Enomoto and Sakai classified IE-closed subcategories over hereditary algebras via twin rigid modules. However, this classification inherently relies on the vanishing of second extension spaces, thus failing for arbitrary finite-dimensional algebras. In this paper, we generalize their classification to arbitrary finite-dimensional algebras by introducing the notions of canonical twin support $τ$-tilting modules and canonical Ext-pairs. By utilizing functorially finite torsion pairs, we provide a homological characterization of these modules. Furthermore, we establish explicit bijections up to isomorphism among functorially finite IE-closed subcategories, canonical twin support $τ$-tilting modules, and canonical Ext-pairs. Finally, we provide a constructive algorithm to canonicalize any given twin support $τ$-tilting module.

It was recently shown that the decoupling limits leading to matrix (gauge) theories on D-branes give rise to non-Lorentzian target space geometries. Perturbatively, matrix theory describes a quantum gravity theory whose low-energy supergravity description exhibits non-Lorentzian behavior. Focusing on the D-particle case associated with the Banks-Fischler-Shenker-Susskind matrix theory, and using techniques from ambitwistor string theory, we show evidence that the dynamics of this non-Lorentzian gravity should be related to anomalies in the current algebra of the associated fundamental string worldsheet theory. At large N, the D-particle backreaction deforms the non-Lorentzian supergravity to the Lorentzian IIA theory, providing a holographic description of the BFSS matrix theory. At a moderately large N such that the D-particles decouple at the leading order, this non-Lorentzian supergravity maps holographically to the leading-order contribution of weakly coupled bulk gravity. This approximately non-Lorentzian regime is related to the null reduction of eleven-dimensional supergravity. Within the non-Lorentzian supergravity, non-trivial dynamics arises from the backreaction of extended brane objects that form BPS states with the D-particles. Finally, we generalize these results to other D-brane and string soliton holographic constructions.

We demonstrate that TeV-scale heavy neutral leptons (HNLs) responsible for inverse-seesaw neutrino mass generation can simultaneously fix the cosmological abundance and decay properties of dark matter (DM). The spontaneous breaking of lepton number gives rise to a pseudo-Nambu-Goldstone boson that serves as a light DM candidate, whose mass originates from a small explicit symmetry-breaking term. The same HNLs that generate neutrino masses produce the DM via freeze-in and mediate its decay into neutrinos, leading to a tight correlation among neutrino masses, DM relic abundance, and DM lifetime. For collider-accessible TeV-scale HNLs, the observed relic density and lifetime constraints point to sub-GeV DM, yielding observable neutrino signals at JUNO and next-generation detectors such as Hyper-Kamiokande and DUNE. This framework establishes a predictive and experimentally testable link between neutrino mass generation and DM.

Non-Display Smart Glasses hold the potential to support everyday activities by combining continuous environmental sensing with voice-only interaction powered by large language models (LLMs). Understanding how conversational successes and breakdowns arise in everyday contexts can better inform the design of future voice-only interfaces. To investigate this, we conducted a month-long collaborative autoethnography (n=2) to identify patterns of successes and breakdowns when using such devices. We then compare these patterns with prior findings on voice-only interactions to highlight the unique affordances and opportunities offered by non-display smart glasses.

The topological properties of field configurations in gauge theory contain important data about the (generalized) global symmetries of the theory as well as potential inconsistencies in the form of gauge anomalies. In this work we modify the topological classes of Abelian $p$-form fields, generating new global variants of gauge theories. These modifications implement constraints directly on the classifying space of the gauge field and its cohomology classes via homotopy fiber construction. This general approach allows us to investigate the universal effects of the constraints on the conserved global charges encoded in gauge characteristic classes. We further demonstrate that this procedure generically leads to new topological sectors introducing additional global charges and anomalies in the modified gauge theories.

Edge magnetoplasmons provide a natural platform for chiral electrodynamics, where broken time-reversal symmetry enforces unidirectional propagation. When probed at microwave frequencies, they offer a route to compact non-reciprocal devices. So far, implementations have suffered from large losses or required complicated matching networks. Here we show that the circulating modes coupled to capacitive gates give rise to a gyrator response, characterized by directional π phase difference between forward and reverse transmission. By engineering a three-terminal capacitive geometry, we realize a self-impedance matched gyrator in which the gyration points coincide with transmission maxima, enabling nearly lossless gyration without external matching networks. Our devices are implemented on a GaAs 2D gas, operate from 0.2 to 2 GHz, tuned by magnetic field, with sub-millimeter footprints and insertion loss as low as 2 dB. This is a factor of 100 smaller and less lossy than commercial and plasmon units, respectively. A dissipative model, in agreement with experiment, provides the fundamental physics and delivers the key materials parameters, leading the way to even less lossy devices approaching ideal operation by materials improvement. The self-impedance matched concept is broadly applicable to a variety of devices, thus providing a foundation for a new generation of high-quality microwave plasmon technology.

The Martian brain terrain (MBT), characterized by its unique brain-like morphology, is a potential geological archive for finding hints of paleoclimatic conditions during its formation period. The morphological similarity of MBT to self-organized patterned ground on Earth suggests a shared formation mechanism. However, the lack of quantitative descriptions and robust physical modeling of self-organized stone transport jointly limits the study of the thermal and aqueous conditions governing MBT's formation. Here we established a specialized quantitative system for extracting the morphological features of MBT, taking a typical region located in the northern Arabia Terra as an example, and then employed a numerical model to investigate its formation mechanisms. Our simulation results accurately replicate the observed morphology of MBT, matching its key geometric metrics with deviations <15%. Crucially, however, we find that the self-organized transport can solely produce relief <0.5 m, insufficient to explain the formation of MBT with average relief of 3.29 \pm 0.65 m. We attribute this discrepancy to sculpting driven by late-stage sublimation, constraining cumulative subsurface ice loss in this region to ~3 meters over the past ~3 Ma. These findings demonstrate that MBT's formation is a multi-stage process: initial patterning driven by freeze-thaw cycles implying liquid water followed by vertical sculpting via sublimation requiring a dry environment. This evolution provides physical evidence for the transition of the ancient Martian climate from a wetter period to a colder hyper-arid state.

We study the computational properties of two canonical planted average-case problems -- noisy planted $k$-XOR and Tensor PCA -- by formally unifying them into a family of planted problems parametrized by tensor order $k$, number of entries $m$, and noise level $δ$. We build a wide range of poly-time average-case reductions within this family, across all regimes $m \in [1, n^k]$. In the denser $m \geq n^{k/2}$ regime, our reductions preserve proximity to the computational threshold, and, as a central application, reduce conjectured-hard $k$-XOR instances with $m \approx n^{k/2}$ to conjectured-hard instances of Tensor PCA. Additionally, we give new order-reducing maps at fixed densities (e.g., $5\to 4$ for $k$-XOR with $m \approx n^{k/2}$ entries and $7\to 4$ for Tensor PCA). In the sparser $m \leq n^{k/2}$ regime, we relate instances of different orders, reducing, for example, $7$-XOR with $m = n^{3.4}$ to the classical setting of $3$-XOR with $m = \widetildeΘ(n^{1.4})$. Taken together, these results establish a hardness partial order in the space of planted tensor models.

To estimate the causal effect of an endogenous treatment using clustered data, the canonical two-stage least squares (2sls) estimates a linear regression of the outcome on treatment status using an instrumental variable (IV) and conducts inference with cluster-robust standard errors. When both the treatment and the IV vary within clusters, an alternative two-stage least squares with fixed effects (2sfe) additionally includes cluster indicators in the regression, thereby incorporating cluster information into point estimation as well. This paper studies the trade-off between these approaches within the local average treatment effect (LATE) framework. When clusters are homogeneous, we show that both approaches yield valid large-sample inference for the LATE, and that 2sfe is more efficient than canonical 2sls only when the variation in cluster-specific effects dominates idiosyncratic variation and the IV has sufficient within-cluster variation. When clusters are heterogeneous, we show that 2sfe identifies a weighted average of cluster-specific LATEs, whereas the canonical 2sls generally does not. We further propose a test for detecting cluster heterogeneity.

The Electric Autonomous Dial-a-Ride Problem (E-ADARP) involves routing and scheduling electric autonomous vehicles under battery capacity and partial recharging constraints, aiming to minimize total travel cost and excess ride time. In practice, operational data for time and state-of-charge (SoC) are often available only at a coarse granularity. This raises a natural question: can discretization be exploited to improve computational performance by enabling alternative formulation structures? To investigate this question, we develop three formulations reflecting different levels of discretization. The first is an improved event-based formulation (IEBF) with arc-flow SoC variables for the continuous-parameter E-ADARP, serving as a strengthened baseline. The latter two are fragment-based formulations designed for discretized inputs. The second is a time-space fragment-based formulation with continuous SoC arc-flow variables (TSFFCS), which discretizes time while keeping SoC continuous. The third is a battery-time-space fragment-based formulation (BTSFF), which discretizes both time and SoC. Here, an event denotes a tuple consisting of a location and a set of onboard customers, while a fragment denotes a partial path. Computational results show that IEBF improves upon the existing event-based formulation for the original E-ADARP. Under discretized settings, TSFFCS tends to outperform IEBF, particularly when recharging is frequent and time discretization is relatively coarse, indicating that time discretization can improve computational performance across a wide range of settings. In contrast, BTSFF rarely outperforms TSFFCS unless the number of reachable SoC levels is limited, suggesting that explicit SoC discretization is beneficial only in relatively restricted settings.

Binary neutron star merger (BNSM) ejecta are considered a primary repository of $r$-process nucleosynthesis and a source of the observed heavy-element abundances. We implement composition mixing into ray-by-ray radiation-hydrodynamic simulations of BNSM ejecta, coupled with an online nuclear network (NN). We model mixing via a gradient-based mixing approximation that evolves simultaneously with the hydrodynamics. We find that mixing occurs in regions where the electron fraction changes rapidly. While mixing smooths composition gradients in transition regions, it has a negligible impact on the heavy-element yields. This is because the primary $r$-process site (the equatorial ejecta) is initially homogeneous in free neutrons, leaving no strong gradients for mixing to act upon. In each angular ray, the abundances of the most produced elements are robust under mixing, while the less abundant ones are more affected. The total global abundances change only slightly from mixing, since each angular ray contributes its most abundant elements. Furthermore, the predicted kilonova light curves show only minor reddening, with differences below the detectability of state-of-the-art telescopes. In general, we do not observe significant effects from mixing in the time span of the $r$-process. Consequently, mixing only leads to minor variations in abundances and light curves in ray-by-ray simulations.

The two-dimensional $O(N)$ nonlinear sigma model (NLSM) is asymptotically free for $N>2$: it exhibits neither a nontrivial fixed point nor spontaneous symmetry-breaking. Here we show that a nontrivial fixed point generically does exist in the complex coupling plane and is described by a complex conformal field theory (CCFT). This CCFT fixed point is generic in the sense that it has a single relevant singlet operator, and is thus expected to arise in any non-Hermitian model with $O(N)$ symmetry upon tuning a single complex parameter. We confirm this prediction numerically by locating the CCFT at $N = 3$ in two non-Hermitian spin-1 antiferromagnetic Heisenberg chains, and in a non-Hermitian spin-$1/2$ ladder, finding good agreement between the complex central charge and scaling dimensions and those obtained by analytic continuation of real fixed points from $N\leq 2$. We further construct a realistic Lindbladian for a spin-1 chain whose no-click dynamics are governed by the non-Hermitian Hamiltonian realizing the CCFT. Since the CCFT vacuum is the eigenstate with the smallest decay rate, the system naturally relaxes under dissipative dynamics toward a CFT state, thus providing a route to preparing long-range entangled states through engineered dissipation.

Studies of Higgs boson properties are crucial for the understanding the Standard Model (SM), as it could couple to new particles and provide hints to physics Beyond the Standard Model (BSM). Different future colliders are proposed, among them the Muon Collider project would allow to perform unprecedented precision measurements of the Higgs boson parameters. The goal of this study is to estimate the statistical uncertainty of the cross section of the $H\rightarrowτ^+τ^-$ process at a 10 TeV center-of-mass energy Muon Collider. In order to reconstruct $τ$ leptons in different decay modes, the TauFinder algorithm is used. The efficiency of hadronic $τ$ ($τ_h$) lepton identification is estimated to be above 80% for 1-prong and 50% for 3-prong decay modes. This study focuses on the signal process $H\rightarrowτ^+τ^-$ in which the $τ$ leptons decay hadronically ($τ_h$). The main background processes are discussed and compared with the signal. The visible invariant mass is reconstructed and template fits are performed with Monte Carlo toy experiments. A statistical uncertainty on the cross section of the signal process: $Δσ/σ=$1.3% is obtained. Finally, comparisons are made with the sensitivities at other future colliders, and possible improvements to the analysis are discussed.

This paper considers the family of Schrödinger operators on $\ell^2(\mathbb{Z})$ given by independent but not necessarily identically distributed and possibly unbounded potentials. We assume a finite exponential moment and allow the choice of distributions to come from any compact set away from deterministic distributions. With these assumptions we prove spectral localization with exponentially decaying eigenfunctions as well as dynamical localization. One of the main tools is a Furstenberg-type theorem for non-stationary matrix products.

We develop a novel framework to build quantum many-body scar states in bipartite systems characterized by perfect correlation between the Hamiltonians governing the two sides. By means of a Krylov construction, we build an interaction term which supports a tower of equally-spaced energy eigenstates. This gives rise to finite-time revivals whenever the system is initialized in a purification of a generic equilibrium state. The dynamics is universally characterized, and is largely independent of the specific details of the Hamiltonians defining the individual partitions. By considering the two-sided chord states of the double-scaled SYK model, we find an approximate realization of this framework. We analytically study the revival dynamics, finding rigid motion for wavepackets localized on the spectrum of a single SYK copy. These findings are tested numerically for systems of finite size, showing excellent agreement with the analytical predictions.

We study anisotropic superconductivity in the nearly quarter-filled $α$-$\mathcal{T}_3$ lattice. We analyze an extended Hubbard model with off-site attractive interactions within the mean-field framework and find two distinct chiral $d+id'$-wave superconducting phases characterized by different Chern numbers. We further investigate the superconducting mechanism mediated by spin fluctuations arising from purely repulsive interactions by applying the fluctuation-exchange (FLEX) approximation to the Hubbard model. The gap symmetry obtained by solving the linearized Eliashberg equation is $d$-wave, which corresponds to a $d+id'$-wave superconducting state with a Chern number of $8$, including the spin degree of freedom. The $\mathbf{q}=\mathbf{0}$ antiferromagnetic spin fluctuation, which possesses the largest spectral weight at finite energies arising from the incipient flat band, gives rise to an effective spin-singlet pairing glue between rim sites.

We construct automata with input(s) in base $k$ recognizing some basic relations and study their number of states. We also consider some basic operations on $k$-automatic sequences $(h(i))_{i \geq 0}$ and discuss their state complexity. We find a relationship between subword complexity of the interior sequence $(h'(i))_{i \geq 0}$ and state complexity of the linear subsequence $(h(ni+c))_{i \geq 0}$. We resolve a recent question of Zantema and Bosma about linear subsequences of $k$-automatic sequences with input in most-significant-digit-first format. We also discuss the state complexity and runtime complexity of using a reasonable interpretation of Büchi arithmetic to actually construct some of the studied automata recognizing relations or carrying out operations on automatic sequences.

A unique feature of gas xenon electroluminescent time projection chambers (GXeEL TPCs) in $0νββ$ searches is their ability to reconstruct event topology, in particular to distinguish "single-electron" from "double-electron" tracks, the latter being the signature of a $0νββ$ decay near the decay endpoint $Q_{ββ}$. Together with excellent energy resolution and the t$_0$ provided by primary scintillation, this topological information is key to suppressing backgrounds. Preserving EL, however, requires operation in pure xenon (with helium as the only benign additive), where electron diffusion is large. Consequently, reconstructed track fidelity is limited by diffusion and intrinsic EL blurring. We propose augmenting the detector with the ability to image not only the electron track but also the corresponding mirror ion track. Introducing trace amounts of NH$_3$ ($\sim$100 ppb) converts primary xenon ions into ammonium ions, NH$_4^+$, via a fast two-step ion-molecule process involving charge transfer followed by proton transfer, while leaving EL unaffected. Electrons drift rapidly to the anode, producing the standard EL image, whereas NH$_4^+$ ions drift slowly toward the cathode, allowing time to determine the event energy and barycenter. For events in the region of interest, an ion sensor near the cathode at the projected barycenter captures the ions. Laser interrogation of the sensor's molecular layer then reveals an ion-track image with sub-millimeter diffusion and no EL-induced smearing. Combined electron-ion imaging strengthens topological discrimination, improving background rejection by about an order of magnitude and significantly extending the discovery potential of GXeEL TPCs for very long $0νββ$ lifetimes.

In general relativity, the dynamics of spinning particles is governed by the Mathisson-Papapetrou-Dixon equations, which are most commonly applied to massive bodies, but the framework also works in the massless case. Such massless versions naturally arise, for example, in the description of energy centroids of high-frequency wave packets. In this work, we consider massless spinning particles in spacetimes with hidden symmetries and we derive the generalized conservation laws associated with conformal Killing-Yano tensors. We then show that the spin Hall equations, a particular case of the Mathisson-Papapetrou-Dixon equations restricted to massless particles with longitudinal angular momentum, are completely integrable in a large class of type D spacetimes. Additionally, we also show that for massive spinning particles, the generalized Carter constant associated with Killing-Yano tensors is conserved independently of the choice of spin supplementary condition.

Noise characteristics of state-of-the art light sources are crucial parameters in understanding their limitations towards quantum applications. This work describes a method to study the electrical noise transfer of current driver sources to the intensity noise of mid-infrared emission by commercial quantum and interband cascade lasers (QCLs and ICLs, respectively). A current driver with sub-shot electrical noise in a specific frequency range (up to 10 dB below the shot noise level) was developed for this purpose. This enables testing the performance of mid-infrared lasers when driven via such a quiet pump source. By using this novel current driver, we identify the fundamental noise of a QCL and an ICL, that is the laser intensity noise resulting solely from the internal dynamics of the laser under test. The proposed methodology allows us to retrieve the noise transfer function from current to light, showing that the main limitations in observing the quantum properties of the emitted photons come from laser excess noise and poor matching between laser and detection system in terms of bandwidth and optical power. From the analysis of the measured parameters, we highlight current technological limitations and suggest which key features should be optimized in mid-infrared systems for matching the performance required by quantum applications.

Bistability-two distinct stable states under identical parameter-is not only a fundamental physical concept but also of importance in practical applications. While plasmon-polaritonic bistability representing history-dependent stable states within plasmonic systems has been theoretically predicted, it has yet to be demonstrated experimentally due to challenges in realizing suitable nonlinearity at feasible electric-field strengths. Here, we report the experimental observation of electrically driven plasmon-polaritonic bistability in graphene/hexagonal-boron-nitride/graphene tunneling transistors, achieved through momentum-conserving resonant tunneling of Dirac electrons. Using a small twist angle between graphene layers, we engineered devices exhibiting both electronic and plasmon-polaritonic bistability. This bistable plasmonic behavior can be precisely tuned through load resistance and electrostatic gating. Our findings open new pathways for exploring nonlinear optical and electronic phenomena in van der Waals heterostructures and mark a significant advance in nanoplasmonics, with potential applications in optical memory, sensing, and optoelectronic switching.

The Integrable Optics Test Accelerator (IOTA) at Fermilab provides a versatile platform for studying the interplay of space-charge, impedance, and non-linear optics in high-intensity hadron beams within synchrotrons and storage rings. This report examines the parameters and dynamics of 2.5 MeV proton beam operations in two configurations of the bare IOTA lattice (dipoles, quadrupoles, sextupoles, and rf cavity only): one for demonstrating Non-linear Integrable Optics with the Danilov-Nagaitsev magnet, and the other for use with electron cooling. We offer order-of-magnitude estimates of the transverse emittance growth rate as a function of beam intensity, highlighting contributions from residual gas scattering, intra-beam scattering, and space-charge effects. Under nominal conditions, the beam lifetime is projected to be less than 7 minutes at low intensity with the current vacuum quality, and fewer than 100,000 turns at high intensity due to strong space-charge effects. The calculations presented here will guide strategies to mitigate emittance growth and inform future IOTA experiments.

In this paper, we propose a suboptimal and reduced-order Model Predictive Control (MPC) architecture for discrete-time feedback-interconnected systems. The numerical MPC solver: (i) acts suboptimally, performing only a finite number of optimization iterations at each sampling instant, and (ii) relies only on a reduced-order model that neglects part of the system dynamics, either due to unmodeled effects or the presence of a low-level compensator. We prove that the closed-loop system resulting from the interconnection of the suboptimal and reduced-order MPC optimizer with the full-order plant has a globally exponentially stable equilibrium point. Specifically, we employ timescale separation arguments to characterize the interaction between the components of the feedback-interconnected system. The analysis relies on an appropriately tuned timescale parameter accounting for how fast the system dynamics are sampled. The theoretical results are validated through numerical simulations on a mechatronic system consisting of a pendulum actuated by a DC motor.

Using generating functions quadratic at infinity for Lagrangian submanifolds of twisted cotangent bundles, we define spectral selectors for compactly supported lcs Hamiltonian diffeomorphisms of the locally conformal symplectizations $S^1 \times \mathbb{R}^{2n+1}$ and $S^1 \times \mathbb{R}^{2n} \times S^1$ of $\mathbb{R}^{2n+1}$ and $\mathbb{R}^{2n} \times S^1$, and obtain several applications: the construction of a bi-invariant partial order on the group of compactly supported lcs Hamiltonian diffeomorphisms of $S^1 \times \mathbb{R}^{2n+1}$ and $S^1 \times \mathbb{R}^{2n} \times S^1$, of an integer-valued bi-invariant metric on the group of compactly supported lcs Hamiltonian diffeomorphisms of $S^1 \times \mathbb{R}^{2n} \times S^1$, and of an integer-valued lcs capacity for domains of $S^1 \times \mathbb{R}^{2n} \times S^1$. The lcs capacity is used to prove a lcs non-squeezing theorem in $S^1 \times \mathbb{R}^{2n} \times S^1$ analogous to the contact non-squeezing theorem in $\mathbb{R}^{2n} \times S^1$ discovered in 2006 by Eliashberg, Kim and Polterovich. Along the way we introduce for Liouville lcs manifolds the notions of essential Lee chords between exact Lagrangian submanifolds and of essential translated points of exact lcs diffeomorphisms. We prove that essential translated points always exist for time-$1$ maps of sufficiently $C^0$-small lcs Hamiltonian isotopies of compact Liouville lcs manifolds and for all compactly supported lcs Hamiltonian diffeomorphisms of $S^1 \times \mathbb{R}^{2n+1}$ and $S^1 \times \mathbb{R}^{2n} \times S^1$. We also obtain an existence result for essential Lee chords between the zero section of a twisted cotangent bundle with compact base and its image by any lcs Hamiltonian isotopy, which can be thought of as a lcs analogue of the Lagrangian and Legendrian Arnold conjectures on usual cotangent and $1$-jet bundles.

The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. While the approach has seen previous success, we here derive it rigorously from an open quantum system master equation, whereas it was previously introduced only on phenomenological grounds. We further show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we show that below the laser threshold, stochastic fluctuations in the numerical solution to the Langevin equations can drive populations to unphysical negative values, requiring the introduction of population bounds, which in turn skew the noise statistics, leading to inaccuracies. The Laser Markov Chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.

Relations between the kinematical tensors (the expansion, the shear, and the vorticity) and the polarization modes of gravitational waves are studied within the context of metric theories of gravity by considering freely falling test particles. After analyzing exact relations, we consider slowly moving particles under the influence of a weak gravitational field. Linearized plane waves of theories representative of those determined by a general second-order Lagrangian, including General Relativity, are shown to exemplify the following interconnections: between the transverse components of the shear and the transverse tensor polarization mode; between the expansion, and both the transverse scalar and the longitudinal polarization modes; and between the longitudinal-transverse components of both the shear and the vorticity, and the vector polarization mode. These relations, from the theoretical point of view, offer a novel insight into the interpretation of the polarization modes in terms of the kinematical tensors. Additionally, the inclusion of the kinematical tensors in the study of gravitational waves might provide a new outlook on their phenomenology.

We study pointwise free and finitely-generated persistence modules over a principal ideal domain, indexed by a (possibly infinite) totally-ordered poset category. We show that such persistence modules admit interval decompositions if and only if every structure map has free cokernel. We also show that, in torsion-free settings, the integer persistent homology module of a filtration of topological spaces admits an interval decomposition if and only if the associated persistence diagram is invariant to the choice of coefficient field. These results generalize prior work where the indexing category is finite.

We study confidence interval construction for linear regression under Huber's contamination model, where an unknown fraction of noise variables is arbitrarily corrupted. While robust point estimation in this setting is well understood, statistical inference remains challenging, especially because the contamination proportion is not identifiable from the data. We develop a new algorithm that constructs confidence intervals for individual regression coefficients without any prior knowledge of the contamination level. Our method is based on a Z-estimation framework using a smooth estimating function. The method directly quantifies the uncertainty of the estimating equation after a preprocessing step that decorrelates covariates associated with the nuisance parameters. We show that the resulting confidence interval has valid coverage uniformly over all contamination distributions and attains an optimal length of order $O(1/\sqrt{n(1-ε)^2})$, matching the rate achievable when the contamination proportion $ε$ is known. This result stands in sharp contrast to the adaptation cost of robust interval estimation observed in the simpler Gaussian location model.

Surety bonds are financial agreements between a contractor (principal) and obligee (project owner) to complete a project. However, most large-scale projects involve multiple contractors, creating a network and introducing the possibility of incomplete obligations to propagate and result in project failures. Typical models for risk assessment assume independent failure probabilities within each contractor. However, we take a network approach, modeling the contractor network as a directed graph where nodes represent contractors and project owners and edges represent contractual obligations with associated financial records. To understand risk propagation throughout the contractor network, we extend the celebrated Friedkin-Johnsen model and introduce a stochastic process to simulate principal failures across the network. From a theoretical perspective, we show that under natural monotonicity conditions on the contractor network, incorporating network effects leads to increases in the average risk for the surety organization. We further use data from a partnering insurance company to validate our findings, estimating an approximately 2% higher exposure when accounting for network effects.

We present a general analytical framework for quasi-static quantum Stirling engines operating across ground-state level crossings (GLC). In the low-temperature regime, we derive the Primarch Formula, an exact universal expression linking extracted work and efficiency directly to macroscopic ground-state degeneracies. We analytically prove that these engines achieve Carnot efficiency without a classical regenerator, and that thermal excitations strictly degrade this performance. Validated against exact numerical simulations of generalized \textit{N}-th spin-1/2 Heisenberg models with nontrivial interactions, the framework is applied to the one-dimensional antiferromagnetic Ising model, revealing a profound connection to number theory. Governed by Fibonacci, Lucas, and parity-dependent critical degeneracies, the engine exhibits distinct operational regimes that permanently violate classical thermodynamic extensivity while operating at the absolute Carnot limit, regardless of macroscopic system size.