We provide a framework for interpreting Discrete Exterior Calculus (DEC) numerical schemes in terms of Finite Element Exterior Calculus (FEEC). We demonstrate the equivalence of cochains on primal and dual meshes with Whitney and generalized Whitney forms which allows us to analyze DEC approximations using tools from FEEC. We demonstrate the applicability of our framework by rigorously proving convergence with rates for the Hodge-Laplacian problem in full $k$-form generality on well-centered meshes. We also provide numerical results illustrating optimality of our derived convergence rates. Moreover, we demonstrate how superconvergence phenomena can be explained in our framework with corresponding numerical results.

In this work, we designed and experimentally verified a highly integrated broadband entropy source for a quantum random number generator (QRNG) based on vacuum fluctuations. The core of the entropy source is a hybrid laser-and-silicon-photonics chip, which is only 6.3 $ \times $ 2.6 $ \times $ 1.5 mm$^{3}$ in size. A balanced homodyne detector based on cascaded radio-frequency amplifiers in the entropy source achieves a 3 dB bandwidth of 2.4 GHz and a common-mode rejection ratio above 25 dB. The quantum-to-classical-noise ratio is 9.51 dB at a photoelectron current of 1 mA. The noise equivalent power and equivalent transimpedance are 8.85$\,\text{pW}/\sqrt{\text{Hz}}$ , and 22.8 k$Ω$, respectively. After optimization using equalizer technology that eliminates the dependence of adjacent samples, the quantum random number generation rate reaches 67.9 Gbps under average conditional minimum entropy and 61.9 Gbps under the worst-case conditional minimum entropy. The developed hybrid chip enhances the integrability and speed of QRNG entropy sources based on vacuum fluctuations.

Accurate fetal birth weight prediction is a cornerstone of prenatal care, yet traditional methods often rely on imaging technologies that remain inaccessible in resource-limited settings. This study presents a novel machine learning-based framework that circumvents these conventional dependencies, using a diverse set of physiological, environmental, and parental factors to refine birth weight estimation. A multi-stage feature selection pipeline filters the dataset into an optimized subset, demonstrating previously underexplored yet clinically relevant predictors of fetal growth. By integrating advanced regression architectures and ensemble learning strategies, the model captures non-linear relationships often overlooked by traditional approaches, offering a predictive solution that is both interpretable and scalable. Beyond predictive accuracy, this study addresses a question: whether birth weight can be reliably estimated without conventional diagnostic tools. The findings challenge entrenched methodologies by introducing an alternative pathway that enhances accessibility without compromising clinical utility. While limitations exist, the study lays the foundation for a new era in prenatal analytics, one where data-driven inference competes with, and potentially redefines, established medical assessments. By bridging computational intelligence with obstetric science, this research establishes a framework for equitable, technology-driven advancements in maternal-fetal healthcare.

Integrable differential identities, together with ensemble-specific initial conditions, provide an effective approach for the characterisation of relevant observables and state functions in random matrix theory. We develop this approach for the unitary and orthogonal ensembles. In particular, we focus on a reduction where the probability measure is induced by a Hamiltonian expressed as a formal series of even interaction terms. We show that the order parameters for the unitary ensemble, that is associated with the Volterra lattice, provide a solution of the modified KP equation. The analogous reduction for the orthogonal ensemble, associated with the Pfaff lattice, leads to a new integrable chain. A key step for the calculation of order parameters for the orthogonal ensemble is the evaluation of the initial condition by using a map from orthogonal to skew-orthogonal polynomials. The thermodynamic limit leads to an integrable system (a chain for the orthogonal ensemble) of hydrodynamic type. Intriguingly, we find that the solution to the initial value problem for both the discrete system and its continuum limit are given by the very same semi-discrete dynamical chain.

Distributed architectures are a route to scalable quantum computing, but the performance of fault-tolerant operations across noisy inter-module links remains poorly characterized. We present circuit-level simulations of two key distributed primitives: transversal non-local CNOT and logical teleportation using surface and bivariate-bicycle codes. We then simulate the use of these distributed primitives in a major subroutine of common quantum algorithms. The results, enabled by our scalable library Transversal Multiple CodeBlock Simulator, demonstrate that on appropriate devices distributed qLDPC transversal operations can outperform surface code lattice surgery and enable efficient parallel computation with lower Bell pair consumption. Notably, we find that the non-local CNOT achieves up to an order of magnitude lower logical error rates than teleportation at the same code distance and noise levels. We further show that code distances of $d \approx 11$ at physical error rate $p \sim 10^{-4}$ and $d \approx 29$ at $p \sim 10^{-3}$, with $p_{\mathrm{ebit}}=10p$, are sufficient to achieve logical error rates below $10^{-12}$, enabling large-scale algorithms. These results provide critical guidance for architecture and code selection in distributed quantum computing.

We solve the dynamical Mordell-Lang problem in positive characteristic for automorphisms of projective surfaces.

We construct and give a complete classification of all the differential symmetry breaking operators $\mathbb{D}_{λ, ν}^{N,m}: C^\infty(S^3, \mathcal{V}_λ^{2N+1}) \rightarrow C^\infty(S^2, \mathcal{L}_{m, ν})$, between the spaces of smooth sections of a vector bundle of rank $2N+1$ over the $3$-sphere $\mathcal{V}_λ^{2N+1} \rightarrow S^3$, and a line bundle over the $2$-sphere $\mathcal{L}_{m, ν} \rightarrow S^2$ in the special case $|m| = N$.

Spin-orbit torque (SOT) presents a promising avenue for energy-efficient spintronics devices, surpassing the limitations of spin transfer torque. While extensively studied in heavy metals, SOT in antiferromagnetic quantum materials remains largely unexplored. Here, we investigate SOT in epitaxial FeSn, a collinear antiferromagnet with a kagome lattice. FeSn exhibits intriguing topological quantum features, including two-dimensional flat bands and Dirac-like surface states, making it an ideal platform for investigating emergent SOT properties. Using spin-torque ferromagnetic resonance, we uncover a six-fold symmetric damping-like SOT in epitaxial-FeSn/Py heterostructures, reflecting the six-fold symmetry of the epitaxial [0001]-oriented FeSn films. Additionally, we observe a substantial unconventional field-like torque, originating from spin currents with out-of-plane spin polarization. This torque exhibits a unique angular dependence-a superposition of six-fold crystalline symmetry and uniaxial symmetry associated with the antiferromagnetic spin Hall effect. Notably, the unconventional field-like torque is enhanced when the RF current flows along the Neel vector in FeSn. Our findings reveal an unconventional spin current anisotropy tunable by crystalline and magnetic symmetry, offering a novel approach for controlling SOT in antiferromagnetic spintronics.

Coherent nonlinear tripartite interactions are critical for advancing quantum simulation and information processing in hybrid quantum systems, yet they remain experimentally challenging and still evade comprehensive exploration. Here, we predict a nonlinear tripartite coupling mechanism in a hybrid setup comprising a single trapped electron and a nearby micromagnet. The tripartite coupling here leverages the electron's intrinsic charge (motional) and spin degrees of freedom interacting with the magnon modes of the micromagnet. Thanks to the large spatial extent of the electron zero-point motion, we show that it is possible to obtain a tunable and strong spin-magnon-motion coupling at the single quantum level, with two phonons simultaneously interacting with a single spin and magnon excitation. This enables, for example, magnons to mediate coupling among distinct degrees of freedom of two electrons, which can be used for the rapid preparation of few-body entangled states. This protocol can be readily implemented with the well-developed techniques in electron traps and quantum magnonics, and may open new avenues for quantum simulations and hybrid quantum information processing by introducing a versatile platform for exploring multipartite interactions and nonclassical state generation.

In the kagome superconductors AV3Sb5 (A=Cs,Rb,K), a cascade of correlated electron phases cause exotic symmetry-breaking quantum states. In particular, the dissipationless chiral loop-current phase has been attracting increasing attention. A crucial clue is offered by the chirality of the quasiparticle interference signal observed in scanning tunneling microscopy. However, the connection between loop-current chirality and quasiparticle interference chirality remains poorly understood. Here, we reveal theoretically that a pronounced chiral quasiparticle interference signal emerges in the extremely dilute impurity regime ($lesssim$ 0.1 %). A single impurity at site Z induces a quasiparticle interference chirality $χ_Z=\pm1$, determined by the direction of the Z3 nematicity, itself set by the relative position of the loop-current order in the star-of-David charge-density-wave phase. Notably, even a small magnetic field can smoothly switch the chirality, leading to field-induced shear lattice strain consistent with recent experiments. Our theoretical study provide key insights into the nature of the loop-current-induced symmetry-breaking states in kagome metals.

In this paper, we study several properties of Sasaki-Ricci solitons as singularity models of the Sasaki-Ricci flow. First, we establish several fundamental equations for Sasaki-Ricci solitons, which enable us to derive potential estimates and prove the positivity of the scalar curvature. Then we present two criteria for the transverse rigidity of Sasaki-Ricci solitons. As essential applications, we prove that any low-dimensional Sasaki-Ricci soliton with constant scalar curvature must be Sasaki-Einstein, and that any Sasaki-Ricci soliton with harmonic Weyl tensor is a finite quotient of the sphere.

We show the 2-Local Stoquastic Hamiltonian problem on a 2D square qubit lattice is StoqMA-complete. We achieve this by extending the spatially sparse circuit construction of Oliveira and Terhal, as well as the perturbative gadgets of Bravyi, DiVincenzo, Oliveira, and Terhal. Our main contributions demonstrate StoqMA circuits can be made spatially sparse and that geometrical, stoquastic-preserving, perturbative gadgets can be constructed, without an increase to particle dimension.

This paper introduces a direct differentiation-based framework that unifies the derivation of influence functions across parametric, nonparametric, and semiparametric models. We show that the Riesz representer of the functional derivative is obtained by orthogonally projecting the identification function onto the subspace of mean-zero functions. Consequently, the influence function emerges as a linear transformation of this centered moment function. The approach extends seamlessly to infinite-dimensional parameters, revealing a common algebraic form for influence functions across both finite- and infinite-dimensional parameters. Applied to semiparametric multi-step plug-in estimation, our method automatically yields locally robust moment functions and provides an explicit closed-form expression for the adjustment term. Finally, we leverage this framework to revisit the joint versus plug-in estimation debate, establishing verifiable sufficient conditions for their semiparametric efficiency equivalence even when nuisance parameters are over-identified.

We establish a semi-orthogonal decomposition for the weighted blowup of an algebraic stack along a Koszul-regular weighted centre, generalising the classic result of Orlov. Our approach is based on the work of Bergh-Schnürer.

Marine organisms manipulate their surrounding flow through their swimming dynamics, which affects the transport of their own odor cues. We demonstrate by direct numerical simulations how a group of swimmers, moving at intermediate Reynolds numbers, immersed in a turbulent flow, alter the shape of the odor plume they release in the water. Odor mixing is enhanced by increased velocity fluctuations and a swimmer-induced flow circulation that widens the odor plume at close range while speeding up dilution of the chemical trace. Beyond a short-range increase in the likelihood of being detected, swimming considerably reduces detections with effects that can persist at distances on the order of ten times the size of the group or more. We find that pullerlike swimmers are more effective at olfactory shielding than pusherlike swimmers. We trace this difference back to the dynamics at the swimmer location, which tends to trap odor at the source for pushers and to dilute it for pullers. Olfactory shielding is robust to changes in the conditions, and is more pronounced for weak turbulent Reynolds numbers and large swimmer Reynolds numbers. Our results suggest that olfactory shielding may play a role in the emergence of different swimming modalities by marine organisms.

Activity, which represents the kinetic property of dynamics, plays a central role in obtaining thermodynamic speed limits (TSLs). In this paper, we discuss a unified framework that provides the existing TSLs based on different activities such as dynamical activity and dynamical state mobility. This unification is based on generalized means that include standard means such as the arithmetic, logarithmic, and geometric means, the first two of which respectively correspond to the dynamical activity and the dynamical state mobility. We also derive an infinite variety of TSLs for Markov jump processes and deterministic chemical reaction networks using different activities. The lower bound on the entropy production given by each TSL provides the minimum dissipation achievable by a conservative force. We numerically and analytically discuss the tightness of the lower bounds on the EPR in the various TSLs.

Predictive processing theories propose that the brain continuously anticipates upcoming input. However, direct neural evidence for predictive pre-activation during natural language comprehension remains limited and debated. Previous studies using large language model (LLM)-based encoding models with fMRI and ECoG have reported pre-onset signals that appear to encode upcoming words, but these effects may instead reflect dependencies in the stimulus or autocorrelations in neural activity. Here, we re-examined this question by aligning LLM-derived word embeddings with neural activity recorded during naturalistic listening using magnetoencephalography (MEG) and electrocorticography (ECoG). We replicated pre-onset encoding effects previously observed in ECoG across both modalities, and found that they persist even after controlling for stimulus correlations. Crucially, temporal generalization analyses revealed no stable overlap between pre- and post-onset representations, indicating that pre-onset activity does not reflect pre-activation of the next word. Consistent with this, long-range predictive effects previously reported in fMRI did not replicate in our higher-temporal-resolution data. While we found no evidence for predictive pre-activation, we observed clear signatures of postdiction, with neural activity reflecting persistent encoding of prior words. These results suggest that reported apparent predictive signals do not reflect pre-activation of upcoming input. They call for caution in interpreting LLM-based encoding models and highlight the need for a more nuanced understanding of what constitutes "prediction" in language comprehension.

We prove that there exist functions $f,g:\mathbb{N}\to\mathbb{N}$ such that for all nonnegative integers $k$ and $d$, for every graph $G$, either $G$ contains $k$ cycles such that vertices of different cycles have distance greater than $d$ in $G$, or there exists a subset $X$ of vertices of $G$ with $|X|\leq f(k)$ such that $G-B_G(X,g(d))$ is a forest, where $B_G(X,r)$ denotes the set of vertices of $G$ having distance at most $r$ from a vertex of $X$.

Let $E/\mathbb{Q}$ be an elliptic curve. We study the behavior of the Tate--Shafarevich group of $E$ under quadratic extensions $\mathbb{Q}(\sqrt{D})/\mathbb{Q}$. By analyzing the cokernel of the restriction map, without assuming the finiteness of the Tate--Shafarevich group, we prove that the ratio $\frac{\#\Sha(E/\mathbb{Q}(\sqrt{D}))[4]}{\#\Sha(E_D/\mathbb{Q})[2]}$ and $\#\Sha(E_D/\mathbb{Q})[2]$ can, under some conditions on $E/\mathbb{Q}$, grow arbitrarily large simultaneously, where $E_D$ denotes the quadratic twist of $E$ by $D$. For elliptic curves of the form $E : y^2 = x^3 + px$ with $p\equiv 1 \bmod 4$ being an odd prime, assuming the finiteness of the relevant Tate--Shafarevich groups, we prove that $\#\Sha(E/\mathbb{Q}(\sqrt{D}))[2] \leq 4$ and $\Sha(E_D/\mathbb{Q})[2] = 0$ for infinitely many square-free integers $D$ with $-D$ being a prime number. Additionally, $\Sha(E/\mathbb{Q}(\sqrt{-D}))[2]\neq 0$ for all $D$ when $p=257$.

Among these, D-peptides are resistant to proteolysis, exhibit greater in vivo stability, and are easier to synthesize. Despite advances in deep learning for peptide discovery, the scarcity of natural D-protein data limits the transfer of existing generative models to the D-peptide chemical space. We propose D-Flow, a full-atom flow-based framework for de novo D-peptide design. Conditioned on receptor binding, D-Flow uses structural representations incorporating backbone frames, side-chain angles, and discrete amino acid types. A mirror-image algorithm is implemented to address the lack of training data for D-proteins by converting the chirality of L-receptors. Furthermore, we enhance D-Flow's capacity by integrating protein language models (PLMs) with structural awareness through a lightweight structural adapter that injects structural representations into PLM embeddings. This enables D-Flow to learn conformational priors in the D-peptide chemical space and to accommodate the chiral selectivity of binding sites, thereby mitigating the scarcity of D-peptide data. A two-stage training pipeline and a control toolkit enable D-Flow to transition from general protein design to targeted binder design while preserving pre-training knowledge. Results on the PepMerge benchmark show D-Flow's effectiveness. D-peptides generated by D-Flow align more closely with native sequences and structures, with sequence identity improving by 10.2% over the best baseline, and the top affinity score reaching 24.31%. Overall, D-Flow shows potential for D-peptide design, facilitating the development of bioorthogonal and stable molecular tools and diagnostics. Code is available at https://github.com/smiles724/PeptideDesign.

We consider a variant of the set covering problem with uncertain parameters, which we refer to as the chance-constrained set multicover problem (CC-SMCP). In this problem, we assume that there is uncertainty regarding whether a selected set can cover an item, and the objective is to determine a minimum-cost combination of sets that covers each item $i$ at least $k_i$ times with a prescribed probability. To tackle CC-SMCP, we employ techniques of enumerative combinatorics, discrete probability distributions, and combinatorial optimization to derive exact equivalent deterministic reformulations that feature a hierarchy of bounds, and develop the corresponding outer-approximation (OA) algorithm. Additionally, we consider reducing the number of chance constraints via vector dominance relations and reformulate two special cases of CC-SMCP using the ``log-transformation" method and binomial distribution properties. Theoretical results on sampling-based methods, i.e., the sample average approximation (SAA) method and the importance sampling (IS) method, are also studied to approximate the true optimal value of CC-SMCP under a finite discrete probability space. Our numerical experiments demonstrate the effectiveness of the proposed OA method, particularly in scenarios with sparse probability matrices, outperforming sampling-based approaches in most cases and validating the practical applicability of our solution approaches.

Among all materials, mono-crystalline diamond has one of the highest measured thermal conductivities, with values above 2000 W/m/K at room temperature. This stems from momentum-conserving `normal' phonon-phonon scattering processes dominating over momentum-dissipating `Umklapp' processes, a feature that also suggests diamond as an ideal platform to experimentally investigate phonon heat transport phenomena that violate Fourier's law. Here, we introduce dilute nitrogen-vacancy color centers as in-situ, highly precise spin defect thermometers to image temperature inhomogeneities in single-crystal diamond microstructures heated from ambient conditions. We analyze cantilevers with cross-sections in the range from about 0.2 to 2.6 $μ$m$^2$, observing a strong reduction of the cantilevers' conductivity as the width decreases. We use first-principles simulations based on the linearized phonon Boltzmann transport equation and viscous heat equations to quantitatively predict the cantilevers' thermal transport properties, rationalizing how the interplay between intrinsic and extrinsic phonon scattering mechanisms determines the observed non-diffusive behavior. Our temperature-imaging method paves the way for the exploration of unconventional, non-diffusive heat transport phenomena in devices and nanostructures of arbitrary geometries.

The decoy-state method is a prominent approach to enhance the performance of quantum key distribution (QKD) systems that operate with weak coherent laser sources. Due to the limited transmissivity of single photons in optical fiber, current experimental decoy-state QKD setups increase their secret key rate by raising the repetition rate of the transmitter. However, this usually leads to correlations between subsequent optical pulses. This phenomenon leaks information about the encoding settings, including the intensities of the generated signals, which invalidates a basic premise of decoy-state QKD. Here we characterize intensity correlations between the emitted optical pulses in two industrial prototypes of decoy-state BB84 QKD systems and show that they significantly reduce the asymptotic key rate. In contrast to what has been conjectured, we experimentally confirm that the impact of higher-order correlations on the intensity of the generated signals can be much higher than that of nearest-neighbour correlations.

In this paper, we prove a new Rogers-Ramanujan-type identity, involving grounded partitions, by computing a character of the affine Kac-Moody algebra $D_4^{(3)}$ in two different ways. The product side is derived using Lepowsky's product formula, while the sum side is obtained using perfect crystals with a technique of Dousse and Konan.

Assume that the generalized Ramanujan conjecture holds on the automorphic $L$-function $L(s, π)$ on $\GL_d$ over $\mathbb{Q}$ with $d\geq 3$, we can obtain a small log-saving non-trivial bound on the second integral moment of $L(1/2+it, π)$. Specifically the bound \[ \int_{T}^{2T}\Big|L\big(\frac{1}{2}+it, π\big)\Big |^2 \dd t\ll_π \frac{T^{\frac{d}{2}}}{\log^{η_d}T} \] holds for a small constant $η_d>0$.

We present the first complete two-loop calculation of the electric dipole moment of the electron, as well as the rates of the lepton-flavor violating decays $μ\to e + γ$ and $τ\to e/μ+ γ$, in the unconstrained two-Higgs doublet model. We include the most general Yukawa interactions of the Higgs doublets with the Standard Model fermions up to quadratic order, and allow for generic phases in the Higgs potential. A python implementation of our results is provided via a public git repository.

Large Language Models (LLMs) are transforming programming practices, offering significant capabilities for code generation activities. While researchers have explored the potential of LLMs in various domains, this paper focuses on their use in programming tasks, drawing insights from user studies that assess the impact of LLMs on programming tasks. We first examined the user interaction behaviors with LLMs observed in these studies, from the types of requests made to task completion strategies. Additionally, our analysis reveals both benefits and weaknesses of LLMs showing mixed effects on the human and task. Lastly, we looked into what factors from the human, LLM or the interaction of both, affect the human's enhancement as well as the task performance. Our findings highlight the variability in human-LLM interactions due to the non-deterministic nature of both parties (humans and LLMs), underscoring the need for a deeper understanding of these interaction patterns. We conclude by providing some practical suggestions for researchers as well as programmers.

Gaussian random fields (GFs) are fundamental tools in spatial modeling and can be represented flexibly and efficiently as solutions to stochastic partial differential equations (SPDEs). The SPDEs depend on specific parameters, which enforce various field behaviors and can be estimated using Bayesian inference. However, even under in-fill asymptotics, the likelihood only provides limited insights into the covariance structure. In response, it is essential to leverage priors to achieve appropriate, meaningful covariance structures in the posterior. This study introduces a smooth, invertible parameterization of the correlation length and diffusion matrix of an anisotropic GF and constructs penalized complexity (PC) priors for the model when the parameters are constant in space. The formulated prior is weakly informative, effectively penalizing complexity by pushing the correlation range toward infinity and the anisotropy to zero.

Polarization-entangled photon pairs are a widely used resource in quantum optics and technologies, and are often produced using a nonlinear process. Most sources based on spontaneous parametric downconversion have relatively narrow optical bandwidth because the pump, signal and idler frequencies must satisfy a phase-matching condition. Extending the bandwidth, for example to achieve spectral multiplexing, requires changing some experimental parameters such as temperature, crystal angle, poling period, etc. Here, we demonstrate broadband (tens of THz for each photon) generation of polarization-entangled photon pairs by spontaneous four-wave mixing in a diamond crystal, with a simple colinear geometry requiring no further optical engineering. Our approach leverages the quantum interference between electronic and vibrational contributions to the $χ^{(3)}$ tensor. Entanglement is characterized in a single realization of a Bell test over the entire bandwidth using fiber dispersion spectroscopy and fast single-photon detectors. The results agree with the biphoton wavefunction predicted from the knowledge of the $χ^{(3)}$ and Raman tensors and demonstrate the general applicability of our approach to other crystalline materials.

We prove that harmonic maps into Euclidean buildings, which are not necessarily locally finite, have singular sets of Hausdorff codimension 2, extending the locally finite regularity result of Gromov and Schoen. As an application, we prove superrigidity for algebraic groups over fields with non-Archimedean valuation, thereby generalizing the rank 1 $p$-adic superrigidity results of Gromov and Schoen and casting the Bader-Furman generalization of Margulis' higher rank superrigidity result in a geometric setting. We also prove an existence theorem for a pluriharmonic map from a Kähler manifold to a Euclidean building.