In 1962, Bateman and Horn conjectured precise asymptotics for the count of positive integers n \le x for which f_1(n), ..., f_k(n) are all prime, where (f_1, ..., f_k) is an admissible k-tuple of polynomials in one variable. We prove that certain random sets of integers almost surely satisfy the Bateman-Horn asymptotics in full generality and with a strong error term, where we have replaced "f_1(n), ..., f_k(n) are all prime" with "f_1(n), ..., f_k(n) all lie in the random set." In particular, sets of integers satisfying Bateman-Horn are plentiful.

Human computer interaction is shifting from screen-based systems to multimodal interfaces where artificial intelligence powered systems increasingly interpret user intent through speech, gesture, and gaze. Yet users rarely understand how these interpretations are made, compromising trust and control. Existing approaches treat multimodal alignment, explainability, and human agency as separate concerns, leaving critical gaps in transparency and user oversight. We propose a Human Artificial Intelligence collaboration framework integrating these three principles as interdependent design requirements: 1) multimodal alignment for accurate intent interpretation, 2) interaction centric explainability delivering real time visual, textual, and audio feedback, and 3) agency preserving mechanisms enabling users to accept, reject, or modify artificial intelligence suggestions at any time. We presented the framework through two scenarios, collaborative design and extended reality warehouse robot collaboration, chosen to span differences in time pressure and error reversibility, with the latter situated in a domain where misinterpretation carries documented safety consequences. This approach reframes collaboration as a continuous interaction property, benefiting designers, researchers, and end users by ensuring that as artificial intelligence systems grow more proactive, user understanding and control remain first class design properties.

Synchronized chaos has previously been predicted and observed in a small number (3) of mutually coupled lasers. In this work, we demonstrate that this phenomenon can theoretically persist in significantly broader scenarios, extending to complex coupled arrays of up to 11 lasers and arrays with finite built-in disorder. We quantify the resulting high-dimensional dynamics by computing Lyapunov spectra and the associated Lyapunov dimension, confirming that the observed states are chaotic rather than quasi-periodic. Furthermore, we uncover a regime of transient synchronized chaos where the system eventually escapes from perfectly synchronized chaotic state into an asynchronous state. We find that the lifetime of these transient states follows a bi-exponential distribution.

Two-dimensional bootstrap percolation is usually characterized by bulk observables, but whether increasing the activation threshold qualitatively reorganizes the geometry of the absorbing state has remained unclear. Here we show that the response undergoes a threshold-controlled geometric crossover. At low thresholds, the extrema of bulk and boundary-sensitive observables remain confined to a single collective low-$p$ window. At high thresholds, they split into distinct branches, revealing multiple geometric response scales. Over the accessible system sizes, the dominant finite-size signatures shift from fluctuations of the final active density to non-singleton boundary observables, while the fluctuation peak itself decreases. Time-resolved mechanism traces show that this crossover is accompanied by a progression from extended collective propagation to frontier exhaustion and, at the highest threshold, to quasi-one-step stabilization. Our results identify boundary organization as the dominant structural signature of high-threshold bootstrap percolation and show that conventional bulk observables alone do not capture the full reorganization of the absorbing state.

Window decoding, first proposed to reduce decoding complexity for real-time decoding, is an essential component to realize scalable, universal-fault tolerant computation. Prior work has focused on improving throughput through parallelization and reducing reaction time via speculation on window boundaries. However, these methods use a fixed window size d, paying a fixed decoding time overhead for each window. In practice, we find this overhead of a fixed window size unnecessary in many cases due to the sparsity of average-case errors in QEC. Leveraging this insight, in this paper we propose an adaptive window decoding technique based on decoder confidence. This technique reduces the overhead in decoding time thus reducing reaction time without compromising on logical error rates. We benchmark adaptive window decoding across different codes and hardware inspired noise models. Our results show that this adaptive technique reaches the target error rate while maintaining a low decoding time overhead across different codes, and under different noise models.

The study of X-ray pulsar accretion columns helps us characterize accretion physics in this extreme regime of strong gravity and strong magnetic fields. Previous observations of the X-ray pulsar Hercules X-1 revealed a highly broadened Fe K emission line, associated with Doppler motions exceeding 0.1c, suggesting its origin in the accretion column. We obtained a high-spectral resolution view of the Fe K energy band of Hercules X-1 thanks to a 200 ks observation with the XRISM observatory. The XRISM/Resolve microcalorimeter spectra allow us to separate the different spectral components and accurately model them with phenomenological models. We confirm the presence of a broad line near 6.5 keV with a typical $1σ$ width of 1 keV. Performing a pulse-phase-resolved analysis, we find that the feature is strongly variable with Her X-1 pulse phase. This is consistent with the proposed origin due to collisional recombination or by reprocessing of the primary X-ray emission in the accretion column, where strong variability with pulse phase is expected due to the rotation of the columns alongside with the neutron star. Additionally, the Fe K line pulsation pattern evolves with the 35-day cycle of Hercules X-1, supporting the scenario that the neutron star and its accretion columns undergo precession, in agreement with recent polarimetric results from the IXPE observatory. We discuss the future applications of modeling of this broad line in X-ray pulsars with physical spectral models. This could be used to detect and track neutron star precession, advancing our understanding of neutron star interiors.

Having been extensively studied during last decades in the fields of thermoelectics and ionic conductors, the $α$ phase of Cu$_{2}$Se with antfluoride crystal structure has recently emerged as a topological zero-gap semimetal with a quadratic contact point which exists at the Fermi surface of its bulk electronic spectrum. Here we argue based on density functional electronic structure calculation that the $β$ phase of Cu$_{2}$Se realized in a recently discovered rhombohedral structure shows a Dirac semimetal behavior of the electrons near the Fermi level. These topological semimetals are currently generating a lot of interest due to unusual transport phenomena, such as strong quantum oscillations, large magnetoresistance effect and ultrahigh carrier mobilities with their Fermi velocities potentially exceeding graphene. We show that there exist Fermi arc states at the surface spectrum of $β-$Cu$_{2}$Se that are topologically protected by the bulk Dirac points. Their shape and spin properties should be resilient to the back- and side scattering effects in the surface transport, suggesting new ways for realizing high-mobility electronic devices.

Colloidal quantum dots (QDs) and their thin-films are increasingly used in electronic and photonic devices replacing traditional bulk semiconductors. However, thermal properties of the QDs are comparatively underexplored relative to device development efforts. This study shows the use of time-resolved X-ray diffraction as a contact-free method to probe the thermal response of QDs in device-like environments, providing in-situ insights for future thermal management strategies. Through the extraction of Debye-Waller Factors on a sub-nanosecond timescale, we use time-resolved X-ray diffraction to directly capture the heating and cooling of core/shell CdSe/CdS QDs following pulsed optical excitation. In a QD thin-film that actively provides optical gain, the thermal conductivity is found to be as low as 0.55 $\mathrm{W\,m^{-1}\,K^{-1}}$, because of the poor heat flow within close-packed QD solids. For QDs dispersed in liquids, interfacial thermal conductance is found to dominate the thermal relaxation with a conductance on the order of 15 $\mathrm{MW\,m^{-2}\,K^{-1}}$.

Array-of-structures (AoS) to structure-of-arrays (SoA) is a classic compiler transformation that improves memory locality and enables data-parallel execution. Existing AoS-to-SoA transformations primarily target regular, array-based programs in imperative languages like C and C++. In contrast, many applications manipulate tree-shaped data structures, for example, ASTs in compilers, DOM trees in browsers, and k-d trees in scientific workloads. Prior work improves the performance of functional programs operating on such data by serializing algebraic datatypes (ADTs) into contiguous memory buffers. However, these representations interleave fields within a single buffer, similar to AoS layouts. We introduce factored, multi-buffer layouts that store different ADT fields in separate buffers, enabling SoA-like layouts for serialized recursive data structures. We formalize this approach in SoCal, a language for generating factored ADT representations, and implement it in a compiler called Colobus. Colobus automatically transforms functional programs to operate over a serialized, factored layout of recursive ADTs. Our evaluation shows a 1.46x geometric mean speedup on a suite of tree-processing benchmarks.

Ab initio wavefunction methods provide accurate molecular simulations but their computational scaling restricts applications to small systems. We develop a workflow combining quantum embedding to decompose a molecule into fragments with a heterogeneous quantum-classical (HQC) method to simulate fragments. We sample fragment electronic configurations on two 156-qubit quantum processors (ibm$\_$cleveland, ibm$\_$kobe), using up to 94 qubits, running 9,200 circuits for over 100 hours, collecting $1.3 \cdot 10^9$ measurement outcomes - the most resource-intensive HQC computation for quantum chemistry to date. We compute fragment wavefunctions via optimized subspace diagonalization on two supercomputers (Fugaku, Miyabi-G), achieving 72.5$\%$ parallel efficiency with scalable distributed linear algebra kernels. We simulate two protein-ligand complexes spanning dispersion- and electrostatics-dominated regimes (11,608 and 12,635 atoms), demonstrate $>40\times$ increase in system size and up to $210\times$ improvement in accuracy over the previous state-of-the-art, with HQC matching coupled-cluster (CCSD) accuracy in fragment energies, and establish a scalable pathway for systematically improvable biomolecular simulations.

A new design for an open-hardware Digital-to-Analog Converter System-on-Module is presented for low-noise ion-trap electrode control. The design specifications were established to fill the technical needs of a modular, scalable DC electrode control platform with sufficient bandwidth, noise characteristics and control flexibility. Critically, a priority was placed on supply-chain management considerations and cost effectiveness for scaling. The system is based upon the Texas Instruments DAC81416 and AMD Xilinx Spartan-7 FPGA for the analog signal and compute architecture respectively. Performance characterization of a prototype device suggests the design is suitable for a variety of ion-trap physics experiments and quantum computing applications.

Reinforcement-learning (RL) solutions for dynamic spectrum access and radio resource management in Open Radio Access Networks (O-RAN) depend critically on the fidelity of the throughput signal used for training. Analytical or physical-layer (PHY)-only simulators scale well but often miss protocol-stack effects such as signaling overhead and retransmissions, whereas exhaustive throughput profiling on a standards-compliant 5G stack is slow and can be unstable under software execution constraints. This paper presents MORPH, a measurement-grounded multi-environment RL pipeline {for slice-aware PRB-level spectrum allocation (spectrum sharing and slice isolation within a single gNB)} built on OpenAirInterface (OAI) 5G-NR RF-simulator mode. MORPH leverages three complementary throughput sources: (i) application-layer throughput measured via \texttt{iPerf} on the OAI stack under controlled AWGN pathloss settings, (ii) empirical MCS-selection distributions conditioned on path loss, enabling a distribution-aware theoretical throughput estimator that reflects standards-compliant link adaptation, and (iii) scalable throughput estimates from a 3GPP-parameterized PHY-fidelity OFDM simulator. Using these components, we train and compare agents that differ only in the origin of their throughput feedback: an OAI-grounded practical agent, a simulator-driven agent, and MORPH, which fuses real and synthetic throughput signals for policy optimization. Evaluation on the OAI execution harness across heterogeneous slicing scenarios shows that MORPH yields more robust slice-wise performance and improved SLA compliance than single-source training, providing a practical foundation for PRB-level spectrum sharing and slice isolation within a single-cell stack and a stepping stone toward multi-cell spectrum coordination and interference management.

Rapid and controllable reduction of graphene oxide (GO) remains a critical challenge for realizing its full technological potential. Here, we report efficient reduction of GO by a synergistic electron-beam-assisted single-pulse near-infrared (NIR) laser process. Time-resolved electron energy-loss spectroscopy measured with a dynamic transmission electron microscope (DTEM) is used to locally track the oxygen concentration evolution after NIR laser pulse irradiation. This finds an oxygen diffusivity of 1.6 +/- 0.4 x 10$^{-8}$ m$^2$/s, which corresponds to 90% reduction of a 46-nm thick film within 960 ns. Electron beam irradiation is found to change the optical absorptivity of GO in the NIR region and the thermal heating cycle resulting from the laser pulse is simulated. Structural characterization via selected-area electron diffraction (SAED) and high-resolution transmission electron microscopy (HRTEM) finds localized restoration of sp$^2$ bonding accompanied by turbostatic disorder in the reduced GO. Together, these results point to a mechanism involving the creation of defects and vacancies produced by electron beam irradiation, which increases the efficiency of NIR light absorption and oxygen diffusion normal to the layers. This study demonstrates the important role of such defects in controlling the photochemistry of GO and its response to NIR illumination.

Optimizing compilers have become a cornerstone for high-performance program generation in research and industry. Optimizations, including those implemented manually by a user and those target-specific and non-target-specific, are used to transform programs to achieve good performance. Although these optimizations are necessary for performance, assessing their correctness has remained a major challenge; the risk of incorrect code being deployed increases with unproven optimization flows. In this work, we target the formal verification of correctness of a transformed program by computing whether a pair of programs are semantically equivalent, one being a transformed version of the other. We restrict the class of programs supported to enable a hybrid concrete-symbolic interpretation approach to equivalence, which in turn is mostly agnostic to how the programs are implemented (syntax, schedule, storage, etc.). This approach can show equivalence in linear time with respect to the operations executed by the programs. We develop a verifier for a meaningful subset of MLIR, and report on the verification of the AMD MLIR-AIR and MLIR-AIE toolchains, as well as the standard mlir-opt on hundreds of benchmarks variants.

Freight Signal Priority (FSP) systems have emerged as a promising strategy to enhance freight mobility and reduce corridor delays in urban networks. While extensive research has focused on priority control algorithms and operational performance evaluation, comparatively limited attention has been devoted to the architectural design of sensing processes that shape reliable priority decisions. In practice, uncertainties in vehicle detection, communication, and estimated time of arrival (ETA) may propagate within the sensing-to-decision process, affecting priority timing and downstream signal performance. This paper presents a systematic review of FSP systems from a sensing-to-decision perspective. We propose a generic two-layer architecture consisting of a sensing-to-decision layer and a control execution layer. The sensing-to-decision layer transforms sensing inputs into priority decisions, while the control execution layer implements approved actions within traffic controllers. Within this architecture, we systematically compare major sensing modalities, including loop detectors, vision sensors, and V2I, across dimensions such as classification capability, state estimation accuracy, latency, and information richness. We further examine representative FSP systems to analyze how modality-specific characteristics and uncertainties influence ETA computation, priority triggering, and decision reliability. By linking sensing design to decision outcomes, this review identifies key deployment challenges and research gaps in reliability-aware sensing-to-decision design. Ultimately, this work provides a conceptual foundation for developing scalable and robust FSP systems that explicitly account for sensing imperfections rather than assuming idealized inputs.

In this paper we theoretically and numerically investigate transport signatures of quantum interference on the current through a single molecule magnet transistor tunnel coupled to oppositely polarized leads in the presence of a local transverse and longitudinal magnetic field. Our calculations are based in a density matrix approach where we treat the ground state energy splitting induced by tunneling of the spin between different paths with the aid of perturbation theory. Using this approach we show that it is possible to use an effective Hamiltonian which describes the Berry phase interference as a function of the transverse magnetic field which completely blocks the current flow when we place the single molecule magnet between oppositely polarized leads. Finally, we use this effective Hamiltonian in an open source Python software (QmeQ) that allows us to calculate the current through the single molecule magnet with oppositely polarized leads tunnel coupled to the single molecule magnet. The analytical results are well reproduced by our numerical simulations.

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of semiparametric methods that are designed to work better than the kernel estimator in a broad nonparametric neighbourhood of a given parametric class of densities, for example the normal, while not losing much in precision when the true density is far from the parametric class. The idea is to multiply an initial parametric density estimate with a kernel type estimate of the necessary correction factor. This works well in cases where the correction factor function is less rough than the original density itself. Extensive comparisons with the kernel estimator are carried out, including exact analysis for the class of all normal mixtures. The new method, with a normal start, wins quite often, even in many cases where the true density is far from normal. Procedures for choosing the smoothing parameter of the estimator are also discussed. The new estimator should be particularly useful in higher dimensions, where the usual nonparametric methods have problems. The idea is also spelled out for nonparametric regression.

We place geo-targeted advertisements on Facebook to encourage users to fill out an online survey, following a process known as river sampling. We discovered a large number and variety of users also came to our survey through snowball sampling, including shared social media posts and other word-of-mouth referral methods. In this article, we analyze the differences between the respondents from river and snowball sampling. We present evidence that the respondents obtained by snowball sampling are more likely to complete the survey and contain a higher fraction of new users and women than those obtained by river sampling. Additionally, the evidence indicates that users from snowball sampling give shorter responses and take less time on the survey than users from river sampling. We hope these findings provide insight for other researchers who incorporate social media strategies when fielding surveys.

Motivated by the indications of high-Tc superconductivity in natural graphite enriched in the rhombohedral phase, we study the band structure of several stacking configurations that combine two of the three graphite structures as well as modifications of the rhombohedral sequence (from ABCABC... to CBACBA...), using first-principles calculations. We focus in particular on the possible emergence of flat bands near the Fermi level. When the two different rhombohedral orderings are combined, flat bands of topological origin emerge at the interface between the two domains, near the K and K' points of the Brillouin zone. Mapping a simple tight-binding model of a rhombohedral slab along the direction perpendicular to the graphene layers onto a Su-Schrieffer-Heeger chain provides a transparent understanding of the underlying physics.

Difference-in-differences (DiD) identification relies mainly on a parallel trends assumption about untreated potential outcomes. Researchers often relax this assumption by assuming conditional parallel trends within units with the same covariate values. However, the process of selecting which covariates to include in this assumption is often \emph{ad hoc}. We propose a formal approach to select the variables that support conditional parallel trends based on graphical criteria. We show that the parallel trends assumption is rarely justified without conditioning on covariates, and that unconditional and conditional parallel trends can conflict with one another. We also demonstrate that a time-invariant covariate with a time-invariant effect on the outcome, which might not ordinarily be considered a confounder in DiD, may be a useful conditioning variable. We clarify that adjustment for a post-treatment covariate depends on what causes that covariate to change. Extending our framework to multiple time periods, we distinguish between treatment type and rollout strategy and examine the problem of treatment-confounder feedback. On the estimation side, we argue that the difficulty of incorporating covariates in DiD, often framed as an estimator problem, is more accurately understood as a misalignment between the adjustment set used by the estimator and the adjustment set required for identification. This misalignment affects several popular estimation procedures, and resolving it requires not a change of estimator, but a change in how covariates enter the estimation procedure. We show how to achieve this alignment for all estimators we evaluate.

Inter-cell interference is a persistent issue in dense 5G deployments, especially in heterogeneous Open Radio Access Network (O-RAN) environments where coordination between base stations is limited. This paper presents AIIM, an adaptive inter-cell interference mitigation xApp for the O-RAN near-real-time RAN Intelligent Controller (near-RT RIC) that performs coordinated physical resource block (PRB) allocation across multiple base stations under diverse traffic demands and channel conditions. Unlike prior studies that rely primarily on simulation or fully hardware-centric testbeds, AIIM is developed and evaluated in a full-stack O-RAN system built on srsRAN, Open5GS, and O-RAN Software Community (ORAN-SC), and deployed on a hybrid experimental platform that simultaneously combines software defined radio (SDR)-based and virtual gNodeBs (gNBs) and user equipment (UEs). This design preserves realistic PHY-layer interactions while substantially improving scalability, reproducibility, and cost-effectiveness for multi-cell interference experiments. AIIM explicitly models overlapping PRB regions across neighboring cells and learns coordinated allocation policies that adapt to per-user QoS demand and pathloss variation across the network. Experimental results show that AIIM improves QoS satisfaction and reduces interference-induced PRB loss relative to proportional-fair scheduling baselines while maintaining comparable aggregate network throughput. These results demonstrate the promise of scalable, learning-driven O-RAN control for practical interference management in heterogeneous multi-gNB 5G networks.\footnote{A video demonstration of the running system can be found at https://github.com/sireinders/AIIM-Multi-gNB-Interference.git.}

The growing popularity of AI writing assistants creates exciting opportunities to support diverse writers. This study examines how personality shapes expectations for AI writing companions and how personality-informed design can enhance human-AI teaming in writing. Through exploratory co-design workshops with 24 writers representing different personality profiles, we elicited values and design ideas for AI writing companions spanning functionality, interaction dynamics, and visual representation. These insights informed two contrasting prototypes reflecting distinct writing orientations, used as design provocations in review-and-refinement workshops with eight participants to prompt reflection on fit, priorities, and writing practices. Our findings reveal both shared foundational needs across writers and meaningful personality-driven preferences that influence how writers engage with AI. This work underscores the importance of team matching in human-AI collaboration and demonstrates how aligning AI companions with individual cognitive and interpersonal needs can improve engagement and perceived collaboration effectiveness.

Galactic winds shape galaxy evolution; however, the outflowing gas is complex: it consists of multiple ionization phases, and its properties vary spatially. Therefore, methods that combine high-fidelity observations with state-of-the-art galactic-wind models are limited. Here we investigate methods for fitting the column density profiles derived from high-quality outflow observations with the multiphase, multiscale wind model from Fielding & Bryan 2022. We identify three key outflow parameters: the initial hot-phase mass-loading factor ($η_\text{ M,hot,0}$), the initial cool-phase mass-loading factor ($η_\text{ M,cool,0}$), and the initial cool-cloud mass. We obtain good fits for most galaxies, with tight constraints on $η_\text{ M,cool,0}$ and moderate constraints on the other two parameters. We find the inferred $η_\text{ M,cool,0}$ and $η_\text{ M,hot,0}$ are mostly of order unity, with significant scatter. The constraints on $η_\text{ M,hot,0}$ suggest that the interaction between the cool and hot phases allows us to indirectly constrain the properties of the hot wind from cool-outflow observations. The model also predicts various radial trends. First, for all galaxies, the cool-phase outflow velocity increases between $1-2$ times of the half-light radius, then reaches a plateau. Second, most galaxies exhibit increasing $η_\text{ M,cool}$ and decreasing $η_\text{ M,hot}$ with radius, with a few showing the reverse trends. These results are effective, model-conditional constraints, and are consistent with other recent multiphase simulations and observations. This highlights that the velocity-radius mapping encoded in UV absorption profiles enables recovery of outflow spatial structures from spatially integrated spectra. Our method paves the way for future broad parameter studies and guides updates of outflow simulations in future work.

We simulate a self-interacting three-flavor neutrino system within a core-collapse supernova using a hybrid classical-quantum algorithm on a qutrit computer. Based on the Dirac-Frenkel evolution equations, we employ a variation of the quantum-assisted simulator (QAS) to calculate the system's time evolution operator by performing qutrit Hadamard tests to find expectation values of unitary operators in the Hamiltonian. The time evolution simulation is then done classically. We find that the hybrid algorithm produces results comparable to an exact numerical integration out to times of $t \approx 30 \,ω_0^{-1}$ with time step $δt = 0.005 \,ω_0^{-1}$, where $ω_0$ is the energy scale of the single neutrino vacuum oscillations. We discuss the lessons learned in simulating neutrino systems using this hybrid quantum-classical algorithm, along with the advantages it offers over quantum Trotterization.

Evaluating DAG task schedulers for wireless edge computing requires jointly modeling compute placement and wireless interference, yet existing tools treat them in isolation. This gap leads to rank inversions: the scheduler that appears optimal under an interference-free model can be the worst choice under realistic wireless conditions. We present ncsim, a lightweight discrete-event simulator that bridges this gap by combining DAG workflow scheduling with physically-grounded IEEE 802.11 CSMA/CA interference modeling in a single Python package. A 108-run factorial experiment reveals rank inversions in 27.8% of scenarios, with the interference-free-optimal scheduler producing up to 2.7x worse makespan than a simple round-robin baseline; scaling to a 100-node random geometric graph raises the inversion rate to 50%. These rank inversions show that interference-free evaluation can select the wrong algorithm entirely, justifying the design and use of ncsim.

Let $\{X, X_{n}; n \geq 1 \}$ be a sequence of i.i.d. $\mathbf{B}$-valued random variables and set $S_{n} = \sum_{i=1}^{n}X_{i},~n \geq 1$. This note is devoted to study the classical central limitr theorem for subsequences of sums of i.i.d. $\mathbf{B}$-valued random variables. We show that, under the assumption that $\mathbf{B}$ is of cotype $2$ space, $\left(\frac{S_{n}}{\sqrt{n}} \right)_{n \geq 1}$ converges weakly if and only if $\left(\frac{S_{m_{n}}}{\sqrt{m_{n}}} \right)_{n \geq 1}$ converges weakly for a subsequence $\{m_{n}; ~n \geq 1\}$ of positive integers. We conjecture that this result is false if $\mathbf{B}$ is not of cotype $2$ space. In addition, we show that, if $\left(\frac{S_{m_{n}}}{\sqrt{m_{n}}} \right)_{n \geq 1}$ converges weakly for a subsequence $\{m_{n}; ~n \geq 1\}$ of positive integers. and $\left(\frac{S_{n}}{\sqrt{n}} \right)_{n \geq 1}$ does not converge weakly, then $\displaystyle \left(S_{n}/a_{n} \right)_{n \geq 1}$ does not converge weakly to a non-degenerate probability measure for any sequence $\{a_{n}; n \geq 1 \}$ of positive real numbers.

For $0 \leq α< n$ and $m \in \mathbb{N} \cap \left(1 - \fracα{n}, +\infty \right)$, we consider certain fractional type operators $T_{α, m}$ generated by $m$-orthogonal matrices and prove that, for $0 < α< n$, $T_{α, m}$ can be extended to a bounded operator $H_X \to Y$ and, for $α= 0$, $T_{0, m}$ can be extended to a bounded operator $H_X \to X$, where $X$ and $Y$ are certain ball quasi-Banach spaces related to each other and $H_X$ is the Hardy space associated with $X$. In particular, our results apply to weighted Lebesgue spaces, variable Lebesgue spaces, Lorentz spaces and Orlicz spaces, the last two are new. Our proofs rely on the ssumption that $X$ is $\mathcal{O}(n)$-invariant, the theory of weighted Hardy spaces, the Rubio de Francia iteration algorithm and the finite atomic decomposition of $H_X$.

Closed-loop bioelectronic regulation of engineered secretory cell systems is challenging because electric-field (EF) stimulation acts indirectly through transcription-factor activation, in the presence of delayed, nonlinear, and noisy intracellular dynamics, sparse measurements, and constrained burst-based actuation. We develop a framework for robust closed-loop endocrine regulation in electrically stimulated engineered cell factories, illustrated through extracellular thyroid hormone \(T_4\) production in engineered thyroid-like cells. The plant is modeled by a control-oriented ODE formulation combining a reduced mechanistic \(T_4\) pathway, an EF-responsive Hill module, and a linear-chain Erlang cascade representing distributed intracellular delay. On this basis, we design a sampled-data adaptive proportional-integral-derivative (PID) controller with derivative filtering, anti-windup, saturation and rate limits, and hysteretic band-locking, together with a robust adaptive extension that accounts for parameter mismatch, sensor noise and bias, actuator mismatch, delay/jitter, and exogenous rhythmic disturbance through a scenario-based risk-aware update. We provide local sampled-data input-to-state stability interpretations for both APID and RAPID, showing that, under standard local Lyapunov and bounded-disturbance conditions, the sampled tracking error is ultimately bounded by a disturbance-dependent constant. In silico experiments demonstrate sustained regulation of extracellular \(T_4\) across prescribed targets despite significant uncertainty.

Altermagnets are a class of materials with compensated magnetic moments, in which spin sublattices are related by specific symmetries other than inversion or translation. This allows time-reversal symmetry to be broken without a net magnetization. Here, we synthesize single crystals of Fe1-xCrxSb2 and investigate their electrical transport and magnetic properties, with a focus on Fe0.85Cr0.15Sb2. Magnetization measurements suggest spin-compensated ordering below ~ 3.5 K, where magnetic moments align along the crystallographic b-direction. Transport measurements reveal a crossover from large positive to negative magnetoresistance, while an anomalous Hall response emerges below 3.5 K, indicating time-reversal symmetry breaking below TN. Muon spin relaxation measurements demonstrate bulk magnetic order below 3.5 K, confirming that the low temperature ordering is intrinsic rather than due to an impurity phase. These results support a potential altermagnetic ground state in Cr-doped FeSb2 with time-reversal symmetry breaking without net magnetization.

Electrochemical metallization (ECM) memristors have potential applications in future neuromorphic computing hardware. The set, reset, and variable-resistance features of these devices originate in the formation and breakup of metal filaments in a solid-state electrolyte. While the performance characteristics of these devices are widely investigated, the driving principles behind the morphology of the filament formation process remain unclear. In this study, we propose an approach motivated by the extremal principles found in non-equilibrium thermodynamics and observe an entropy production and energy dissipation rate minimization during the filament-forming process in kinetic Monte Carlo simulations.