 0.3$, and for very precise data corresponding to a forecasted Year-5 DESI survey (or other stage IV dark energy galaxy surveys). We present several ways to correct for this effect, suitable for a variety of applications. We therefore recommend that analyses exploring such parameter regimes either apply the proposed corrections or include an appropriate systematic error budget.

The rapid proliferation of autonomous AI agents is driving a shift toward agentic commerce, where agents are expected to autonomously invoke and pay for services. While blockchain-based payments offer a programmable foundation for such interactions, the recently proposed x402 standard fails to enforce end-to-end atomicity across service execution, payment, and result delivery. In this paper, we present A402, a trust-minimized payment architecture that securely binds cryptocurrency payments to service execution. A402 introduces Atomic Service Channels (ASCs), a new channel protocol that integrates service execution into payment channels, enabling real-time, high-frequency micropayments for agentic commerce. Within each ASC, A402 employs an atomic exchange protocol based on TEE-assisted adaptor signatures, ensuring that payments are finalized if and only if the requested service is correctly executed and the corresponding result is delivered. To further ensure privacy, A402 incorporates a TEE-based Liquidity Vault that privately manages the lifecycle of ASCs and aggregates their settlements into a single on-chain transaction, revealing only aggregated balances. We implement A402 and evaluate it against x402 with integrations on both Bitcoin and Ethereum. Our results show that A402 delivers orders-of-magnitude performance and on-chain cost improvements over x402 while providing trust-minimized security guarantees.

This paper introduces an uncertainty compensation-based robust adaptive model predictive control (MPC) framework for linear systems with nonlinear time-varying uncertainties. The framework integrates an L1 adaptive controller to compensate for the matched uncertainty and a robust feedback controller, designed using linear matrix inequalities, to mitigate the effect of unmatched uncertainty on target output channels. Uniform bounds on the errors between the system's states and control inputs and those of a nominal (i.e., uncertainty-free) system are derived. These error bounds are then used to tighten the actual system's state and input constraints, enabling the design of an MPC for the nominal system under these tightened constraints. Referred to as uncertainty compensation-based MPC (UC-MPC), this approach ensures constraint satisfaction while delivering enhanced performance compared to existing methods. Simulation results for a flight control example and a spacecraft landing on an asteroid demonstrate the effectiveness of the proposed framework.

NGC 4051 is a nearby (16.7 Mpc), Narrow Line Seyfert 1 galaxy (NLS1), which has a low black hole mass of $10^6$ M$_{\odot}$. It is also known for its rapid X-ray variability, on timescales of kilo-seconds and has a complex, multi component wind in both the soft X-ray and Fe K bands. Here we present the first high resolution XRISM Resolve spectrum of NGC 4051, which was captured in a historically bright state for a 150 ks exposure. XRISM resolves two blue-shifted Fe K shell absorption troughs in the mean spectrum, which can be ascribed to H-like iron and arises from two outflow components with outflow velocities of 0.025c and 0.04c. A time dependent spectral analysis shows that the iron K absorption is variable on timescales of less than a day, increasing in velocity over the duration of the observation. The velocity changes may be explained either by the passage of two separate transiting absorbers, of different velocities, or by a single accelerating outflow of approximately constant column density. In the latter case, the wind acceleration is likely to be too large to be caused by radiation pressure and instead magnetic driving is favored to accelerate the wind up to 0.04c. The outflow can originate from an accretion disk wind, whose kinetic power is sub-Eddington in contrast to recent examples of winds from powerful, luminous quasars observed by XRISM.

Next generation quantum technologies will need to rely on efficient transduction between electrical, optical, and mechanical quantum degrees of freedom to generate large-scale entanglement over large distances. The performance of such transducers is fundamentally limited by the cryogenic properties of the underlying materials. Here, we demonstrate that engineering strain in ferroelectric thin-film strontium titanate ($\mathrm{SrTiO_3}$) not only results in an exceptionally large Pockels coefficient, but also in a robust linear piezoelectric response at cryogenic temperatures, surpassing previous thin-film benchmarks. We measure piezoelectric tensor elements of $d_{15} = 151.8 \pm 1.5$ pm/V and $d_{33} = 54.8 \pm 4$ pm/V, and an effective photoelastic coefficient of $p_{\mathrm{eff}}$ = 0.56 at 5~K. Utilizing these enhanced properties, we demonstrate the first $\mathrm{SrTiO_3}$-on-oxide acousto-optic modulator with a voltage-length product ($V_πL$) of $0.874 \pm 0.084$ V cm, outperforming state-of-the-art unreleased modulators that typically feature a $V_πL$ of a few V cm. Our results establish thin-film $\mathrm{SrTiO_3}$ as a promising material system for integrated quantum photonics operating at cryogenic temperatures.

For an $(n\times N)$-matrix $A$ of rank $n$ with integer entries, Gelfand, Kapranov and Zelevinsky introduce a system of differential equations, called the $A$-hypergeometric system. We define the stable GKZ hypergeometric $\mathcal D$-module using cohomological functors, which is closely related to the $A$-hypergeometric $\mathcal D$-module and the $\mathcal D$-module underlying the better behaved GKZ system introduced by Borisov and Horja. We prove the stable GKZ hypergeometric $\mathcal D$-module is holonomic and is an integrable connection of rank $n!\mathrm{vol}(Δ_\infty)$ on the Zariski open subset parametrizing nondegenerate Laurent polynomials, where $Δ_\infty$ is the Newton polytope at $\infty$.

AI agents increasingly perform agentic exploration: pursuing multiple solution paths in parallel and committing only the successful one. Because each exploration path may modify files and spawn processes, agents require isolated environments with atomic commit and rollback semantics for both filesystem state and process state. We introduce the branch context, a new OS abstraction that provides: (1) copy-on-write state isolation with independent filesystem views and process groups, (2) a structured lifecycle of fork, explore, and commit/abort, (3) first-commit-wins resolution that automatically invalidates sibling branches, and (4) nestable contexts for hierarchical exploration. We realize branch contexts in Linux through two complementary components. First, BranchFS is a FUSE-based filesystem that gives each branch context an isolated copy-on-write workspace, with O(1) creation, atomic commit to the parent, and automatic sibling invalidation, all without root privileges. BranchFS is open sourced in https://github.com/multikernel/branchfs, along with a Python integration library, BranchContext, that provides ready-to-use agent exploration patterns. Second, branch() is a proposed Linux syscall that spawns processes into branch contexts with reliable termination, kernel-enforced sibling isolation, and first-commit-wins coordination. Preliminary evaluation of BranchFS shows sub-350 us branch creation independent of base filesystem size, and modification-proportional commit overhead (under 1 ms for small changes).

The impact of routine smaller outages on distribution system customers in terms of customer minutes interrupted can be tracked using conventional reliability indices. However, the customer minutes interrupted in large blackout events are extremely variable, and this makes it difficult to quantify the customer impact of these extreme events with resilience metrics. We solve this problem with the System Average Large Event Duration Index SALEDI that logarithmically transforms the customer minutes interrupted. We explain how this new resilience metric works, compare it with alternatives, quantify its statistical accuracy, and illustrate its practical use with standard outage data from five utilities.

Thermal equilibrium states of many-body Hamiltonians are essential for probing quantum chaos, finite-temperature phases of matter, and training quantum machine learning models, yet generating large collections of such states across different Hamiltonians remains costly with existing methods. We introduce a powerful operation, the quantum thermal-drift channel, to construct a measurement-controlled sampling algorithm that autonomously generates thermal states together with their system Hamiltonians as labels for general physical models. We prove that our algorithm is efficient: the total gate count scales polynomially with system size and quadratically with inverse temperature, providing the first polynomial resource bound for random thermal state generation. We characterize the distribution of sampled Hamiltonians as a normal distribution reweighted by partition functions, which quantifies a trade-off between sampling accuracy and effective label range. Level-spacing statistics computed from sampled thermal states of a 2D transverse-field Ising model show a crossover to Wigner-Dyson universality, confirming that the sampler captures nontrivial chaotic correlations. Finally, a variational quantum classifier trained on the generated dataset achieves near-optimal accuracy in predicting Hamiltonian properties of unseen states. These results establish a scalable, quantum-native route for thermodynamic simulation and labeled quantum data generation in many-body systems.

Generative AI blurs the lines of authorship in computing education, creating uncertainty around how students should attribute AI assistance. To examine these emerging norms, we conducted a factorial vignette study with 94 computer science students across 102 unique scenarios, systematically manipulating assessment type, AI autonomy, student activity, prior knowledge, and human refinement effort. This paper details how these factors influence students' perceptions of ownership and disclosure preferences. Our findings indicate that attribution judgments are primarily driven by different levels of AI assistance and human refinement. We also found that students' perception of authorship significantly predicts their policy expectations. We conclude by proposing a shift from statement-style policies to process-oriented attribution, transforming disclosure into a pedagogical mechanism for fostering critical engagement with AI-generated content.

Recently, numerical examples of stable soap bubble clusters with multiple torus bubbles have been presented. The geometry of these clusters is based on the Platonic solids whose vertices have valence $3$ (in order to fulfill Plateau's laws): the tetrahedron, the cube, the dodecahedron. The clusters respectively contain a bubble of genus $3, 5, 11$. The construction is quite generic and can be used with any convex polyhedron. If stable, the cluster obtained using a polyhedron with $n$ faces has $3n+2$ bubbles and one of these bubbles has genus $n-1$. We propose here to show that is it possible to get stable soap bubble clusters with multiple torus bubbles using a geometry based on prisms and Archimedean solids as well.

The Ermakov Pinney equation and its associated invariant are shown to arise naturally in stationary quantum mechanics when the Schrodinger equation is expressed in Bohm Madelung form and the Hamiltonian is diagonal and separable. Under these conditions, the stationary continuity constraint induces a nonlinear amplitude equation of Ermakov Pinney type in each degree of freedom, revealing a hidden invariant structure that is independent of whether the evolution parameter is time or space. By reformulating the separated stationary equations in Sturm Liouville form and applying Liouville normalization, we demonstrate that the quantum potential is encoded as a curvature contribution of the self adjoint operator rather than appearing as an additional dynamical term. This correspondence preserves the standard probabilistic predictions of quantum mechanics while yielding exact stationary Bohmian amplitudes and their associated invariants. The resulting invariant-based formulation provides stationary guiding fields and clarifies the ontological status of Bohmian amplitudes as geometrically encoded structures rather than auxiliary dynamical additions. The results further show that stationary constrained Bohm Madelung systems naturally admit variational formulations whose extremals preserve the Ermakov Lewis invariant.

Schadenfreude, or the pleasure derived from others' misfortunes, has become a visible and performative feature of online news engagement, yet little is known about its prevalence, dynamics, or social patterning. We examine schadenfreude on Facebook over a ten-year period across nine major news publishers in the United States, the United Kingdom, and India (one left-leaning, one right-leaning, and one centrist per country). Using a combination of human annotation and machine-learning classification, we identify posts describing misfortune and detect schadenfreude in nearly one million associated comments. We find that while sadness and anger dominate reactions to misfortune posts, laughter and amusement form a substantial and patterned minority. Schadenfreude is most frequent in moralized and political contexts, higher among right-leaning audiences, and more pronounced in India than in the United States or United Kingdom. Temporal and regression analyses further reveal asymmetric relationships between political power and schadenfreude: left-leaning outlets display "power-licensed" schadenfreude that increases when their party governs, while right-leaning outlets exhibit "power-compensatory" schadenfreude that intensifies in opposition. Together, our findings move beyond anecdotal accounts to map schadenfreude as a dynamic, context-dependent feature of digital discourse, revealing how it evolves over time and across ideological and cultural divides.

We thoroughly investigate nonanalytic terms in the finite-temperature effective potential in one-loop approximation on a $D$-dimensional spacetime, $S_τ\times R^{D-(p+1)}\times \prod_{i=1}^p S_i^1$, using a mode recombination formula. Such nonanalytic terms cannot be expressed as positive powers of field-dependent mass squared. The formula provides a clear separation of the effective potential into a part that contains the nonanalytic terms and a part that is purely analytic, and clarifies the origin of the nonanalytic terms. We obtain all the nonanalytic terms and show that only two types of nonanalytic terms arise from the modes with zero Matsubara frequency. For a real scalar field with periodic boundary conditions, if the number of noncompacted spatial dimensions is odd (even), there are odd powers of $M$ ($\log M$ terms) but no $\log M$ terms (no odd powers of $M$). For fermions with general boundary conditions, we find that neither of the two types appears. These results clarify the nonanalytic structure of the finite-temperature effective potential on the spacetime with compactified spatial dimensions.

We study the formation of solitons in a uniform quasi-one-dimensional (quasi-1D) spin-orbit (SO) coupled self-repulsive pseudo spin-half and spin-one dipolar Bose-Einstein condensates (BEC), using the mean-field Gross-Pitaevskii equation. The dipolar atoms are taken to be polarized along the quasi-1D $x$ direction. In the pseudo spin-half case, for small SO-coupling, one can have dark-bright and bright-bright solitons. For large SO coupling, the dark-bright and bright-bright solitons may acquire a spatially-periodic modulation in density; for certain values of contact interaction paramerers there is only the normal bright-bright soliton without spatially-periodic modulation in density. In the spin-one anti-ferromagnetic case, for small SO coupling, one can have bright-bright-bright, dark-bright-dark, and bright-dark-bright solitons; and for large SO coupling, the dark-bright-dark and bright-dark-bright solitons are found to have spatially-periodic modulation in density. In the spin-one ferromagnetic case, for both small and large SO coupling, we find only bright-bright-bright solitons. All these solitons, specially those with a dark-soliton component, are dynamically stable as demonstrated by real-time propagation using the converged stationary solution obtained by imaginary-time propagation as the initial state.