The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of fluids with different densities and subjected to a Boussinesq physical regime in each layer. Well-posedness of the periodic initial-value problem (ivp) of the systems is first analized. Then, a discretization in space based on the spectral Fourier-Galerkin method is introduced and error estimates for the semidiscrete approximation are derived. Using an efficient time integrator, some numerical experiments to illustrate the performance of the discretization are presented.

We present measurements of near-infrared (NIR) terrestrial airglow produced by helium and oxygen in the exosphere as observed by SPHEREx. Using eight months of survey data obtained from a 680 km low-Earth orbit, emission from HeI $λ$10830, OI $λ$8446, and OI $λ$11287 is mapped with both global spatial and multi-season temporal coverage. These measurements are obtained along upward looking lines of sight as part of the astrophysical survey, in contrast to conventional nadir-viewing Earth remote sensing, which probes the behavior of low-density material in the thermo- and exosphere. We describe an analytical framework to extract atmospheric emission lines in the presence of astrophysical backgrounds including stars, resolved galaxies, and the diffuse Zodiacal light. The resulting global measurements reveal temporal variability over the survey period and systematic dependencies on geographic location. We interpret these variations in the context of the variable Solar illumination and seasonal effects. SPHEREx, an astrophysical space observatory, is demonstrated to be a promising new platform for monitoring NIR airglow and investigating its coupling to Solar activity and global geophysical processes.

We provide a computable criterion for selecting among Fourier, wavelet, and time-frequency analysis by extending the algebraic diversity (AD) framework to Lie groups acting on $L^2(\mathbb{R})$. To our knowledge, there is no other criterion that provides this selection capability. The group-averaged estimator generalizes from a finite sum over group elements to an integral with respect to Haar measure. A Continuous Replacement Theorem establishes signal-noise separation under equivariance and ergodicity conditions, with a noise operator $\mathcal{N}_G = C_ρ^{-2}$ determined by the Duflo-Moore operator that explains the frequency-dependent noise floor in wavelet analysis as a consequence of the affine group's non-unimodularity. A Unification Theorem shows that classical spectral analysis corresponds to the translation group, wavelet analysis to the affine group, time-frequency analysis to the Heisenberg-Weyl group, and spherical harmonics to SO(3). The commutativity residual $δ$, extended to Hilbert-Schmidt operator norms, provides a principled selection criterion among these groups. A double-commutator generalized eigenvalue problem solves the blind group matching problem in polynomial time. A Discretization Recovery Theorem establishes that all discrete AD results are sampling approximations to the continuous theory, with $\mathbb{Z}_M \to (\mathbb{R},+)$ as $M \to \infty$.

Indian Railway workshops form a critical component of rolling stock maintenance infrastructure, employing more than 2.5 lakh personnel across 44 major workshops nationwide. However, safety management in many workshops still relies on fragmented manual processes, resulting in delayed approvals, incomplete documentation, and increased exposure to operational hazards. Field safety observations indicate that lacerations (28.7%) and abrasions (21%) remain among the most frequent workplace injuries, highlighting the need for structured digital safety workflows. This paper presents the Integrated Digital Management System for Railway Workshops, a modular multi-workflow digital platform developed to improve safety governance and workflow transparency. The proposed system integrates four primary modules: Machine and Plant Management, Permit-to-Work (PTW) Management, Contract Management, and Incident Management. The Permit-to-Work module digitizes hazardous work authorization in accordance with IS 17893:2022, while the Contract Management module supports workforce validation and regulatory oversight. The Incident Management module enables rapid reporting, investigation tracking, and corrective action workflows. Functional evaluation in a railway workshop-oriented deployment scenario demonstrated measurable operational improvements, including a reduction in permit processing time by approximately 35%, improved incident reporting response time by nearly 40%, and enhanced workflow traceability across multiple safety modules. The proposed system establishes a scalable foundation for digital safety governance in large-scale railway workshop environments.

Graph representation is a powerful abstraction of real-world objects and relations. Computing the Graph Edit Distance (GED) between graphs is critical in domains such as bioinformatics, machine learning, and pattern recognition. GED measures the minimum number of edit operations required to transform one graph into another. However, the high computational complexity of optimal and near-optimal methods limits their applicability to large-scale graphs, making high-performance parallel GED computation essential. To address this, we propose FAST-GED, a fast and scalable open-source framework for GED computation on GPUs. FAST-GED overcomes existing limitations by combining high accuracy with fast execution through GPU-friendly algorithmic design and efficient mapping to GPU hardware, minimizing host-device communication. The implementation is optimized and tested across multiple GPU architectures. We validate FAST-GED on real and synthetic datasets with diverse graph sizes and densities. It achieves speedups of several orders of magnitude over the Python NetworkX library while reaching optimal solutions in most cases. Moreover, it outperforms state-of-the-art approximate methods in both accuracy and scalability. We show that FAST-GED enables broader adoption of GED-based solutions in real-world applications.

Social media has become a critical source of situational awareness during disasters, providing real-time insights into evolving impacts and emerging needs. To support crisis response at scale, recent work has increasingly leveraged large language models (LLMs) to automatically classify and summarize situational information from social media streams. However, existing approaches implicitly assume that extracted situational claims are equally plausible, despite information quality varying substantially as a crisis unfolds. In this work, we propose an uncertainty-aware framework for automated situational awareness reporting that explicitly accounts for the plausibility of social media claims. First, we classify social media posts according to an established situational awareness schema. Second, we introduce an uncertainty assessment layer that evaluates whether individual situational claims plausibly reflect real-world conditions when conditioned on external proxy data, while explicitly eliciting the model's confidence in this judgment. Third, we use these uncertainty assessments to generate crisis reports that communicate not only what is being reported, but how certain those reports are. We apply this framework to over 200,000 earthquake-related Twitter/X posts, using impact summaries from the USGS PAGER as a representative external proxy. We argue that explicitly representing uncertainty supports human crisis communicators in prioritizing information under time pressure, and provides a framework for integrating external proxy data into LLM-based situational awareness pipelines.

Canonical LST (sTEZ) is an enshrined, protocol-native mechanism designed to mitigate the centralization risks associated with liquid staking intermediaries. Intended to complement direct staking rather than replace it, Canonical LST provides a neutral, public alternative managed directly by the Tezos protocol. It allows any tez holder to participate in aggregated staking without reliance on third-party operators. sTEZ follows an accrual-based design: all slashing events and rewards are reflected in the token's exchange rate to tez, keeping balances fungible while exposing holders to the precise economics of staking. This approach ensures that liquid staking functions as fundamental network infrastructure--with deterministic lifecycle rules, transparent on-chain data, and governance anchored in the amendment process--rather than as a discretionary commercial product. This white paper summarises the motivation for enshrining liquid staking, the core mechanics, exchange-rate model, regulatory touchpoints, risk posture, and forward-looking roadmap for Canonical LST.

We present a minimal agent-based model of interacting agents characterized by their wealth to study taxation and inequality in a non-conservative economy. Wealth evolves through an extremal stochastic replacement process in which the poorest agent has its wealth replaced by a new random value, financed through a collective taxation mechanism. We explore taxation regimes ranging from regressive to progressive schemes and tune the overall redistribution strength. Under regressive taxation, the system self-organizes into two distinct stationary phases when changing the total tax collected: a non-ergodic, high-inequality regime characterized by wealth condensation in a subset of agents that permanently escape replacement, and a more homogeneous ergodic phase in which all agents participate in the dynamics. Increasing taxes drives an abrupt transition between these phases. The transition is discontinuous and exhibits hysteresis and bistability, consistently detected through the Gini index, the Top $1\%$ wealth share, the entropy, and the Binder cumulant. In contrast, neutral and progressive taxation suppress persistent wealth concentration, preventing the emergence of strongly unequal states and eliminating hysteretic behavior. These results show that minimal stochastic redistribution mechanisms alone can produce discontinuous transitions, metastability, and non-ergodicity, demonstrating that taxation structure can determine the emergence and stability of macroscopic inequality.

We consider smooth convex minimization over compact convex sets, i.e., $\min_{x \in C} f(x)$ with the (vanilla) Frank-Wolfe algorithm. Well-known lower bounds establish a worst-case $Ω(1/t)$ primal-gap barrier in the general smooth convex case, and faster convergence usually requires favorable function properties such as Hölder error bounds or strong convexity. We present a new Local Dual Sharpness (LDS) condition, essentially a property of the feasible region and its LMO, under which the Frank-Wolfe algorithm converges in $o(1/t)$ for any smooth convex function, ruling out an $Ω(1/t)$ lower bound under LDS. The condition is a generalization (and localization) of uniform convexity of sets and it is satisfied by any uniformly convex set. To our knowledge, this is the first unconditional $o(1/t)$ convergence result for uniformly convex sets. Combining LDS with stronger function properties, e.g., a local variant of Hölder error bounds, allows us to quantify the actual rates.

We associate a musical instrument, a "hyperbolic marimba", to every pair $(X,Γ)$ where $X$ is a hyperbolic surface and $Γ\subset X$ a simple multicurve labeled with musical keys. It works as follows: take a geodesic and every time it hits $Γ$, play the corresponding note. In this paper we investigate to which extent the so-produced melodies characterize $(X,Γ)$ up to isometry. In the accompanying website "HyperMarimba" (available at https://ludox73.github.io/HyperMarimba/story.html ), the reader can actually listen to the produced melodies. They can also visualize some of the phenomena we investigate.

The accurate simulation of interface-dominated solid mechanics problems on complex microstructures remains challenging, particularly when interface-fitted quadrilateral or hexahedral meshes are difficult to generate. We extend the shifted boundary method (SBM) to cohesive-zone formulations and introduce the Shifted Cohesive Zone Method (SCZM), with applications to crystal plasticity on non-interface-fitted meshes. By shifting the enforcement of traction-separation laws from the true interface to a nearby surrogate interface, SCZM enables the use of standard finite element spaces while avoiding the meshing burden associated with interface-conformal discretizations. We present a simplified SCZM weak form defined on the surrogate interface, leading to a straightforward implementation of the nonlinear residual and consistent tangent matrix. The method is implemented in the open-source MOOSE framework and coupled with constitutive models from NEML2, enabling simulations with linear elasticity, multiple traction-separation laws, and history-dependent crystal plasticity. We further develop a geometry-aware, PCA-enhanced point classification algorithm to accelerate surrogate-domain construction. Verification and benchmark studies in two and three dimensions demonstrate that SCZM achieves first-order convergence for non-interface-fitted interface problems and closely matches interface-fitted reference solutions in terms of reaction forces, surface energy release, deformation, stress fields, and damage evolution. These results indicate that SCZM provides an accurate and efficient framework for modeling interface mechanics in complex microstructures without requiring interface-fitted meshes.

Deploying Large Language Models (LLMs) on resource-constrained edge devices faces critical bottlenecks in memory bandwidth and power consumption. While ternary quantization (e.g., BitNet b1.58) significantly reduces model size, its direct deployment on general-purpose hardware is hindered by workload imbalance, bandwidth-bound decoding, and strict data dependencies. To address these challenges, we propose \textbf{VitaLLM}, a hardware-software co-designed accelerator tailored for efficient ternary LLM inference. We introduce a heterogeneous \textbf{Dual-Core Compute Strategy} that synergizes specialized TINT-Cores for massive ternary projections with a unified BoothFlex-Core for mixed-precision attention, ensuring high utilization across both compute-bound prefill and bandwidth-bound decode stages. Furthermore, we develop a \textbf{Leading One Prediction (LOP)} mechanism to prune redundant Key-Value (KV) cache fetches and a \textbf{Dependency-Aware Scheduling} framework to hide the latency of nonlinear operations. Implemented in TSMC 16nm technology, VitaLLM achieves a decoding throughput of 70.70 tokens/s within an ultra-compact area of 0.223 mm$^2$ and a power consumption of 65.97 mW. The design delivers a superior Figure of Merit (FOM) of 17.4 TOPS/mm$^2$/W, significantly outperforming state-of-the-art accelerators. Finally, we explore an extended bit-serial design (BoothFlex-BS) to demonstrate the architecture's adaptability for precision-agile inference.

We show the existence of energies exhibiting dynamical delocalization in discrete 2D Chern insulators perturbed by a random potential in a general setting. Our proof exploits two main features of the model: jumps in the integer value of the Chern character and continuity of averaged spectral projections in both energy and disorder parameters. This allows us to show robustness of the topological index in the presence of disorder, which, combined with existing methods to prove dynamical localization, allows us to provide detailed information on the phase diagram of the model. The novelty of our approach is that we are able to show dynamical delocalization in the disorder parameter, and not only in the energy parameter, which allows to prove Anderson metal-insulator transition even when spectral gaps close due to the strength of disorder.

The microscopic origin of the de Sitter entropy remains a central puzzle in quantum gravity related to the cosmological constant problem. Within $\mathcal{H}$olographic $\mathcal{N}$aturalness, we propose this entropy is carried by light, coherent degrees of freedom - "hairons" - emerging as moduli of gravitational instantons on orbifolds. From the Euclidean de Sitter instanton ($S^4$), we construct a new class of orbifold gravitational instantons, $S^4/\mathbb{Z}_N$, where $N$ corresponds to the de Sitter entropy. The moduli space dimension scales linearly with $N$, and we identify these moduli with hairon fields. A $\mathbb{Z}_N$ symmetry from Wilson loops ensures mode distinguishability, yielding the correct entropy. Hairons acquire a mass of the order of the Hubble scale with negligible interactions, suggesting the de Sitter vacuum is a Bose-Einstein condensate of these excitations. We then unify the neutrino mass generation with the cosmological constant via gravitational topology. The small neutrino mass emerges naturally without new physics beyond the Standard Model. The gravitational Chern-Simons structure and anomaly force a topological Higgs mechanism, leading to neutrino condensation via $S^4/\mathbb{Z}_N$ instantons. The topological degrees $N \sim M_\text{P}^2/Λ\sim 10^{120}$ provide both a holographic entropy counting and a $1/N$ information see-saw mechanism for neutrino masses. Predictions: (i) neutrino superfluid condensation forming Cooper pairs below meV as cold dark matter; (ii) resolution of the strong CP problem via a QCD composite axion; (iii) time-varying neutrino masses tracking th dark energy evolution; (iv) signatures in astroparticle physics, ultra-high-energy cosmic rays and high magnetic field experiments.

We showed a positive energy theorem for asymptotically flat initial data sets with the concept of spectral PSC by He-Shi-Yu, Bi-Hao-He-Shi-Zhu and Brendle-Wang; and the Jang equation in Schoen-Yau, Eichmair and Jang. Then, we proved a quantitative shielding theorem concerning the causal property of the energy-momentum vector of an asymptotically hyperbolic manifold. As a result, we established the positive mass theorem for complete asymptotically hyperbolic manifolds satisfying the dominant energy condition. As corollaries, we also obtained corresponding results for manifolds with asymptotically locally hyperbolic ends with a certain symmetry.

The widespread claim that violations of Bell inequalities establish the nonlocality of nature is critically reexamined. It is argued that this conclusion is not logically compelled by either the Einstein-Podolsky-Rosen (EPR) argument or Bell's theorem. The analysis highlights the central role of counterfactual reasoning--the assumption that outcomes of unperformed measurements possess definite values--in the derivation of Bell inequalities. It is shown that these inequalities follow not from locality alone, but from the conjunction of locality with a global assignment of values across incompatible measurement contexts. Their experimental violation therefore signals the impossibility of such a global assignment, i.e. contextuality, rather than necessarily implying nonlocal causation. This perspective is further illustrated within Nelson's stochastic mechanics, where entanglement is encoded in a joint stochastic process and measurement corresponds to Bayesian conditioning, thereby sharpening the distinction between contextual correlations and nonlocal dynamical influence.

We prove that if a small Hankel operator on the product Hardy space belongs to some Schatten class $S^p$, $p < \infty$, then it has a symbol in product BMO. In other words, the conclusion of Nehari's theorem holds under the hypothesis that the operator belongs to a Schatten class.

Laser annealing offers a promising route to back end of the line fabrication of ferroelectric thin film transistors based on hafnium-zirconium oxide (HZO). Due to the wide band gap of this material, previous reports have studied the crystallization of HZO using ultraviolet or infrared light. In contrast, we monitor its crystallization in a Si$_3$N$_4$/TiN/Hf$_{0.5}$Zr$_{0.5}$O$_2$ thin film heterostructure upon irradiation with visible nanosecond laser pulses. This geometry mimics the structure of CMOS devices and harnesses the absorption of TiN in the visible regime to generate the heat necessary for the transformation. Through a series of local in situ measurements using a modified transmission electron microscope, we quantify the relationship between the HZO film thickness, critical laser energy density and the ferroelectric HZO phase fraction, finding a sharp threshold behavior in the laser pulse energy necessary to crystallize HZO. The optimal condition of irradiating an 8-nm HZO film with a single laser pulse with an energy density of 177 mJ/cm$^2$ is found to produce 86% of the ferroelectric orthorhombic phase. Heat transfer dynamics within the heterostructure during laser annealing are revealed by finite element simulations, where the partial melting of the silicon nitride substrate is found to play an important role limiting the temperature to 1900 °C. This finding as well as the observed laser pulse energy threshold behavior support a kinetic crystallization pathway involving the tetragonal phase. More generally, these findings show how laser-driven phase engineering can lead to scalable design and enhanced performance of ferroelectric materials in advanced electronic applications.

Advances in generative artificial intelligence, particularly agentic coding systems capable of autonomous software development, are disrupting the economics of the make-or-buy decision for enterprise applications. The "SaaSocalypse" narrative predicts that AI will render large segments of the Software-as-a-Service market obsolete by enabling firms to build software in-house at a fraction of historical cost. This paper adopts a conceptual research approach, combining transaction cost economics and the resource-based view with an assessment of current AI capabilities, to systematically re-evaluate the factors underlying the make-or-buy decision. It makes three contributions. First, it provides a factor-level analysis of how AI reshapes seven canonical decision determinants: cost, strategic differentiation, asset specificity, vendor lock-in, time-to-market, quality and compliance, and organizational capability. Second, it develops a typology of enterprise applications by their sensitivity to AI-induced shifts in make-or-buy economics. Third, it demonstrates that AI fundamentally transforms the governance properties of the Make option, shifting it from Williamson's pure hierarchy to a hybrid governance form that combines code ownership with external AI infrastructure dependency, with qualitatively different economics, capability requirements, and governance structures than pre-AI in-house development. The analysis finds that the SaaSocalypse thesis is overstated for most enterprise application categories; Make is most compelling for commodity utilities and differentiating custom applications in the AI era, while regulated and mission-critical systems remain predominantly in the buy domain.

Schroedinger's equation gave early quantum theory a visual language that looked like physics again: a wave evolving by a linear differential equation. This essay argues that the same success also seeded a recurring impulse to keep quantum theory "classical-looking" by treating the wave function as a physical wave. Schroedinger quickly realized that, for many-particle systems, the wave function is naturally defined on configuration space rather than ordinary physical space, blocking any straightforward reading of it as a literal classical wave. Read through Mach and Boltzmann, who shaped his intellectual outlook most deeply, his achievement appears double-edged: it provided an extraordinarily powerful picture for calculation and discovery, while also warning against taking that picture too literally. I argue that this tension never fully disappeared. It still reappears in modern physics whenever the wave function, or in quantum field theory the field itself, is treated as ontology rather than as part of a representation tied to measurement and observational context, a point sharpened by Bell-type no-go theorems. The centenary moral is: use pictures boldly, but demote them ontologically.

Rapid environmental change and advances in data-driven analysis highlight the need not only to use computational tools, but also to foster understanding of the natural world and inspire creativity. Photosynthesis, the process that fuels nearly all life on Earth, provides a compelling context for such learning, particularly in understanding how plants alter their photosynthetic strategies in response to environmental changes. However, existing tools for studying photosynthesis are often inaccessible or limited to demonstrating its presence, rather than capturing its temporal dynamics. We present PhytoBits, a frugal in situ gas-exchange sensing toolkit for distinguishing and teaching photosynthetic strategies. PhytoBits combines leaf enclosure with accessible materials, an off-the-shelf CO2 sensor, and a low-cost microcontroller, to support multi-day monitoring of plant gas-exchange in educational and research contexts. We validated PhytoBits against research-grade gas-exchange systems, confirming that it identifies C3 and CAM (Crassulacean Acid Metabolism) photosynthetic pathways. In addition to obligate CAM, PhytoBits also resolves facultative CAM and developmental CAM dynamics in plants. This work presents an early-stage hardware validation; user deployment studies, open-source code dissemination, and automated pathway classification are planned as future work.

For any Tychonoff space $X$ let $C_p(X)$ (resp., $C^*_p(X)$) be the set of all continuous (resp., and bounded) functions on $X$ with the pointwise convergence topology. Given Tychonoff spaces $X$ and $Y$, Uspenskij \cite{us} proved that if $C_p(X)$ is uniformly homeomorphic to $C_p(Y)$, then $X$ is pseudocompact if and only if $Y$ is pseudocompact. The author and Vuma \cite{valvu} have shown that linear homeomorphisms between $C_p^*(X)$ and $C_p^*(Y)$ preserve pseudocompactness. Recently Baars-van Mill-Tkachuk \cite{bmt} gave another proof of that result and raised the question if the same remains true provided $C_p^*(X)$ and $C_p^*(Y)$ are uniformly homeomorphic. In the present paper we answer that question positively. This, together with a result of Krupski \cite{k}, implies that $κ$-pseudocompactness is also preserved by uniform homeomorphisms between $C_p^*$-spaces.

We prove the following estimate \[ \|{e^{it\partial_x^2}f}\|_{L_{(t,x)\in \mathbb{T}^2}^6}\leq C (\log N)^{1/6} \|f\|_{L^2_x(\mathbb{T})}, \] assuming $\mbox{supp} (\hat f)\subset [-N,N]$ for $N>1$. The bound $(\log N)^{1/6}$ is sharp in view of the lower bound by Bourgain \cite{Bourgain}.

Water exhibits an anomalous nonlinear temperature-density ($ρ$-$T$) relation as it approaches freezing, along with an increase in viscosity, and a decrease in thermal conductivity. These departures from the standard Oberbeck--Boussinesq approximation, which assumes constant material properties and a linear $ρ$-$T$ relation, can modify convection in ice-bounded aquatic systems, yet their effects remain unexplored. Here, we examine these effects via the canonical Rayleigh--Bénard convection framework using direct numerical simulations. We show that non-Oberbeck--Boussinesq effects lower the mean fluid temperature relative to the standard case and break the classical symmetry of the mean temperature profile. The magnitude of this symmetry breaking depends on both the Rayleigh number $Ra$ and the temperature-dependent material properties retained in the governing equations. We further identify a small but measurable shift in the critical Rayleigh number, $Ra_c$. After accounting for this shift, the nondimensional heat transfer rate, $Nu$, follows the classical scaling with supercriticality, while $Re$ remains consistent with the Grossmann--Lohse unifying theory, $Re\propto (Ra-Ra_c)^{1/2}$ for low-$Ra$ convection (regime $\mathrm{I}_u$) and $Re\propto (Ra-Ra_c)^{4/7}$ at high-$Ra$ (regime $\mathrm{III}_u$). Unlike the classical expectation that the latter scaling arises at high Prandtl number, here it is obtained at an intermediate Prandtl number, $Pr\sim 10$. Our results establish how near-freezing material anomalies affect both local and global properties of convection, with implications for heat distribution and mixing in cryospheric liquid waters.

The mechanisms underlying magnon damping are of fundamental and technological interest in low-damping materials. We find low-damping ferrimagnetic insulator Li$_{0.5}$Al$_{1.0}$Fe$_{1.5}$O$_4$ (LAFO) thin films to be a promising model system for probing these mechanisms because of its distinct temperature dependent spin diffusion length (SDL) trends for electrically and thermally generated magnons. With increasing temperature, the electrical SDL shows minimal change, while the thermal SDL decreases. We attribute these trends to distinct magnon populations and scattering mechanisms: thermally generated high $k$ magnons are limited by magnon-phonon scattering, whereas electrically generated low $k$ magnons are limited by relaxational scattering from magnetic impurities.

This chapter provides an overview of chaotic billiard lasers as a prominent branch of quantum chaos. These lasers offer an ideal experimental platform for demonstrating the principles of quantum chaos within a physical system. We begin by introducing the fundamental principles of chaotic ray dynamics in optical microcavities, where the transition from regular to fully chaotic dynamics fundamentally alters the underlying wavefunctions and lasing properties. A central focus is placed on "chaos-assisted light emission," which serves as a practical manifestation of "chaos-assisted tunneling" -- a hallmark phenomenon in the study of quantum chaos. We discuss both theoretical frameworks and experimental validations, demonstrating how chaotic orbits facilitate the coupling between evanescently localized modes and far-field emission. Furthermore, exploring how the presence of a gain medium influences established results from quantum chaos research remains a fundamental and intriguing problem in physics. To address this, we establish a rigorous and comprehensive derivation of the Maxwell-Bloch equations for two-dimensional microcavity lasers, specifically examining their application to fully chaotic, stadium-shaped billiard lasers. By bridging the gap between nonlinear lasing processes and chaotic wavefunctions, this chapter highlights the unique potential of chaotic billiards for controlling light-matter interactions and shaping the next generation of unconventional coherent light sources.

We study quantum tunneling through a potential barrier whose height fluctuates in time and is modeled by Gaussian white noise. We map the stochastic dynamics onto an equivalent time-independent Lindblad equation for the density matrix, allowing fully analytical solutions. For Schrödinger particles, noise introduces dissipation that suppresses Fabry-Pérot oscillations and yields an exponentially decaying transmission. Applying the same formalism to graphene, we demonstrate that noise induces a complex longitudinal wavevector within the barrier, leading to a strong suppression of transmission and Klein tunneling, even at normal incidence. Our approach promises improved control over Klein tunneling. These results demonstrate that noisy barriers can act as tunable dissipative elements, offering a pathway to enhanced control of electron transport in graphene-based devices. We also briefly discuss how our results could guide the design of graphene quantum dots for potential use in spin qubit devices.

Classical design theory treats the type of an object as a given: the designer decides in advance that this will be a cup, then optimizes its parameters. This paper argues that object type is not a presupposition but an inference, something that can be determined from physical data and functional requirements jointly. We call this problem requirement-steered interface type inference and show that it is inexpressible within existing design frameworks. This paper makes two contributions that are jointly necessary and individually incomplete. The first is the problem itself, which classical design cannot pose because it presupposes the very thing our problem seeks to determine. The second is C-DMBD, a constrained extension of the Dynamic Markov Blanket Detection algorithm, which makes requirement-steered inference computationally tractable. Drawing on the free-energy principle and active inference, established frameworks in theoretical neuroscience and Bayesian mechanics, we model a product's surface as a Markov blanket: the minimal boundary through which all causal exchange between object and environment must pass. Different blanket structures correspond to different object types; different parameterizations of the same structure correspond to different functional modes of the same type. This paper is a proof of concept and a theoretical proposal. It reframes design as inference rather than optimization, and as a relation between generative models rather than a specification of parameters.

We develop a Weierstrass-Kenmotsu type representation for conformal immersions of constant mean curvature $0\le H<1$ in hyperbolic $3$-space $\HH$. The construction is based on the Hermitian model of $\HH$, a balanced spectral deformation, and Iwasawa splitting of $\SL$. We show that such immersions arise locally from a rank-one $(1,0)$-form $η$ and a constant complex parameter $λ\in\C^*$ through a flat $\SL$-connection of the form \[ S^{-1}dS=η-λ\,η^*, \] with mean curvature \[ H=\frac{1-|λ|^2}{1+|λ|^2}. \] Conversely, every conformal CMC immersion with $0\le H<1$ is locally obtained from such flat rank-one data. We establish an explicit correspondence with the representation of Aiyama and Akutagawa via a gauge transformation, and interpret the construction in terms of Kokubu's adjusted normal Gauss map. We further discuss the role of the flatness condition, present simple local and cylindrical model examples, and outline aspects of monodromy and numerical implementation within this framework.

We introduce R package iglm, which implements a comprehensive framework for studying relationships among predictors and outcomes under interference. The implemented regression framework facilitates the study of spillover and other phenomena in connected populations and has important advantages over existing packages, among them scalability and provable theoretical guarantees. On the computational side, the regression framework relies on scalable methods that can be applied to small and large data sets, by solving a convex optimization program based on pseudo-likelihoods using Minorization-Maximization and Quasi-Newton algorithms. On the statistical side, the regression framework comes with provable theoretical guarantees. To increase the versatility of iglm, users can add custom-built model terms. We showcase iglm using two data sets, including hate speech on the social media platform X and communications among students.