We propose a sparse delay-Doppler NOMA scheme resilient to intentional jamming. The transmitter places user data on a small random subset of delay-Doppler bins, spreads the result through a unitary precoder, and re-draws the active subset per frame from a pseudo-random seed shared with the receiver. The receiver detects and discards jammed bins, recovers the sparse signal by least squares, and decodes per bin via SIC. Hadamard, DFT, and Haar-random precoders all yield essentially the same BER, because a Marchenko-Pastur conditioning argument controls any random unitary submatrix. The closed-form BER has no jammer-induced floor, unlike the well-known partial-band floor of conventional OTFS-NOMA. The same argument shows that compromising the shared seed does not break the system: random unitary submatrices remain well-conditioned, so BER stays within the unjammed envelope. For more than two users we use a superincreasing power allocation (Merkle-Hellman knapsack) and prove the resulting low-complexity SIC matches maximum-likelihood detection exactly, removing the usual SIC propagation ceiling. For more than four users we partition them into pairs assigned to disjoint bin subsets; this OMA-friendly NOMA rule reaches floor BER at eight users by SNR around 20 dB. We extend the framework to Rician fading and show the jammer-independence property holds for arbitrary Rician K-factor. Monte Carlo simulations track the analytical predictions within 3 dB and show at least a 40 dB BER-ratio improvement against pattern-aware jammers, with about 24 dB of cumulative gain over conventional OTFS-NOMA under oracle jamming.

We construct the double-current deformations of two-dimensional quantum field theories whose partition functions have background gauge-field anomalies. Extending the path integral construction of [1], we couple the seed theory to dynamical gauge fields and compact Stueckelberg fields and insert parallel transport in the anomaly line bundle. The deformed partition function then has the same anomaly as the undeformed one. For flat background gauge fields the Stueckelberg non-zero modes localize the dynamical gauge fields to flat connections, reducing the deformation to a finite-dimensional holonomy integral. We derive the integral kernel on the torus and its higher-genus generalization. For the compact boson, or equivalently the Abelian $U(1)$ WZW model, the kernel gives a Gaussian transform of the torus partition function: at zero background the spectrum is obtained by $k\to K_λ$, while contact terms and spectral-flow data remain controlled by the original anomaly. We also formulate the anomaly-compatible non-Abelian and homogeneous Yang-Baxter generalization.

Many works have attempted to estimate the correlation and integral timescales associated with turbulent fluctuations in the solar wind, which are interpreted as length scales based on Taylor's~Hypothesis. However, accurate estimates of these timescales from spacecraft observations heavily rely on the accurate estimation of autocorrelation functions (ACF), which have been recently shown to depend strongly on the interval length used to estimate them. In this Letter, we show that this dependence on interval length may be artificial because common ACF estimators do not correctly capture the long-lag behavior of the true ACF of the underlying turbulence. We introduce a new ergodicity-based methodology to unambiguously estimate the integral timescale, and a new ACF estimator with better ergodic convergence than current ones. Due to its ergodic properties, the new ACF estimator properly captures the long-lag behavior, and is independent of the interval length. We use this approach to estimate the integral and correlation scales of magnetic fluctuations in the solar wind near $1~{\rm au}$.

We introduce a family of homotopy theories for generalized metric spaces with natural number distances, via the magnitude-path spectral sequence (MPSS). The first page of the MPSS is known as magnitude homology; the second page is known as bigraded path homology, and contains GLMY path homology as its top row. For each natural number r, we define a class of maps of metric spaces called r-quasi-isomorphisms: those maps that induce a quasi-isomorphism at page r of the MPSS. We show that every page of the spectral sequence satisfies a suitable metric analogue of each of the Eilenberg-Steenrod axioms. In particular, we introduce the notion of r-cofibration and prove a Mayer-Vietoris theorem for page r with respect to r-cofibrations. We establish a family of Brown category structures on generalized metric spaces which allow us to explicitly compute homotopy colimits. We apply this to describe r-suspension and r-spheres of dimension n, and compute their spectral sequences. Finally we prove that for r = 1 the entire theory restricts to directed graphs.

Using the open source MPI-AMRVAC framework, we study oscillatory reconnection in a laboratory plasma, which occurs when a magnetic null is perturbed by incoming fast magnetoacoustic waves driven by an alternating current. The magnetic null region collapses to first form a $y$-directed current sheet that later changes its orientation to the $x$-direction. The $x$-directed current sheet has smaller enhanced thermal pressure and out-of-plane current than the $y$-directed current sheet. The Hall effect produces an out-of-plane plasma flow that evolves with a time lag with respect to the enhanced thermal pressure and out-of-plane current density. Increasing the amplitude of the alternating current produces higher thermal pressure, out-of-plane current density, and out-of-plane plasma flow, while the first peaks of thermal pressure and out-of-plane current density occur earlier.

The goal of this paper is to establish polynomial Fourier decay for images of self-similar measures $μ$ on $\mathbb{R}^k$ under sufficiently nonlinear real-analytic maps $f \colon \mathbb{R}^k \to \mathbb{R}^d$. For example, we prove that if $f$ is analytic on $\mathbb{R}^k$, its graph does not lie in an affine hyperplane in $\mathbb{R}^{k+d}$, and $μ$ is not supported in an affine hyperplane in $\mathbb{R}^k$, then the image measure has polynomial Fourier decay. Key steps in the proof include establishing a uniform Lojasiewicz-type inequality for self-similar measures, and using the decay of the Fourier transform of $μ$ outside a very small exceptional set of frequencies. As an application of our results, we prove polynomial Fourier decay for self-conformal measures on $\mathbb{C}$ for a large class of complex analytic IFSs which are not self-similar but are conjugate to a linear IFS via an analytic map.

Lovász' famous Hamiltonicity conjecture (1969) states that every connected vertex-transitive graph has a Hamiltonian path. A stronger version of the conjecture, often attributed to Thomassen (1978), states that every sufficiently large such graph even has a Hamiltonian cycle. Despite the great amount of attention these conjectures have attracted over the past decades both in the combinatorial and algebraic communities, for more than 40 years the best known lower bound for the maximum length of a cycle (path) in a connected vertex-transitive graph of order $n$ remained of the form $Ω(\sqrt{n})$, due to Babai (1979). A series of recent works has successively improved the exponent in this lower bound further. In this paper, improving the previous state-of-the-art bound $Ω(n^{9/14})$ due to Norin et al.~(2025), we prove that every connected vertex-transitive graph of order $n$ contains a cycle of length at least $n^{2/3-o(1)}$. This hits a natural barrier for several existing approaches from previous work. Our proofs combine recent embedding techniques for paths in sublinear expanders, sublinear expander decompositions of almost-regular graphs, and several additional combinatorial ideas.

Dense sampling records what an animation system actually evaluated, but it produces a poor final representation: every sampled frame can become a key, edit handles become noisy, and animated vector paths remain hard to adjust. Existing reducers usually treat the two axes separately: animation-curve reducers reduce key timing, while curve and path simplifiers reduce geometry. When applied independently to animated paths, these methods can break point identity across frames, change vertex structure over time, or provide no single error budget that covers both timing and shape. bbsolver frames the task as tolerance-bounded spatiotemporal reduction. A host application, such as After Effects or Blender, samples temporal and spatial animation into a documented JSON bundle; the standalone solver chooses sparse keys, interpolation metadata, and path representation; and the output is accepted only if replayed samples remain within the requested worst-case error. The same solver core can be used by any application that can export samples and write back returned keys or paths. In After Effects validation, solved keys written back into AE and re-sampled from AE playback reduce a DUIK humanoid walk cycle from 12,684 samples to 540 keys at epsilon=1, a 23.5x reduction, and an ant rig from 11,956 samples to 653 keys, an 18.3x reduction, with maximum errors below 1 px and 1 degree. A Blender-sampled FBX mocap retarget reaches 214 keys from 13,455 samples at epsilon=3; baselines tuned to matched measured accuracy require 4.5x to 27.5x more scalar key entries. For vector paths, bbsolver supports reduction when vertex identity/order is constant over time and diagnostics for variable-vertex-count streams, including a 6.7x After Effects-compatible procedural-path compression and exact transition-timing recovery in a diagnostic case.

In this paper, we study the monogeneity of a special class of composed polynomials of the form $ (f \circ g)(x) = (x^m + c)^n + a(x^m + c)^{n-1} + d(x^m + c)^{n-2} + b,$ where \( f(x) = x^n + a x^{n-1} + d x^{n-2} + b \in \mathbb{Z}[x] \) satisfies \( a^2 = 4d \) and \( g(x) = x^m + c \in \mathbb{Z}[x] \). Assuming that \( (f \circ g)(x) \) is irreducible over \( \mathbb{Q} \), we obtain necessary and sufficient conditions on the parameters \( a, b, c, d, m, n \) for the polynomial to be monogenic. These conditions help to identify when the set \( \{1, θ, \dots, θ^{mn-1}\} \) forms an integral basis of the number field \( \mathbb{Q}(θ) \), where \( θ\) is a root of \( (f \circ g)(x) \). We also provide lower bound for the counting of such monogenic polynomials. Furthermore, we study the behaviour of solutions to certain related differential equations and present a class of polynomials with non-square-free discriminants as an application of the main results.

We study an online version of the robust mean change point detection problem under a dynamic Huber contamination model with arbitrary contamination distribution and inlier distribution possessing exponentially- or polynomially-decaying tails. This robustness framework is systematically studied for the first time in the change point literature. For univariate data, we characterise the detection delay by partitioning the parameter space into four regimes, in terms of the true change location, signal size and contamination level. Efficient detection procedures are accompanied by matching lower bounds, up to poly-logarithmic factors. For the multivariate setting, we devise an efficient robust mean testing procedure and apply this to the robust online change point problem. The theoretical analysis of the robust mean testing procedure is the first in dealing with both Huber contamination and heavy-tailedness, and is thus of independent interest. Extensive numerical experiments are conducted to support our theoretical findings.

The triangle packing number $ν(G)$ of a graph $G$ is the maximum size of a set of edge-disjoint triangles in $G$. Tuza conjectured that in any graph $G$ there exists a set of at most $2ν(G)$ edges intersecting every triangle in $G$. We show that Tuza's conjecture holds in the random geometric graph for a large range of densities. We also study the problem of covering almost all edges of the random geometric graph with edge-disjoint copies of some fixed graph $F$. In particular, we show the existence of almost-perfect packings for an infinite family of $F$, and state some negative results as well.

For a clique $K_r$, a graph is $K_r$-saturated if it contains no copy of $K_r$ and the addition of any edge from its complement creates a $K_r$. A classical result of Erdős-Hajnal-Moon and Zykov shows that the number of edges of an $n$-vertex $K_r$-saturated graph is at least $(r-2)n-\binom{r-1}{2}$. In this paper, we focus on the number of edges of the $K_r$-saturated graphs with a fixed matching number. Let $G$ be an $n$-vertex $K_r$-saturated graph with matching number $ν(G) = s$. For sufficiently large $n$, we prove that the number of edges \begin{equation*} e(G)\geq \left\{\begin{array}{cl}{(r-1)n-\frac{r}{2}(r-1)-1,}&{\quad\mathrm{if}~s=r-1;}\\{(r-1)n + (s-r)^2 - \frac{1}{2}(r+2)(r-3) - 5,}&{\quad\mathrm{if}~s>r-1.}\\\end{array}\right. \end{equation*} Moreover, we completely characterize the graphs attaining the equality.

We calculate the ``kinematic'' corrections $t/P_z^2$ and $m_N^2/P_z^2$ to the short distance expansion of gauge-invariant nonlocal quark-antiquark operators sandwiched between nucleon states with different momenta. Here $t$ is the momentum transfer, $m_N$ is the nucleon mass and $P_z$ is the momentum component in the direction of the quark-antiquark separation, which is assumed to be large. These matrix elements can be calculated in lattice QCD and, at leading twist, expressed in terms of moments of the generalized parton distrubutions (GPDs). Our results allow one to control one of principal uncertainties in such calculations and extend their region of applicability to larger momentum transfers, which is important in the quest to access the three-dimension image of the proton. The calculated corrections turn out to be significant for a realistic lattice QCD setup.

We introduce a stochastic probing problem with correlated items. In our model, which we call Bayesian Probing, the correlations are modeled by an underlying graph $G$. Each vertex is independently active with a known probability. Each item corresponds to an edge in the graph. Probing an edge has some cost, gives some reward if both endpoints are active, and also reveals the state of its endpoints. Hence a probe induces a Bayesian update on the remaining edges. The goal is to adaptively probe items/edges subject to a knapsack constraint to maximize the expected total reward obtained from the probed edges. Bayesian Probing generalizes stochastic knapsack and stochastic probing by allowing correlations between items. Moreover, it gives a tractable model for the Bayesian Active Search problem, a popular problem considered in the machine learning community. In Bayesian Active Search, the goal is to find items in a particular class by adaptively probing at most, say $k$, items. Given a prior distribution over items, we want to compute a Bayesian policy to maximize the number of such items found. For this general problem with arbitrary priors, there are strong lower bounds on efficiently computing good policies. In this paper, we design efficient approximation algorithms for Bayesian Probing. These results give the first efficient approximation algorithms for Bayesian Active Search, for a class of practically-relevant prior distributions.

In this paper, we continue a line of research initiated by Basu, Brakensiek, and Putterman [2026] studying the sparsifiability of Hamiltonians. We focus particularly on the sparsifiability of the widely-studied Quantum Cut (QC) Hamiltonians. Our main result is that in an $n$-qubit system, any $n$-qubit QC Hamiltonian can be sparsified to $\widetilde{O}(n /\varepsilon^2)$ many terms while preserving the energy of every state up to a factor of $1 \pm \varepsilon$. Our result can be interpreted as giving an importance sampling scheme for the edges of an arbitrary graph $G$ such that the \emph{Kikuchi} graph at level $\ell$ of the sampled graph is a spectral approximation to the Kikuchi graph of $G$. Importantly, the \emph{same} sampling scheme works simultaneously for all $\ell$. The natural approach of leverage score sampling, analyzed via matrix concentration inequalities, yields a polynomially worse bound in our setting because the underlying matrices have dimension $\sim 2^n$. Instead, our approach relies on decomposing the action of these matrices into invariant subspaces. Then, by using an operator-valued inequality of Alon and Kozma [Ann. Henri Poincaré, 2020], itself building on an \emph{octopus inequality} of Caputo, Liggett, and Richthammer [J. AMS, 2010], we extend our sparsification technique to all expander graphs. We then invoke expander decomposition to extend our sparsifier to all graphs.

We study driven and open quantum systems described by a time-periodic Lindblad master equation. In closed systems, the stroboscopic dynamics can always be described by an effective time-independent Floquet Hamiltonian; this idea is the basis of Floquet engineering. However, in the presence of dissipation, the existence of an effective time-independent Floquet Lindbladian is not guaranteed due to the non-unitary nature of the evolution. Using Floquet theory, we construct a well-defined time-independent Floquet Lindbladian in an extended Sambe-Liouville space, transforming the initial time-dependent problem to a static and non-Hermitian eigenvalue problem. For harmonic driving, we introduce a matrix continued fraction method to nonperturbatively resum multiphoton processes and construct an effective Floquet Lindbladian acting only on the physical Liouville space. Compared to other high-frequency expansions, this method has the advantage of providing the whole infinite series expansion at once. Using a resolvent formalism, we show how to obtain a spectral Floquet representation of correlation functions of an open quantum system. As an application, we consider a dissipating two-level system in a linearly polarized field and calculate its resonance fluorescence spectrum. Furthermore, we consider a parametrically driven quantum dot with pump and loss for which we calculate its spectral function and current-voltage characteristics.

We investigate the demography of little red dots (LRDs) using 37 objects at $z\sim3$-$7$ with JWST/NIRSpec PRISM and grating spectra compiled from various JWST programs. We focus on spectroscopic quantities of the broad H$α$ luminosity $L_\mathrm{Hα,broad}$ (and the broad H$β$ luminosity $L_\mathrm{Hβ,broad}$ where available) and the bolometric luminosity $L_\mathrm{bol}$ represented by modified blackbody emission, avoiding quantities contaminated by host-galaxy emission (e.g., total H$α$ luminosity). We identifiy a tight scaling relation between $L_\mathrm{Hα,broad}$ and $L_\mathrm{bol}$, supporting the interpretation that these emissions are primarily powered by the central engine. Interestingly, the $L_\mathrm{Hα,broad}$-$L_\mathrm{bol}$ scaling relation of LRDs is enhanced by a factor of $\sim40$ in $L_\mathrm{Hα,broad}$ relative to that of low-$z$ Type 1 AGN. A similar trend is found in the $L_\mathrm{Hβ,broad}$-$L_\mathrm{bol}$ relation, although the enhancement in $L_\mathrm{Hβ,broad}$ is smaller, only by a factor of $\sim10$. We explore the physical origin of these enhancements and find that \textsc{Cloudy} photoionization modeling within the classic locally optimally-emitting cloud (LOC) framework can explain them through an increase in the covering factor from $\sim20$\% (Type 1 AGN) to $\sim100$\% (LRDs), together with an increase in the hydrogen column density from $N_\mathrm{H}\sim10^{23}\,\mathrm{cm}^{-2}$ to $\gtrsim10^{24}\,\mathrm{cm}^{-2}$, with a preferred gas density of $\sim10^{10}\,\mathrm{cm}^{-3}$, successfully reproducing the modified blackbody emission. Such a nearly unity covering factor without requiring a gas density increase may result from a significant increase in the BLR filling factor or size, corresponding to a ``stuffed BLR" or ``giant BLR," respectively.

Bidirectional quantum key distribution (QKD) protocols face persistent challenges related to classical disclosure, confinement of the signal space to predictable subspaces, and limited detectability under substitution or entanglement-swapping attacks. In this work, we present a Bell-state extension of the Loop-Back QKD architecture that improves efficiency and detectability while preserving its defining feature of a simplified, measurement-free remote terminal. The protocol employs entangled Bell states together with deterministic local Pauli encoding at the remote node. A central element is that Alice privately prepares and knows the initial Bell state, which serves as a hidden reference enabling her to interpret the Bell-state transition induced by Bob, while preventing an adversary from reconstructing the encoding without access to this reference. By exploiting both intra- and inter-family Bell transitions, the scheme expands the effective signal space beyond the subspace restrictions of earlier two-way protocols. Alice performs a Bell-state measurement to deterministically infer Bob's operation without any basis sifting. Although the traveling subsystem remains locally maximally mixed, concealing the initial Bell family amplifies disturbance under separable substitution strategies, yielding an intrinsic detection probability of approximately 3/4 per round. From an efficiency perspective, the protocol lifts the intrinsic post-selection limitation of single-qubit Loop-Back schemes: the effective throughput is bounded only by the Bell-state measurement success probability, reaching up to 50% in linear-optical implementations. These features make the proposed scheme particularly suitable for mobile or edge-based QKD scenarios, where passive remote nodes must operate under high loss and limited interaction times.

Superconducting resonators coupled to semiconductor quantum dots provide a powerful platform to investigate light-matter interaction and decoherence mechanisms in solid-state quantum systems. Here we study a hybrid circuit quantum electrodynamics architecture consisting of a GaAs double-quantum-dot charge qubit capacitively coupled to a high-impedance, frequency-tunable SQUID-array resonator. By tuning the qubit transition frequency over the range $ω_\mathrm{q}/2π\sim 3$-$6$ GHz, we perform frequency-resolved decoherence spectroscopy of the charge qubit across a broad energy window. Time-resolved measurements enable us to disentangle relaxation and pure dephasing processes and to identify distinct decoherence regimes as a function of qubit frequency. We find that at lower frequencies ($\leq 4.5$ GHz) dephasing dominates the qubit linewidth, whereas at higher frequencies energy relaxation becomes the leading contribution. The measured frequency dependence of the relaxation rate exhibits a cubic scaling, consistent with charge-qubit decay dominated by coupling to a piezoelectric phonon bath and providing frequency-resolved access to the corresponding phonon-induced spectral density. Our results show that hybrid semiconductor--superconducting circuits can serve as sensitive spectroscopic tools to probe microscopic decoherence mechanisms relevant for a wide range of hybrid quantum devices.

We present a comprehensive study of Little Red Dots (LRDs) at 2.3 < z < 7.4 using NIRCam photometry and NIRSpec MSA/PRISM spectra from the ongoing NEXUS program. Photometric selection combining several commonly adopted methods yields a high completeness of about 85% for LRD selection over this redshift range and for a flux limit of F444W < 26. The overall purity is about 60%, with contamination from emission-line galaxies and normal active galactic nuclei (AGNs), as well as dwarf stars. Most (>90%) of the spectroscopically confirmed LRDs have robust broad-line detection. Our spectroscopic sample of 36 LRDs displays the full range of spectral diversity of LRDs. It includes objects with extreme Balmer breaks similar to the LRD "Cliff", as well as objects with moderately reddened rest-optical continua that can be fit with low-temperature blackbody components in the recent BH* model framework. The broad H$α$ emission is correlated with the continuum emission at 5100 Angstrom, suggesting common origins for these emission components; the narrow [O III] emission, however, is poorly correlated with the optical continuum. We do not find evidence of redshift evolution in these spectral properties. The space density of LRDs declines toward z about 2, opposite to the trend for normal AGNs, although low-luminosity LRDs at z about 2-4 may be more abundant than currently probed by ground-based searches. The clustering of LRDs suggests that they live in dark matter halos of several times $10^{11}\ h^{-1}$ solar masses, albeit with large uncertainties. Overall, these results are consistent with recent observations of LRDs and with the emerging picture of accreting SMBHs enshrouded in dense gas envelopes as the origin of LRDs.

We present an FPGA-based implementation of a scanning transfer cavity lock (STCL) for laser frequency stabilization, allowing for the simultaneous stabilization of multiple laser sources with respect to a single reference laser by means of a continuously scanned Fabry-Perot cavity. By exploiting the FPGA architecture to simultaneously perform cavity scanning, peak detection, and feedback actuation, we minimize latency and allow independent control loops for several lasers within a single device, offering direct scalability. The system performance is analyzed through heterodyne measurements from short ($<1\,$s) to long ($\sim20\,$hours) timescales. The end-to-end locking performance is validated through atomic spectroscopy of ytterbium atoms in a magneto-optical trap, demonstrating sub-MHz absolute frequency stability over several hours for the stability transfer across $\sim 150\,$nm in the visible-wavelength range. Importantly, we demonstrate a novel fast-scanning approach based on acousto-optic modulator (AOM) frequency modulation, enabled by the low detection latency of our FPGA implementation. This increases significantly the effective locking bandwidth and reduces the intrinsic noise of the system with respect to standard piezo-actuated scanning of the cavity length, allowing to reach sub-$100\,$kHz long-term stability and offering perspectives for laser-line narrowing. Owing to its modularity, low cost and ease of implementation within the open-source PyRPL firmware package for the STEMlab Red Pitaya platform, our architecture offers a compact and flexible alternative to existing STCL and locked-cavity implementations, providing a practical approach to the operation of a state-of-the-art cold-atom experiment without relying on any atomic references for laser stabilization.

We show that strongly amplified dynamical responses in cavity optomechanical systems can be harnessed for enhanced quantum sensing. By tuning the optomechanical interaction to a regime of enhanced susceptibility, weak perturbations produce disproportionately large changes in the system response, leading to substantially improved estimation precision. Using Gaussian estimation theory, we demonstrate that the quantum Fisher information exhibits a divergent scaling as the perturbation strength decreases, implying a corresponding suppression of the estimation error. We further show that heterodyne detection of the output cavity field yields the classical Fisher information with the same asymptotic scaling as the quantum Fisher information, demonstrating that the enhanced sensitivity is accessible with a standard measurement protocol. These results identify amplified optomechanical dynamics as a controllable resource for quantum enhanced sensing and metrology.

We characterize the integrand numerators that give rise to locally finite or evanescent Feynman integrals for the massless pentabox. We provide compact expressions for the generators of the corresponding ideal in terms of an adapted momentum basis and also in terms of Gram determinants. We also compute the integrals corresponding to the lowest-rank numerators in terms of polylogarithms using the HyperInt package, and in terms of pentagon functions.

Domain walls provide an excellent fit to Pulsar Timing Array (PTA) data. A distinctive feature of the associated gravitational-wave (GW) spectrum is its ultraviolet (UV) tail, which can extend into the mHz band and thereby make cross-detection with space-based interferometers such as LISA and Taiji possible. In this work, we explore the PTA-compatible parameter space of domain-wall models and study both the reconstruction prospects at LISA and Taiji and the information gain achievable through joint PTA--LISA and PTA--Taiji analyses. We find that LISA and Taiji can probe an extended region of parameter space yielding an ultraviolet tail in the milli-Hz band, even in the presence of astrophysical foregrounds. Within the PTA-supported region, however, the genuinely informative regime is more restricted and concentrated toward the high-signal edge. In the space-based-detector-only analysis, the posterior is strongly degenerate in the underlying model parameters, although one principal parameter combination can be reconstructed with high precision where the signal is sufficiently strong. When PTA-informed priors are incorporated, the additional information gain is localized to the same high-signal region: there the space-based data produce a non-negligible posterior update and strongly suppress the catastrophic LISA(Taiji)-only degeneracy, while the final posterior often retains an axis ratio comparable to that of PTA alone. Our analysis is based on a 10-dimensional Bayesian inference with two domain-wall signal parameters and eight nuisance parameters describing instrumental noise and astrophysical foregrounds. We use 49 grid injections for the LISA-only and Taiji-only analyses and 65 injections from the PTA-supported region for the joint analyses, with Clough--Tocher interpolation used to construct posterior heat maps.

We propose an analog quantum simulation of chiral magnetic dynamics using ultracold atoms in an optical superlattice. The massive Schwinger model in the zero gauge coupling limit maps onto the Rice-Mele model, with the fermion mass and topological angle encoded in the superlattice parameters. We study the real-time dynamics of the vector current following two quench protocols that drive continuous chirality injection and chirality relaxation. Simulations with realistic superlattice parameters and experimental noise demonstrates clear mass dependence of the current dynamics in both protocols, robust against experimental imperfections. The vector current may be directly measurable via single-bond-resolved detection, establishing cold atom superlattices as a viable platform for probing non-equilibrium chiral phenomena.

Diabatic quantum annealing with variationally optimized schedules can exhibit exponential speedups over conventional adiabatic quantum annealing, as was demonstrated numerically for a frustrated Ising ring model by C{ô}t{é} et al. Here we identify Landau-Zener-St{ü}ckelberg interference as the underlying mechanism for this speedup, and based on this insight we propose a variational schedule ansatz with far fewer parameters. This simplified ansatz allows us to show analytically that the classical optimization of the schedule parameters can be done in polynomial time and discuss conditions when we expect this type of mechanism to provide speedups over adiabatic annealing. Furthermore, we provide an analytical argument that coherence is an essential resource for this mechanism, which we verify numerically. We perform extensive numerical tests of the proposed ansatz and observe substantial improvements over adiabatic annealing and competitive performance in particularly challenging problem instances, including a well-studied MAXCUT instance commonly used for benchmarking. Our work shows that explicitly leveraging physical mechanisms can lead to more effective designs of variational annealing algorithms.

Cation-disordered AgBiS2 is a promising lead-free optoelectronic material, but both its ordered structure and the microscopic origin of its favorable electronic properties remain debated. Theory has proposed a mixed-coordination tendency with tetrahedral AgS4 and octahedral BiS6 units, whereas experiments mainly report octahedrally coordinated ordered and cation-disordered phases, together with local cation off-centering. Here, we combine a machine-learning interatomic potential with a deep-learning Hamiltonian to resolve the coupled structural and electronic evolution of AgBiS2 at large length scales. We identify the three-dimensional Bi-S network as the central structural motif governing both disorder stability and band-edge electronic states. At weak disorder, Ag/Bi exchange competes with the off-centering tendency of the Ag sublattice, producing strongly distorted local environments and convoluted diffraction signatures that hinder the identification of the ordered phase. With increasing disorder, BiS6-like units connect into a continuous Bi-S network, which stabilizes the rocksalt-like disordered phase. Despite strong cation disorder, AgBiS2 retains clear semiconductor-like band dispersion and develops a direct band gap. The connected Bi:p-S:p states supported by the Bi-S network preserve a dispersive conduction-band edge and a small electron effective mass. In contrast, mobile Ag disrupts the long-range periodicity of Ag-S bonding, leading to strongly localized valence states. These results clarify the structural controversy in ordered AgBiS2 and establish a unified physical picture of disorder stability and optoelectronic response in nonisovalent semiconductor alloys.

Fluid-immersed hair beds are ubiquitous in biology-from the endothelial glycocalyx and primary cilia to intestinal microvilli-where they serve as mechanosensors that transduce dynamic flow signals into biochemical regulatory responses. Despite the inherently dynamic nature of physiological flows, the dynamic mechanical properties of fluid-immersed hair beds under time-varying conditions remain poorly characterized. Here we investigate the transient rheological response of elastic hair beds to large-amplitude oscillatory shear flows at low to intermediate Reynolds number. While the hairs and fluid themselves obey linear constitutive laws, their coupled interaction produces a dynamic nonlinear response that depends sensitively on driving frequency and amplitude. We identify a crossover from a stress-lagging regime to a stress-leading regime, which is governed by an interplay between fluid viscosity, fluid inertia, and hair elasticity. A simplified rigid-beam model qualitatively captures the crossover behavior. Characterizing the dynamic flow response of soft hair beds has direct biological implications, since the lag time sensitively determines the stability of mechanosensory signaling in the feedback loops underlying essential biological processes such as vasodilation, ciliary remodeling, and tubular reabsorption. Our results establish a framework for understanding how the physical properties of biological hair beds optimize dynamic information transmission during mechanotransduction.

The second homology group is of central importance in the study of profinite rigidity of $3$-manifold groups. Although general and deep results imply that the integral homology of cocompact hyperbolic $3$-orbifold groups is computable in principle, the resulting algorithm is not practical. We develop an effective method for computing $H_2$ in the case of orbifold groups arising as finite extensions of the fundamental group of hyperbolic rational homology $3$-spheres. As a special case, this yields explicit computations of the second homology groups of all cocompact lattices between $π_1(\mathcal{W})$ and its normalizer in $\mathrm{PSL}_2(\mathbb C)$, where $\mathcal{W}$ is the Weeks manifold. We also show that these lattices are absolutely profinitely rigid, completing work by Bridson, McReynolds, Reid & Spitler in this setting. As a special case, we determine that $H_2(Γ_{\mathcal{O}}, \mathbb Z) \cong \mathbb{Z} / 2\mathbb{Z}$, where $Γ_{\mathcal{O}}$ is the normalizer of the group of units $Γ_{\mathcal{O}}^1$ in a choice of maximal order $\mathcal{O}$ of the quaternion algebra associated to $\mathcal{W}$, thereby answering a question of Bridson & Reid. Although this non-vanishing obstructs one possible construction of Grothendieck pairs in $Γ_{\mathcal{O}}^1 \times Γ_{\mathcal{O}}^1$, we use our computations to show the vanishing of the second homology of another lattice whose derived subgroup is $Γ_{\mathcal{O}}^1$, which then yields Grothendieck pairs in this direct product by a theorem of Bridson & Reid. Finally, to showcase the generality of the techniques, we also compute the second homology of some finite extensions by orientable isometries of the fundamental group of some Fibonacci manifolds $M_n$.

We study the problem of optimally sending a real-valued source through multiple uses of a channel with feedback. First, we state a set of conditions that are sufficient for an encoder to achieve maximal mutual information between the source and all the channel outputs. This set of conditions are also necessary when the channel is input-identifiable, a condition widely satisfied by common channel models. More notably, we further study the information maximization-distortion minimization problem, where the mutual information between the source and all channel outputs still needs to be maximized, while at each step, the MMSE of estimating the source from the channel outputs so far also needs to be minimized. We derive a solution to this problem for discrete channels with certain symmetries, e.g. $k$-ary symmetric or $k$-ary erasure channels. We show that for such channels the famous posterior matching scheme, while not necessary for information maximization alone, is sufficient and essentially necessary for achieving both information maximization and distortion minimization. This work also provides a new perspective of regularizing distortion-minimizing feedback communication through information maximization, which enables us to find the optimal solution that otherwise would be intractable.