Given a non-zero polynomial $P(x)$, we study Fuchsian differential operators of the form $L=\partial_x^2-u(x)$ such that for all $λ\in\mathbb{C}$ the operator $L+λP(x)$ is monodromy free. We prove that all such operators are obtained from populations of critical points of ${\widehat{\mathfrak{sl}}_2}$ master functions. Moreover, we show that the reproduction procedure of critical points corresponds to a Darboux transformation of operator $P^{-1}(x)L$. As a result, we obtain a classification of all operators $L$ with such properties in the case of $P(x)=x^k$.

Neural Architecture Search (NAS) has become an important approach for automatically designing neural networks under task-specific and hardware-specific constraints. However, many existing NAS frameworks tightly couple search space definitions, model implementations, and deployment pipelines, making extension to new hardware platforms and custom operators difficult. In this paper, we present the elasticAI.explorer, an extensible Python framework for hardware-aware NAS built on top of Optuna. The framework introduces a YAML-based search space specification that dynamically translates into executable neural network models during sampling. The approach supports layer-wise, cell-based, and hierarchical search spaces while maintaining a unified interface for optimization and deployment. Beyond architecture generation, the framework integrates hardware-specific code generation, Docker-based cross-compilation toolchains, and automated creation of on-device benchmarking binaries, enabling hardware-in-the-loop NAS workflows. The system further provides extensible evaluators for FLOPs, parameter count, and latency estimation. The elasticAI.explorer aims to reduce the engineering overhead of embedded AI deployment and accelerate research on hardware-aware NAS for heterogeneous accelerator platforms

1D-CNNs play a crucial role for time-series analysis on tiny smart sensor systems, e.g. for biosignal analysis, predictive maintenance, or structural health monitoring. LUTbased precomputation has emerged as an interesting optimization technique to implement such neural networks on FPGAs. The core idea is to precompute all possible outputs of a neural network layer and store them directly in the lookup tables of the FPGAs. This enables highly resource-efficient networks with ultra-low latency but suffers from poor scalability. Previous work has explored using depthwise-separable convolutions to improve scalability. In this paper, we generalize this approach to consider additional forms of grouped convolutions. Based on this, we propose a novel type of convolutional block and an algorithm to guide the choice of hyper parameters for this block. We evaluate our approach on a medical time-series dataset for predicting atrial fibrillation using the MIT-BIH database (ECG recordings). The resulting hardware accelerators are small enough to be deployed on an AMD Spartan 7 S15. They achieve a F1-Score of up to 95% while only requiring 2,844 LUTs and no DSPs or BRAM.

We study the complex spectrum of the partial theta function \[ Θ(q,x)=\sum_{j=0}^{\infty}q^{j(j+1)/2}x^j, \qquad |q|<1, \] where a spectral value is a parameter for which \(Θ(q,\cdot)\) has a multiple zero. Since the function is defined here only for \(|q|<1\), all spectral values are strictly inside the unit disk; boundary points on \(|q|=1\) occur only as accumulation points of the spectrum. The paper combines two complementary points of view. Near the unit circle we prove that every point of \(|q|=1\) is an accumulation point of the spectrum; the proof uses explicit spectral factors of truncations, the Jacobi triple product, and a boundary-window lifting argument near roots of unity. Inside a fixed subdisk, illustrated for \(|q|\leq 0.8\), the true spectrum is locally finite and must be separated carefully from the much larger branch loci of truncations and Jensen polynomials. We give a truncation-seeded Newton procedure which produces a discrete list of candidate spectral values, explain the caustic/escaping-root mechanism in finite approximants, and record numerical monodromy experiments using a radial convention: for a spectral point \(q_*\), roots are labelled at the point \(0.1q_*/|q_*|\) on the small circle and then continued along the straight radial segment to \(q_*\). This convention gives a coherent set of collision labels in the disk, treats negative real spectral values from the base point \(-0.1\), and leads to a preliminary rational-direction heuristic for radial monodromy.

Let $X$ be a proper smooth rigid analytic variety over a complete algebraically closed field $p$-adic field $\mathbf C$. Fix an continuation $\mathrm{Exp}$ of $\exp$. Faltings (in the curve case) and Heuer showed that any lifting $\widetilde X$ of $X$ over $\mathbf{B}_{\rm dR}^+/t^2$ induces an equivalence bewteen the category of Higgs bundles on $X_{\mathrm{\acute{e}t}}$ and the category of $v$-bundles on $X_v$. In this paper, we aim to study how the equivalence depends on the choice of such a lifting $\widetilde X$ when $X$ is a curve of genus $g\geqslant 2$. More precisely, we call a Higgs bundle lift-independent if it always corresponds to the same $v$-bundle under $p$-adic Simpson correspondence with respect to any lifting $\widetilde X$ and then we will show that (1) There exists some $r(g)\geqslant \sqrt{g-1}$ such that any semistable lift-independent Hitchin-small Higgs bundle of rank $r\leqslant r(g)$ has zero Higgs field. (2) There always exists a semistable Higgs bundle of degree $0$ with non-zero Higgs field that is lift-independent.

We propose and demonstrate a dynamical mirror compensation scheme to restore velocity immunity in a large-area dual-atom-interferometer gyroscope. In an ideal Mach-Zehnder configuration, the phase shift is inherently immune to atomic velocity, but this property is broken by the Earth's rotation via the Coriolis effect. We overcome this by actively rotating the Raman mirrors during the pulse sequence to cancel the time-dependent angular offset. The implementation relies on a decouplable calibration-compensation chain to remove rotation-induced time-dependent terms. The scheme is validated on a dual-atom-interferometer gyroscope with an interference area of 21.1 cm^2. After compensation, the phase's dependence on atomic velocity is reduced 40-fold, and the velocity contribution to scale-factor stability is evaluated to be 0.13 ppm. The sensor achieves a rotation sensitivity of 1.3\times10^{-8} rad/s/Hz^{1/2} and a stability of 1.9\times10^{-10} rad/s at 4500 s integration, together with a common-mode noise rejection ratio of up to 459, demonstrated in a seismic event. This work removes a key obstacle to scale-factor stabilization in atom-interferometer gyroscopes and paves the way for their applications in inertial navigation and geophysics.

This work presents a high-resolution X-ray microtomography system that uses commercial off-the-shelf (COTS) CMOS image sensors as direct detectors, relying on the sensor s intrinsic resolution to achieve tomographic reconstructions without optical components. The system employs a microfocus X-ray source in cone-beam geometry, enabling both absorption-contrast and propagation-based phase-contrast imaging. A dynamic flat-field correction algorithm mitigates radiation-induced degradation during long acquisitions, helping to overcome limitations of consumer-grade hardware. The setup provides voxel sizes from 3.9 micron to 5.2 micron. Phase contrast visualizes soft tissue boundaries that would be undetectable by conventional radiography. Compared to synchrotron or nanofocus systems, our solution is simpler, lower-cost, and avoids complex optics or slow scans. COTS CMOS sensors appear as a viable alternative for laboratory-scale high-resolution microtomography.

Artificial Intelligence (AI)-powered Radio Access Network (RAN) networks have attracted significant attention from both industry and academia. Meanwhile, Digital Twins offer a safe playground for experimenting with AI/Machine Learning (ML)-based solutions for advanced AI-RAN research. By enabling the testing of online algorithms before deployment on the RAN, they reduce costs and safety risks associated with physical field testing. In this article, we propose ARIADNE, an online Reinforcement Learning (RL)-based module that seamlessly integrates with SIONNA and is tasked with performing link adaptation. We explore different design choices and demonstrate how ARIADNE can surpass industry-standard and state-of-the-art methods by achieving up to 11% and 20% improvements in Spectral Efficiency, respectively. Finally, we show that RL learns a Modulation and Coding Scheme (MCS) selection strategy that diverges from Outer Loop Link Adaptation (OLLA), exhibiting either more conservative or more aggressive behavior depending on the configuration, a trend further corroborated by training offline on 5th generation (5G) over-the-air (OTA) measurements.

Large recommendation models have demonstrated substantial potential gains under scaling laws, yet these gains are difficult to realize in industrial recommendation systems because real-world deployment requires lightweight models with strict serving efficiency and latency guarantees. This creates a fundamental gap between offline model scaling and online deployment. In this work, we present Rec-Distill, an industrial distillation pipeline that transfers the performance gains of large-scale recommendation modeling to efficient serving models. Rec-Distill combines large-teacher scaling with student-side transfer optimization through decoupled training, black-box distillation, debiasing mechanism, and a hybrid batch-streaming pipeline for dynamic recommendation environments. Across multiple recommendation and advertising scenarios on real-world platforms, our framework scales teacher models up to 24B dense parameters and 20K behavior sequence length, while enabling lightweight students to recover a substantial portion of teacher gains, with distillation transferability exceeding 60% in the best setting. Extensive offline and online experiments further show that these transferred gains consistently translate into measurable business improvements under industrial constraints. These results demonstrate that Rec-Distill provides a practical framework for distilling large-scale recommendation models into deployable, cost-efficient serving systems, while also establishing a reliable path toward scaling recommendation models to even larger regimes in the future.

Adjacent GEMM problems that differ by a single 128-element step in N can show 30% different throughput on the same GPU. This pervasive performance ruggedness - invisible to roofline analysis and peak-FLOPs intuition, yet dominant for every non-peak workload - is the subject of this paper. We propose performance ruggedness analysis as an analytical framework complementary to roofline: rather than summarizing GPU performance with a scalar bound, treat the full multidimensional performance surface as the object of study, decompose its texture into mechanism-attributable components and separate software-removable contributions from hardware-bound ones. The framing is directly analogous to deep-learning loss landscapes - a continuous quantity (the idealized time 2MNK / compute_throughput_peak) made rugged by interaction with discrete hardware substrates (tiles, sub-groups, cache lines, DRAM channels). We apply the framework to BF16 NN (no transpose) GEMM on Intel Battlemage (Arc B580, sycl-tla) via a 32,768-configuration sweep (M, N, K) belongs to {128, ..., 4096}^3. The peak is 110.8 TFLOPs at the non-square shape M=3840, N=2048, K=4096 with the default tile size; the initial landscape roughness is 16.8 TFLOPs per 128-step against an ideal of 2.0. A two-stage software stack - (i) best-of-six dynamic tile selection and (ii) a novel dynamic-programming based padding-and-splitting optimizer with O(1) runtime lookup - reduces roughness by 70% and raises mean throughput by 30%. Cross-tile experiments establish that the residual sawtooth period scales exactly with software tile size, ruling out cache set conflicts and attributing the remaining variance to four hardware-bound sources (per-kernel base overhead, wave quantization, DPAS atom geometry and GDDR6 channel-hash interactions).

The Wiedemann-Franz law couples electrical and thermal conductivity, making high electrical conduction with low thermal conduction a major challenge. To overcome this, we designed an active thermal metasurface (ATMS) - based thermal invisible gateway that decouples thermal and electrical paths. Built on a copper substrate with a dumbbell-shaped bridge, the structure suppresses heat flow via directional compensation while allowing unimpeded electrical conduction. Room-temperature experiments show an effective thermal conductivity below 10^-3 W m^-1 K^-1 (near zero, air-like insulation) and an electrical conductivity up to 2.8x10^7 S m^-1 (metal-level). Unlike conventional material-modification approaches, our work uses macroscopic structural design to break the intrinsic coupling, offering a promising solution for applications like on-chip interconnects and wearable electronics.

Long-term observations indicate that the relative intensity of cosmic-ray anisotropy remains below $0.1\%$ for energies less than $\sim 1$ PeV. Measuring such faint signals poses a significant challenge in data analysis, requiring careful removal of instrumental and atmospheric artifacts. The all-distance equi-zenith angle method is widely employed to extract cosmic-ray anisotropies, as it effectively suppresses the instantaneous variations arising from the instrument and atmosphere. \textcolor{black}{However, instability in the detector efficiency makes precise measurements of anisotropy challenging with this method.} In this work, we present an enhanced all-distance equi-zenith angle method for cosmic-ray anisotropy measurement. Unlike previous implementations, our improved approach enables the simultaneous measurement of anisotropies over multiple time frames and allows the detection efficiency to be determined directly from the data. This feature makes the method especially suitable for applications where the detector array does not operate with long-term stability\textcolor{black}{, and thus allows for the measurement of anisotropy with high-precision}. Moreover, our enhanced method is also feasible when the data do not span complete tropical years.

Meta-analyses of observational studies often show substantial between-study heterogeneity, limiting the interpretability of pooled estimates. Meta-regression can be used to explore heterogeneity, but it is often underpowered to handle multiple effect modifiers. We propose a novel framework that integrates large language models (LLMs) with deep metric learning to infer study-level similarity prior to meta-analysis. Study-level clinical and methodological characteristics were processed by an LLM to generate study triplets (anchor, similar, dissimilar). These triplets were constructed by treating each study as an anchor and comparing it with pairs of other studies to identify, in each instance, the study most similar to the anchor. Then, the triplets were used into an embedding model trained with triplet loss; a deep learning approach that learns an embedding space where clinically and methodologically similar studies are clustered together. We apply our framework to a meta-analysis dataset of 58 observational studies comparing cognitive outcomes between preterm- and term-born children. Subsequently, we fit meta-analysis models within the identified study clusters and compare the results with those of the overall analysis. Results suggested three clusters two of which retained considerable between-study heterogeneity. The remaining cluster comprised the most homogeneous group of studies and exhibited a more extreme pooled effect estimate together with a narrower prediction interval compared with the overall analysis. This work presents a novel approach for exploring heterogeneity in meta-analysis by incorporating study characteristics prior to model fitting. By transforming study information into a similarity space, the framework identifies coherent subgroups and supports more precise inference in heterogeneous real-world evidence.

Radio arrays provide a scalable route to detecting extensive air showers from ultra-high-energy cosmic rays, but trigger studies for candidate layouts are expensive when every energy, arrival direction, core position and trigger configuration is evaluated with full radio simulations. We present FARSim, a fast surrogate framework that reuses a reduced library of ZHAireS reference footprints to reconstruct ground-plane radio emission and to estimate trigger-relevant observables. The method combines vector geomagnetic and charge-excess field decomposition, geomagnetic-angle and energy scaling, geometrical projection, contour-based core sampling and event-rate integration. We validate the reconstructed field footprints and trigger regions against dedicated ZHAireS simulations, and quantify the computational gain obtained by replacing repeated full shower simulations with fast footprint queries. We further extend the peak-field surrogate to time-domain electric-field synthesis by combining the predicted three-component peak-field vector with geometry-dependent normalized pulse templates. Propagating these traces through an RF-chain response enables voltage-domain threshold and L1-trigger diagnostics. For the validation samples considered here, the time-domain extension reaches a median vector-waveform R^2 of 0.986 over 2112 held-out ZHAireS traces when tested at the true peak amplitude. FARSim is therefore intended as a rapid, physics-informed screening layer for array-layout and trigger studies; absolute exposure predictions and detector commissioning remain the role of full end-to-end simulations.

We improve upon the Johnson-type bound of Hayashi and Yasunaga for insertion-deletion codes by encoding each local list into a binary constant-weight code. The resulting local list-size bound is tight for sufficiently large alphabets. Applying the McEliece--Rodemich--Rumsey--Welch bound to this constant-weight formulation yields an asymptotic rate bound that strictly improves on Yasunaga's Elias-type bound in the nontrivial range.

In holography, the complexity--momentum correspondence relates the increasing momentum of a point particle falling into an eternal black hole to the rate of growth of the Krylov complexity of the dual boundary state, a conjecture established exactly for the BTZ black hole in AdS$_{3}$ at the semiclassical level. We examine possible extensions of the correspondence by considering boundary higher Krylov complexities and Krylov correlators encoding fluctuations and temporal correlations of the spreading quantum state. To this end, we derive exact results for Krylov correlators in quantum systems with $\mathfrak{sl}(2,\mathbb{R})$ or Heisenberg-Weyl symmetry and apply them to the complexity--momentum correspondence. We show that certain out-of-time-ordered correlators of two or more Krylov speed operators at different times are proportional to combinations of the proper radial momenta of a particle falling into the BTZ black hole in AdS$_{3}$, evaluated at those times. This represents a first step in the generalization of the original complexity--momentum relation.

Generative recommendation has recently emerged as a promising paradigm for sequential recommendation. It formulates the task as an autoregressive generation process, predicting tokens of the next item conditioned on user interaction histories. Existing generative recommendation models are typically trained with token-level likelihood objectives such as cross-entropy loss, while employing beam search during inference to generate ranked candidates. However, this leads to a fundamental training-inference inconsistency: standard training assumes ground-truth tokens are always available, while beam search prunes low-probability branches during inference, causing the correct item to be prematurely discarded when its prefixes receive low scores. To address this issue, we propose the Adaptive Prefix-Aware Optimization (APAO) framework, which introduces prefix-level optimization losses to better align the training objective with the inference setting. Furthermore, we design an adaptive worst-prefix optimization strategy that dynamically focuses on the most vulnerable prefixes during training, thereby enhancing the model's ability to retain correct candidates under beam search constraints. We provide theoretical analyses to demonstrate the effectiveness and efficiency of our framework. Extensive experiments show that APAO consistently alleviates the training-inference inconsistency and improves performance across generative recommendation backbones. The source code is publicly available at https://github.com/yuyq18/APAO.

We present the winning strategy for the EVA2025 Data Challenge, which aimed to estimate the probability of extreme precipitation events. These events occurred at most once in the dataset making the challenge fundamentally one of extrapolating extreme values. Given the scarcity of extreme events, we argue that a simple, robust modeling approach is essential. We adopt univariate models instead of multivariate ones and model Peaks Over Thresholds using Extreme Value Theory. Specifically, we fit an exponential distribution to model exceedances of the target variable above a high quantile (after seasonal adjustment). The novelty of our approach lies in using martingale testing to evaluate the extrapolation power of the procedure and to agnostically select the level of the high quantile. While this method has several limitations, we believe that framing extrapolation as a game opens the door to other agnostic approaches in Extreme Value Analysis.

The GW plus Bethe-Salpeter equation (GW-BSE) formalism is a well-established approach for calculating excitation energies and optical spectra of molecules, nanostructures, and crystalline materials. We implement GW-BSE in the CP2K code and validate the implementation for a standard organic molecular test set, obtaining excellent agreement with reference data, with a mean absolute error in excitation energies below 3 meV. We then study optical spectra of nanographenes of increasing length, showing excellent agreement with experiment. We further compute the size of the excitation of the lowest optically active excitation which converges to about 7.6 $Å$ with increasing length. Comparison with time-dependent density functional theory using functionals of varying exact-exchange fraction shows that none reproduce both the size of the excitation and optical spectra of GW-BSE, underscoring the need for many-body methods for accurate description of electronic excitations in nanostructures.

Parton distributions encode the momentum-space structure and, in their generalizations, the spatial tomography of quarks and gluons inside hadrons, the building blocks of visible matter. We present a unified neural-network approach that learns these distributions directly from matrix elements calculated via numerical simulations of quantum chromodynamics (QCD) on the lattice by fitting two complementary inputs simultaneously: data matched to physical quantities via known momentum-space and coordinate-space formalisms. Utilizing data from both methods stabilizes the extraction and mitigates biases that can arise when either is used alone. We validate the method on controlled mock data and apply it to lattice-QCD matrix elements to extract parton distribution functions (PDFs). We show benefits of such an approach for determining the physical quantities. We further extend the framework to zero-skewness generalized parton distributions and demonstrate nucleon tomography within the same neural-network parameterization. Our results provide an adaptable and systematically improvable approach for extracting partonic distributions from Euclidean correlators. It can incorporate polarization, additional channels, and future experimental constraints from current and future facilities, such as the Electron-Ion Collider.

In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners on its boundary exhibits a universal corner-dependent contribution. We study this contribution through the lens of lattice discretization, and demonstrate that this corner dependence emerges naturally from the geometric structure of infinite projected entangled pair states (iPEPS) on discrete lattices. Using a rigorous counting argument, we show that the bond dimension of an iPEPS representation exhibits a corner-dependent term that matches the predicted term in gapped continuous systems. Crucially, we find that this correspondence only emerges when averaging over all possible lattice orientations and origin positions, revealing a fundamental requirement for properly discretizing continuous systems. Our results provide a geometric understanding of entanglement corner laws and establish a direct connection between continuum field theory predictions and the structure of discrete tensor network representations. We extend our analysis to gauge-invariant systems, where lattice corners crossed by the bipartition boundary contribute an additional corner-dependent term. These findings offer new insights into the relationship between entanglement in continuous and discrete quantum systems.

We study relatively hyperbolic group pairs whose boundaries are Schottky sets. We characterize the groups that have boundaries where the Schottky sets have incidence graphs with 1 or 2 components.

The 21-cm emission line from neutral hydrogen during the cosmic Dark Ages can be a powerful probe of cosmological models and early universe physics. This work provides a quantitative forecast for the design requirements of a lunar far-side interferometer array aimed at measuring the 21-cm power spectrum and constraining inflationary models through the running of the spectral index $α_s$. During the Dark Ages, larger collapsed objects have not yet formed, allowing linear perturbation theory to remain valid down to much smaller scales than is possible in current large-scale structure or CMB surveys. We first validate this linearity assumption by quantifying the contribution of minihalos to the 21-cm signal. We then establish a generalized and flexible analytical framework for the baseline density distribution of interferometers that may consist of an arbitrary number of stations or sub-arrays. Incorporating a realistic noise model, we determine the configurations necessary to reach the detection threshold and demonstrate that distributing the total collecting area into multiple stations can improve the signal-to-noise ratio of the power spectrum at a tunable small scale of interest by up to two orders of magnitude. We then show that a lunar array requires at least $\sim30,000$ probed Fourier modes to achieve a constraint on inflation of $σ(α_s) = 0.034$, a result competitive with the Planck 2018 results and capable of distinguishing between different inflationary scenarios. We quantitatively explain how thermal noise severely erodes modes at high redshifts and small scales -- scales previously considered easily accessible to Dark Ages observations in the literature -- and discuss the prospects for Dark Ages observations as a new and independent probe despite this limitation.

Visible light communication (VLC) provides a unified framework for wireless data transmission and illumination, but its practical deployment requires transmission schemes that jointly satisfy communication and lighting constraints. In color-shift keying (CSK) systems, dimming remains a challenging and underexplored problem because the average optical power must be controlled without altering the perceived chromaticity. This paper proposes a dimming space-time code (DSTC) for CSK-based VLC systems, where a structured dimming matrix introduces controlled temporal power variations while satisfying physical feasibility, color preservation, and identifiability conditions. Two receiver architectures are developed: a pilot-assisted zero-forcing (ZF) receiver and a tensor-based semi-blind PARAFAC receiver that jointly estimates the channel and transmitted symbols using only one training time slot. Simulation results show that the proposed DSTC provides diversity gains and substantial BER reductions with respect to conventional CSK, while the tensor-based receiver improves spectral efficiency by reducing training overhead, with particular benefits in large-scale MIMO configurations.

In this paper, we consider the expansion of power grids under emerging large loads from data centers and electrified manufacturing. We develop a multi-period grid capacity expansion model to determine optimal investment profiles for power generation, storage, and transmission capacity while accounting for hourly power dispatch, such that electricity demand is satisfied and the total planning and operation cost is minimized. We also propose a new modeling approach regarding the spatial distribution of demand from large loads. The model is used to analyze the expansion of a synthetic grid that follows key characteristics of the ERCOT system over a seven-year planning horizon, under loads from data centers and electrified oil refining, which account for 17.5% and 4.7% of total annual electricity demand by the end of the planning horizon. The optimal investment policy leads to an 83.6% increase in generation capacity and exploits the short construction times of solar and storage as well as the operational flexibility of thermal generators. Finally, sensitivity analysis reveals that the construction time of grid assets substantially impacts investment timing, generation technology mix, and transmission capacity expansion. The proposed modeling framework is general and can be extended to other grid systems, enabling the exploration of diverse demand scenarios, policy assumptions, and regional characteristics.

Can a Laughlin anyon fluid become a topological superconductor? We answer this question for a $ν=1/3$ fractional Chern insulator (FCI) using a $U(3)$ infrared parton theory. Three charge-$e/3$ constituents form the electron, while three constituent pairs form a gauge-invariant charge-$2e$ Cooper pair. The resulting superconductors share an ordinary charge-$2e$ sector but differ in their neutral color response, giving an SC$^\ast$ with the parent Laughlin $U(1)_3$ order, a chiral topological superconductor with $c_-=3/2$, and a strong-pairing anyon superconductor with $c_-=3$. The same framework organizes a nearby $σ_{xy}=0$ charge density wave (CDW) state. At commensurate filling, the normal state and the $c_-=3$ and $c_-=3/2$ superconducting descendants are naturally tied to a period-three density order background, while the SC$^\ast$ branch can preserve microscopic translations. Away from commensuration, a chargon metal can pair into the same $c_-=3/2$ topological superconductor. The FCI, reentrant CDW, and chiral superconductivity are unified in the $U(3)$ parton theory.

Let $K$ be a number field, $k\geq 2$ an integer, $(K^*)^k$ the $k$-fold direct product of $K^*$ with coordinatewise multiplication, and $Γ$ a finitely generated subgroup of rank $r$ of $(K^*)^k$. Further, let $H(α)$ denote the absolute exponential height of an algebraic number $α$. Fix non-zero elements $a_1,\ldots , a_k\in K$. We give asymptotic formulas for the number of $\mathbf{x}=(x_1,\ldots , x_k)\inΓ$ with $H(a_1x_1+\cdots +a_kx_k)\leq X$ as $X\to\infty$ such that no non-empty subsum of $a_1x_1+\cdots +a_kx_k$ vanishes. By the same method of proof, we obtain an asymptotic formula as $X\to\infty$ for the number of non-negative integers $n$ with $H(u_n)\leq X$, where $\{ u_n\}$ is a linear recurrence sequence.

We develop a systematic framework for the quantum and thermal properties of a Klein-Gordon scalar field subject to an inverted harmonic potential $-{1\over2} m^2ω^2 x^2$. Starting from a non-Hermitian momentum substitution $P \to P - mωx$, we employ a symplectic phase-space rotation $V = \exp\!\left[-\tfracπ{8}(xp+px)\right]$ to map the system onto an analytically tractable effective harmonic oscillator evaluated at $xe^{iπ/4}$. This allows us to define a well-regulated partition function $Z(β,ω,m)$ and derive closed-form expressions for the free energy, entropy, and thermal correlation functions. We then apply this framework to three physical settings: (i) scalar field fluctuations during cosmological inflation, (ii) quantum fields near black-hole horizons, and (iii) order-parameter dynamics near second-order phase transitions in condensed matter. Our results unify previously scattered results in the literature and provide new predictions for the finite-temperature spectral density and entanglement entropy of unstable quantum systems.

Superconducting microstrip resonators, which leverage kinetic inductance to probe electrodynamics, are sensitive tools for studying superconducting thin films at microwave frequencies. However, extracting the absolute superconducting penetration depth from these measurements remains challenging. In this work, we present a hybrid method to determine the absolute value of penetration depth over a wide temperature range by combining resonator measurements with finite-element electromagnetic simulations in COMSOL Multiphysics. We demonstrate this approach by extracting the penetration depth of NbN films by fabricating resonators from films of various thicknesses. Furthermore, we extend the technique to materials with lower critical temperatures by employing a flip-film geometry. By placing a sample above a NbN resonator, separated by a thin Mylar dielectric, we create a coupled structure where changes in the sample's penetration depth shift the resonant frequency. This non-destructive method provides a reliable, high-sensitivity platform for characterizing the penetration depth of diverse superconducting thin films.

We present a method of studying few-body nuclear scattering by means of neural quantum states, without requiring time-evolution. A recently developed family of stable minimum principles for Schrodinger's equation provides conservative uncertainties on cross sections and partial wave amplitudes computed in this way. We use this method to study both elastic and inelastic neutron-deuteron scattering with realistic nuclear two-body forces.