This thesis generalizes the study of $C\cap(C + α)$ where $C$ is the middle third Cantor set to self-affine sets in $\mathbb{R}^{n}$. We present sufficient and necessary conditions for when the translation $α$ produces a self-affine intersection for a particular class of self-affine sets. In the case where the attractor is self-similar, we improve results concerning the function from $α$ to the fractal dimension of the intersection. This lends itself to a case study of the complex number system $(-n + i, \{0, 1, . . . , n^{2}\})$, when $n$ is an integer greater than or equal to $2$. Lastly, we present a definition of multiplicative invariance for subsets of $\mathbb{Z}^{n}$ and establish a connection, known in the one-dimensional case, between them and invariant sets of the $n$-dimensional torus.

We study how electoral rules shape polarization dynamics when voters and candidates both adapt to repeated election outcomes. We introduce two geometric primitives for comparing rules under this feedback: the \emph{winner radius} $R_t = \max_i \|x_i - w^{(t)}\|$, the distance from the winner to the farthest voter, and the \emph{supporter centroid radius} $S_t = \max_j \|c_j - s_j^{(t)}\|$, the largest gap between any candidate and their support base. We show that $R_t$ controls a one-step contraction bound on voter disagreement and $S_t$ plays the analogous role for candidate dispersion, and that these two objectives are in tension. Rules that reduce $R_t$ tend to increase $S_t$, and vice versa. A winner close to the voter median does not resolve the tension, since proximity to the median and proximity to the Chebyshev center are different objectives. We use this framing to organize a simulation study across seven standard electoral rules and one convex-combination benchmark, comprising 1000+ runs across diverse electorate profiles, voter mechanisms, and camp-balance settings. The empirical results confirm the theoretical tradeoff: winner-take-all rules achieve small $S_t$ at the cost of large $R_t$ and weaker voter depolarization, while convex-combination rules reverse this. An oracle comparison further shows that minimizing $R_t$ per step and minimizing voter disagreement per step are distinct objectives with different long-run consequences for both voter and candidate dynamics.

Spatial join is a fundamental operation in spatial databases. With the rapid growth of 3D data in applications such as LiDAR-based object detection and 3D digital pathology, there is an increasing need to support spatial join over 3D datasets. However, existing techniques are largely designed for 2D data, leaving 3D spatial join underexplored and computationally expensive. We present 3DPipe, a pipelined GPU framework for scalable spatial join over polyhedral objects. 3DPipe exploits GPU parallelism across both filtering and refinement stages, incorporates a multi-level pruning strategy for efficient candidate reduction, and employs chunked streaming to handle datasets exceeding GPU memory. Its pipelined execution overlaps CPU data preparation, host-device data transfer, and GPU computation to improve throughput. Experiments show that 3DPipe achieves up to 9.0$\times$ speedup over the state-of-the-art GPU solution, TDBase, while maintaining excellent scalability. 3DPipe is open-sourced at https://github.com/lyuheng/3dpipe.

We study the notion of debiasability for cost functions arising in optimal transport. We call a symmetric cost function $c:\mathscr{X}\times\mathscr{X}\to\mathbb{R}\cup\{+\infty\}$ debiasable if it satisfies $c(x,y)\ge \tfrac{1}{2}c(x,x)+\tfrac{1}{2}c(y,y)$ for all $x,y\in\mathscr{X}$. Building on an equivalent characterization by an inf-representation $c(x,y)=\inf_{z\in\mathscr{Z}}ψ(x,z)+ψ(y,z)$ for some set $\mathscr{Z}$ and some function $ψ: \mathscr{X}\times \mathscr{Z} \to \mathbb{R} \cup \{+\infty\}$, interpreted as a generalization of the midpoint identity for squared geodesic distances, we investigate the debiasability of costs defined on spaces of probability measures. Our primary focus is the entropic regularization of optimal transport across different regimes of the regularization parameter $\varepsilon \in [0,+\infty]$, encompassing classical optimal transport ($\varepsilon=0$), entropic optimal transport ($\varepsilon>0$), and the Maximum Mean Discrepancy ($\varepsilon=+\infty$). For $\varepsilon \in (0,+\infty]$, we investigate sufficient conditions, such as negative definiteness of the ground cost or continuity and positive definiteness of the induced kernel, handled then via a convex-nonconcave minimax argument. All our results extend naturally to unbalanced optimal transport settings and we generalize in this way the findings of \cite{feydy2019interpolating} and \cite{sejourne2019sinkhorn}. As a byproduct, we derive novel decomposition formulas for entropic optimal transport, which may be of independent interest.

We propose \emph{PRISM} (\textbf{Pseudorandom Residue-based Indexed Scheduling Method}), a deterministic topology-discovery framework for single-hop wireless networks with bounded interference. Each receiver has at most \(L\) interfering transmitters among \(K\) transmitters and identifies them through singleton transmissions. PRISM assigns finite-field labels to transmitters and schedules transmissions via modular multiplication and a second prime modulus. It achieves full discovery in \(O(L(1+δ)\log K)\) rounds in expectation with failure probability \(K^{-δ}\), and in \(O(L^2\log K)\) rounds deterministically. Simulations show \(\approx 0.9L\log K\) scaling, with \(q/L\approx1.2\) minimizing mean completion time and \(q/L\approx1.4\text{--}1.6\) improving tail performance.

Learning about causal effects in target populations and their subsets may be facilitated by combining information from multiple sources. One major class of study designs that combine information involves appending an index study with data from an external comparator, which may facilitate head-to-head comparisons of treatments initially studied in different populations. We delineate external comparator analyses under two distinct, but related, identification strategies. The first strategy relies on exchangeability (transportability) of potential outcome means, which uses information only on the treatments that are to be compared. The second strategy relies on transportability in effect measure, requiring additional use of information on a third treatment common to the populations that have been combined. In a time-fixed setting with a point treatment and non-failure time outcome, we examine identification and estimation under a basic setup where information from an index trial is combined with a second, and external to the index trial, data source. We propose estimators for identifying observed data functionals, with a particular focus on semiparametric efficient augmented weighting estimators that incorporate models for the probability of trial participation, the probability of treatment, and conditional outcome means. We derive the asymptotic properties of these augmented weighting estimators -- including robustness to model misspecification and slower rates of convergence for some nuisance function models -- and use simulation to compare their finite sample performance to estimators based only on outcome modeling or weighting. Last, we provide a practical demonstration of the proposed methods by combining the ACCEPT and PHOENIX 1 randomized trials to evaluate the effect of various biologic agents on plaque psoriasis, a chronic inflammatory disorder.

Eruptive accretion events are expected to play an important role in the mass buildup stage of individual star formation. FU Ori objects (FUors) experience the most extreme eruptive outbursts, which raise the accretion rate of the disk from $10^{-9}-10^{-8} \ M_\odot \ \mathrm{yr}^{-1}$ to $10^{-5}-10^{-4} \ M_\odot \ \mathrm{yr}^{-1}$ and last for decades. During an outburst, the disk is approximately 100 times brighter than the star, making direct study of the central star impossible. However, the disk is expected to be in Keplerian rotation around the star, enabling indirect constraints on properties of the central source via observations of the disk. Using $1-2.4 \ μ$m high resolution spectra of several tens of FUors, we demonstrate the expected Keplerian rotation in their inner disks. We then adopt a Keplerian rotational broadening profile to model the line profiles of spectral lines, and focussing on the H-band region, we infer the mass distribution of FUors. We finally show that this mass distribution is consistent with inferred Solar neighborhood initial mass functions, suggesting all young stars undergo a period of FUor outbursts in their pre main-sequence evolution.

Stationary states of quantum many-body Hamiltonians are invariant under the Hamiltonian evolution. Besides ground and thermal states, this class includes microcanonical ensembles that are of fundamental importance in statistical physics. We consider the preparation of general stationary states by leveraging recent advances in the field of open-system dynamics. In particular, constructions based on exact KMS-detailed balance with respect to Gibbs states of noncommuting Hamiltonians have only recently been proposed as a tool for their efficient preparation and, by extension to small temperatures, for ground state preparation. We extend these constructions to the problem of stationary state preparation, providing general criteria that characterize when such states have efficient implementations, along with specific results on the approximation of microcanonical ensembles. An interesting application of our work are tests of conjectured ensemble equivalences for local observables between microcanonical and Gibbs ensembles.

In many applications, the data lie on a type of cone, where there is a distinction between an overall scale variable and the remaining scale-free structure. For example, the joint size and shape of objects are points on a cone, where size represents scale, and shape is the scale-free structure. Dimension reduction is central in such applications, as shape data are often high-dimensional. Interactions between shape and size are widespread and of significant interest in real-world applications. However, most existing methods either lack a single notion of size or focus solely on shape, effectively removing size information. We propose Principal Nested Cones (PNC), a nonlinear dimension reduction framework that preserves both shape and size. PNC represents data through a sequence of nested hypercones and progressively projects observations onto lower-dimensional cone spaces. The resulting PNC scores provide low-dimensional representations that jointly capture size-shape variation in an interpretable manner. To enable scalable computation in ultra-high-dimensional settings, we develop a fast approximation combining PCA-based transformation with standard PNC. Simulation studies and real data applications demonstrate that PNC captures nonlinear size-shape structure, improves representation and reconstruction, and yields interpretable insights across morphometric, developmental, and molecular datasets.

In this paper, we conduct a systematic literature review of (semi-) automated approaches to Quantum Software Engineering (QSE) and Quantum Artificial Intelligence (QAI). Prior work in the literature indicated that both Software Engineering (SE) and Artificial Intelligence (AI) practices may become more efficient by using (semi-) automated approaches. This also holds in the Quantum Computing (QC), Quantum Information Science (QIS), and Quantum Engineering (QE) world, as well as in hybrid quantum-classical applications. In fact, automation is even more crucial in such cases since there is a limited number of developers and AI experts (e.g., data scientists) who possess the required knowledge and skills in QC. Moreover, in hybrid setups, automation may help decide what part of the application should be deployed on quantum hardware and on which of the available quantum platforms, if applicable. This can be a significant help to achieve productivity leap and efficiency even for subject matter experts. Unlike prior literature reviews and surveys, this work focuses on automation in SE and AI for quantum and hybrid quantum-classical applications and identifies the recent trends and future directions through a systematic literature review. We are interested in methods and techniques that can enable a broader development and deployment of quantum and hybrid AI-enabled software systems.

Standard intergenerational measures have been shown to understate the long-run persistence of socioeconomic advantages in developed countries. We study theoretically and empirically whether this pattern extends to less developed settings, using Indonesia as a case study. Using the Indonesian Family Life Survey (IFLS) and Census data, we study multigenerational correlations in education across three generations. Contrary to previous findings, we observe greater multigenerational mobility than parent-child correlations alone would suggest. We develop a theoretical framework to highlight two key factors influencing multigenerational dynamics in developing countries: (1) financial and credit constraints, and (2) cultural norms related to marital sorting. To confirm their relevance, we exploit regional variations in exposure to the 1997-98 Asian financial crisis and in marital customs.

Traditional macroeconomic growth models rely on general equilibrium and continuous, frictionless institutional transitions, failing to account for the catastrophic structural collapses observed in empirical economic history. We propose the Stochastic Networked Governance (SNG) model, a discrete-time, agent-based framework that bridges econophysics, network science, and institutional economics. By defining jurisdictions through a binary institutional genome, the model formalizes institutional complementarity, endogenous growth, and the non-linear macroeconomic penalties of structural reform (the "J-Curve"). Using the CEPII Gravity Database and the IMF Systemic Banking Crises dataset, we move beyond theoretical topologies to execute an empirical historical simulation from 1970 to 2017 across the top 100 global economies. Through Monte Carlo ensembles, we demonstrate how scale-invariant exogenous shocks and spatial capital flight drive global phase transitions, exposing the mathematical mechanics of the 1989-1991 Soviet collapse, the Hub-Risk Paradigm, and the emergent resilience of spatially firewalled market networks.

In the vicinity of the young star FN Tau, we have detected a microjet and four Herbig-Haro objects, whose positions and kinematics indicate the presence of a bipolar collimated outflow from the star - HH 1267. The stellar jet does not propagate rectilinearly, and we discuss the possibility that the curved shape of the jet, whose axis is inclined to the line of sight at an angle $<20^\circ$, results from the precession of the inner regions of the FN Tau protoplanetary disk. Approximately 60 years ago, the star underwent outbursts with an amplitude of $Δm_{\rm pg} \sim 2^{\rm m}$ lasting several months, which we associate with the onset of the microjet.

Recent years have experienced growing contributions of AI coding agents that assist human developers in various software engineering tasks. However, this growing AI-assisted autonomy raises questions about security and trust. In this paper, we analyze more than 33,000 AI-generated pull requests (PRs) and identify 675 security-related submissions made by agentic AIs. Then we examine the security-related PRs with a focus on recurring security weaknesses, review outcomes and latency, commit message quality, and rejection reasons. The results show that security-related AI PRs introduce a small set of recurring weaknesses such as regex inefficiencies, injection flaws, and path traversal. Many flawed contributions are still merged, while rejections often arise from social or process factors such as inactivity or missing test coverage. The commit message quality of AI PRs has a limited effect on acceptance or latency, in contrast to human PRs reported in previous studies. We also extend existing rejection taxonomies by adding categories that are unique to AI-generated security contributions. These findings offer new insights into the strengths and shortcomings of autonomous coding systems in secure software development.

Path optimization methods have been widely used and highly successful for the analysis of chemical reactions. Yet, they can fail to capture intrinsically multidimensional features of potential energy surfaces (PES). We introduce the nudged elastic membrane method, a framework for constructing two-dimensional reduced potential-energy surfaces in chemically relevant regions of a PES using only energies and forces without requiring more costly Hessian information. The method is demonstrated for a three-dimensional prototype model and for the triplet formaldehyde molecular system. In both cases, the resulting membrane captures one-dimensional reaction-path features as well as genuinely two-dimensional structures such as a yet unreported reported second-order saddle point in the PES of triplet formaldehyde. The method further provides direct access to structures that can serve as starting points for subsequent refinement. Our results show that the method offers a practical route to exploring multidimensional PES topography beyond the single-path picture.

In this paper, we consider combining the ideas of forbidden random context grammars as well as of ordered grammars with cooperating distributed grammar systems (CDGS). We focus on investigating their generative capacities. Both ideas can be added to CDGS in two ways: either having (e.g.) a strict order of the rules in each component, or having a strict order on the components. This leads to four different scenarios, only some of them have been addressed in the literature before. While in the area of CDGS, many inclusions among language classes have been %are still open questions for decades, the proposed addition of forbidden random context and ordered regulation variants leads to a clear picture which allows us to get down to only five different classes of languages well known from classical regulated rewriting. This way, we also solve some open problems from the literature.

Guiding others through authentic scientific research outside of PhD programs has been practiced for decades in specialized secondary schools, undergraduate research programs, and independent settings. These practitioners work in the middle, between the classroom science teacher and the PhD advisor, guiding learners with aptitude or serious interest. Sport and music have dedicated professions for this middle position (the school-team coach and the school band director); research does not. This paper names that missing profession the Research Guide: the practitioner who develops another person's capacity to do research, from framing a question to communicating findings. Hundreds of thousands of middle and high school students already pursue authentic research each year, even more college undergraduates participate in research with a faculty member, and millions of adults engage in citizen science. In current practice, the programs that serve this middle group mostly default to a simplified version of the PhD apprenticeship model structured around one mentor with a few students at a time, without systematic training; they overwhelmingly frame research as the hypothetico-deductive cycle alone. The role calls for cognitive apprenticeship, a pedagogical approach in which an expert's tacit moves on open-ended problems are made visible and scaffolded, then faded as the learner develops, while the research outcomes themselves remain unpredictable. It spans multiple modes of inquiry (not only the hypothetico-deductive cycle) and demands a combination that no existing training program produces: pedagogy, research methodology, developmental assessment, risk and productive struggle management, domain flexibility, and community building. Together these demands warrant a dedicated profession: a named role, a training pathway, a career ladder, hiring standards, and institutional recognition.

In a previous submission, we established a fundamental relation between tone networks and configurations. It was shown that the Eulerian tonnetz can be represented by a $\{12_3\}$ of Daublebsky von Sterneck type D222. We also constructed a tonnetz for Tristan-genus chords (dominant sevenths and half-diminished sevenths) and we showed that this tonnetz can be represented by a $\{12_3\}$ of type D228. In both of these constructions the associated Levi graphs play an important role. Here we look at the tonnetze associated with some other musical systems, thereby offering several concrete examples of an abstract view of music as combinatorial geometry. First, we look at the tonal harmonies typical of the classical period. In the case of diatonic triads, we show the existence of a bipartite graph of type $\{7_3\}$ and girth four that represents the well-known relations between the seven diatonic degrees and their pitch classes. In the case of diatonic seventh chords, we obtain a Fano configuration $\{7_3\}$ which gives a complete characterization of the voice-leading relations that hold between such chords. Next, we construct a tonnetz for pentatonic music based on the Desargues configuration $\{10_3\}$ and we construct a tonnetz for the 12-tone system based on the Cremona-Richmond configuration $\{15_3\}$. Both can be used as a resource for musical compositions. Finally, we show that the relation between the chromatic pitch class set and the major triad set is also represented by a D222. The minor triads are in one-to-one correspondence with the members of a certain class of hexacycles in the Levi graph of this configuration. In this way, the characteristic duality between major and minor triads in the tonnetz can be broken.

We explore the sensitivity of neutrino observatories and direct dark matter detection experiments to boosted sub-GeV dark matter produced by inelastic cosmic ray collisions in the atmosphere. We revisit earlier approaches and extend the sensitivity to higher mass by modeling the proton bremsstrahlung production mode via initial state radiation. For vector-mediated dark matter models, the peak of the cosmic ray flux allows for enhanced DM production for mediator masses near the $ρ/ω$ resonances. We determine and compare the ensuing sensitivity of direct detection experiments LZ and PandaX-4T and the neutrino detectors Borexino and Super-K.

Earth-observation satellites are emerging as distributed edge platforms for time-critical tasks, yet orbital scheduling remains challenged by intermittent energy harvesting and temporal coupling where eager execution risks future battery depletion. Existing schedulers rely on static priorities and lack mechanisms to adaptively shed work. We present Equinox, a lightweight, decentralized runtime for resource-constrained orbital systems. Equinox enables adaptive scheduling by compressing time-varying constraints, including battery charge, thermal headroom, and queue backlog, into a single state-dependent marginal cost of execution. Derived from a barrier function that rises sharply near safety limits, this cost encodes both instantaneous pressure and future risk. This local signal serves as a constellation-wide coordination primitive. Tasks execute only when their value exceeds the current cost, enabling value-ordered load shedding without explicit policies. If local costs exceed a neighbor's, tasks are dynamically offloaded over inter-satellite links, achieving distributed load balancing without routing protocols or global state. We evaluate Equinox using a multi-day simulation of a 143-satellite constellation grounded in physical Jetson Orin Nano measurements. Equinox improves scientific goodput by 20% and image-processing throughput by 31% over priority-based scheduling while maintaining 2.2x higher mean battery reserves. Under high demand, Equinox achieves 5.2x the execution rate of static scheduling by gracefully shedding work rather than collapsing under contention.

We present ab initio calculations using the $R$-matrix with time dependence (RMT) method for high-order harmonic generation (HHG) in argon in a short, intense pulse regime. The calculations employ a $6$-cycle $\sin^2$ pulse at $850$ nm with peak intensity $2.3\times 10^{14}$ W/cm$^2$ and, for comparison with the experiment by Guo et al. [J. Phys. B: At. Mol. Opt. Phys. 51, 034006 (2018)], a Gaussian pulse with the same frequency and peak intensity. Both pulse shapes yield the expected harmonic structure in the region above the ionization threshold (approximately $15.82$ eV in $LS$-coupling). The spectra exhibit strong carrier-envelope-phase (CEP) sensitivity. The energy region leading up to the ionization threshold contains spectral features arising from residual coherent dipole oscillations (free-induction decay) that strongly depend on spectral windowing and the post-pulse propagation time. We show that the HHG spectrum, particularly below the ionization threshold, is a defined quantity that depends on analysis choices rather than being a uniquely determined observable. Comparison between theoretical predictions and experimental observations in this energy regime, therefore, requires explicit specification of these parameters.

Blockchain technology is widely expected to reduce transaction costs by automating contract enforcement and eliminating intermediaries; yet, the execution costs imposed by network congestion have received little attention in the operations management literature. We study on-chain peak shaving, the systematic scheduling of Ethereum transactions toward low-congestion windows to reduce gas fee exposure. We use transaction-level data from seven firms across seven industries (N = 62,142 transactions, January-March 2026). Gas fees vary significantly throughout the day: the peak-hour premium at 10 AM Eastern Time reaches USD 0.220 per transaction above the overnight baseline, driven primarily by speculative-arbitrage demand rather than operational activity. Firm-level scheduling responses are heterogeneous and not uniformly disciplined. Only three of seven firms transact disproportionately during off-peak hours; four transact counter-cyclically, concentrated in peak windows due to external deadlines or governance cycles. This heterogeneity is explained by two moderators: transaction deferrability and gas intensity. We formalize these into an On-Chain Scheduling Matrix that maps firms to four regimes: 1) full peak shaving, 2) selective peak shaving, 3) cost provisioning, and 4) accept-market-rate, with regime membership predicting both fee savings and residual cost floors (40-92 percent of actual expenditure). Theoretically, we extend Transaction Cost Economics to account for time-varying execution costs imposed by congestion externalities. In addition to extending Williamson's original cost taxonomy, we introduce a dual classification of gas fees as execution costs in timing but maladaptation costs in origin. The findings reposition on-chain gas-fee management alongside energy procurement and foreign exchange hedging as a domain requiring systematic operational planning.

Shot noise has been used to measure fractional charges of anyons. The value of the charge imposes constraints on fractional statistics but does not determine it. This issue is particularly important in multi-component systems. For example, the zero charge of neutral anyons in bilayer graphene gives no information about their statistics at all. We propose a protocol to probe the statistics of charged and neutral anyons in multi-component systems with layer-resolved or spin-resolved noise. The protocol applies to the fractional quantum spin Hall effect in MoTe$_2$, topological states in multi-layer graphene and bilayer GaAs, and to recently discovered fractional excitons in bilayer graphene. The approach relies on the relation between statistics and the distribution of the anyon charge over the components. Information about statistics can also be extracted from a simpler measurement of the layer-resolved electric current through a narrow constriction in a Hall bar even in the presence of long-range interactions and other non-universal effects.

Generative AI has demonstrated significant potential in creative design, enabling the rapid generation of visual content and imaginative concepts. Although deep AI models achieve effective featurization in the latent space, navigating the space remains a challenge. Current techniques, such as GANSlider and SliderSpace, use multiple sliders to generate high-dimensional vectors in generative AI's latent space. Despite applying (global) PCA to reduce the number of sliders, these approaches struggle with scalability and usability as the number of control dimensions increases. In this paper, we introduce LatentGandr, a visual analytics technique that facilitates latent space exploration by extracting locally linear dimensions from embeddings in high-dimensional latent spaces. By analyzing the topology and local curvature of the embeddings, LatentGandr automatically identifies local neighborhoods and computes their principal components using localized PCA. These local principal components are visualized as interactive image grids, allowing users to efficiently explore and control the generative process, providing an intuitive means to refine the generation of novel content and concepts. To evaluate the effectiveness of LatentGandr, we conducted a study comparing it to GANSlider, the current state-of-the-art visualization interface for generative AI models. The results offer insights into how localized exploration techniques can enhance user interaction with these models.

The deflection angle of a light ray passing the Schwarzschild (spherically symmetric vacuum) black hole was calculated by Charles Galton Darwin in 1959 in terms of the elliptic integral of the first kind. This calculation has been repeated many times and has also been given approximately in terms of elementary functions for impact parameters that either are not too small or are close to the critical impact parameter. Here I present Padé 2-point approximants of order [2,2] (quadratic numerators and denominators), relating the critical impact parameter divided by the actual impact parameter to the exponential of the negative of the deflection angle, that fairly accurately cover the full range of impact parameters greater than the critical impact parameter, which is the case for all photon trajectories that remain outside the black hole. I also present a simpler quadratic approximation that works as well in the middle of the range but not so well at the extremes.

Mimicking the collective excitatory and inhibitory behaviors of biological neurons remains a critical challenge in the development of neuromorphic computing systems that rival the complexity and performance of the human brain. Volatile high-to-low resistance switching in insulator-to-metal transition (IMT) materials produces an abrupt increase in current flow, resembling neuronal excitation. This electrical excitation enables IMT materials to be driven into a neuron-like spiking self-oscillation regime using simple RC circuits. Here, we report a new type of self-oscillation dynamics that occurs in the opposite class of metal-to-insulator transition (MIT) materials. Electrical triggering of the MIT suppresses current flow, resembling neuronal inhibition. Using a prototypical MIT material, we experimentally demonstrate inhibitory-like self-oscillations in two-terminal switching devices incorporated into a simple RL circuit. Our results show robust ~0.1 - 1 MHz electric current oscillations with minimal cycle-to-cycle variation, which can be controlled by varying the applied DC voltage, temperature, and inductance. This work demonstrates a new type of inhibitory MIT-based artificial neuron that can complement the excitatory functionalities of IMT-based neuristors in biologically plausible neuromorphic systems.

We establish a framework to determine the linear completeness of families of non-linear trajectories in Hilbert spaces, which relies on an infinite analytic block Toeplitz operator formulation. By means of this approach, we show the linear completeness in Sobolev spaces of two families of classical functions. One is the moving family of dilated Weierstrass functions. The other is the family of eigenfunctions of the Gross-Pitaevskii equation with trapping potential in an infinite square well. Our results provide a new insight on the formulation of general methods to examine this intriguing concept, bridging classical non-linear analysis and linear approximation theory.

The rapid advancement of Audio Large Language Models (ALMs), driven by Neural Audio Codecs (NACs), has led to the emergence of highly realistic speech deepfakes, commonly referred to as CodecFakes (CFs). Consequently, CF detection has attracted increasing attention from the research community. However, existing studies predominantly focus on English or Chinese, leaving the vulnerability of Indic languages largely unexplored. To bridge this gap, we introduce Indic-CodecFake (ICF) dataset, the first large-scale benchmark comprising real and NAC-synthesized speech across multiple Indic languages, diverse speaker profiles, and multiple NAC types. We use IndicSUPERB as the real speech corpus for generation of ICF dataset. Our experiments demonstrate that state-of-the-art (SOTA) CF detectors trained on English-centric datasets fail to generalize to ICF, underscoring the challenges posed by phonetic diversity and prosodic variability in Indic speech. Further, we present systematic evaluation of SOTA ALMs in a zero-shot setting on ICF dataset. We evaluate these ALMs as they have shown effectiveness for different speech tasks. However, our findings reveal that current ALMs exhibit consistently poor performance. To address this, we propose SATYAM, a novel hyperbolic ALM tailored for CF detection in Indic languages. SATYAM integrates semantic representations from Whisper and prosodic representations from TRILLsson using through Bhattacharya distance in hyperbolic space and subsequently performs the same alignment procedure between the fused speech representation and an input conditioning prompt. This dual-stage fusion framework enables SATYAM to effectively model hierarchical relationships both within speech (semantic-prosodic) and across modalities (speech-text). Extensive evaluations show that SATYAM consistently outperforms competitive end-to-end and ALM-based baselines on the ICF benchmark.

We study the periodic homogenization of the viscous Hamilton--Jacobi equation \[ u_t^\varepsilon + \frac{1}{2}|Du^\varepsilon|^2 + V\!\left(\frac{x}{\varepsilon}\right) = \frac{\varepsilon}{2}Δu^\varepsilon \qquad \text{in } \mathbb{R}^n \times (0,\infty), \] with initial datum $g \in W^{1,\infty}(\mathbb{R}^n)$, where $V$ is Lipschitz continuous and $\mathbb{Z}^n$-periodic. We prove the sharp global estimate \[ |u^\varepsilon(x,t)-u(x,t)| \leq \varepsilon\!\left(C+\frac{n}{2}\log\!\left(\frac{\max\{t,\varepsilon\}}{\varepsilon}\right)\right) \qquad \text{for all } (x,t)\in \mathbb{R}^n \times [0,\infty), \] where $\varepsilon \in (0,1]$, $u$ solves the limiting (homogenized) equation and $C>0$ is a constant depending only on $\|Dg\|_{L^\infty(\mathbb{R}^n)}$, $\|DV\|_{L^\infty(\mathbb{R}^n)}$, and $n$. We further show that if $g$ is locally semiconcave, then \[|u^\varepsilon(x,t)-u(x,t)| \leq C_{x,t}\varepsilon \qquad \text{for a.e. } (x,t)\in \mathbb{R}^n \times (0,\infty),\] where $C_{x,t}$ depends on $(x,t)$, $\|Dg\|_{L^\infty(\mathbb{R}^n)}$, and $\|DV\|_{L^\infty(\mathbb{R}^n)}$. More precisely, the above improved rate holds at every point $(x,t)$ where $u(\cdot,t)$ is twice differentiable at $x$. In particular, this occurs for a.e. $x\in \mathbb{R}^n$, since $u(\cdot,t)$ is locally semiconcave. We conclude by raising the open problem of whether the same $O(\varepsilon |\log \varepsilon|)$ rate remains valid for general strictly convex Hamiltonians or general periodic diffusions.

We present a search for small Kochen-Specker (KS) sets in dimension 3, specifically targeting extensions of the 13-ray Yu-Oh set, which has been proven to be the minimal witness to state-independent contextuality. To enable this search, we introduce a novel SAT-based orderly generation framework integrating recursive canonical labeling (RCL) with the graph isomorphism tool NAUTY. We demonstrate that previous SAT approaches relying on lexicographical canonicity suffer from exponential scaling on canonical graphs. This limitation renders them intractable on the large instances (25 to 33 vertices) encountered in our search, whereas our RCL check maintains consistent millisecond-level performance, effectively eliminating the bottleneck. Overcoming this bottleneck allows us to perform the first exhaustive enumeration of all KS sets with up to 33 rays containing the complete 25-ray state-independent contextuality (SI-C) set obtained by rigid extensions of the Yu-Oh set in 1,641 CPU hours. We found and verified that the 33-ray set discovered by Schütte is the smallest three-dimensional KS set containing the complete 25-ray SI-C set. All non-existence results are backed by independently verifiable proof certificates via an extension of the DRAT proof format.