Materials deform elasto-plastically and fail under various loading conditions, typically quantified by the stress triaxiality, which is the ratio between the dilatational (hydrostatic) stress and the deviatoric (shear-like) one. We show that the elasto-plastic deformation of glasses approaching failure qualitatively differ for large and small stress triaxiality levels. Specifically, in the former limit, glasses reveal a strong hyperelastic (nonlinear elastic) response with minute plasticity, largely independently of the quenching rate across the glass transition. Yet, glassy disorder gives rise to significant elastic (reversible) nonaffine deformation, accompanied by the formation of micro-cavities. A small fraction of the latter is irreversible, i.e., survives unloading prior to the onset of failure, and may serve as nucleation sites for failure in the form of large-scale cavitation, involving a topological transition accompanied by the formation of an internal free surface, upon which the glass loses a significant fraction of its load-bearing capacity. These results are contrasted with glass behavior in the limit of vanishing stress triaxiality and their universality across different glass formers is demonstrated. Finally, the implications of our findings for understanding glass deformation and failure under realistic stress conditions are discussed.

We extend the Weak Adversarial Neural Pushforward Method (WANPM) to fractional Fokker-Planck equations, in which the classical Laplacian diffusion operator is replaced by the fractional Laplacian of order alpha in (0, 2]. The solution distribution is represented as the pushforward of a simple base distribution through a neural network, and the weak formulation is discretized entirely via Monte Carlo sampling without any temporal mesh. A key computational advantage is that plane-wave test functions are eigenfunctions of the fractional Laplacian, making the operator cost identical to that of classical diffusion for any alpha. We validate the method on seven benchmark problems with alpha = 1.5, spanning one and two spatial dimensions: the steady-state fractional Ornstein--Uhlenbeck (OU) process, a harmonic confining potential, a double-well potential, and a triple-well potential in one dimension, a steady-state 2D double-peak distribution, a time-dependent 2D ring distribution with rotational drift, and a five-dimensional harmonic potential. Each case is benchmarked against particle simulations using symmetric alpha-stable Lévy increments, and robust statistics confirm close agreement throughout. The method is mesh-free, requires no density evaluation or non-local quadrature, and provides a promising foundation for high-dimensional anomalous diffusion solvers.

Quantum oscillation with nontrivial Berry phase is one of the characteristics of topological materials. As a Dirac semimetal candidate, zirconium pentatelluride ($\text{ZrTe}_5$) stands out as an intriguing material for investigating topological phase transitions and Dirac fermion physics; however, the extreme sensitivity of its electronic properties to stoichiometric variations and crystalline defects has hindered consistent experimental observation. Here, we report an optimized Te-flux synthesis method designed to produce centimeter-scale, high-quality single crystals meanwhile minimizing extrinsic carrier contamination. Comprehensive morphology, structural and chemical characterizations, including scanning electron microscopy, Laue backscattering and Rietveld refinement, confirm a high-purity $Cmcm$ phase with excellent crystallinity. Furthermore, magnetotransport measurements reveal a remarkably low Shubnikov-de Haas oscillation onset field ($B_{int} \approx 0.38$ T) with an ultra-high mobility of $5.58\times10^5$cm$^2$V$^{-1}$s$^{-1}$ and access to the the quantum limit at $B \approx 1.3$ T, attesting to the superior crystalline quality and the efficacy of this growth optimization. These results demonstrate that growth control is crucial for stabilizing intrinsic electronic behavior in $\text{ZrTe}_5$, establishing a robust platform for exploring topological phase transitions and exotic quantum phenomena in topological semimetals.

The need to reduce datacenter carbon footprint is urgent. While many sustainability techniques have been proposed, they are often evaluated in isolation, using limited setups or analytical models that overlook real-world dynamics and interactions between methods. This makes it challenging for researchers and operators to understand the effectiveness and trade-offs of combining such techniques. We design OpenDC-STEAM, an open-source customizable datacenter simulator, to investigate the individual and combined impact of sustainability techniques on datacenter operational and embodied carbon emissions, and their trade-off with performance. Using STEAM, we systematically explore three representative techniques - horizontal scaling, leveraging batteries, and temporal shifting - with diverse representative workloads, datacenter configurations, and carbon-intensity traces. Our analysis highlights that datacenter dynamics can influence their effectiveness and that combining strategies can significantly lower emissions, but introduces complex cost-emissions-performance trade-offs that STEAM can help navigate. STEAM supports the integration of new models and techniques, making it a foundation framework for holistic, quantitative, and reproducible research in sustainable computing. Following open-science principles, STEAM is available as FOSS: https://github.com/atlarge-research/OpenDC-STEAM.

Topological flat bands (FBs) offer an ideal platform for realizing exotic topological phases, such as fractional Chern insulators, yet their realization with both exact flatness and stable topology in local lattice models has been long hindered by fundamental no-go theorems. The obstruction to topological FBs is also manifested as the absence of exact Gaussian tensor-network state (TNS) representations for topological insulators and superconductors. Here, we overcome this barrier by demonstrating the existence of critical topological FBs (CTFBs) in finite-range hopping models. They saturate the no-go theorems via a unique structure of Bloch wavefunctions: While continuous over the whole Brillouin zone, the projector $P(\mathbf{k})$ onto FBs are non-analytic at isolated band touching points, thereby relaxing the inherent restrictions on the coexistence of exact flatness and stable topology. We establish a general principle to construct CTFBs, as well as their parent Hamiltonians, that carry desired topological invariants in given space groups. Explicit examples exhibiting Chern numbers 1, 2, 3 in 2D, strong $\mathbb{Z}_2$ index in 2D, and strong $\mathbb{Z}_2$ index in 3D are provided. Furthermore, an automated algorithm identifies more than 50,000 symmetry-indicated CTFBs. Achieved without fine-tuning, these FBs host nontrivial topology that is robust against arbitrary symmetry-preserving perturbations such as gap-opening terms. Filling such CTFBs yields short-range entangled topological states that exhibit power-law correlations. Crucially, all filled CTFB states admit exact TNS representations with finite bond dimensions, providing a tractable starting point for exploring strongly correlated topological matter.

We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for compact-group representations on Banach spaces, and relies in part on Riemann-Lebesgue-type decay properties for Fourier coefficients of elements in minimal tensor products with compact-quantum-group function algebras.

We revisit quantum tomography of $H \to ZZ$ and $H \to WW$ in the presence of higher-order corrections. We verify that neither the use of an effective spin analysing power (only for $ZZ$) or a photon veto are sufficient to render the naively-constructed spin density operators physical. A subtraction of higher-order corrections is thus necessary to perform consistent quantum tomography. Such corrections are small when compared to expected experimental uncertainties with current data. As a by-product, we point out the striking possibility to observe parity-violating effects in $H \to WW$.

We prove that the kissing number in 19 dimensions is at least 11948, improving the bound of Cohn and Li by 256. By the odd-sign construction of Cohn and Li, it is enough to find a binary code of length 19 and minimum distance 5 inside the ambient 5-punctured extended binary Golay code. We construct such a code explicitly, of size 1280. The construction is organized around a chain of linear codes $M\le K\le D$, $|M|=64$, $|K/M|=16$, and $|D/K|=4$. The 21 words of $D$ of weight 3 or 4 lie in exactly five nonzero $M$-cosets inside $K$. Those five cosets define a Cayley graph on $K/M\cong\mathbb F_2^4$ with connection set $\{e_1,e_2,e_3,e_4,e_1+e_2+e_3+e_4\}$, hence the Clebsch graph. A 5-coclique in that quotient lifts first to a 320-word code in $K$ and then, by taking all four cosets of $K$ in $D$, to the desired 1280-word code.

Observational evidence, together with practical computations and modeling, supports a Euclidean spatial sector in the current cosmological model based on the FLRW metric. This, however, would imply that the total amount of matter and energy immediately after the Big Bang must have been infinite, an implication that could only be avoided through a transition from a closed to an open universe, a process forbidden in standard FLRW models. In this article, we investigate the spacetimes resulting from promoting the spatial curvature $k$ in FLRW spacetimes to a time-dependent function, $k \to k(t)$, allowing it to change sign and thereby allowing changes in the topology of the constant-$t$ slices. Although previously dismissed due to a classical theorem by Geroch, such transitions are shown to be consistent with global hyperbolicity when the comoving time is distinct from a Cauchy time, as recent work by one of the authors demonstrates. We construct three distinct geometries exhibiting this behavior using different representations of constant-curvature spaces. We analyze their global properties and identify mild conditions under which they remain globally hyperbolic. Furthermore, we characterize their Killing vectors, proving a general result for spherically symmetric spacetimes and compare them with known geometries in the literature.

As Large Language Models (LLMs) scale to handle massive concurrent traffic, optimizing the infrastructure required for inference has become a primary challenge. To manage the high cost of GPU resources while ensuring strict service-level objectives (SLOs), operators increasingly deploy models across heterogeneous hardware clusters that multiplex latency-sensitive online requests and throughput-oriented offline requests. However, traditional resource-centric autoscalers like the Kubernetes horizontal pod autoscaler (HPA) do not consider application-specific SLOs, hardware heterogeneity, or internal engine state (like KV cache utilization) globally. This leads to unnecessary scaling, severe resource underutilization, and disrupted stateful inference. To address these limitations, we introduce the Workload Variant Autoscaler (WVA), a specialized control plane co-designed with \texttt{llmd} that tightly couples scaling decisions with the inference server's internal saturation state. By utilizing proactive headroom-based scaling and fragmentation-aware scale-down, our experiments demonstrate that WVA achieves a \textbf{37\% improvement in effective throughput} and a \textbf{10x reduction in request failures} compared to HPA. Furthermore, WVA's cost-aware tiering intrinsically reduces overall power consumption by prioritizing lower-cost, energy-efficient hardware variants over homogeneous scaling on high-end accelerators.

Unravelling two-electron correlation is a long-standing challenge at the heart of few-body quantum physics, underlying correlated phenomena across atomic, molecular and condensed-matter science. In prototypical three-body Coulomb systems, such strong correlation in doubly excited states (DESs) of planetary atomic systems leaves distinct signatures in nonsequential above-threshold double ionization (NS-ATDI) driven by coherent laser fields, yet such targeted study has long remained elusive. Here we present kinematically complete measurements of multi-photon double ionization in cold strontium atoms. Our results reveal a dominant NS-ATDI channel exhibiting well-defined band structures that encode pronounced energy and angular correlations between the two emitted electrons. Autoionization spectra confirm the presence of DESs as transition states that effectively promote the NS-ATDI process. These observations provide direct evidence that both electrons are synchronously excited and ionized via resonant high-lying DES transitions, meaning the structure-linked two-electron correlation of DES is preserved and propagated in the laser-driven time-dependent three-body system. Our work transcends the traditional paradigm of multi-photon double ionization, and fundamentally reshapes the core understanding of intrinsic electron correlation governing many-body systems in nature.

Stepsize selection remains a critical challenge in the practical implementation of distributed optimization. Existing distributed algorithms often rely on restrictive prior knowledge of global objective functions, such as Lipschitz constants. While centralized Polyak stepsizes have recently gained attention for their parameter-free adaptability and fast convergence. However, their extension to distributed settings is hindered by the requirement for local function values at the global optimum, which are typically unavailable to individual agents. To bridge this gap, we design a novel distributed adaptive Polyak stepsize algorithm with level-value adjustment (DPS-LA), where each agent only needs to solve a computationally efficient linear feasibility problem, thereby eliminating the dependency on global optimal values. Theoretical analysis proves that DPS-LA guarantees network consensus and achieves a linear speedup convergence rate of $\mathcal{O}(1/\sqrt{nT})$. Numerical results confirm the efficiency of the proposed algorithm.

In this paper, we study congruences of Hecke eigenvalues between Hermitian Klingen-Eisenstein series and cusp forms on the unitary group $\mathrm{U}_{n,n}$ defined over the rational number field $\mathbb{Q}$. We also prove the rationality of the space of Hermitian automorphic forms and the integrality of their Hecke eigenvalues.

The NIST Handbook of Mathematical Functions (2010) and the NIST Digital Library of Mathematical Functions (2025) classify classical orthogonal polynomials through Bochner's 1929 algebraic-differential characterisation and its discretisation. Yet this classification rests on a narrow reading of Bochner's work and on a restricted notion of orthogonality that becomes inadequate once polynomials are characterised by their algebraic properties. As a result, algebraically equivalent families are treated as distinct, parameter domains are restricted, and families already implicit in Bochner's scheme are excluded. In the mid-1980s, Maroni challenged this view by extending the notion of classical orthogonal polynomials through duality theory on locally convex spaces, thereby reaching the algebraic limits latent in Bochner's framework. Yet when the notion was later enlarged to include further families, Maroni's criteria and rationale were largely set aside. To clarify this history, we revisit a less familiar line of development and use it to obtain a classification of classical orthogonal polynomials on linear lattices within Maroni's functional-analytic setting, beyond the positive-definite case. This classification recovers all known families as special cases, preserves orthogonality and the defining algebraic properties, places supposedly new families in their proper structural context, and shows that algebraically identical polynomials are often treated as distinct. Moreover, through a limit process in the weak topology of the continuous dual, we recover families implicit in Bochner's work and unify the continuous and discrete cases within a dual-topological framework. Thus, neither Bochner's classical characterisation nor its discrete analogue is modified to produce ad hoc families; both are recovered at the level of their intrinsic algebraic structure.

IT systems are facing an increasing number of security threats, including advanced persistent attacks and future quantum-computing vulnerabilities. The move towards crypto-agility and post-quantum cryptography (PQC) requires a reliable inventory of cryptographic assets across heterogeneous IT environments. Due to the sheer amount of packets, it is infeasible to manually detect cryptographically relevant software. Further, static code analysis pipelines often fail to address the diversity of modern ecosystems. Our research explores the use of large language models (LLMs) as heuristic tools for cryptographic asset discovery. We propose a collaborative framework that employs multiple LLMs to assess software relevance and aggregates their outputs through majority voting. To preserve data privacy, the approach operates on-premises without reliance on external servers. Using over 65,000 Fedora Linux packages, we evaluate the reliability of this method through statistical analysis, inter-model agreement, and manual validation. Preliminary results suggest that~LLM ensembles can serve as an efficient first-pass filter for identifying cryptographic software, resulting in reduced manual workload and assisting PQC transition. The study also compares on-premises and online LLM configurations, highlighting key advantages, limitations, and future directions for automated cryptographic asset discovery.

We investigate static, spherically symmetric black hole spacetimes induced by the spontaneous Lorentz--symmetry breaking of a Kalb--Ramond (KR) two--form field, non--minimally coupled to gravity, coexisting with an anisotropic fluid. By adopting a general equation of state where the radial pressure relates to the energy density via $w_1 = -1$ and the tangential pressure via an arbitrary parameter $w_2$, we derive exact analytical solutions representing black holes surrounded by diverse matter fields, including dust ($w_2=0$), radiation ($w_2=1/3$), and dark energy--like distributions ($w_2=-1/2$). A rigorous analysis of curvature invariants confirms a genuine core singularity, while the global geometry and adherence to standard energy conditions are shown to be highly sensitive to the interplay between the KR coupling ($\ell$), the fluid density parameter ($K$), and $w_2$. Furthermore, we analyze null geodesics in detail to determine the photon sphere and shadow radii. Using the Gibbons--Werner geometrical approach and the Gauss-Bonnet theorem applied to the optical metric, we compute the weak deflection angle of light and demonstrate that both the KR field and the anisotropic fluid significantly enhance light bending, particularly in dark--energy--like backgrounds. In the strong deflection limit (SDL), we calculate the lensing observables--$θ_\infty$, $s$, and $r_{\mathrm{mag}}$--for the supermassive black holes Sgr A* and M87*. Using EHT observations, we obtain constraints on the model parameters: for dust ($w_2=0$), the data of Sgr A* restricts $0\le \ell \le 0.065$ and $0\le K \le 0.04$, while for radiation ($w_2=1/3$), $K$ lies in $0.65\le K \le 0.85$ with $\ell$ unconstrained. We also derive similar bounds from M87*.

Automated Vulnerability Repair (AVR) systems, especially those leveraging large language models (LLMs), have demonstrated promising results in patching vulnerabilities -- that is, if we trust their patch validation methodology. Ground-truth patches from human developers often come with new tests that not only ensure mitigation of the vulnerability but also encode extra semantics such as root cause location, optimal fix strategy, or subtle coding styles or conventions. And yet, none of the recent AVR systems verify that the auto-generated patches additionally pass these new tests (termed as $\text{PoC}^+$ tests). This is a subtle yet critical omission. To fill this gap, we constructed a benchmark, $\textrm{PVBench}$, with 209 cases spanning 20 projects. Each case includes basic tests (functional tests before the patch and the PoC exploit) as well as the associated $\text{PoC}^+$ tests. Evaluated on three state-of-the-art AVR systems, we find that over 40\% of patches validated as correct by basic tests fail under $\text{PoC}^+$ testing, revealing substantial overestimation on patch success rates. Analyzing these patches that are falsely labeled as correct, we suggest that AVR tools should improve in three critical areas: root cause analysis, adherence to program specifications, and capturing developer intention.

We consider the following Choquard equation $$ -Δ_γu + u = \left(d(z)^{-μ} \ast |u|^p\right)|u|^{p-2}u, \text{ in } \mathbb{R}^N, $$ where $Δ_γ$ is the Grushin operator. For a suitable range of the parameter $p$ we prove the existence of a mountain pass solution of the equation and we establish that the solution belongs to $L^q(\mathbb{R}^N)$ for all $q\in [2,\infty]$ and to $C^{0,α}_{\textrm{loc}}(\mathbb{R}^N)$ for some $α\in (0,1)$. Additionally, we provide a Poho\v zaev type identity, which allows us to derive a nonexistence result for smooth solutions to our equation.

A system of spins coupled to a bath is a traditional setup in open quantum systems. Through Heisenberg's equation, the spin dynamics can be modeled by a set of first-order differential equations. Interpreting the terms as colored noise and non-Markovian damping, one can write them as quantummechanical Heisenberg-Langevin (HL) equations. These are notoriously difficult to solve because of the high dimensionality of the Hilbert space. Classical generalized Langevin equations, involving non-Markovian damping and colored noise, are well understood and can be treated numerically with relative ease. Thus, a classical ansatz can be made by substituting quantum expectation values with classical functions. This allows the application of standard methods developed for classical stochastic dynamical systems to tackle spin dynamics. However, this approach is uncontrolled and should be benchmarked against known quantum dynamics. In this investigation, a Hamiltonian for spin dynamics is modified to obtain a setup analogous to the Weisskopf-Wigner (WW) theory of spontaneous emission, enabling a comparison of the results. This will be compared for T = 0 and with a slight adaptation in the high-temperature limit.

The conventional description of transport through the interface between a normal conductor and a superconductor reduces the system to a one-dimensional problem treating Andreev reflection based on a zero-dimensional Sharvin type point-contact model, and effectively neglects all considerations of device geometry. While this has been successful in systems where conductance in the normal material is in the diffusive transport regime, such an over-simplification of the problem fails in other transport regimes. In particular, when transport is ballistic as in a typical semiconductor-superconductor hybrid structure, geometrical effects are inherently important, and a proper description must consider a one-dimension contact injecting into a two-dimensional ballistic cavity. We present the first study of this regime and explore the bias-voltage dependence of Andreev transport in a cavity-type device comprised of a high mobility HgTe quantum well side-contacted by one superconducting and one normal contact, each creating a one-dimensional interface. The enhanced conductance from Andreev transport features two finite bias conductance peaks, observed at energies within the energy gap of the superconductor. Interestingly, these two peaks respond differently to the application of a perpendicular-to-plane magnetic field. Using a semi-classical model for the quantum transport within the cavity, we are able to attribute each peak to a different class of ballistic trajectories. One class is dominated by normal reflection, and its interference condition is independent of magnetic field, whereas the other one contains retro-reflected Andreev processes at the superconductor interface. These create closed trajectories that are strongly suppressed by magnetic field due to Aharonov-Bohm and Doppler shift effects.

The cosmohedron was recently proposed as a polytope underlying the cosmological wavefunction for $\text{Tr}(Φ^3)$ theory. Its faces were conjectured to be in bijection with Matryoshkas, which are obtained from a subdivision of a polygon by sequentially wrapping groups of polygons into larger polygons. In this paper we prove the correctness of this construction, and elucidate its combinatorial structure. Cosmohedra generalize to a wider class of $\mathcal{X}$ in $Y$ polytopes, where we chisel a polytope from the family $\mathcal{X}$ at each vertex of a polytope $Y$. We sketch a new application of these chiseled polytopes to the physics of ultraviolet divergences in loop-integrated Feynman amplitudes.

Objective: The percentage of long-term survival in out of hospital cardiac arrest cases is remarkably low. One approach would be to increase the effectiveness of cardiopulmonary resuscitation (CPR), which is currently not measurable in a quantifiable way. The most significant challenge in providing a mobile solution for CPR evaluation is a mobile, hazard free sensor attachment with high usability. Methods: We present a sensor attachment solution usable for semiautomatic ultrasonic (US) Doppler measurements. Components are attached to a Stifneck Select Collar$^{\mathrm{TM}}$ (Laerdal). An inflatable cushion (TR-Band$^{\mathrm{TM}}$, Terumo) allows adjustable contact pressure. A clinical study was conducted in which the system was evaluated based on comfort, pain, sensor support, the viability of Doppler signals, and the absence of skin irritations. Results: The system was utilized in a prospective study involving 102 healthy probands. On a scale between 1 (Low) and 10 (Intense), ratings were 1.19 (SD 0.46), 6.52 (SD 1.78), and 9.95 (SD 0.32) for pain, comfort, and support, respectively. The average duration of application was 31.19 minutes (SD 16.75 minutes). Audible Doppler signals were achieved in 92.2 % of the probands, and Doppler curve evaluation was usable in 73.5 %. No skin irritations were observed. Conclusion: A hands free sensor attachment for a US probe was developed that caused no significant complaints by healthy study volunteers. Medical users assessed its attachment as robust. Significance: With its adjustable positioning and easy attachment, the Stifneck modification can form a basis for a mobile US Doppler device, capable of evaluating carotid artery flow during CPR.

Sub-GeV thermal dark matter weakly interacting with the Standard Model through vector-portal mediators provides a well-motivated and predictive framework that remains challenging to probe with conventional direct detection experiments. Motivated by the rapid development of neutrino facilities based on spallation neutron sources, we study the sensitivity of future coherent elastic neutrino-nucleus scattering experiments to light dark matter produced in neutral pion decays. We consider scalar dark matter interactions mediated by two different vector portals, a generic dark photon and a baryophilic vector mediator. The neutral pion yield is calculated through a GEANT4 simulation and the results are compared with those obtained with the Sandford-Wang parametrization. We show that predictions based on either approach do not produce significant differences. Our results demonstrate that upcoming low-threshold neutrino detectors at the European Spallation Source (ESS), the Japan Proton Accelerator Research Complex (J-PARC) and the China Spallation Neutron Source (CSNS) may test regions in parameter space not yet explored, or be competitive with existing bounds. We point out that these facilities will strengthen the global experimental program searching for secluded sectors.

The relation between the effective degrees of freedom (EDOF) and the trace anomaly is studied in the hadron resonance gas (HRG) model. If we regard the thermodynamical relation as the evolution equation and define the EDOF as P/T^4, where P and T are the pressure and the temperature, respectively, we obtain the equation which relates to the trace anomaly. The structure of the equation resembles that of the so-called c-theorem, which asserts that the EDOF should not increase as the energy scale parameter decreases, in the two dimensional conformal field theory. There is a stationary point where the trace anomaly (modified trace anomaly) vanishes, and the scale symmetry is restored. To investigate the limiting temperature of the HRG model with the excluded volume effects, we consider two types of the c-theorem like conditions for the EDOF. The first condition requires that the EDOF should not decrease when T increases. This condition is equivalent to the condition that the trace anomaly (modified trace anomaly) should not be negative. The second condition requires that the EDOF should be convex downwards as a function of T. It is found that the first condition gives the limiting temperature of the HRG model with the excluded volume effect which is much higher than the crossover transition temperature obtained by the lattice QCD calculation and, at zero baryon number density, is close to the transition temperature in the pure gluonic theory, while the second one gives the limiting temperature which almost coincides with the one obtained by using the normalized baryon number fluctuation in the previous study and is consistent with the critical point predicted by the lattice QCD calculation.

Distributed quantum computing (DQC) is being actively investigated as a means of scaling the number of qubits across multiple connected quantum devices. This includes quantum circuit compilation and execution management on multiple quantum devices in the network. The latter aspect is very challenging because, while reducing the makespan of job batches remains a relevant objective, novel quantum-specific constraints must be considered, including QPU utilization, non-local gate rate, and the latency associated with queued DQC jobs. In this work, a range of scheduling strategies is proposed, simulated, and evaluated, including heuristics that prioritize resource maximization for QPU utilization, node selection based on heterogeneous network connectivity, asynchronous node release upon job completion, and a scheduling strategy based on reinforcement learning with proximal policy optimization. These approaches are benchmarked against traditional FIFO and LIST schedulers under varying DQC job types and network conditions for the allocation of DQC jobs to devices within a network.

In this paper, we introduce a translation that combines the $j$-translation with Kripke forcing in the internal logic of an elementary topos. First, we show that our translation is sound for intuitionistic first-order logic and Heyting arithmetic. Furthermore, its interpretation in the effective topos provides an extension of the sheaf model of realizability introduced by de Jongh and Goodman. As an application, we systematically investigate translations for semi-classical axioms. Based on this investigation, we establish a separation result on semi-classical arithmetics, which cannot be obtained using the usual $j$-realizability.

We theoretically study surface superconductivity in a nodal-line semimetal by combining a minimal tight-binding model with a layer-resolved Bogoliubov-de Gennes approach. In the normal state, the model realizes a bulk nodal loop and an associated drumhead surface band in a slab geometry with open boundaries in the $z$ direction: the central layers reproduce the bulk-like density of states, whereas the surface layer exhibits a sharp zero-energy peak originating from the drumhead states. On top of this band structure we introduce chiral $p$-wave and $d_{x^2-y^2}$-wave superconducting channels and determine the layer-dependent gap amplitudes self-consistently. The chiral $p$-wave order parameter is strongly enhanced at the outermost layers and decays within only a few layers towards the interior, while the $d$-wave order parameter is more than an order of magnitude smaller on all layers. The quasiparticle dispersion and surface local density of states in the chiral $p$-wave state show that the drumhead band is efficiently gapped out and that the zero-energy peak in the normal surface spectrum is split into two coherence peaks, directly reflecting the induced superconducting gap. These results demonstrate that superconductivity driven by drumhead surface states is naturally biased toward a surface-localized chiral $p$-wave pairing symmetry and may offer qualitative guidance for interpreting surface-sensitive experiments on Pd-doped CaAgP.

We generalize the seminal framework of Kyle (1985) to a many-asset setting, bridging the gap between informed-trading theory and modern trading practices. Specifically, we formulate an infinite-dimensional Bayesian trading game in which the informed trader's private information may concern arbitrary aspects of the cross-sectional payoff structure across a continuum of traded assets. In this general setting, we obtain a parsimonious equilibrium characterized by a single scalar fixed point, which yields closed-form characterizations of equilibrium trading strategy, price impact within and across markets, and the information efficiency of equilibrium prices.

In this article, we demonstrate the phenomenon of thermal transpiration in a bounded convex domain. We employ the stationary Boltzmann equation with a cutoff potential. For boundary condition, we partition the boundary into diffuse reflection and incoming regions. We establish the existence of solution in a weighted $L^\infty$ space. Furthermore, we consider a convex domain with diffuse reflection boundary condition in the middle and incoming boundary condition at the two ends. We first consider Maxwellians with the same pressure but different temperatures at the two ends. We prove that the total flux $U(x)$ is directed toward the hot end. Furthermore, we derive an estimate for the total flux: \begin{align} U(x)\geq C\left(1-\frac{1}{\sqrt{T_2}}\right). \end{align} In addition, we show that when the pressures and temperatures on the two ends satisfy the relation \begin{align} \frac{P_1}{P_2}=\sqrt{\frac{T_1}{T_2}}, \end{align} the total flux of the solution is of order $\mathcal{O}(\frac{1}κ)$. This result is consistent with Knudsen's finding of thermomolecular pressure difference in 1909.

We study topology, particularly compactness, as an extension of Shulman's work on constructive mathematics via affine logic, while allowing propositional impredicativity. We introduce a notion of compactness in affine logic and prove the fundamental properties of compactness, including the extreme value theorem and the Heine-Borel theorem for 'cuts', which are a version of Dedekind cuts in affine logic. Moreover, from the antithesis translation of the Heine-Borel theorem for cuts to intuitionistic logic, we derive the Heine-Borel theorem for one-sided reals intuitionistically, and have verified the proof with an interactive theorem prover. The code is available at https://github.com/hziwara/CutsHeineBorel.