In recent years, several notions of non-rigidity of horizontal vectors in Carnot groups have been proposed, motivated, in particular, by the characterization of monotone sets and Whitney extension properties. In this note we compare some of these notions.

In this article, we study the $G$-autoequivalences of the derived category $\mathbf{D}^b_G(A)$ of $G$-equivariant objects for an abelian variety $A$ with $G$ being a finite subgroup of $\mathrm{Pic}^0(A)$. We provide a result analogue to Orlov's short exact sequence for derived equivalences of abelian varieties. It can be generalized to the derived equivalences of abelian varieties for a same $G$ in general. Furthermore, we find derived equivalences of generalized Kummer varieties by lifting derived equivalences of abelian surfaces using the $G$-equivariant version of Orlov's short exact sequence and some ``splitting" propositions.

We propose the unitary variational quantum-neural hybrid eigensolver (U-VQNHE), which improves upon the original VQNHE by enforcing unitary neural transformations. The non-unitary nature of VQNHE causes normalization issues and divergence of the loss function during training, leading to exponential scaling of measurement overhead with qubit number. U-VQNHE resolves these issues, significantly reduces required measurements, and retains improved accuracy and stability over standard variational quantum eigensolvers.

Every matrix polynomial $\mathbf{f}_n$ can be written in the form \[ \mathbf{f}_n(z)=\mathbf{h}(z^2)+z\,\mathbf{g}_n(z^2). \] The matrix polynomial $\mathbf{f}_{2m}$ is said to be of Hurwitz type if the expression $\mathbf{g}_{2m}(z)\mathbf{h}_{2m}^{-1}(z)$ admits a representation as a finite continued fraction with positive definite matrix coefficients. Similarly, the odd-degree matrix polynomial $\mathbf{f}_{2m+1}$ is of Hurwitz type if $\frac{1}{z}\mathbf{h}_{2m+1}(z)\mathbf{g}_{2m+1}^{-1}(z)$ has the same property. We derive an explicit form of the Bezoutian associated with Hurwitz-type matrix polynomials. Using this explicit form, we provide an explicit proof that Hurwitz-type matrix polynomials are Hurwitz matrix polynomials. In [52], the Hurwitzness of Hurwitz-type matrix polynomials was also studied. Finally, we propose an extension of the class of Hurwitz-type matrix polynomials by adding to a non--Hurwitz-type matrix polynomial another matrix polynomial so that the resulting matrix polynomial is of Hurwitz type.

A subset $S$ of a topological gyrogroup $G$ is said to be a {\it suitable set} for $G$ if $S$ is discrete, the gyrogroup generated by $S$ is dense in $G$, and $S\cup \{0\}$ is closed in $G$, where $0$ is the identity element of $G$. In this paper, it is proved that every locally compact strongly topological gyrogroup has a suitable set, which gives an affirmative answer to a question posed by F. Lin, et al. in \cite{key14}.

We present the implementation of simplified and full likelihood models for multibin signal regions in CheckMATE. A total of 13 searches are included from ATLAS and CMS, and several methods are presented for the implementation and evaluation of likelihood functions. Statistical combinations increase the sensitivity of searches and open up the possibility of combining orthogonal search channels in the CheckMATE framework.

RNA function is deeply intertwined with its conformational dynamics. In this review, we survey recent advances in the use of atomistic molecular dynamics simulations to characterize RNA dynamics in diverse contexts, including isolated molecules and complexes with ions, small molecules, or proteins. We highlight how enhanced sampling techniques and integrative approaches can improve both the precision and accuracy of the resulting structural ensembles. Finally, we examine the emerging role of artificial intelligence in accelerating progress in RNA modeling and simulation.

Given a Calderbank-Shor-Steane (CSS) code, it is sometimes necessary to modify the code by adding an arbitrary number of physical qubits and parity checks. Motivations may include concatenating codes, embedding low-density parity check (LDPC) codes into finite-dimensional Euclidean space, or reducing the weights of parity checks. During this embedding, it is essential that the modified code possesses an isomorphic set of logical qubits as the original code. However, despite numerous explicit constructions, the conditions of when such a property holds true is not known in general. Therefore, using the language of homological algebra, we provide a unified framework that guarantees a natural isomorphism between the output and input codes. In particular, we explicitly show how previous works fit into our framework.

We build a modified universal Kolyvagin system for the Galois representation attached to a Hida family of modular forms, starting from the big Heegner point Euler system of Longo--Vigni built in towers of Shimura curves. We generalize the work of Büyükboduk to a quaternionic setting, relaxing the classical \emph{Heegner hypothesis} on the tame conductor of the family. As a byproduct of this construction, we give a proof of one divisibility of the anticyclotomic Iwasawa main conjecture for Hida families.

For the bipartite Bell scenario with two inputs and two outputs, a nonlinear witness of dimensionally restricted nonlocality is introduced. Popescu-Rohrlich (PR) box fraction of dimensionally restricted nonlocality is then introduced and studied using the aforementioned witness and a nonlinear measure of correlations. This PR box fraction is also nonzero for certain Bell-local correlations. It is shown that any nonsignaling correlation shared by Alice and Bob that has dimensionally restricted nonlocality contains secrecy against any third party, Eve, who is also dimensionally restricted. In this context, for the specific Bell scenario considered, it is demonstrated that the PR box fraction of dimensionally restricted nonlocality can be used as a resource for secure quantum key distribution, even if entanglement is not certified.

This paper introduces a new, highly energy-efficient, Adiabatic Capacitive Neuron (ACN) hardware implementation of an Artificial Neuron (AN) with improved functionality, accuracy, robustness and scalability over previous work. The paper describes the implementation of a \mbox{12-bit} single neuron, with positive and negative weight support, in an $\mathbf{0.18μm}$ CMOS technology. The paper also presents a new Threshold Logic (TL) design for a binary AN activation function that generates a low symmetrical offset across three process corners and five temperatures between $-55^o$C and $125^o$C. Post-layout simulations demonstrate a maximum rising and falling offset voltage of 9$mV$ compared to conventional TL, which has rising and falling offset voltages of 27$mV$ and 5$mV$ respectively, across temperature and process. Moreover, the proposed TL design shows a decrease in average energy of 1.5$\%$ at the SS corner and 2.3$\%$ at FF corner compared to the conventional TL design. The total synapse energy saving for the proposed ACN was above 90$\%$ (over 12x improvement) when compared to a non-adiabatic CMOS Capacitive Neuron (CCN) benchmark for a frequency ranging from 500$kHz$ to 100$MHz$. A 1000-sample Monte Carlo simulation including process variation and mismatch confirms the worst-case energy savings of $\>$90$\%$ compared to CCN in the synapse energy profile. Finally, the impact of supply voltage scaling shows consistent energy savings of above 90$\%$ (except all zero inputs) without loss of functionality.

We consider collections of hyperplanes in $\mathbb{R}^n$ covering all vertices of the $n$-dimensional hypercube $\{0,1\}^n$, which satisfy the following nondegeneracy condition: For every $v\in \{0,1\}^n$ and every $i=1,\dots,n$, we demand that there is a hyperplane $H$ in the collection with $v\in H$ such that the variable $x_i$ appears with a non-zero coefficient in the hyperplane equation describing $H$. We prove that every collection $\mathcal{H}$ of hyperplanes in $\mathbb{R}^n$ covering $\{0,1\}^n$ with this nondegeneracy condition must have size $|\mathcal{H}|\ge n/2$. This bound is tight up to constant factors. It generalizes a recent result concerning the intensively studied skew covers problem, which asks about the minimum possible size of a hyperplane cover of $\{0,1\}^n$ in which all variables appear with non-zero coefficients in all hyperplane equations. As an application of our result, we also obtain an essentially tight bound for an old problem about collections of hyperplanes slicing all edges of the $n$-dimensional hypercube, in the case where all of the hyperplanes have bounded integer coefficients.

We investigate the geodesic orbit property of pseudo-Riemannian nilmanifolds, specifically those known in the literature as pseudo $H$-type Lie groups -- i.e., 2-step nilpotent Lie groups of Heisenberg type equipped with a left invariant pseudo-Riemannian metric. The study of homogeneous geodesics on Riemannian $H$-type Lie groups was completed by C.~Riehm in 1984. In this work, we extend these results to the pseudo-Riemannian $H$-type Lie groups and provide a complete characterization of the geodesic orbit property for the case where the underlying Lie algebras are constructed from the admissible Clifford modules of minimal dimension.

We consider a coded distributed computing problem in a ring-based communication network, where $N$ computing nodes are arranged in a ring topology and each node can only communicate with its neighbors within a constant distance $d$. To mitigate the communication bottleneck in exchanging intermediate values, we propose new coded distributed computing schemes for the ring-based network that exploit both ring topology and redundant computation (i.e., each map function is computed by $r$ nodes). Two typical cases are considered: all-gather where each node requires all intermediate values mapped from all input files, and all-to-all where each node requires a distinct set of intermediate values from other nodes. For the all-gather case, we propose a new coded scheme based on successive reverse carpooling where nodes transmit every encoded packet containing two messages traveling in opposite directions along the same path. Theoretical converse proof shows that our scheme achieves the optimal tradeoff between communication load, computation load $r$, and broadcast distance $d$ when $N\gg d$. For the all-to-all case, instead of simply repeating our all-gather scheme, we delicately deliver intermediate values based on their proximity to intended nodes to reduce unnecessary transmissions. We derive an information-theoretic lower bound on the optimal communication load and show that our scheme is asymptotically optimal under the cyclic placement when $N\gg r$. The optimality results indicate that in ring-based networks, the redundant computation $r$ only leads to an additive gain in reducing communication load while the broadcast distance $d$ contributes to a multiplicative gain.

Physics-Informed Neural Networks (PINNs) have emerged as a promising approach for solving partial differential equations (PDEs) by embedding the governing physics into the loss function associated with a deep neural network. In this work, a Quantum PINNs (QPINN) framework is proposed to solve two-dimensional (2D) time-dependent Maxwell's equations. Our approach utilizes a parametrized quantum circuit in conjunction with the classical neural network architecture and enforces physical laws, including a global energy conservation principle, during training. A quantum simulation library, TorQ, was developed to efficiently compute circuit outputs and derivatives by leveraging GPU acceleration based on PyTorch, enabling end-to-end training of the QPINN. The method was evaluated on two 2D electromagnetic wave propagation problems: one in free space (vacuum) and the other has an added dielectric medium. Multiple quantum circuit ansätze, input scales, and an added loss term were compared in a thorough ablation study. Furthermore, recent techniques to enhance PINN convergence, including random Fourier feature embeddings and adaptive time weighting, have been incorporated. Our results demonstrate that the QPINN achieves accuracy comparable to, and even greater than, the classical PINN baseline, while using a significantly smaller number of trainable parameters. This study also shows that adding an energy conservation term to the loss stabilizes training and improves the physical fidelity of the solution in the lossless free-space case. This added term helps mitigate a new kind of barren plateau (BP) related phenomenon - ``black hole'' (BH) loss landscape for the quantum experiments in that scenario. By optimizing the quantum-circuit ansatz and embedding energy-conservation constraints, our QPINN achieves up to a 19% higher accuracy on 2D Maxwell benchmark problems compared to a classical PINN.

This study presents a comprehensive analysis of the elliptic flow coefficient, $v_2$, for charged hadrons at mid-rapidity in d+Au collisions at $\sqrt{s_{\mathrm{NN}}} = 200\mathrm{~GeV}$. Utilizing the AMPT model in both default and string melting modes, we examine the dependence of $v_2$ on transverse momentum, collision centrality, and particle type. Furthermore, we present $v_2$ scaled by participant eccentricity, which indicates a similar level of collectivity across different centrality intervals in d+Au collisions at $\sqrt{s_{\mathrm{NN}}} = 200\mathrm{~GeV}$ within the AMPT-SM model. Our results indicate that the early-stage partonic phase significantly influences $v_2$, as observed by variations in parton scattering cross-section, while the later stage hadronic rescattering shows minimal impact. Comparisons with STAR and PHENIX experimental data show that the AMPT model effectively captures the transverse momentum dependence of $v_2$, underlining the importance of parton scattering mechanisms and the need for careful interpretation of experimental results in asymmetric systems.

We present the first broadband spectral and timing study of the Be/X-ray pulsar XTE J0111.2$-$7317 (SXP31.0) during the first major outburst since its discovery in 1998. This giant type II outburst, observed between April and September 2025, marks the source's return to activity after nearly three decades of quiescence. Using NuSTAR observations together with data from Swift/XRT and SRG/ART-XC, we followed the outburst's evolution, with the source reaching a bolometric luminosity of $L_{\rm bol} = 3.6 \times 10^{38}$ erg s$^{-1}$. The broadband spectra are well described by an absorbed cutoff power law, two blackbody components (hot and soft), and a narrow Fe K$α$ line. No cyclotron absorption features were detected in either the phase-averaged or phase-resolved spectra in the 5-50 keV band. Most notably, we report the discovery of a previously undetected quasiperiodic oscillation (QPO) at $0.8 \pm 0.1$ mHz, characterized by a fractional root-mean-square (rms) amplitude of 14% at a super-Eddington bolometric luminosity of $L_{\rm bol} = 2.5 \times 10^{38}$ erg s$^{-1}$. In contrast, the previously reported 1.27 Hz QPO was not detected. While the 0.8 mHz QPO is present, the pulsed fraction (PF) is low in soft X-rays, which is consistent with other super-Eddington pulsars exhibiting mHz QPOs; however, it rises above 20 keV to reach 35%. The QPO vanishes in subsequent observations coinciding with a sharp increase in the PF and a distinct change in pulse profile morphology. It was not observed in any follow-up observations at luminosities above or below its initial detection, suggesting it is a transient phenomenon.

A dissipationless supercurrent state in superconductors can be destroyed by thermal fluctuations. Thermally activated phase slips provide a finite resistance of the sample and are responsible for dark counts in superconducting single photon detectors. The activation barrier for a phase slip is determined by a space-dependent saddle-point (instanton) configuration of the order parameter. In the one-dimensional wire geometry, such a saddle point has been analytically obtained by Langer and Ambegaokar in the vicinity of the critical temperature, $T_c$, and for arbitrary bias currents below the critical current $I_c$. In the two-dimensional geometry of a superconducting strip, which is relevant for photon detection, the situation is much more complicated. Depending on the ratio $I/I_c$, several types of saddle-point configurations have been proposed, with their energies being obtained numerically. We demonstrate that the saddle-point configuration for an infinite superconducting film at $I\to I_c$ is described by the exactly integrable Boussinesq equation solved by Hirota's method. The instanton size is $L_x\simξ(1-I/I_c)^{-1/4}$ along the current and $L_y\simξ(1-I/I_c)^{-1/2}$ perpendicular to the current, where $ξ$ is the Ginzburg-Landau coherence length. The activation energy for thermal phase slips scales as $ΔF^\text{2D}\propto (1-I/I_c)^{3/4}$. For sufficiently wide strips of width $w\gg L_y$, a half-instanton is formed near the boundary, with the activation energy being 1/2 of $ΔF^\text{2D}$.

This paper deals with a problem which describes tuberculosis granuloma formation \begin{align*} \begin{cases} u_t = Δu - \nabla \cdot (u \nabla v) - uv - u + β, &x \in Ω,\ t>0, \\ v_t = Δv + v -uv + μw, &x \in Ω,\ t>0, \\ w_t = Δw + uv - wz - w, &x \in Ω,\ t>0, \\ z_t = Δz - \nabla \cdot (z \nabla w) + f(w)z -z, &x \in Ω,\ t>0 \end{cases} \end{align*} under homogeneous Neumann boundary conditions and initial conditions, where $Ω\subset \mathbb{R}^n$ ($n\ge 2$) is a smooth bounded domain, $β,μ>0$ and $f$ is some function, and shows that if initial data are small in some sense then the solution $(u,v,w,z)$ of the problem exists globally and convergences to $(β,0,0,0)$ exponentially when $β>1$ and the reproduction number $R_0 := \frac{μβ+ 1}β$ satisfies $R_0<1$.

Fluctuating hydrodynamics provides a framework connecting mesoscopic fluctuations with macroscopic transport behavior. To bridge mesoscopic and macroscopic transport from microscopic dynamics, we introduce a wavenumber-dependent viscosity, defined via the equilibrium correlation of time-averaged Fourier components of the fine-grained shear stress field. Two-dimensional molecular dynamics simulations reveal its small-wavenumber divergence characteristic of the renormalized viscosity, while its large-wavenumber behavior determines the bare viscosity, thereby establishing a link between mesoscopic and macroscopic transport based on microscopic dynamics.

We study periodic orbits in the spatial rotating Kepler problem from a symplectic-topological perspective. Our first main result provides a complete classification of these orbits via a natural parametrization of the space of Kepler orbits, using angular momentum and the Laplace-Runge-Lenz vector. We then compute the Conley-Zehnder indices of non-degenerate orbits and the Robbin-Salamon indices of degenerate families, establishing their contributions to symplectic homology via the Morse-Bott spectral sequence. To address coordinate degeneracies in the spatial setting, we introduce a new coordinate system based on the Laplace-Runge-Lenz vector. These results offer a full symplectic-topological profile of the three-dimensional rotating Kepler problem and connect it to generators of symplectic homology.

Turbulence poses challenges for numerical simulation due to its chaotic, multiscale nature and high computational cost. Traditional turbulence modeling often struggles with accuracy and long-term stability. Recent scientific machine learning (SciML) models, such as Fourier Neural Operators (FNO), show promise in solving PDEs, but are typically limited to one-step-ahead predictions and often fail over long time horizons, especially in 3D turbulence. This study proposes a framework to assess the reliability of neural operator models in turbulent flows. Using three-dimensional forced homogeneous isotropic turbulence (HIT) as a benchmark, we evaluate models in terms of uncertainty quantification (UQ), error propagation, and sensitivity to initial perturbations. Statistical tools such as error distribution analysis and autocorrelation functions (ACF) are used to assess predictive robustness and temporal coherence. Our proposed model, the factorized-implicit FNO (F-IFNO), improves long-term stability and accuracy by incorporating implicit factorization into the prediction process. It outperforms conventional LES and other FNO-based models in balancing accuracy, stability, and efficiency. The results highlight the importance of prediction constraints, time interval selection, and UQ in developing robust neural operator frameworks for turbulent systems.

We investigate the correlation between quantum depletion and Hawking temperature in a ringshaped Bose-Einstein condensate featuring an analog black hole-white hole horizon pair, using the Bogoliubov approach. The presence of horizons is found to enhance the quantum depletion compared to horizon-free configurations, indicating a correlation between depletion and horizon dynamics. Via tuning the Hawking temperature, we observe its effect on the depletion profile. Our results show that depletion increases with Hawking temperature, and beyond a certain threshold, backreaction effects emerge, challenging the validity of the Bogoliubov approximation. We identify a viable parameter regime where the system remains both theoretically controlled and experimentally accessible, offering insight into horizon-induced quantum fluctuations, with implications for future studies of backreaction.

The goal of our work is to study the decomposition of the joint action of $\mathscr{G} = \text{SpO}(2n|1)$ and $\mathfrak{g}' = \mathfrak{osp}(2|2)$ on the supersymmetric algebra $\text{S} = \text{S}(\mathbb{C}^{2n|1} \otimes \mathbb{C}^{1|1})$. As proved by Merino and Salmasian, we have a one-to-one correspondence between irreducible representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing as subrepresentations of $\text{S}$. In this paper, we obtained an explicit description of the highest weights and joint highest weight vectors for the representations of $\mathscr{G}$ and $\mathfrak{g}'$ appearing in the duality.

We derive a local, crossing symmetric dispersion relation (CSDR) for 2-2 scattering amplitudes with a parametric ambiguity motivated by string theory. Various limits of the parameter lead to the fixed-t, fixed-s, and other known CSDRs. We also present formulae for higher-subtracted cases. Several examples are discussed for illustration. In particular, for the Veneziano and the Virasoro-Shapiro amplitudes, we derive parametric series representations which manifest poles in all channels and converge everywhere. We then discuss applications of our formalism for bootstrapping weakly-coupled gravitational EFTs. We demonstrate that even in the presence of the graviton pole, one can derive bounds on the Wilson coefficients while working in the forward limit, with the parameter acting as the IR regulator instead. Finally, we derive series representations for multi-variable, totally symmetric generalisations of the Veneziano and Virasoro-Shapiro amplitudes that manifest poles in all the variables. This is a first step towards dispersion relations for n-particle scattering amplitudes.

The flip symmetry on knot diagrams induces an involution on Khovanov homology. We prove that this involution is determined by its behavior on unlinks; in particular, it is the identity map when working over $\mathbb{F}_2$. This confirms a folklore conjecture on the triviality of the Viro flip map. As a corollary, we prove that the symmetries on the transvergent and intravergent diagrams of a strongly invertible knot induce the same involution on Khovanov homology. We also apply similar techniques to study the half sweep-around map.

Bayesian optimization (BO) struggles in high dimensions, where Gaussian-process surrogates demand heavy retraining and brittle assumptions, slowing progress on real engineering and design problems. We introduce GIT-BO, a Gradient-Informed BO framework that couples TabPFN v2, a tabular foundation model that performs zero-shot Bayesian inference in context, with an active-subspace mechanism computed from the model's own predictive-mean gradients. This aligns exploration to an intrinsic low-dimensional subspace via a Fisher-information estimate and selects queries with a UCB acquisition, requiring no online retraining. Across 60 problem variants spanning 20 benchmarks-nine scalable synthetic families and ten real-world tasks (e.g., power systems, Rover, MOPTA08, Mazda)-up to 500 dimensions, GIT-BO delivers a stronger performance-time trade-off than state-of-the-art GP-based methods (SAASBO, TuRBO, Vanilla BO, BAxUS), ranking highest in performance and with runtime advantages that grow with dimensionality. Limitations include memory footprint and dependence on the capacity of the underlying TFM.

For each braided category $\mathcal{C}$ we show that, under mild hypotheses, there is an associated category of "half braided algebras" and their bimodules internal to $\mathcal{C}$ which is not only monoidal but even braided and balanced. We use this in the case where $\mathcal{C}$ is the category of modules over a ribbon Hopf algebra to interpret stated skeins as a TQFT, namely a braided balanced functor from a category of cobordisms to this category of algebras and their bimodules. Although our construction works in full generality, we relate in the special case of finite-dimensional ribbon factorizable Hopf algebras the stated skein functor to the Kerler-Lyubashenko TQFT by interpreting the former as the "endomorphisms" of the latter.

We discuss the possible topological order/topological quantum field theory of different quantum Hall systems. Given the value of the Hall conductivity, we constrain the global symmetry of the low-energy theory and its anomaly. Specifically, the one-form global symmetry and its anomaly are presented as the organizing principle of these systems. This information is powerful enough to lead to a unique minimal topological order (or a small number of minimal topological orders). Almost all of the known experimentally discovered topological orders are these minimal theories. Since this work is interdisciplinary, we made a special effort to relate to researchers with different backgrounds by providing translations between different perspectives.

Quantum spin models are ubiquitous in solid-state physics, but classical simulation of them remains extremely challenging. Experimental testbed systems with a variety of spin-spin interactions and measurement channels are therefore needed. One promising potential route to such testbeds is provided by microwave-photon-mediated interactions between superconducting qubits, where native strong light-matter coupling enables significant interactions even for virtual-photon-mediated processes. In this approach, the spin-model connectivity is set by the photonic mode structure, rather than the spatial structure of the qubit. Lattices of coplanar-waveguide (CPW) resonators have been demonstrated to allow extremely flexible connectivities and can therefore host a huge variety of photon-mediated spin models. However, large-scale CPW lattices with non-trivial band structures have never before been successfully combined with superconducting qubits. Here we present the first such device featuring a quasi-1D CPW lattice with multiple transmon qubits. We demonstrate that superconducting-qubit readout and diagnostic techniques can be generalized to this highly multimode environment and observe the effective qubit-qubit interaction mediated by the bands of the resonator lattice. This device completes the toolkit needed to realize CPW lattices with qubits in one or two Euclidean dimensions, or negatively-curved hyperbolic space, and paves the way to driven-dissipative spin models with a large variety of connectivities.