We explore a simple and predictive dark matter scenario involving a complex scalar field, $ϕ$, coupled to the Higgs portal with no additional field content. In the UV, the field possesses a global $U(1)$ symmetry which is broken by mass terms and Higgs portal interactions. In the mass basis, the complex field splits into a pair of real scalars with a small mass splitting (in analogy to pseudo-Dirac fermions), such that the Higgs portal acquires both diagonal and off-diagonal terms with respect to these eigenstates. In the parameter space where the off-diagonal interaction predominates, this scenario is safe from direct detection constraints. Moreover, this model provides a viable explanation for the longstanding Galactic Center gamma-ray excess. Additionally, this model influences the Higgs potential in a way that could facilitate a strong first-order electroweak phase transition in the early universe, potentially leading to a stochastic gravitational wave background that could fall within the reach of upcoming space-based detectors.

Identifying scalable circuit architectures remains a central challenge in variational quantum computing and quantum machine learning. Many approaches have been proposed to mitigate or avoid the barren plateau phenomenon or, more broadly, exponential concentration. However, due to the intricate interplay between quantum measurements and classical post-processing, we argue these techniques often fail to circumvent concentration effects in practice. Here, by analyzing concentration at the level of measurement outcome probabilities and leveraging tools from hypothesis testing, we develop a practical framework for diagnosing whether a parameterized quantum model is inhibited by exponential concentration. Applying this framework, we argue that several widely used methods (including quantum natural gradient, sample-based optimization, and certain neural-network-inspired initializations) do not overcome exponential concentration with finite measurement budgets, though they may still aid training in other ways.

We describe an explicit presentation of the ring of integral piecewise-exponential functions on a unimodular fan as a quotient of the Stanley-Reisner ring of the fan. This gives rise to a presentation of K-rings of smooth toric varieties that is parallel to the well-known presentation of integral Chow rings as quotients of Stanley-Reisner rings.

In complex systems research, the study of higher-order interactions has exploded in recent years. Researchers have formalized various types of group interactions, such as public goods games, biological contagion, and information broadcasting, showing how higher-order networks can capture group effects more directly than pairwise models. However, equating hyperedges-edges involving more than two agents-with groups can be misleading, as it obscures the polysemous nature of ``group interactions''. For instance, many models of higher-order interactions focus on the internal state of the hyperedge, specifying dynamical rules at the group level. These models often neglect how interactions with external groups can influence behaviors and dynamics within the group. Yet, anthropologists and philosophers remind us that external norms, factors, and forces governing intergroup behavior are essential to defining within-group dynamics. In this paper, we synthesize concepts from social ontology relevant to the emerging physics of higher-order networks. We propose a typology for classifying models of group interactions based on two perspectives. The first focuses on individuals within groups engaging in collective action, where shared agency serves as the binding force. The second adopts a group-first approach, emphasizing institutional facts that extend beyond the specific individuals involved. Building on these perspectives, we introduce four dimensions to classify models of group interactions: persistence, coupling, reducibility, and alignment. For the physics of higher-order networks, we provide a hierarchy of nested mathematical models to explore the complex properties of social groups. We highlight social interactions not yet explored in the literature on higher-order networks and propose future research avenues to foster collaboration between social ontology and the physics of complex systems.

Low-altitude wireless networks (LAWNs) have been envisioned as flexible and transformative platforms for enabling delay-sensitive control applications in Internet of Things (IoT) systems. In this work, we investigate the real-time wireless control over LAWNs, where an aerial drone is employed to serve multiple mobile automated guided vehicles (AGVs) via finite blocklength (FBL) transmission. Toward this end, we adopt the model predictive control (MPC) to ensure accurate trajectory tracking, while we analyze the communication reliability using the outage probability. Subsequently, we formulate an optimization problem to jointly determine control policy, transmit power allocation, and drone trajectory by accounting for the maximum travel distance and control input constraints. To address the resultant non-convex optimization problem, we first derive the closed-form expression of the outage probability under FBL transmission. Based on this, we reformulate the original problem as a quadratic programming (QP) problem, followed by developing an alternating optimization (AO) framework. Specifically, we employ the projected gradient descent (PGD) method and the successive convex approximation (SCA) technique to achieve computationally efficient sub-optimal solutions. Furthermore, we thoroughly analyze the convergence and computational complexity of the proposed algorithm. Extensive simulations and AirSim-based experiments are conducted to validate the superiority of our proposed approach compared to the baseline schemes in terms of control performance.

We consider polynomial optimization problems on Cartesian products of basic compact semialgebraic sets. The solution of such problems can be approximated as closely as desired by hierarchies of semidefinite programming relaxations, based on classical sums of squares certificates due to Putinar and Schmüdgen. When the feasible set is the bi-sphere, i.e., the Cartesian product of two unit spheres, we show that the hierarchies based on the Schmüdgen-type certificates converge to the global minimum of the objective polynomial at a rate in $O(1/t^2)$, where $t$ is the relaxation order. Our proof is based on the polynomial kernel method. We extend this result to arbitrary sphere products and give a general recipe to obtain convergence rates for polynomial optimization over products of distinct sets. Eventually, we rely on our results for the bi-sphere to analyze the speed of convergence of a semidefinite programming hierarchy approximating the order $2$ quantum Wasserstein distance.

Let $w$ be a string of length $n$. The problem of counting factors crossing a position -- Problem 64 from the textbook ``125 Problems in Text Algorithms'' [Crochemore, Lecroq, and Rytter, 2021] -- asks to count the number $\mathcal{C}(w,k)$ (resp. $\mathcal{N}(w,k)$) of distinct substrings in $w$ that have occurrences containing (resp. not containing) a position $k$ in $w$. The solutions provided in their textbook compute $\mathcal{C}(w,k)$ and $\mathcal{N}(w,k)$ in $O(n)$ time for a single position $k$ in $w$, and thus a direct application would require $O(n^2)$ time for all positions $k = 1, \ldots, n$ in $w$. Their solution is designed for constant-size alphabets. In this paper, we present new algorithms which compute $\mathcal{C}(w,k)$ in $O(n)$ total time for general ordered alphabets, and $\mathcal{N}(w,k)$ in $O(n)$ total time for linearly sortable alphabets,for all positions $k = 1, \ldots, n$ in $w$. We further derive model-dependent optimal bounds by separating the algorithms into preprocessing and linear-time postprocessing: for $\mathcal{C}$ the preprocessing is run reporting, and for $\mathcal{N}$ it is preprocessing based on longest previous non-overlapping factors (LPnF) and longest next factors (LNF). In particular, all values $\mathcal{C}(w,k)$ can be computed in $O(n\log n)$ time over general unordered alphabets in which direct accesses to alphabet characters are restricted to equality tests, and in $O(n\logσ)$ time in the word RAM model, where $σ$ denotes the number of distinct characters occurring in $w$. For $\mathcal{N}(w,k)$, the equality-testing complexity over general unordered alphabets is $Θ(n^2)$. We also show that our upper bounds are optimal for all of the aforementioned alphabet assumptions and computation models.

We present 6GHz radio continuum observations of the galaxy cluster Abell 2744 ($z = 0.307$) obtained with the Karl G. Jansky Very Large Array (VLA) as part of the VLA Frontier Fields program, the goal of which is to explore the radio continuum emission from high-redshift galaxies that are magnified by foreground massive galaxy clusters. With an rms noise of $\approx 1 μ$Jy beam$^{-1}$, in the image plane, and sub-arcsec angular resolution ($θ_{1/2}=0.82''$), this is the deepest and most detailed radio image of Abell 2744 ever obtained. A total of 93 sources is detected with a peak signal-to-noise ratio $\geq5$, of which 46 have optical/near-infrared (IR) counterparts with available redshift, magnification ($μ$), and stellar mass (${M}_*$) estimates. The radio sources are distributed over a redshift of 0.15 to 3.55, with a median redshift value of $z = 0.93^{+1.48}_{-0.63}$ and with a range mass from $5.5\times 10^{9} \,\rm{M}_{\odot}$ to $1.3\times 10^{11} \,\rm{M}_{\odot}$. A comparison between the radio-based star formation rates (SFRs) and those derived from ultraviolet-to-near IR data reveals that radio SFRs are typically an order of magnitude higher. This discrepancy is likely a result of strong dust obscuration affecting the UV-to-NIR tracers. We look for radio counterparts of the so-called ``Little Red Dots (LRDs)'' galaxies at $z\approx6$ seen behind Abell 2744, but find no significant detections. After stacking, we derive a 3$σ$ upper limit to the 6GHz radio luminosity of LRDs of $4.1\times 10^{39}\,\rm erg\,s^{-1}$. Finally, we present a sample of 22 moderately/strongly lensed galaxies ($μ\gtrsim 2$) in the VLA Frontier Fields survey, which provides a zoomed view of the star formation processes within main sequence galaxies at $z\approx 1-2$.

We introduce a novel and flexible framework for constructing locally adaptive Hamiltonian Monte Carlo (HMC) samplers by Gibbs sampling the algorithm's tuning parameters conditionally based on the position and momentum at each step. For adaptively sampling path lengths, our Gibbs self-tuning (GIST) approach encompasses randomized HMC, multinomial HMC, the No-U-Turn Sampler (NUTS), and the Apogee-to-Apogee Path Sampler as special cases. We exemplify the GIST framework with a novel alternative to NUTS for locally adapting path lengths, evaluated with an exact Hamiltonian for a high-dimensional, ill-conditioned Gaussian measure and with the leapfrog integrator for a suite of diverse models.

We establish the theoretical foundation for a variant of the method of fundamental solutions (MFS), where the source points $\{q_j\}_{j=1}^\infty$ accumulate towards the domain in a Whitney fashion, meaning that their separation is proportional to the distance to the domain. We prove that the normalized Lusin wavelets $ψ_j(w) = b_j(w-q_j)^{-2}$ constitute a generalized basis, known as a frame, for the Hardy subspace of $L_2$-traces of holomorphic functions on the domain. Consequently, our method, where $ψ_j$ are used as basis functions in the MFS, enables a numerically stable approximation of solutions to Laplace boundary value problems, even when the solutions lack analytic continuation across the boundary. Despite the source points accumulating towards the domain, our computations achieve at least 12 digits of accuracy uniformly up to the boundary, including cases when the solution lacks analytic continuation or when the boundary has corners.

The matrix exponential restricted to skew-symmetric matrices has numerous applications, notably in view of its interpretation as the Lie group exponential and Riemannian exponential for the special orthogonal group. We characterize the invertibility of the derivative of the skew-restricted exponential, thereby providing a simple expression of the tangent conjugate locus of the orthogonal group. In view of the skew restriction, this characterization differs from the classic result on the invertibility of the derivative of the exponential of real matrices. Based on this characterization, for every skew-symmetric matrix $A$ outside the (zero-measure) tangent conjugate locus, we explicitly construct the domain and image of a smooth inverse -- which we term \emph{nearby logarithm} -- of the skew-restricted exponential around $A$. This nearby logarithm reduces to the classic principal logarithm of special orthogonal matrices when $A=\mathbf{0}$. The symbolic formulae for the differentiation and its inverse are derived and implemented efficiently. The extensive numerical experiments show that the proposed formulae are up to $3.9$-times and $3.6$-times faster than the current state-of-the-art robust formulae for the differentiation and its inversion, respectively.

In this paper, we develop a unified theory of reducibility and indecomposability for Shen-Larsson modules over the Witt, special and Hamiltonian type Lie algebras on a torus. Our approach is based on a rank-one mechanism governing irreducible submodules, Loewy filtrations, rank reduction, uniseriality and mixed complex structures. We first provide a uniform intrinsic characterization of the trivial and fundamental representations of $gl_N, sl_N, sp_{2n}$ in terms of quadratic relations satisfied by rank-one elements of these matrix Lie algebras and utilize it to determine the irreducibility of Shen-Larsson modules over $W_N, S_N, H_{2n}$. Using the rank-one operators arising from these relations, we then construct rank-reducing operators corresponding to distinguished lattice directions and apply them to show that the submodule structure of the reducible Shen-Larsson modules over $W_N, S_N, H_{2n}$ attached to the fundamental representations of $gl_N, sl_N, sp_{2n}$ respectively are generically uniserial. In the Hamiltonian case, we show that the submodules of these reducible Shen-Larsson modules come from kernels and images of differentials of the de Rham and Koszul-type complexes. These differentials anti-commute and thus endow the tensor field modules with a mixed complex structure, which also admit a natural interpretation formally analogous to the de Rham differential and co-differential type operator appearing in symplectic Hodge theory. In particular, we provide complete answers to the questions recently posed by Pei-Sheng-Tang-Zhao [J. Inst. Math. Jussieu 2023] concerning the structure of Shen-Larsson modules over $H_{2n}$.

This paper studies semiparametric Bayesian inference for the average treatment effect on the treated (ATT) within the difference-in-differences (DiD) research design. We propose two new Bayesian methods with frequentist validity. The first one is the semiparametric Bayesian outcome regression, where we place a Gaussian process prior on the conditional mean function of the control group. The second method is a doubly robust Bayesian procedure that adjusts the prior distribution of the conditional mean function and subsequently corrects the posterior distribution of the resulting ATT. We prove new semiparametric Bernstein-von Mises (BvM) theorems for both proposals. Monte Carlo simulations and an empirical application demonstrate that the proposed Bayesian DiD methods exhibit strong finite-sample performance. We also present extensions of the canonical DiD approach, incorporating clustered data and staggered entry with multiple periods.

The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum processes in computer science. In this work, I determined the lower bound of the computational complexity of knapsack problems. I investigated the origin of nontrivial topological structures in these hard problems. It was uncovered that the nontrivial topological structures arise from the contradictory between the three-dimensional character of the lattice and the two-dimensional character of the transfer matrices used in the quantum statistics mechanism. I illustrated a phase diagram for the non-deterministic polynomial (NP) vs polynomial (P) problems, in which a NP-intermediate (NPI) area exists between the NP-complete problems and the P-problems, while the absolute minimum core model is at the border between the NPI and the NP-complete problems. The absolute minimum core model of the knapsack problem cannot collapse directly into the P-problem. Under the guide of the results, one may develop the best algorithms for solving various optimum problems in the shortest time, being in subexponential and superpolynomial. This work illuminates the road on various fields of science ranging from physics to biology to finances, and to information technologies.

We establish a quantitative version of the isoperimetric inequality for the torsion of multiply connected domains, among sets with given area and with given joint area of the holes. Since the optimal shape is the annulus, we investigate how a given domain approaches an annular configuration when its torsion is close to the optimal value. Our result shows that when the torsional rigidity is nearly optimal, the domain $Ω$ must be close to an annulus.

Achieving robust and scalable remote quantum entanglement is a fundamental challenge for the development of distributed quantum networks and modular quantum computing systems. Along this, perfect state transfer (PST) and fractional state transfer (FST) have emerged as promising schemes for quantum state transfer and remote entanglement generation using only nearest-neighbor couplings. However, the current implementations suffer from quantum loss and limited parameter tunability. In this work, we propose a new quantum state transfer scheme based on a zig-zag configuration, which introduces a controlling parameter for PST and FST. We show that this new parameter can suppress the population in the intermediate qubits, thereby reducing losses. We experimentally demonstrate the dynamics of different configurations on a superconducting quantum processor, achieving an $18\%$ reduction in error for remote Bell state generation in a 1D ($1\times5$) qubit chain, and exhibit robustness against certain types of noise. Then we extend our approach to a 2D network, successfully generating a W state among the four corner qubits. These results highlight the potential of our enhanced quantum state transfer scheme for scalable and noise-resilient quantum communication and computing.

Spreadsheet tools are widely accessible to and commonly used by K-12 students and teachers. While spreadsheets are not ideal for many types of statistical analysis, they have an important role in data collection and organization. From a pedagogical standpoint, spreadsheets make data visible and easy to interact with, facilitating student engagement in data exploration, analysis, and computation. Though not suitable for all tasks, spreadsheets can facilitate learning and practicing data and computing skills for K-12 students. This paper 1) demonstrates the potential utility of spreadsheets in K-12; 2) reviews prior frameworks and standards that are relevant for K-12 data tools; and 3) proposes data-driven data skills to help develop data acumen and computational fluency. We provide some example activities, identify challenges and barriers to adoption, suggest pedagogical approaches to ease the learning curve for instructors and students, and discuss the need for professional development to facilitate deeper use of spreadsheets for data science and STEM disciplines.

In this work, the computational complexity of a spin-glass three-dimensional (3D) Ising model (for the lattice size N = lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that an absolute minimum core (AMC) model consisting of a spin-glass 2D Ising model interacting with its nearest neighboring plane, has its computational complexity O(2^mn). Any algorithms to make the model smaller (or simpler) than the AMC model will cut the basic element of the spin-glass 3D Ising model and lost many important information of the original model. Therefore, the computational complexity of the spin-glass 3D Ising model cannot be reduced to be less than O(2^mn) by any algorithms, which is in subexponential time, superpolynomial.

In this paper, we introduce two flexible extensions of the classical Gini index, referred to as the extended lower and upper Gini indices. The proposed measures are based on the differences between an observation and the minimum and maximum order statistics in samples of size $m\geqslant 2$ and reduce to the classical Gini coefficient when $m=2$. Unlike conventional Gini-type measures, they provide a position-oriented assessment of inequality relative to the lower and upper tails of the distribution. We establish the consistency and asymptotic normality of the proposed estimators under mild regularity conditions. For gamma-distributed populations, we derive exact expressions for their expectations and prove their unbiasedness, thereby extending previous results of [Deltas, G. 2003. The small-sample bias of the gini coefficient: Results and implications for empirical research. Review of Economics and Statistics 85:226-234] and [Baydil, B., de la Peña, V. H., Zou, H., and Yao, H. 2025. Unbiased estimation of the gini coefficient. Statistics & Probability Letters 222:110376]. The finite-sample performance of the estimators is investigated through Monte Carlo simulations, and an application to 2023 GDP per capita data from South American countries illustrates the practical usefulness of the proposed measures. The results show that the extended lower and upper Gini indices provide a richer and more informative characterization of inequality than traditional Gini-type measures.

We introduce $Σ$-Attention, a Transformer-based operator-learning framework to address a key computational challenge in correlated materials. Our approach utilizes an Encoder-Only Transformer as an ansatz to approximate the self-energy operator of strongly correlated electronic systems. By creating a batched dataset that combines results from three complementary approaches: many-body perturbation theory, strong-coupling expansion, and exact diagonalization, each effective in specific parameter regimes, $Σ$-Attention is applied to learn a universal approximation for the self-energy operator that is valid across all regimes. This hybrid strategy leverages the strengths of existing methods while relying on the transformer's ability to generalize beyond individual limitations. More importantly, the scalability of the Transformer architecture allows the learned self-energy to be extended to systems with larger sizes, leading to much improved computational scaling. Using the 1D Hubbard model, we demonstrate that $Σ$-Attention can accurately predict the Matsubara Green's function and hence effectively captures the Mott transition at finite temperature. Our framework offers a promising and scalable pathway for studying strongly correlated systems with many possible generalizations.

Abért and Virág proved in 2005 that the Hausdorff dimension of a non-trivial normal subgroup of a level-transitive 1-dimensional subgroup of the group of $p$-adic automorphisms $W_p$ is always 1. They further asked whether the same holds replacing 1-dimensional with positive dimensional. On the one hand, we provide a negative answer in general by giving counterexamples where the non-trivial normal subgroups are not all 1-dimensional. Furthermore, these counterexamples are pro-$p$ subgroups of $W_p$ with positive Hausdorff dimension in $W_p$ but with non-trivial center, and thus not weakly branch. On the other hand, we restrict ourselves to the class of self-similar groups and answer the question of Abért and Virág in the positive in this case. Along the way, we generalize a result of Abért and Virág on the closed subgroups of $W_p$ being perfect in the sense of Hausdorff dimension to closed subgroups of any iterated wreath product $W_H$ and show that self-similar positive-dimensional subgroups of $W_H$ do not satisfy any group law.

This paper presents our submission to the PROCESS Challenge 2025, focusing on spontaneous speech analysis for early dementia detection. For the three-class classification task (Healthy Control, Mild Cognitive Impairment, and Dementia), we propose a cascaded binary classification framework that fine-tunes pre-trained language models and incorporates pause encoding to better capture disfluencies. This design streamlines multi-class classification and addresses class imbalance by restructuring the decision process. For the Mini-Mental State Examination score regression task, we develop an enhanced multimodal fusion system that combines diverse acoustic and linguistic features. Separate regression models are trained on individual feature sets, with ensemble learning applied through score averaging. Experimental results on the test set outperform the baselines provided by the organizers in both tasks, demonstrating the robustness and effectiveness of our approach.

Recent breakthroughs in Automatic Speech Recognition (ASR) have enabled fully automated Alzheimer's Disease (AD) detection using ASR transcripts. Nonetheless, the impact of ASR errors on AD detection remains poorly understood. This paper fills the gap. We conduct a comprehensive study on AD detection using transcripts from various ASR models and their synthesized speech on the ADReSS dataset. Experimental results reveal that certain ASR transcripts (ASR-synthesized speech) outperform manual transcripts (manual-synthesized speech) in detection accuracy, suggesting that ASR errors may provide valuable cues for improving AD detection. Additionally, we propose a cross-attention-based interpretability model that not only identifies these cues but also achieves superior or comparable performance to the baseline. Furthermore, we utilize this model to unveil AD-related patterns within pre-trained embeddings. Our study offers novel insights into the potential of ASR models for AD detection.

Atomic packing is an important metric for characterizing protein structures, as it significantly influences various features including the stability, the rate of evolution and the functional roles of proteins. Packing in protein structures is a measure of the overall proximity between the proteins' atoms and it can vary notably among different structures. However, even single domain proteins do not exhibit uniform packing throughout their structure. Many different methods have been used to measure the quality of packing in proteins, identify factors that influence it, and their possible implications. In this work, we examine atomic density distributions derived from 21,255 non-redundant protein structures and show that statistically significant differences between those distributions are present. The biomolecular assembly unit was chosen as a representative for these structures. Several protein structures deviate significantly and systematically from the average packing behavior. Hierarchical clustering indicated that there are groups of structures with similar atomic density distributions. Search for common features and patterns in these clusters showed that some of them include proteins with characteristic structures such as coiled-coils and cytochromes. Certain classification families such as hydrolases and transferases have also a preference to appear more frequently in dense and loosely-packed clusters respectively. Regarding factors influencing packing, our results support knowledge that larger structures have a smaller range in their density values, but tend to be more loosely packed, compared to smaller proteins. We also used indicators, like crystallographic water molecules abundance and B-factors as estimates of the stability of the structures to reveal its relationship with packing.

The common feature for a nontrivial hard problem is the existence of nontrivial topological structures, non-planarity graphs, nonlocalities, or long-range spin entanglements in a model system with randomness. For instance, the Boolean satisfiability (K-SAT) problems are nontrivial, due to the existence of non-planarity graphs, nonlocalities, and the randomness. In this work, the relation between a spin-glass three-dimensional (3D) Ising model with the lattice size N = mnl and the K-SAT problems is investigated in detail. With the Clifford algebra representation, it is easy to reveal the existence of the long-range entanglements between Ising spins in the spin-glass 3D Ising lattice. The internal factors in the transfer matrices of the spin-glass 3D Ising model lead to the nontrivial topological structures and the nonlocalities. At first, we prove that the absolute minimum core (AMC) model exists in the spin-glass 3D Ising model, which is defined as a spin-glass 2D Ising model interacting with its nearest neighboring plane. Any algorithms, which use any approximations and/or break the long-range spin entanglements of the AMC model, cannot result in the exact solution of the spin-glass 3D Ising model. Second, we prove that the dual transformation between the spin-glass 3D Ising model and the spin-glass 3D Z2 lattice gauge model shows that it can be mapped to a K-SAT problem for K > = 4 also in the consideration of random interactions and frustrations. Third, we prove that the AMC model is equivalent to the K-SAT problem for K = 3.

RR Lyrae stars (RRLs) are valuable probes of both Milky Way assembly and stellar-evolution physics. Using a sample 6,240 RRLs obtained in the first year of the Dark Energy Spectroscopic Instrument (DESI) survey, we investigate the metallicity of RRLs and its correlation with their pulsation properties. We find that (1) a clear correlation between period and [Fe/H] reinforces the view that the long-standing Oosterhoff dichotomy arises from the scarcity of intermediate-metallicity Galactic globular clusters hosting sizeable RRL samples; (2) high-amplitude short-period and small-amplitude short-period variables are comparatively metal-rich, with mean [Fe/H] = $-1.39 \pm 0.27$ and $-1.30 \pm 0.28$, respectively; (3) in double-mode pulsators (RRd) the metallicity declines smoothly with increasing fundamental-mode period, and anomalous RRd stars occupy a remarkably narrow [Fe/H] range relative to classical RRd stars; (4) this spectroscopic sample let us, for the first time, place empirical constraints on the metallicity-dependent topology of the instability strip using phase-corrected effective temperatures and a large number of RRLs, where we observe an instability strip that moves towards cooler $T_{\rm eff}$ with declining [Fe/H] with a width roughly consistent with stellar-evolution models; and (5) a subset of metal-rich RRLs exhibits orbits consistent with disk membership and halo kinematics. Our results confirm the tantalizing potential of DESI for Galactic and stellar astrophysics and highlight the importance of the even larger samples of RRLs and data-processing improvements forthcoming in future DESI data releases.

We study synchronizing partial DFAs, which extend the classical concept of synchronizing complete DFAs and are a special case of synchronizing unambiguous NFAs. A partial DFA is called synchronizing if it has a word (called a \emph{reset word}) whose action brings a non-empty subset of states to a unique state and is undefined for all other states. The class of strongly connected partial DFAs is precisely the class of DFAs recognizing the Kleene star of prefix codes. While in the general case the problem of checking whether a partial DFA is synchronizing is PSPACE-complete, we show that in the strongly connected case, this problem can be efficiently reduced to the same problem for a complete DFA. Using combinatorial, algebraic, and formal languages methods, we develop techniques that relate main synchronization problems for strongly connected partial DFAs to the same problems for complete DFAs. In particular, this includes the Černý and the rank conjectures, the problem of finding a reset word, and upper bounds on the length of the shortest reset words of literal automata of finite prefix codes. We conclude that solving fundamental synchronization problems is equally hard in both models, as an essential improvement of the results for one model implies an improvement for the other.

A family of simplicial complexes connected by simplicial maps and indexed by a finite poset $P$ is called a poset tower. Poset towers subsume multi-parameter filtrations, zigzag filtrations, and one-parameter simplicial towers, while allowing arbitrary finite posets and simplicial maps. The homology of a poset tower is a $P$-persistence module. To compute it globally over $P$, we consider the chain complex segment of $P$-persistence modules $C_{\ell-1}\xleftarrow{\partial_{\ell}}C_\ell \xleftarrow{\partial_{\ell+1}}C_{\ell+1}$ induced by the simplices of the tower. Unlike in one-critical multi-filtrations, the chain modules $C_\ell$ need not be projective and may have a complicated structure. We address the problem of replacing this segment by projective modules and $P$-graded matrices while preserving homology. The resulting projective implicit representation (PiRep) plays the role of the graded boundary-matrix representation in the classical persistence algorithm: it converts simplicial data into algebraic input on which persistent homology can be computed globally over $P$. In particular, a PiRep can be used as input to algorithms for computing minimal presentations of persistent homology. We give an efficient algorithm to compute a PiRep from a poset tower. It constructs degreewise minimal presentations and asymptotically minimal second terms of projective resolutions of the chain modules $C_\ell$, lifts the boundary maps $\partial_\ell$ to these resolutions, and assembles the resulting data into a PiRep using an additional correction term. The method is tailored to chain complexes induced by poset towers and computes the required algebraic data combinatorially, exploiting their special structure and avoiding general-purpose algebraic reduction. In the context of poset towers, it is fully general and can serve as a foundation for efficient algorithms on specific posets.

Next-generation gravitational wave (GW) observatories, such as the Einstein Telescope (ET) and Cosmic Explorer, will observe binary neutron star (BNS) mergers across cosmic history, providing precise parameter estimates for the closest ones. Innovative wide-field observatories, such as the Vera Rubin Observatory, will quickly cover large portions of the sky with unprecedented sensitivity to detect faint transients. This study aims to assess the prospects for detecting optical emissions from BNS mergers with next-generation detectors, considering how uncertainties in neutron star (NS) population properties and microphysics may affect detection rates. Starting from BNS merger populations exploiting different NS mass distributions and equations of state (EOSs), we model the GW and kilonova (KN) signals based on source properties. We model KN ejecta through numerical-relativity informed fits, considering the effect of prompt collapse of the remnant to black hole and new fitting formulas appropriate for more massive BNS systems, like GW190425. We include optical afterglow emission from relativistic jets consistent with observed short gamma-ray bursts. We evaluate the detected mergers and the source parameter estimations for different geometries of ET, operating alone or in a network of current or next-generation GW detectors. Finally, we estimate the number of detected optical signals simulating realistic observational strategies by the Rubin Observatory. ET as a single observatory will enable the detection of about ten to a hundred KNe per year by the Rubin Observatory. This improves by a factor of about 10 already when operating in the network with current GW detectors. Detection rate uncertainties are dominated by the poorly constrained local BNS merger rate, and depend to a lesser extent on the NS mass distribution and EOS.

Fe$_2$GeTe$_3$ is a paradigmatic van der Waals magnet with the full microscopic picture of magnetic interactions still under debate. Here, we use scanning tunneling microscopy and spectroscopy at 1.1 K to map out the low-energy physics on the surface. In agreement with previous works, we observe a spatially varying Fano lineshape that has been ascribed to a Kondo resonance. In addition, we identify a small gap of $\approx$ 5 meV width on top of the larger-energy Fano resonance. We suggest that this gap is the signature of a coherent Kondo lattice that has been proposed to originate from hybridization of a strongly dispersing and a flat band both derived from $d$ electrons of the Fe atoms in the lattice. Adding magnetic adatoms on the surface hardly influences the magnetic signatures of the substrate, indicating the robustness of the intralayer Kondo correlations against magnetic adsorbates.