Stable matching theory is the foundation of centralized clearinghouses worldwide, from school choice programs to medical residency allocations. However, incorporating complex distributional goals-such as multi-dimensional diversity quotas or sibling co-assignment guarantees-often compromises stability or renders the problem computationally intractable. The existing literature typically addresses this tension by weakening stability to accommodate distributional constraints. In contrast, the reverse question remains largely unexplored: if we restrict attention to stable matchings, to what extent can such distributional objectives be achieved? In this paper, we resolve this tension by introducing a general, polynomial-time algorithmic framework to optimize arbitrary institutional (or even two-sided) objectives within the set of stable matchings. We prove that for any polynomial-time computable set functions $g_i$ evaluating the assigned students at institutions $i \in I$, a stable matching minimizing either the utilitarian objective $\sum_{i\in I} g_i$ or the egalitarian objective $\max_{i\in I} g_i$ can be found efficiently. Our approach leverages the structural properties of stable matchings, mapping arbitrary set functions to linear edge weights. We apply this theorem to efficiently solve major open practical problems: finding stable matchings that minimally violate overlapping diversity quotas (under both total and maximum violations) and maximizing the number of sibling families assigned to the same institution. Even when the distributional objective is prioritized, our algorithm helps to quantify the ``price of stability'', i.e., the gap between the maximally diverse matching and the maximally diverse stable matching.

We measured the critical temperatures and critical switching and retrapping currents of wide and narrow thin-film quasi-one-dimensional superconducting aluminum structures of the same thickness in zero magnetic field. For the first time, we found that the narrower the structure, the lower the critical temperature and critical current density in the structure. Probably, the influence of depairing centers that are on dirty longitudinal boundaries of the structure, is the stronger than the narrower the structure. It is found for the first time that, in most cases, the temperature-dependent switching critical current in both structures is approximated by two functions. At temperatures below the temperature corresponding to the bottom of the resistive N-S transition of structures, the switching critical current is described by the Kupriyanov-Lukichev theory. At temperatures close to the top of the N-S transition, the switching current is linear with temperature and coincides with the critical Josephson current. At these temperatures, Josephson SNS junctions are formed in structures.

Mixture-of-Experts (MoE) architectures in Large Language Models (LLMs) have significantly reduced inference costs through sparse activation. However, this sparse activation paradigm also introduces new safety challenges. Since only a subset of experts is engaged for each input, model behavior becomes coupled to routing decisions, yielding a difficult-to-control mechanism that can vary across safety-relevant scenarios. At the same time, adapting model behavior through full fine-tuning or retraining is costly, especially when developers need to rapidly configure the same model for different safety objectives. We present MASCing (MoE Activation Steering Configuration), the first framework that enables flexible reconfiguration of MoE behavior across diverse safety scenarios without retraining. MASCing uses an LSTM-based surrogate model to capture cross-layer routing dependencies and map routing logits to downstream behaviors. It then optimizes a steering matrix to identify behavior-relevant expert circuits and, at inference time, applies steering masks to the routing gates to override expert selection. This enables targeted enhancement or suppression of specific behaviors while preserving general language utility. To demonstrate its reconfigurability, we apply MASCing to two different safety-related objectives and observe consistent gains with negligible overhead across seven open-source MoE models. For multi-turn jailbreak defense, it improves the average defense success rate from 52.5% to 83.9%, with gains of up to 89.2%. For adult-content generation, MASCing enables models to comply with such requests that would otherwise be refused, increasing the average generation success rate from 52.6% to 82.0%, with gains of up to 93.0%. These results establish MASCing as a practical, lightweight, and flexible framework for scenario-specific safety reconfiguration in MoE models.

We study square-base Calderbank--Shor--Steane (CSS) hypergraph-product codes as a finite-length class for regular high-girth quantum low-density parity-check (LDPC) design. For base matrices of small column weight, we give checkable conditions for regularity, rank deficiency, and short-cycle exclusion, and we present explicit column-weight-three and column-weight-four examples with Tanner girth 6 and 8. We also analyze circulant permutation matrix (CPM) lifts of this class. Using the standard voltage-sum criterion, we identify orthogonality-forced Tanner 8-cycles and show that CPM lifting cannot raise the Tanner girth beyond 8 when these cycles are present. As a representative finite-length instance, a randomized CPM lift of the girth-8 base construction gives a $[[28800,62]]$ girth-8 $(3,6)$-regular CSS-LDPC code. Under degeneracy-aware belief-propagation decoding with optional ordered-statistics-decoding-lite post-processing, this code produced zero decoding failures in $2.993\times 10^8$ independent trials at depolarizing probability $p=0.1402$; the Wilson 95% upper confidence bound is $1.28\times 10^{-8}$.

We show that the VC-density in certain theories of oriented abelian groups is at most the size of parameter variables, which yields dp-minimality. We further prove that the VC-density of formulas in pairs of such models is bounded by twice the size of parameter variables. This uniform upper bound is shown to be sharp, and as a consequence, we show that such pairs have dp-rank 2.

An asymptotically flat spacetime in $D=4$ can be mapped via Couch-Torrence conformal inversion to the geometry around an extremal non-expanding and non-rotating horizon. At the linearized level, an infinite tower of conserved Newman-Penrose charges can be found at null-infinity, while infinitely many Aretakis charges are conserved in the near-horizon. Couch-Torrence inversion allows one to establish a matching between the two sets of asymptotic charges. In this work we construct the Newman-Penrose and Aretakis scalar charges in higher-dimensional geometries of D3-branes in $D=10$ and D3-brane bound states in $D=4$ and $D=5$ and establish a precise matching between them through the inversion. By exploiting the residual unbroken supersymmetry of Type IIB supergravity, we demonstrate that it is possible to relate scalar (complex dilaton) charges to higher spin charges. In particular, we determine infinite towers of conserved asymptotic spinorial charges associated with the dilatino fluctuations, and determine the map through inversion.

We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be screened may be large $p$ $>>$ $n$, and growing at an exponential rate, provided $\ln (p)$ $=$ $o(n^{a})$ for some $a$ $>$ $0$ that depends on memory decay and the growth of higher moments. We study the problem of correlation screening in a high dimensional marginal regression setting, assuming so-called \textit{physical dependence} in a time series setting. We entirely sidestep covariance matrix estimation and adaptive re-sampling by working with a max-statistic over the many computed parameters. Thus we do not need endogenous selection of the most relevant predictor index yielding non-uniform asymptotics, nor do we need a post-estimation Bonferroni correction. The non-standard limit distribution arising from the maximum of an increasing number of estimators is easily approximated by a multiplier (wild) block bootstrap. The max-test controls for size well, performs well against various deviations from the null, including very slight deviations with a weak or sparse signal. A numerical experiment is performed and an empirical example with the VIX volatility index is provided.

We investigate spin-induced scalarization of Kerr black holes in an Einstein-scalar-Gauss-Bonnet (EsGB) model that does not admit a linear tachyonic instability of the scalar-free solution. The scalarization mechanism is therefore genuinely nonlinear. We first analyze the decoupled scalar dynamics on fixed Kerr backgrounds and show that sufficiently rapid rotation modifies the Gauss-Bonnet invariant such that a negative near-horizon region develops near the poles. This region provides a geometric trapping mechanism for nonlinear scalar growth, which becomes effective above a threshold spin $χ=0.5$. We then construct stationary scalarized black hole solutions with full backreaction and determine their domain of existence. We find that the solutions occupy a finite low-mass high-spin wedge in the spin-mass plane. This is in contrast to spin-induced spontaneous scalarization, where the scalarized solutions form a narrow band. In this wedge, toward the high-spin end, the scalar hair becomes stronger, and the solutions approach a near-extremal regime, while toward the low-spin boundary, the scalar field is strongly suppressed and approaches a weak-hair limit as $χ\to 0.5$.

We investigate the superfluid dynamics of a Josephson junction beyond the mean-field description, incorporating the role of thermal fluctuations as well as quantum fluctuations. Using a formalism that accounts for the fluctuations in a homogeneous gas, and under the assumption that the transport of the non-condensed component is negligible, we derive a corrected equation of motion within the two-site approximation. The resulting corrections for the typical dynamical quantities, like the Josephson frequency, the strength of macroscopic quantum self-trapping, and the threshold for spontaneous symmetry breaking, allow us to predict the effects of both types of fluctuations and assess their relative importance in different regimes in a semianalytical fashion. For all the dynamical quantities, the quantum fluctuations are shown to play an opposite role with respect to the thermal fluctuations. Josephson frequency is decreased by thermal fluctuations and both the critical strenghts of macroscopic quantum self trapping and spontaneous symmetry breaking are increased. We assess the experimentally accessible regimes by calculating the relevant parameters of recent experimental realizations of Bosonic Josephson junction and show that the expected regime is dominated by quantum fluctuations.

High Bandwidth Memory with Processing-in-Memory (HBM-PIM) offers an opportunity to reduce data movement by executing computation directly inside memory, but current commercial platforms expose limited instruction sets and require specialized software stacks. In this work, we investigate whether HBM-PIM can serve as a backend for ISA-level matrix acceleration, using the RISC-V Attached Matrix Extension (AME) as a semantic reference. We propose a PEP-based execution model that maps AME element-wise and matrix instructions to HBM-PIM micro-kernels and data instructions in memory operations. Differently from SoA HBM-PIM, we introduce a reduction-free outer-product dataflow that enables accumulation entirely within memory despite the lack of native reduction support. Our approach supports end-to-end execution of element-wise operations, GEMV, and GEMM in PIM mode, minimizing host involvement and off-chip transfers. An experimental evaluation on Samsung Aquabolt-XL shows that AME matrix tile multiplication achieves up to 14.9 GFLOP/s (59.4 FLOP/cycle) on a single HBM pseudo-channel.

We give a self-contained, modern exposition of Édouard Goursat's 1887 theorem on pseudo-elliptic integrals -- those integrals of the form $\int F(t)\,\d t/\sqrt{R(t)}$ with $R$ a cubic or quartic polynomial that, despite living on a genus-$1$ algebraic curve, admit elementary antiderivatives. After reviewing integration in finite terms and Liouville's theorem, we present Goursat's two main theorems with proofs phrased in the language of Möbius automorphisms of the underlying hyperelliptic curve. We then develop a cube-root analog: for integrals of the form $\int F(t)\,\d t/\sqrt[3]{R(t)}$ with $R$ cubic, an order-$3$ Möbius substitution cyclically permuting the roots of $R$ induces an eigendecomposition into three pieces. Two of the three eigenpieces (eigenvalues $1$ and $ω^2$, where $ω= e^{2πi/3}$) descend through a chain of substitutions to genus-$0$ curves and yield elementary antiderivatives; the middle eigenpiece (eigenvalue $ω$) descends only to the genus-$1$ curve $y^3 = x(x-K)$ and is generically transcendental.

Cross-chain NFT migration refers to the process of transferring digital assets along with their associated functionalities and guarantees between distinct blockchain platforms. However, architectural divergences among these platforms introduce critical challenges, often resulting in features that fail to behave as intended. While protocol-level mechanisms can coordinate data transfer, they are insufficient to resolve deeper compatibility issues arising from fundamental differences in state organization, transaction execution, and ownership representation. Thus, the critical challenge lies in predicting which NFT features can be preserved, which require redesign, and which are fundamentally incompatible, prior to undertaking costly migration attempts. To address this challenge, we first derive a tailored four-layer NFT architecture based on standard blockchain stacks, distinguishing cryptographic, state-management, transaction-processing, and ownership primitives, with explicit upward dependencies. Building on this architecture, we conceptualize an NFT as a bundle of features and define successful cross-chain NFT migration as the preservation of these features. Grounded in this model, we propose a four-phase migration analysis methodology comprising source feature specification, primitive-level dependency mapping, target platform profiling, and compatibility assessment, which classifies each feature as natively preserved, partially mismatched, or completely mismatched. We evaluate this methodology through a proof-of-concept analysis of Ethereum-to-Solana NFT migration, identifying several incompatibility issues that hinder seamless NFT migration.

The verification of bullion coin authenticity is essential for maintaining integrity within the precious metals market; however, the increasing sophistication of counterfeits has rendered traditional inspection methods insufficient. This paper proposes a non-destructive verification framework based on acoustic frequency analysis and deep neural networks. The methodology leverages the unique acoustic fingerprint of a coin, a physical signature determined by its material composition, mass, and geometry, captured through mechanical excitation. We implement a synergistic dual-model architecture consisting of an autoencoder that reconstructs the spectrum for anomaly detection and a deep learning classifier for coin type identification. To address the challenges of environmental noise and limited dataset diversity, a dynamically calculated anomaly threshold and data augmentation techniques were employed. Experimental results demonstrate that the integrated system achieves high precision in distinguishing authentic specimens from high-quality counterfeits, maintaining stability across varying recording conditions and devices. Beyond bullion authentication, the study highlights the scalability of the proposed non-destructive testing method for assessing the safety of critical components in the automotive and aerospace industries.

We study solution discovery, where the goal is to obtain a feasible solution to a problem from an initial configuration by a bounded sequence of local moves. In many applications, however, the graph that defines which vertex sets are feasible is not the same as the graph that governs how tokens, agents, or resources may move. Existing models such as token sliding and token jumping typically do not distinguish the problem graph and the movement graph. Motivated by this mismatch, we introduce a directed weighted two-graph model that cleanly separates feasibility from movement. A problem graph specifies the desired combinatorial objects, while a movement graph specifies admissible relocations and their costs. This yields a flexible framework that captures asymmetry, heterogeneous movement constraints, and weighted transitions, while subsuming classical discovery models as special cases. We investigate this model through \textsc{Path Discovery} and \textsc{Shortest Path Discovery}, where the task is to realize a vertex set containing an $s$-$t$-path or a shortest $s$-$t$-path in the problem graph. These problems are particularly natural in applications, since directed and weighted shortest paths are among the most fundamental algorithmic primitives. At the same time, previous work has already shown that discovery can be computationally hard even when the underlying optimization problem is easy. Our results show that this phenomenon persists, and becomes especially rich, in the two-graph setting. We obtain a detailed complexity picture, identifying tractable cases as well as strong hardness results.

Lattice reduction smooths the Gram-Schmidt profile, and we use majorization to describe the local swap mechanism behind that smoothing. In this language, each non-degenerate Lovász swap acts as a T-transform on the log-norm profile. As a consequence, every strictly Schur-convex measure of profile spread decreases at such a swap. Two structural consequences follow. First, the worst-case GSA envelope admits a variational interpretation. It is the unique minimum-variance profile compatible with the Lovász gap geometry, so its slope is determined by the LLL parameter alone. Second, the realized swap trajectory satisfies an exact telescoping identity for variance dissipation. The same viewpoint also helps organize deep-insertion heuristics. It suggests a thermal family of Schur-convex scoring rules, motivates adaptive selection within that family, and leads to two concrete selectors: Thermal-Adaptive, which reduces operation counts relative to SS-GG on flat profiles in our benchmarks while recovering SS-GG on $q$-ary inputs, and Geodesic Deep-LLL, which reduces equivalent-swap counts on structured lattices in our benchmarks at higher wall-clock cost.

We investigate the charge transport properties of a relativistic drifting plasma using the kinetic theory within the relaxation time approximation. The collective drift induced by electromagnetic fields is described in terms of a suitably modified distribution function. The analysis is done for both constant and time dependent field configurations. For constant electromagnetic fields, we obtain the Hall drift current that arises from the transverse motion of charged particles in electric and magnetic fields. Extending the framework to time dependent electric fields, we show that their temporal variations give rise to polarization drift, which significantly alters the structure of the induced current and introduces additional components along both the conventional drift and polarization directions. We present a quantitative estimate of the Hall drift and polarization induced contributions in the quark gluon plasma and study the temperature dependence of the associated charge transport coefficients in the QCD.

The excitation of plasma wakefields driven by chirped laser pulses is investigated using a reduced relativistic fluid Poisson model supported by fully relativistic particle in cell (PIC) simulations. The study considers exponential, linear, quadratic, and unchirped phase-modulated laser drivers propagating in an underdense plasma. Numerical solutions of the governing equations demonstrate that exponential chirping produces enhanced wakefield amplitudes compared to polynomial and unchirped cases due to nonlinear phase variation across the pulse envelope. The analytical predictions are validated using quasi cylindrical PIC simulations performed under identical plasma and laser parameters. The simulations reveal strong chirp dependent wakefield modification, with positively chirped pulses generating peak accelerating fields exceeding 58 GV per m, accompanied by pronounced density compression and enhanced electron momentum gain. These results demonstrate that exponential chirping provides an effective mechanism for controlling wakefield strength and improving plasma based particle acceleration.

We present a unifying Nearly Asymptotically Invariant Manifold (NAIM) framework for understanding Nesterovs Accelerated Gradient (NAG) method. By lifting the first-order gradient flow into a second-order phase space we construct a NAIM a slow, attracting graph and show that acceleration emerges from a curvature aware perturbation of this graph. The evolving slope of the perturbed manifold is governed by a Differential Riccati Equation (DRE), which enforces strict tangency of the vector field to the manifold surface. In the quadratic case the DRE reduces to an Algebraic Riccati Equation (ARE), and the requirement of spectral resonance equal contraction rates across all curvature modes uniquely determines the damping coefficient, directly yielding the continuous time Nesterov ODE. Fenichels theorem then extends this picture rigorously to general smooth, strongly convex landscapes: normal hyperbolicity guarantees persistence of the accelerated manifold despite varying Hessian curvature. The method is further extended to unified geometric derivation of NAG methods for smooth convex and strongly convex optimization in the discrete case. We exploit the underlying geometric structure and derive both cases from the same principle of preserving the projective structure under discretization process. A Lie Trotter splitting separates the linear dissipative dynamics from the nonlinear gradient flow. The dissipative subsystem is integrated by the Cayley (bilinear) transform, which preserves the underlying projective (Mobius) structure unconditionally and produces the classical Nesterov momentum coefficient as the unique Pade multiplier. For the convex case, projective flatness (vanishing Schwarzian derivative) uniquely selects the time-varying damping recovering the canonical Nesterov ODE for convex functions.

In this paper, we employ the Comisso-Asenjo magnetic reconnection (MR) mechanism to investigate energy extraction from a rapidly rotating five-dimensional Kerr black hole (BH) with single- and two-rotation configurations. We analyze the efficiency, phase-space structure of accelerated and decelerated plasma energies, and the extracted power as functions of the spin parameter, reconnection location, plasma magnetization, and magnetic field orientation. We show that MR significantly enhances energy extraction from a five-dimensional BH with a single rotation and that the extraction efficiency is higher in the single rotation configuration than in the two-rotation case. We also evaluate the extraction rate and compare it with the Blandford-Znajek (BZ) mechanism, showing that the extracted power can exceed that of the BZ process in the single-rotation configuration. Our analysis shows that MR can significantly improve energy extraction in five-dimensional Kerr BHs with a single rotation, making them promising candidates for powering high-energy astrophysical phenomena.

Let $X_1,\ldots,X_n$ be independent random points in the closed unit ball of $\mathbb{R}^d$. Assume that each $X_i$ has a beta distribution with parameter $β_i \ge -1$: if $β_i>-1$, then $X_i$ has Lebesgue density proportional to $(1-\|x\|^2)^{β_i}$ on $\{\|x\|<1\}$, whereas the case $β_i=-1$ corresponds to the uniform distribution on the unit sphere $\{\|x\|=1\}$. Let $[X_1,\ldots,X_n]$ denote the convex hull of these points. Interpreting the unit ball as the Klein model of hyperbolic geometry, we derive closed-form formulas for the expected hyperbolic volume of the random hyperbolic polytope $[X_1,\ldots,X_n]$. As a special case, if $X_1,\ldots,X_n$ are independent and uniformly distributed on the unit sphere in $\mathbb{R}^3$, then for every $n\ge 4$, \[ \mathbb{E}\,\operatorname{Vol}_{3}^{\mathrm{hyp}}\!\bigl([X_1,\ldots,X_n]\bigr) = π\left(\frac{n}{2}-\sum_{j=1}^{n-1}\frac{1}{j}\right). \]

Bayesian variable selection requires sampling from a posterior distribution that combines discrete model indicators with continuously varying parameters, a challenge often addressed through reversible jump Markov chain Monte Carlo (RJMCMC). Despite its generality, RJMCMC is widely regarded as difficult to design and implement correctly. We present mixtures of mutually singular (MoMS) distributions as a transparent alternative in which competing models are represented within a single fixed-dimensional parameter space partitioned into mutually singular subspaces. We show that this formulation reproduces the exact spike-and-slab interpretation of Bayesian variable selection and that, under appropriate constructions, MoMS and RJMCMC share the same Metropolis--Hastings acceptance probability. On a benchmark dataset with ten predictors, both methods recover posterior inclusion probabilities that match full enumeration, while MoMS achieves comparable or superior effective sample size per second relative to a carefully engineered RJMCMC scheme. We further illustrate the approach in a mixed-effects logistic regression for a sleep-and-memory experiment and in factor-loading selection for a multidimensional generalized partial credit model. Together, these results show that Bayesian variable selection can be carried out within standard fixed-dimensional Markov chain Monte Carlo methodology -- without regret.

Rhombohedral graphene with topological flat bands offers an ideal platform for realizing correlated and topological quantum phases. Here we investigate hBN aligned eight-layer rhombohedral graphene moire superlattices, which host a robust quantum anomalous Hall (QAH) state alongside three unconventional superconducting phases. For electron-doped carriers away from the moire potential, we observe QAH Chern number reversal driven by the displacement fields and in plane magnetic fields. For hole-doped carriers near the moire superlattice, the three superconducting phases exhibit distinctively different in plane magnetic field responses: one is weakly enhanced, the second is strongly suppressed, and the third exclusively induced by in plane magnetic field. The isotropic in plane magnetic field response in the QAH regime points to interplay between orbital magnetism and spin-orbit coupling, and the field-emergent superconductivity provides compelling evidence for spin-triplet pairing. Our work demonstrates a highly versatile platform for coexisting topological and superconducting states, and highlights in plane magnetic field as a powerful in-situ control knob for engineering novel quantum devices.

We study when a sound arithmetic theory $\mathcal S{\supseteq}S^1_2$ with polynomial-time decidable axioms efficiently proves the bounded consistency statements $Con_{\mathcal S{+}ϕ}(n)$ for a true sentence $ϕ$. Equivalently, we ask when $\mathcal S$, viewed as a proof system, simulates $\mathcal S{+}ϕ$. The paper's two unconditional contributions constrain possible characterizations. First, for finitely axiomatized sequential $\mathcal S$, if $EA{\vdash}Con_{\mathcal S}{\rightarrow}Con_{\mathcal S{+}ϕ}$, then $\mathcal S$ interprets $\mathcal S{+}ϕ$, implying ${\mathcal S}{\vdash^{n^{O(1)}}}Con_{\mathcal S}(p(n)){\rightarrow}Con_{\mathcal S{+}ϕ}(n)$ for some polynomial $p$, and hence ${\mathcal S}{\vdash^{n^{O(1)}}}Con_{\mathcal S{+}ϕ}(n)$. Second, if $\mathcal S$ fails to simulate $\mathcal S{+}ϕ$ for some true $ϕ$, then for all sufficiently large $k$ it also fails for $ϕ_{BB}(k)$ asserting the exact value of the $k$-state Busy Beaver function. Informally, any argument showing that $\mathcal S$ fails to simulate some $\mathcal S{+}ϕ$ also yields unprovable $ϕ_{BB}(k)$ witnessing the same obstruction. These results suggest that relative consistency strength is a serious candidate for governing when simulation is possible, while leaving open whether it is the correct criterion. The paper's central conjectural proposal is that the above sufficient condition is also necessary: if $EA{\not\vdash}Con_{\mathcal S}{\rightarrow}Con_{\mathcal S{+}ϕ}$, then for every constant $c{>}0$, ${\mathcal S}{\not\vdash^{n^c}}Con_{\mathcal S{+}ϕ}(n)$. Under this proposal, hardness follows in canonical cases where $ϕ$ is $Con_{\mathcal S}$ or a Kolmogorov-randomness axiom. The latter yields further conjectural consequences and extensions.

We propose a novel and generalized mechanism, dubbed stochastic axion mixing. In a multi-axion framework, this mixing occurs naturally provided that the masses of all ultra-light axion-like particles (ALPs) are distinct and lighter than the zero-temperature mass of the QCD axion. Crucially, this mechanism is independent of the relative magnitudes of the axion decay constants. In contrast to the conventional maximal mixing scenario -- which strictly relies on specific decay constant hierarchies -- stochastic mixing represents a significantly broader formalism. Notably, maximal mixing emerges as a specific subset of stochastic mixing under restrictive conditions. This new mechanism offers profound implications for axion cosmology.

This paper addresses the problem of finding the densest $k$-vertex subgraph in an arbitrary graph. This problem is NP-hard and has important applications in social network analysis, fraud detection, recommendation systems, and bioinformatics. We propose two quantum approaches to solve this problem: reduction to Quadratic Unconstrained Binary Optimization (QUBO) and using Grover's quantum search algorithm. For the latter approach, we present an explicit gate-based oracle circuit utilizing Dicke states and Quantum Fourier Transform for edge counting. Numerical simulations demonstrate a quadratic speedup over classical Brute-force search.

AI systems rest on software with low integrity mechanisms, leaving AI systems exposed across every stage from data acquisition to final inference. This paper makes the AI supply chain a first-class object of analysis, decomposing it across four architectural layers: data acquisition, model training, model inference, and a cross-cutting substrate. Within these layers, we identify four structural gaps that traditional supply chain mechanisms do not address: verifiability, versioning, observability, and traceability.Current AI systems fall short on all of them: they carry undeclared behavioral couplings that no resolver enforces; they cannot be reverted back to known working assemblies; they degrade silently rather than surfacing breaking changes; and their lineage can hardly be approximated. To illustrate the scale of the software supply chain of AI, we measure a reference stack of 48 production-grade open-source projects, which declares 4,664 direct dependencies, resolves to 11,508 transitive packages, and totals roughly 392M lines of code.

We model a direct solid-state phase transition through a nucleation-and-growth process in which plates have simple, regular shapes - squares, cubes, or square-faced lamellae - and grow homothetically (self-similarly) until they either reach a randomly assigned maximum size or are stopped by impingement with previously formed plates. The reverse transformation is represented by the preferential disappearance of smaller plates, while larger plates are retained during an incomplete reversion. A subsequent direct transformation therefore produces a modified plate-size distribution, a memory effect that forms the main focus of this study. Building upon an earlier two-dimensional (2D) formulation, we extend the model to cubes (3D) and to lamellar plates (3DL) in order to examine how dimensionality affects transformation memory. We introduce a quantitative descriptor of memory, the size mass ratio, and find that memory is robust in all geometries but overall stronger in 2D than in 3D or 3DL. We provide growth snapshots, arrest-regrowth cycles, size distributions, and differential scanning calorimetry simulations, and we compute the Shannon size-entropy to quantify configurational diversity. Although motivated by the thermal memory effect in shape-memory alloys, the model more generally identifies a purely geometric mechanism for memory in first-order solid-solid transformations, highlighting the role of dimensionality and geometric blocking in controlling the strength of transformation memory.

The main theorem of the paper provides an existence criterion of holomorphic discs for higher $A_\infty$ operations. The key step is to show that if a minimal disc in a Kähler manifold with boundary in a sequence of Lagrangian submanifolds intersecting transversely such that its partial Maslov indices are either all no less than $1$ or all no larger than $-1$, then there is a holomorphic disc with the same image as this minimal disc. As a by-product, we show that all minimal discs in $\C\mathrm{P}^m$ with boundary on $\R\mathrm{P}^m$ are holomorphic.

We present YOSO (You Only Shot Once), a single-frame phase retrieval framework for digital in-line holographic microscopy (DIHM) in which supervised deep learning is used to numerically generate an additional hologram corresponding to different defocus distance, creating a so-called multi-height dataset, which is then conventionally processed with a well-established Gerchberg-Saxton (GS) algorithm. YOSO is trained on computer-generated data derived from natural images, enabling strong generalization. The selected multi-scale ResNet architecture enables rapid training in under two hours on a mid-range workstation, which is done only once, enabling efficient inference thereafter. We further show that YOSO network can process inputs of varying spatial dimensions, allowing training on small inputs and direct inference on full-sized holograms while bypassing patch-and-stitch procedure. A further advantage of YOSO is its physics-consistent hologram padding, which replaces conventional zero or edge-value padding with a physically grounded approach compatible with the GS framework. The YOSO framework is tested on various systems (lens-based and lensless DIHM) and diverse samples: a resolution test target, adherent and suspended biological cells, and a mouse brain slice. The results show that YOSO is compatible with 3D objects and correctly recovers defocused object wave features, enabling holographic postprocessing such as numerical refocusing. The results of this work are available publicly as software for end-to-end implementation.

Photoacoustic imaging is the leading technique for deep tissue optical imaging, allowing single-shot imaging at depths. However, its resolution may be limited by acoustic aberrations, caused by natural unknown heterogeneities in the tissue speed of sound. In recent years, reflection-matrix based scattering-compensation techniques have been successfully employed in ultrasound, optics, and seismology, to computationally correct such distortions. However, they have not been adapted to photoacoustic imaging since they rely on multiple acquisitions under different controlled excitations, such as input plane-wave illuminations, which do not result in signal changes in photoacoustics. Here, we introduce a framework that enables the direct application of the state-of-the-art reflection-matrix based aberration correction techniques to photoacoustic imaging of dynamic targets. Specifically, we show that a covariance matrix analysis of a conventional set of photoacoustic frames of dynamic targets, such as flowing red blood cells in blood vessels, yields a virtual reflection-matrix that is mathematically analogous to a pulse-echo reflection-matrix, and lends itself to direct processing by conventional reflection-matrix based scattering-compensation algorithms. We validate and demonstrate the approach for photoacoustic aberration correction of vessel-mimicking targets containing flowing absorbers in both simulations and experiments.