Prestack elastic parameter inversion is important for reservoir characterization and quantitative seismic interpretation. Most existing deep-learning-based methods have achieved promising results, but they generally require sufficient labeled training data and have limited flexibility in integrating multi-source conditioning information. To address this issue, we propose a multi-condition guided diffusion model for controllable elastic parameter synthesis. Elastic parameter training datasets are first constructed based on well log statistics and geological characteristics of the target area and are used to train the diffusion model. A unified multi-condition guided diffusion framework is then developed to incorporate both implicit and explicit conditioning information. Specifically, iterative latent variable refinement, Adapter-based conditioning, and a diffusion posterior sampling (DPS)-projection guidance strategy are introduced for implicit model-domain constraints, implicit structural constraints, and explicit conditioning-operator constraints, respectively. Synthetic examples demonstrate that the proposed method can generate elastic parameter samples that are consistent with the prescribed conditions under both single-condition and multi-condition guidance. When seismic data are used as conditioning information, the framework can be further adapted to seismic elastic parameter inversion. Experiments show that the proposed method improves the prediction of representative elastic parameters, including P-wave velocity, S-wave velocity, and density, compared with baseline methods. The synthesized samples can also support downstream deep-learning-based inversion under limited labeled data, achieving competitive performance.

ChatGPT was launched on November 30, 2022; the r/ChatGPT subreddit was created just one day later. Since then, chatbot-based AI products have gone from niche proofs-of-concept to widely-used household names. However, the ways in which adoption has developed among the public remains poorly understood. In this paper, we develop a framework for using social media as a data source for understanding the societal impact of widely-adopted consumer AI products, and propose PuLSE (Public and Longitudinal Signals for Evaluation), a general approach to monitoring for societally-impactful trends in real time. We apply our framework to conduct what is, to the best of our knowledge, the first longitudinal study of r/ChatGPT. We find that, overall, r/ChatGPT posts over time illustrate the normalization of ChatGPT as an everyday consumer product rather than an exceptional, novel technology. However, our retrospective analysis also finds that posts about using ChatGPT for mental health support, and posts about developing emotional attachments to ChatGPT, both rise steadily in frequency almost immediately after the launch of GPT-4o in May 2024. We show that PuLSE can detect the increase in emotional engagement as early as October 2024 -- months before OpenAI made any (public) acknowledgment of this impact. An interactive site to explore our results and methods, updated daily with live data, is available at rchatgpt-pulse.github.io.

Cellular networks are undergoing a revolutionary transform with the advent of O-RAN architectures and AI/ML solutions. O-RAN's Non-Real-Time and Near-Real Time RAN Intelligent Controllers open the door to the implementation of automated control-loops that can provide RAN optimisations in numerous scenarios and use cases, and which can be further empowered by AI-driven approaches. Energetic sustainability has raised as one of the main optimisations targets due to the impact of mobile networks on global energy consumption. To this end, the BeGREEN project aims at enhancing the energy efficiency of beyond 5G networks by defining novel AI/ML-based methods at RAN and edge infrastructure. This paper presents BeGREEN Intelligent Plane, a novel framework which implements and exposes AI/ML workflows to O-RAN-based optimisations targeting energy efficiency. We also describe an exemplary application of the Intelligent Plane and its AI Engine, which aims at providing AI-driven cell on/off control.

Within the framework of a quasi-relativistic model of graphene that admits topologically nontrivial Majorana-like quasiparticle excitations, appearance of such vortex states in the frequency dependencies of the complex dielectric permittivity of the system subjected to an external electromagnetic field has been examined. The vortex graphene states possess topological charges (flavours ) being nonzero Zak phases. Interaction effects of Majorana-like modes have been qualitatively related to the formation of Fano resonances in the optical response. The constructed topological model of graphene may be considered as a toy model of three-flavour mass-neutrino oscillations.

Determining the minimal distance between a target channel and a convex hull of predefined set of implementable channels is a fundamental problem in quantum resource theory, and provides key guidance for experimental implementations. In this work, we develop a unified analytical framework for optimal convex approximation of quantum channels based on the quantum $α$-affinity measure. We construct a channel distance metric induced by the α-affinity and the ChoiJamiolkowski isomorphism, which satisfies the required properties of a well-defined channel distance. Subsequently, we present an optimization framework for the convex approximation of quantum channels, and derive analytical solutions for the optimal convex approximation of single-qubit unitary channels over both the SU(2)-covariant and Pauli channel families, obtaining closed-form expressions for the optimal parameters and the minimal approximation distance. This framework is further applied to the amplitude-damping channel, yielding the explicit form of its optimal approximation and the associated minimal α-affinity distance. In contrast to conventional approaches based on the diamond norm, our framework provides a systematic and analytically tractable approach to quantum channel approximation under realistic constraints.

The rapid growth in compute demand from artificial intelligence (AI) has driven a massive surge in data center construction, precipitating an energy and sustainability crisis. Motivated by the abundant solar energy in outer space and the recent sharp reduction in space launch costs, orbital data centers are emerging as a potential pathway for the future scaling of AI compute infrastructure. While the cold background in vacuum seems appealing for cooling, computing systems operating in space without convection ultimately rely on radiative cooling, requiring large-area radiators. Such limitations in thermal management pose a significant challenge for deploying the standard liquid/air-cooled computers in space. In this work, we investigate the impact of the thermal constraints in space on both graphics processing units (GPUs) with high-bandwidth memory (HBM) and the emerging compute-in-memory (CIM) accelerators. We develop a radiator-in-the-loop co-design methodology that directly links the permitted system TOPS (terra-operations per second) with the practical radiator cooling capacity in space. Our thermal simulations reveal that the separately located GPU die and HBMs create severe thermal hotspots under limited radiator capacity, necessitating GPU thermal throttling. In contrast, CIM accelerators exhibit a much more uniform heat distribution and consistently outperform GPUs in TOPS/W across a wide range of radiator budgets. We systematically evaluated the performance of CIM and GPU across various AI workloads and demonstrated that CIM has a magnified advantage for deployment in space under realistic thermal constraints.

In this paper, we establish in Theorem 1.2 the reciprocity of wavefront sets for irreducible admissible representations $π$ of classical groups $G$ over any local field $F$ of characteristic zero if $π$ has a generic local $L$-parameter. Over archimedean local fields, based on the progress made in our previous work (arXiv:2207.04700), we prove in Theorem 1.5 that for an irreducible Casselman--Wallach representation $π$ with a generic local $L$-parameter, the Wavefront Set Conjecture (arXiv:2207.04700, Conjecture 1.2) and its refinement (Conjecture 1.1) hold for the arithmetic wavefront set ${\mathrm{WF}}_{\mathrm{ari}}(π)$ as defined by the associated enhanced local $L$-parameter of $π$ and the wavefront set ${\mathrm{WF}}_{\mathrm{tr}}(π)$ defined by the Harish--Chandra distribution character $Θ_π$ of $π$. Hence the microlocal structure of $Θ_π$ is completely determined by the arithmetic information carried by the enhanced local $L$-parameter of $π$. The relations with the algebraic wavefront set ${\mathrm{WF}}_{\mathrm{wm}}(π)$ defined by the degenerate Whittaker models are extensively discussed by means of the composition law (Theorem 3.4) over all local fields of characteristic zero. Under Conjecture 1.3, the Wavefront Set Conjecture is fully established over archimedean local fields. As a consequence, we prove a refinement of Vogan's maximal-orbit principle (Theorem 1.7).

Extreme space weather poses an existential threat to modern satellite infrastructure, with a Carrington-class solar storm projected to cause economic losses of billions of dollars per day. Due to the rapid proliferation of satellites (with over 70,000 expected to be deployed in the next 5 years), understanding extreme space weather impacts has become essential for global economic stability and national security, and consequently, the lives of millions. However, our current vulnerability to such events remains largely unknown, and existing models rely primarily on statistical populations instead of individual satellite behavior. Through the development of a novel spatiotemporal agent-based model (ABM), this study addresses two critical research challenges: (1) predicting the impacts of extreme space weather disturbances and (2) enabling real-time maneuver guidance for satellites during such events. Utilizing 41,644 satellite records, historical records from 5 recent space weather events, and atmospheric density models, we built individual satellite agents with physics-driven behaviors that make independent decisions by dynamically responding to constraints such as propellant requirements and collision avoidance thresholds. Scenario analysis suggests that 95% of satellites in Low Earth Orbit altitudes would experience enhanced atmospheric drag of 8x baseline levels, increasing collision risks by 2-3x. Monte Carlo simulations also predict direct economic impact per affected satellite on the order of $40M. Furthermore, the model successfully uses real-time conditions to provide maneuver recommendations, with 92% accuracy. This study is thus the first to provide a prototype framework for real-time adaptive decision systems to safeguard satellites against the next Carrington-class disruption.

We prove that a finite, connected, singly connected, locally convex higher-rank tree whose $1$-skeleton is planar and which is \emph{non-degenerate}, in the sense that every edge of each colour forms a commuting square with every other colour, has rank at most four. Under these hypotheses this establishes the planarity conjecture stated in \cite{Pask}. The obstruction side of the argument uses only the non-planarity of $K_5$; it makes no appeal to the four-colour theorem. The engine is a monotonicity property of the set of colours emitted at a vertex (``backward propagation''), which forces, in any finite singly connected non-degenerate $k$-graph, a single vertex emitting all $k$ colours; once $k\ge 5$, local convexity manufactures a subdivision of $K_5$ at such a vertex.

The sPHENIX detector at the Relativistic Heavy Ion Collider will measure a suite of unique jet and Upsilon observables with unprecedented statistics and kinematic reach. A MAPS-based vertex detector upgrade to sPHENIX, the MVTX, will provide a precise determination of the impact parameter of tracks relative to the collision vertex in high multiplicity heavy ion collisions. The MVTX utilizes the latest generation of MAPS technology to provide precision tracking with high tracking efficiency over a broad momentum range in the high luminosity RHIC environment. These new capabilities will enable precision measurements of open heavy flavor observables, covering an unexplored kinematic regime at RHIC. The physics program, its potential impact, and recent detector development of the MVTX will be discussed.

We propose the Metastable Emergent Dark Energy (MEDE) model, a novel phenomenological extension of the Phenomenological (PEDE) and Generalized (GEDE) Emergent Dark Energy frameworks, in which dark energy exhibits a transitionary behavior, appearing at late times and vanishing toward the future. This model naturally enables a smooth crossing of the phantom divide line in the dark energy equation of state, as hinted at by recent observations. The MEDE model is defined by a hyperbolic tangent dark energy equation of state $w(z)=-1-Δ\tanh[\log_{10}((1+z)/(1+z_t))]$, introducing only two free parameters, the transition redshift $z_t$ and the variation amplitude $Δ$, allowing both the emergent and transitionary behavior of dark energy. We constrain the MEDE model using a combined dataset of Planck CMB, DESI DR2 BAO, and different compilations of Type Ia supernovae, obtaining $z_t=0.425^{+0.084}_{-0.120}$ and $Δ=0.87^{+0.29}_{-0.35}$ (for CMB+DESI+PantheonPlus), indicating a statistically significant deviation from the cosmological constant. Statistical comparisons show that the MEDE model is preferred over $Λ$CDM by the combined dataset, with $Δ\rm DIC_{ MEDE-ΛCDM}= -9.29$. The MEDE model performs comparably to the CPL dynamical dark energy parametrization ($Δ\rm DIC_{MEDE-CPL} = 0.74$), with no strong statistical distinction from CPL using current data. Notably, MEDE preserves the success of $Λ$CDM in describing early-universe physics and naturally accommodates the phantom-crossing signature indicated by the latest low-redshift observations. The MEDE scenario provides a compelling dark energy phenomenology that may guide us toward interesting theoretical implications.

Unmanned aerial vehicles-assisted mobile edge computing (UMEC) can execute compute-intensive and latency-critical artificial intelligence (AI) services, which can be provided by multiple UAVs collaborating in the air to perform inference tasks. Completing an AI service requires multiple inferences, each of which is implemented by an AI service chain consisting of multiple virtual network functions (VNFs). The application of AISC relies on an efficient AISC deployment strategy to determine which UAV to deploy VNF on. However, the UMEC network topology is highly dynamic due to the high-speed movement of UAVs or their departure/arrival, which makes the AISC deployment in the UMEC network challenging. In addition, the intricate relationships between UMEC environment and AISC, as well as between individual VNFs in an AISC, can also affect the effectiveness of AISC deployment strategy. Moreover, under the constraints of energy consumption and load balancing, it is also difficult to optimize the AISC strategy to minimize AISC completion time for enhancing the quality of AI service. To address the above challenges, this paper proposes a double deep attention Q-network based on heterogeneous graph neural networks, which incorporates heterogeneous graph to capture diverse relationships in UMEC and utilizes attention mechanisms to adaptively focus on critical nodes and links for intelligent AISC deployment. The experimental results demonstrate that the proposed algorithm performs excellently in AISC completion time, AISC completion rate, load balancing and energy consumption.

The classical problem of Erdős asks for the minimum number of empty convex $k$-gons determined by an $n$-element point set in the plane. The celebrated empty hexagon theorem, proved independently by Gerken and Nicolás, shows that every sufficiently large planar point set contains a $6$-hole, while Horton's famous construction shows the existence of arbitrarily large point sets with no $7$-hole. In this paper, we initiate the study of the maximum number of $k$-holes in planar point sets with no $(k+1)$-hole. More precisely, for each fixed $k\geq 6$, let $h_k(n)$ be the maximum number of $k$-holes determined by a planar point set in general position, of size at most $n$, and with no $(k+1)$-hole. We prove that there are absolute constants $c_1,c_2>0$ such that $(c_1/k)^{\lfloor k/3\rfloor} n^{\lfloor k/3\rfloor} \leq h_k(n)\leq (c_2/k)^{\lceil k/2\rceil} n^{\lceil k/2\rceil}$.

We perform detailed studies of five Hamiltonian variational ansatzes (HVA) based on the Hamiltonian of the $(1+1)$d $\mathbb{Z}_2$ lattice gauge theory. The ansatzes are designed to respect local and global symmetries of the original Hamiltonian and therefore act on a finely segmented state Hilbert space. Following Larocca et al. (2023), we numerically study the dimension of the dynamical Lie algebra (DLA) and the rank of the quantum Fisher information matrix (QFIM) of the ansatzes within specific invariant subspaces. The ansatzes all involve sums of weight-three Paulis in their generators, which is a feature that have so far been underexplored in this context. We also perform numerical experiments to determine the ground state energy of the original Hamiltonian via variational quantum eigensolver (VQE), and observe that overparametrization of the ansatzes coincides with the apparent disappearance of local minima in the loss function, in line with the finding in the reference. Finally, the decay rate of the VQE loss function under gradient descent optimization is revealed to scale linearly with the number of parameters in the ansatz. These results help to enrich the theory of overparameterization of quantum circuits and inform the design of scalable variational ansatzes.

Automatic Audio Captioning (AAC) seeks to generate natural language descriptions of complex acoustic scenes, bridging auditory perception and language understanding. However, word-selection indeterminacy and increasing reliance on large-scale sequence-to-sequence or LLM-based models limit practical deployment. We propose a resource-efficient AAC framework that explicitly grounds caption generation in auxiliary AudioSet semantics. Frame-level acoustic representations extracted using a ConvNeXt encoder are augmented with top-$K$ predicted AudioSet keywords, providing structured contextual cues for decoding. A compact six-layer BART-style decoder conditions on this joint acoustic-semantic representation, enabling caption generation without LLM-scale decoding. The proposed design balances semantic grounding and computational efficiency within a compact architecture. Evaluations on Clotho V2 and AudioCaps confirm competitive caption quality under practical deployment constraints.

This paper develops a political-economy model of artificial general intelligence (AGI) as a technology that progressively substitutes living labor with machine-based productive systems. The model studies the transition from the first moment at which AGI becomes economically capable of replacing labor to the later moment at which AGI becomes technically and actually capable of near-complete replacement. The central distinction is between technical substitutability and actual adoption. Technical substitutability is the feasible replacement ceiling implied by the state of AGI capability, whereas actual adoption is the realized replacement share chosen under cost, profitability, and adoption frictions. Under the strict value-theoretic assumption that AGI transfers value but does not itself create new value, deeper AGI adoption raises the organic composition of capital, reduces the quantity of living labor when adoption outpaces the creation of new labor fields, compresses the source of surplus value, and places downward pressure on the social rate of profit. In the limiting case in which actual AGI adoption approaches complete substitution and new labor fields fail to compensate for displaced labor, living labor tends to zero, surplus value tends to zero, and the profit rate tends to zero. The model therefore identifies near-complete AGI substitution not merely as an efficiency transition, but as a boundary case for value production under a strict political-economy theory of value.

The hyperon-nucleon ($Y$-$N$) interaction, an important ingredient for the nuclear equation-of-state (EoS), remains poorly constrained. Precise measurements of hypernucei intrinsic properties and production yields in heavy-ion collisions are crucial for the understanding of their production mechanisms and the strength of the $Y$-$N$ interaction. Thanks to the high statistics data taken from the STAR BES II program, a series of hypernuclei measurements are carried out at low energies. In these proceedings, we present the kinematic and centrality dependence of light hypernuclei production yields and strangeness population factor ($S_3$, $S_4$) in Au+Au collisions at $\sqrt{s_{\rm NN}}=$ 3 GeV. We also report the energy dependence of $^{3}_Λ{\rm H}$ yields and $S_3$ at mid-rapidity from 3 to 27 GeV Au+Au collisions. Precise measurements of $^{4}_Λ{\rm He}$ lifetime and $^{3}_Λ{\rm H}$ branching ratio are also reported. These results are compared with model calculations and physics implications are discussed.

Underwater vehicles are naturally modelled as rigid bodies on SE(3) subjected to added mass effects. The passivity of the Hamiltonian structure of the system can be exploited to design energy-based stabilising controllers, however, the extension of these control designs to tracking control is not trivial since the error system for the classical error formulations is not itself Hamiltonian. In this paper, we show that a novel choice of error function leads to error dynamics that are Hamiltonian. We go on to derive an energy-based tracking control for a fully coupled model of a submersible vehicle. Asymptotic convergence of the control scheme is proved and the control is demonstrated in a simulation study of the Blue Robotics BlueROV2 Heavy submersible.

The mass-critical NLS on Euclidean space $\R^d$ exhibits a strong mass rigidity: all positive ground states are generated from a single profile and have the same ground state mass $\widehat{M}(Q)$. By appealing to bifurcation methods, Dancer constructed in his seminar paper \cite{DancerSolution} solutions to the corresponding equation on $\R^d\times\T$ which decay in the noncompact directions and are nontrivially periodic in one direction. Such bifurcation approach, however, does not provide any energetic characterization of the solutions, and in particular does not explain their relation to the Euclidean ground-states. By introducing a new strict monotonicity mechanism for the prescribed-mass energy level, combining the semivirial-vanishing geometry framework developed in author's recent work, we prove that for any mass $c\in(0,2π\widehat{M}(Q))$ the semivirial-vanishing variational problem $m_c$ admits a normalized Dancer-type optimizer which also solves the focusing mass-critical NLS on $\R^d\times\T$. This also gives a sharp complement for the existence results deduced in our earlier work \cite{Luo_LegendreFenchel} via the Legendre-Fenchel duality.

We construct $N=1$ supersymmetric (SUSY) vertex algebras from supersymmetric enhancements of Costello--Gwilliam factorization algebras on super Riemann surfaces. Introducing SUSY factorization algebras defined on embedded SUSY disks together with natural symmetry conditions, we prove a SUSY analogue of the Costello--Gwilliam extraction theorem. As an application, we study the holomorphic sigma model in the BV formalism. For a linear target, we obtain the free $bc$-$βγ$ system and recover its structure as a SUSY vertex algebra. For general complex targets, we describe the descent of the theory under coordinate changes and identify the resulting SUSY vertex algebra with the chiral de Rham complex. We further show that Ricci-flat Kähler and hyperkähler targets give rise to $N=2$ and $N=4$ supersymmetric enhancements introduced by Ben-Zvi--Heluani--Szczesny.

Turning a promising economic idea into a credible empirical finding is, in practice, an expensive undertaking: it demands a great deal of specialised computation, and the results are seldom released in a form that others can check or build upon. Econstellar is our response. It is an open, publicly served research engine that runs publication-grade financial econometrics from an ordinary web browser and explains what the results mean, so that a reader does not merely read a finding but can re-run it, vary its inputs, and trace exactly how it was produced. Three choices give the system its character. The heavy computation is placed on the processor that suits it, rather than forced onto hardware ill-matched to the task, which is much of the reason analysis of this kind is so rarely served to the public. An artificial-intelligence assistant selects and interprets the analyses but never originates a number, so every quantity it reports is a real computation the reader can reproduce. And the engine a visitor exercises is the same code that produced the figures in our published research. We expose seventeen econometric methods, each reported with a verified live value and reproducible at the public endpoint, computed under a single discipline: prices are treated as non-stationary and all methods are applied to returns. The system also regenerates, on demand, the headline result of an accompanying study of financial contagion, from the package that generated it. The platform is the working core of an active research programme spanning three software releases and three preprints, and it is available now, free and open-source, at a live public address. Our aim is a simple one: to shorten the distance between a research claim and the moment another person can independently verify it.

Entanglement generation is a central resource for quantum information processing, quantum networking, and quantum sensing. In practical implementations, however, entangling interactions are inevitably subject to uncertainty and fluctuations in the interaction strength. We investigate the robustness of entanglement generation in the presence of such imperfections and establish a direct connection between the robustness of entanglement generation and quantum Fisher information (QFI). For two interacting qubits, we show that the reduction in concurrence caused by fluctuations in the interaction parameter is bounded by the QFI with respect to the interaction strength.

We report the first observation of a large directed flow ($v_1$) of $ϕ$ mesons in mid-central Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=3.0$-4.5 GeV, together with the $\sqrt{s_{\mathrm{NN}}}=7.7$ GeV collider-energy result for the collision-energy dependence, measured by the STAR experiment at RHIC. Despite its mesonic nature, the $ϕ$-meson $v_{1}$ exhibits a magnitude comparable to that of protons and $Λ$ baryons, and is significantly larger (by a factor of $\gtrsim3$) than that of $K^0_S$ mesons at the lowest energies. The midrapidity slope $dv_1/dy$ shows a pronounced energy dependence similar to that observed for protons and $Λ$ baryons, in contrast to lighter mesons, in the high-baryon-density region. Comparisons with hadronic transport calculations indicate that the observed $ϕ$-meson directed flow is consistent with production via high-mass baryon resonances and the collective motion of baryons influenced by baryonic mean-field interactions. Due to its long lifetime and relatively weak effective $ϕ$-$N$ interaction, the $ϕ$ meson can retain sensitivity to collective dynamics established during the dense baryonic stage of the collision. These results provide new experimental constraints on baryon-resonance production and strange-hadron transport dynamics in dense QCD matter.

Ultra-peripheral heavy-ion collisions (UPCs) coherently photo-produce vector mesons through two spatially separated and quantum-mechanically indistinguishable production sites, whose separation far exceeds the lifetime of the created resonance. The superposition of these amplitudes generates production-site entanglement, observed experimentally as entanglement-enabled spin-interference patterns in the angular distributions of the decay products. We show that these interference signatures provide a sensitive probe of spin-alignment transfer in hadronic decay chains, enabling intermediate-state quantum numbers and relative branching ratios to be measured from observed angular modulations. Using the decay $ρ(1450)\!\rightarrow\!π^{+}π^{-}π^{+}π^{-}$ as example, we simulate the $a_{1}(1260)π$, $h_{1}(1170)π$, $ρ(ππ)_{S}$, and $π(1300)π$ channels and demonstrate that each produces a distinct azimuthal $\cos 2ϕ$ modulation. The $π(1300)π$ mode shows a uniquely separated response, allowing its branching fraction to be extracted directly. These results establish production-site entanglement in UPCs as a selective tool for hadron spectroscopy, particularly for broad or overlapping resonances that are otherwise difficult to disentangle.

We study the problem of learning an unknown $n$-qubit Hamiltonian $H$ from $U = e^{-iHt}$ for a single time $t$, where $t$ may be arbitrarily large. For broad families of local Hamiltonians, we prove that, with high probability over $H$ and $t$, any sum of local observables $A$ that is normalized and orthogonal to $H$ satisfies $\tfrac{1}{2^n}\|[U(t),A]\|_F^2 \geq 1/\text{poly}(n)$. The Hamiltonian is therefore the unique approximately conserved local observable, and we can efficiently recover $H$, up to scale, as the approximate null vector of a data matrix built from random product-state inputs and classical shadows. As a corollary, we obtain a weak equilibration statement: the infinite-temperature autocorrelation of every sum of local observables orthogonal to $H$ decays by at least an inverse-polynomial amount.

Optical spectrometers are fundamental to scientific analysis, yet achieving high performance at low cost remains challenging because uncorrected aberrations rapidly degrade spectral resolution and typically necessitate complex, expensive optics. Moreover, to preserve spectral resolution, many compact designs remain fundamentally throughput-limited in terms of having a high f-number and a narrow slit. Here we present SHADES (Stochastic High-throughput Aberration-free Deep-Encoded Spectrometer), a general framework that mitigates the effects of optical aberrations using a stochastic grating array (SGA) coupled with physically grounded deep learning (DL), while substantially increasing optical throughput using encoded multi-slits. We develop a theoretical framework establishing aberration resilient spectroscopy in compact, highly aberrated systems, enabling miniaturization without sacrificing spectral resolution and optical throughput. SHADES utilizes an arbitrary spectrum generator (ASG) for hardware-in-the-loop calibration with a DL-based reconstruction pipeline. We further leverage transfer learning (TL) to reduce calibration data and computation for scalable deployment of SHADES. Experimentally, a micro-SHADES prototype achieves a spectral resolution of 2.4 nm over 450-700 nm and accurately reconstructs fluorescence spectra for chemical identification. Collectively, SHADES provides an aberration-free, high-throughput, low-cost spectrometer architecture suited for compact and scalable sensing applications.

Empirical entropy rates are widely used to quantify unpredictability from symbolic or time-series data, yet their interpretation is subtle in weakly chaotic dynamics, where ordinary Lyapunov exponents vanish and invariant measures are infinite. We address this issue by studying the empirical one-step conditional entropy for the fixed finite partitions considered below in one-dimensional intermittent maps with infinite invariant measures. For the modified Bernoulli map and the Boole transformation in the infinite-measure weak-chaos regime, we prove that this per-step empirical entropy converges to zero. Thus, the usual entropy-rate normalization becomes asymptotically blind to subexponential instability. The finite-time information sum, however, remains informative. Rare transitions between long laminar phases occur on the return-sequence scale, and their empirical self-information contributes an additional logarithmic factor. Under the stated regularity and moment assumptions, this mechanism yields a two-term estimate for the ensemble mean decay, supported by numerical simulations. Although the raw entropy rate vanishes, self-normalized fluctuations remain nontrivial and are numerically consistent with normalized Mittag-Leffler laws. A comparison with generalized Lyapunov sums shows that the corresponding information sum is not a Krengel entropy estimator, but a computable, partition-dependent finite-time measure of sparse symbolic transitions. These results clarify what empirical Markov entropy can, and cannot, measure in infinite-measure weak chaos.

Bowler et al. introduced the concept of torsoids that describes the 1-separations of a directed graph in a canonical way building on previous progress by Lov{á}sz. To fully understand the structure of directed graphs with respect to their 1-separations it remains to find a global structure along which the torsoids are arranged. In this paper, we start the investigation of this global structure for a specific class of directed graphs.

We study statistical inference for deterministic drift structures in Gaussian process models under high-frequency observations.The observed process consists of a centered stationary Gaussian component combined with a broad class of time-inhomogeneous deterministic drifts. To estimate the drift parameter, we introduce a least squares-type contrast based on first-order increments. We establish consistency and asymptotic normality under weak dependence conditions on the Gaussian component. A central feature of the framework is that the rate of convergence of the estimator depends jointly on the local roughness of the Gaussian noise and the long-time information accumulation structure generated by the drift. The theory accommodates a wide range of drift families, including integrable, polynomial-type, and periodic structures. In particular, different drift densities produce qualitatively different statistical regimes, including non-standard rates of convergence and accelerated rates for persistent or growing deterministic structures.

Pearson's correlation coefficient is commonly used as a single-number summary of association between two responses. In many applications, however, the strength of association is itself heterogeneous and may vary with demographic, biological, experimental, or environmental covariates. The regcorr package implements regression models in which a Pearson correlation coefficient is linked to a linear predictor of covariates. The package supports bivariate normal responses and bivariate Bernoulli responses, provides Newton-Raphson estimation routines, includes data generators for simulation studies, and supplies a bootstrap-based subroutine for assessing the significance and power of covariate effects. The implementation follows the likelihood-based framework of Dufera, Liu, and Xu (2023) and exposes it through a lightweight R interface with no compiled code and minimal dependencies. This paper describes the statistical model, the computational design of regcorr, reproducible usage examples, and practical guidance for interpreting covariate-dependent correlations. The package is available from the Comprehensive R Archive Network at https://CRAN.R-project.org/package=regcorr under the MIT license.