Linear-quadratic Gaussian games provide a framework for modeling strategic interactions in multi-agent systems, where agents must estimate system states from noisy observations while also making decisions to optimize a quadratic cost. However, these formulations usually require agents to utilize the full set of available observations when forming their state estimates, which can be unrealistic in large-scale or resource-constrained settings. In this paper, we consider linear-quadratic Gaussian games with sparse interagent observations. To enforce sparsity in the estimation stage, we design a distributed estimator that balances estimation effectiveness with interagent measurement sparsity via a group lasso problem, while agents implement feedback Nash strategies based on their state estimates. We provide sufficient conditions under which the sparse estimator is guaranteed to trigger a corrective reset to the optimal estimation gain, ensuring that estimation quality does not degrade beyond a level determined by the regularization parameters. Simulations on a formation game show that the proposed approach yields a significant reduction in communication resources consumed while only minimally affecting the nominal equilibrium trajectories.

We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on complex-valued functions defined on Q_{p}. These Hamiltonians admit localized wavefunctions and allow long-range interactions, so spooky action at a distance is allowed. These features are not present in the original model. The new model gives the same predictions as the standard one. The p-adic line serves as a discrete model for the physical space; in this type of space, non-locality emerges naturally.

In competitive games with private objectives, actions can reveal information about hidden parameters. Quantifying such information revelation, however, is substantially more challenging, since it depends not only on the opponent's hidden parameter but also on the opponent's model of the game. We study this problem via a two-player linear-quadratic stochastic differential game under partial information, in which each player knows its own coupling parameter and models the opponent's hidden parameter through a prior. Starting from the full-information game, we characterize the Nash equilibrium by coupled Riccati equations. We then define baseline implementable controls by averaging the equilibrium under each player's prior. Building on this baseline, we formulate an alignment-faking control problem in which one player trades off fidelity to its implementable policy against information acquisition about the opponent's hidden parameter. The information incentive is constructed from a proxy Fisher information matrix based only on the player's available model. This leads to a tractable saddle-point formulation with semi-explicit control characterization through Riccati systems. Numerical illustrations show that alignment faking can substantially improve information gain over baseline play when the faker's model is accurate, but often at the cost of greater detectability. They also show that the proxy Fisher information can systematically differ from the true information under model misspecification.

Clumping by streaming instability (SI) leading to gravitational collapse is the leading proposed mechanism for forming planetesimals, the building blocks of terrestrial planets and giant-planet cores. The critical dust-to-gas density ratio above which the SI leads to dust concentration strong enough to result in collapse depends on local dust properties and disk conditions, such as particle Stokes number, pressure gradient, and turbulence. The role of turbulence has recently drawn attention because simulations have shown that even modest levels of istropically forced turbulence can significantly increase the critical dust-to-gas ratio. However, we show that this does not hold for turbulence self-consistently generated by the magnetorotational instability (MRI). We present the first parameter study of the SI in three-dimensional, stratified, shearing-box simulations including non-ideal magnetohydrodynamics with ambipolar diffusion. Modest turbulence yields a clumping boundary similar to pure SI cases, while stronger turbulence does increase the critical dust-to-gas density ratio, though less than in the models where turbulence is isotropically forced. Particle concentration occurs inside zonal flows, large-scale structures generated by the MRI. Our results suggest that self-consistent, MRI-driven turbulence does not necessarily inhibit planetesimal formation.

Two-level systems (TLS) in native Nb and Ta oxides limit superconducting-qubit coherence and SRF-cavity quality factors in the microwave frequency range, yet their microscopic origin remains unclear. We combine MLIP-accelerated sampling of hydrogen configurations and diffusion pathways in amorphous Nb and Ta pentoxides with targeted $\textit{ab initio}$ validation. Hydrogen is the only light interstitial with barrier-distance combinations near the $\sim0.1-10$ GHz tunneling regime, and its ensemble statistics in amorphous oxides produce effective TLS densities and loss estimates consistent with the experimentally observed higher loss in Nb oxide than in Ta oxide. Our results point to H tunneling as a plausible microscopic TLS source in these materials.

Formal specifications, such as pre- and post-conditions provide a solid basis for performing thorough program verification. However, developers rarely provide such formal specifications, hence if AI could help in constructing them, it would make formal verification possible or at least make automated testing much more effective. This paper presents a study on the ability of LLMs in generating formal FULL pre- and post-conditions of a program, given its natural language description. 24 state-of-the-art LLMs were evaluated on a freshly prepared dataset of 40 tasks. The paper investigates specifications of varying difficulty and discusses a set of more refined performance metrics in addition the general accept@1 performance. It also investigates the impact of using automatically generated tests for validation of the solutions proposed by LLMs. The results of the experiment reveal that, in general LLMs can produce valid pre- and post-conditions based on natural language descriptions of programs. Incorrect solutions from proprietary models are also often near correct. A closer inspection shows that open-source models tend to result in a higher proportion of erroneous results while proprietary models tend to have slightly higher false negative rates. Interestingly, the results also show that augmenting the manually prepared dataset with automatically generated tests leads to the exposure of wrong solutions, which would have otherwise been accepted as correct. In general, LLMs perform better in formalizing pre-conditions than on post-conditions and proprietary models perform better than open ones. However, none of the LLMs were able to correctly formalize all the tasks in our benchmark. Overall, the effectiveness and reliability of LLMs in formalizing pre- and post-conditions could be greatly improved by using a good test suite that checks the correctness of the LLM generated formalizations.

Metaphors fundamentally shape how we reason about complex issues like artificial intelligence, yet current approaches to metaphor analysis in political discourse suffer from inconsistent definitions and methodologies. This paper introduces Narrative Frames, a novel categorisation system that addresses these limitations by providing a standardised framework for identifying and analysing metaphors in AI policy debates. Building on Lakoff and Johnson's conceptual metaphor theory, we derive 49 distinct narrative frames through a two-stage process: inductively coding 685 metaphors from the MetaNet database, then cross-referencing findings with 82 critical metaphor analysis studies. This methodology grounds the typology in both empirical data and established theoretical concepts while resolving definitional ambiguities that have hindered cross-study comparison. The Narrative Frames system offers researchers, journalists, and policymakers a shared vocabulary for analysing how metaphors shape public perception and policy priorities in AI governance. By revealing both the frames present and notably absent in discourse, this approach enables more transparent analysis of underlying assumptions and power dynamics. We discuss limitations and propose future applications, including computational scaling using large language models.

This paper develops a multi-period optimization framework to design a voluntary renewable program (VRP) for an electric utility company, aiming to maximize total renewable energy deployments. In the business model of VRP, the utility must ensure it generates renewable energy up to the total amount of contract during each market episode (i.e., a year), while all the revenue collected from the VRP must either be used to invest in procuring renewable capacities or to maintain the current renewable fleet and infrastructure. We thus formulate the problem as an optimal pricing problem coupled with revenue allocation and renewable deployment decisions. We model the demand function of voluntary renewable contracts as an exponential decay function based on survey data. We analytically derive the optimal pricing policy of the VRP as a function of the current grid carbon intensity. We prove that a myopic policy is conditionally optimal, which maximizes renewable capacity in each period, attains the long-run optimum due to the utility's revenue-neutral constraint. We show different binding conditions and marginal values of decision variables correspond to different phases of the energy transition, and that the utility should strategically design its revenue-sharing decisions, balancing investments in renewable expansion and subsidizing existing renewable fleets. Finally, we show that voluntary renewable programs can only extend renewable penetration but cannot achieve net-zero emissions or a fully renewable grid. This pricing-allocation-expansion framework highlights both the potential and limitations of voluntary renewable demand, providing analytical insight into optimal policy design and the qualitative shifts occurring during the energy transition process.

We introduce the notion of density of a rational language with respect to a sequence of probability measures. We prove that if $(μ_n)$ is a sequence of Bernoulli measures converging to a positive Bernoulli measure $\overlineμ$, the sequential density is the ordinary density with respect to $\overlineμ$. We also prove that if $(μ_n)$ is a sequence of invariant probability measures converging in the strong sense to an invariant probability measure $\overlineμ$, then the sequential density of every rational language exists for this sequence.

In many geophysical and planetary environments, such as Earth's ocean and atmosphere as well as subsurface oceans of icy satellites, convection driven by bottom geothermal heating usually coexists with baroclinic eddies driven by lateral buoyancy/temperature gradients. These processes compete against each other, with convection destabilizing the stratification and baroclinic eddies re-stabilizing it, thereby controlling whether the bottom heat flux is significantly redistributed as it is transmitted to the upper surface. Using scaling analysis and numerical simulations, we show that a stratified layer persists near the upper surface up to ${\rm Ra}_{v}\sim {\rm Ra}_h^{5/2}$, where ${\rm Ra}_h\equiv Δb_0/(L_zf^2)$ measures the imposed upper-surface buoyancy contrast $Δb_0$ and ${\rm Ra}_v\equiv B_0/(L_z^2f^3)$ measures the strength of the bottom buoyancy flux $B_0$, $L_z$ is the domain depth and $f$ is the Coriolis parameter. For ${\rm Ra}_v<{\rm Ra}_h^{5/2}$, baroclinic eddies dominate over convection, maintain the upper stratified layer, and completely deflect the bottom buoyancy/heat input into meridional transport. In contrast, when ${\rm Ra}_v>{\rm Ra}_h^{5/2}$, convective plumes penetrate the stratification and transport buoyancy/heat vertically with negligible deflection. Building on these results, we further propose a scaling law for the meridional buoyancy/heat transport in this system. Applications to icy satellites are discussed.

Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $α$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic $α^* = 3.85 \pm 2.32$ across natural muscles and showed that $α^*$ optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in $α$ emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by $α$) shapes population dynamics. Agents of different $α$ compete for resources and reproduce with slight mutations. Without mutations, resource availability drives populations in $α$ toward distinct behaviors: under abundance or scarcity, specialized $α$ survive. However, with mutations and selection, populations evolve toward distributions centered around the characteristic $α^*$ observed in nature. Further, we show that the mutation rate $δ$ governs a balance between adaptability and robustness: large $δ$ generates instability and extinction, small $δ$ prevents feedback, while intermediate $δ$ enables long-term adaptability while remaining robust to short-term noise. Our results suggest that nonlinear actuation provides a general understanding of energy management in actomyosin systems across a wide range of timescales, ranging from the task-specific to evolutionary. These insights may guide the rational design of active materials with adaptive properties.

We use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.

The determination of the neutrino mass ordering is one of the flagship goals in particle physics. A well-known and powerful synergy emerges when combining high-precision measurements of the effective atmospheric mass-squared splitting from electron antineutrino disappearance in reactor experiments with that from muon (anti)neutrino disappearance in accelerator-based long-baseline experiments. To fully exploit this synergy, percent-level precision in the atmospheric mass splitting is required-a target that JUNO is expected to achieve within a few months of data taking. This motivated the formulation of a mass ordering sum rule for neutrino disappearance channels, which shows that by combining data from T2K and NOvA with JUNO after one year of operation, the neutrino mass ordering can be determined at the $3σ$ confidence level. Since JUNO has recently started taking data, it is timely to ask whether this sum rule remains robust in the presence of new physics. We identify the necessary conditions for new physics to affect the sum rule and demonstrate that, in some cases, such effects could lead to an incorrect inference of the mass ordering. As concrete examples, we consider Scalar Non-Standard Interactions (SNSI) and neutrinos coupled to an ultralight scalar field. We find that, for SNSI, current constraints render any modification of the sum rule negligible, whereas in the latter case, the inference of the ordering requires caution. Nevertheless, these effects can be disentangled, illustrating how the sum rule can also be used to search for new physics.

This paper illustrates the Renormalisation Group (RG) approach to singular SPDEs following a framework introduced by Kupiainen \cite{Kupiainen2016}. We study a linear elliptic SPDE with a hierarchical Laplace operator and multiplicative noise, in two dimensions. Although this model is a significant simplification, it captures the core mechanisms of the RG method in a transparent setting. Particular emphasis is placed on the dynamical system governing the flow of the effective force coefficients, the central object of the RG method.

Traditional GPU hash tables preserve every inserted key -- a dictionary assumption that wastes scarce High Bandwidth Memory (HBM) when embedding tables routinely exceed single-GPU capacity. We challenge this assumption with cache semantics, where policy-driven eviction is a first-class operation. We introduce HierarchicalKV (HKV), the first general-purpose GPU hash table library whose normal full-capacity operating contract is cache-semantic: each full-bucket upsert (update-or-insert) is resolved in place by eviction or admission rejection rather than by rehashing or capacity-induced failure. HKV co-designs four core mechanisms -- cache-line-aligned buckets, in-line score-driven upsert, score-based dynamic dual-bucket selection, and triple-group concurrency -- and uses tiered key-value separation as a scaling enabler beyond HBM. On an NVIDIA H100 NVL GPU, HKV achieves up to 3.9 billion key-value pairs per second (B-KV/s) find throughput, stable across load factors 0.50-1.00 (<5% variation), and delivers 1.4x higher find throughput than WarpCore (the strongest dictionary-semantic GPU baseline at lambda=0.50) and up to 2.6-9.4x over indirection-based GPU baselines. Since its open-source release in October 2022, HKV has been integrated into multiple open-source recommendation frameworks.

Early demonstrations of fault tolerant quantum systems have paved the way for logical-level compilation. For fault-tolerant applications to succeed, execution must finish with a low total program error rate (i.e., a low program failure rate). In this work, we study a promising candidate for future fault-tolerant architectures with low spatial overhead: the Gross code. Compilation for the Gross code entails compiling to Pauli Based Computation and then reducing the rotations and measurements to the Bicycle ISA. Depending on the configuration of modules and the placement of code modules on hardware, one can reduce the amount of resulting Bicycle instructions to produce a lower overall error rate. We find that NISQ-based, and existing FTQC mappers are insufficient for mapping logical qubits on Gross code architectures because 1. they do not account for the two-level nature of the logical qubit mapping problem, which separates into code modules with distinct measurements, and 2. they naively account only for length two interactions, whereas Pauli-Products are up to length $n$, where $n$ is the number of logical qubits in the circuit. For these reasons, we introduce a two-stage pipeline that first uses hypergraph partitioning to create in-module clusters, and then executes a priority-based algorithm to efficiently assign clusters onto hardware. We find that our mapping policy reduces the error contribution from inter-module measurements, the largest source of error in the Gross Code, by up to $\sim36\%$ in the best case, with an average reduction of $\sim13\%$. On average, we reduce the failure rates from inter-module measurements by $\sim22\%$ with localized factory availability, and by $\sim17\%$ on grid architectures, allowing hardware developers to be less constrained in developing scalable fault tolerant systems due to software driven reductions in program failure rates.

This paper presents a particle swarm optimization algorithm that leverages surrogate modeling to replace the conventional global best solution with the minimum of an n-dimensional quadratic form, providing a better-conditioned dynamic attractor for the swarm. This refined convergence target, informed by the local landscape, enhances global convergence behavior and increases robustness against premature convergence and noise, while incurring only minimal computational overhead. The surrogate-augmented approach is evaluated against the standard algorithm through a numerical study on a set of benchmark optimization functions that exhibit diverse landscapes. To ensure statistical significance, 400 independent runs are conducted for each function and algorithm, and the results are analyzed based on their statistical characteristics and corresponding distributions. The quadratic surrogate attractor consistently outperforms the conventional algorithm across all tested functions. The improvement is particularly pronounced for quasi-convex functions, where the surrogate model can exploit the underlying convex-like structure of the landscape.

The growing energy demands of computational systems necessitate a fundamental shift from performance-centric design to one that treats energy consumption as one of the primary design considerations. Current approaches treat energy consumption as an aggregate, deterministic property, overlooking the path-dependent nature of computation, where different execution paths through the same software consume dramatically different energy. We introduce the Energy Flow Graph (EFG), a formal model that represents computational processes as state-transition systems with energy costs for both states and transitions. EFG enables various applications in software engineering, including static analysis of energy-optimal execution paths and a multiplicative cascade model that predicts combined optimization effects without exhaustive testing. Our early experiments demonstrate EFG's versatility across domains: in software programs validated through 3.5 million executions, 15.6% of solutions exhibit high path-dependent variance (CV $>$ 0.1), while structural optimization reveals up to 705$\times$ energy reduction. In AI pipelines, the cascade model predicts optimization combinations within 5.1% error, enabling selection from 4.2 million possibilities using only 22 measurements. The EFG transforms energy optimization from trial-and-error to systematic analysis, providing a foundation for green software engineering across computational domains.

Handover optimization in O-RAN faces growing challenges due to heterogeneous user mobility patterns and rapidly varying radio conditions. Existing ML-based handover schemes typically operate at the near-RT layer, which lack awareness of the mobility-mode and struggle to incorporate a longer-term predictive context. This paper proposes a multi-modal mobility-aware optimization framework in which all predictive intelligence, including mobility mode classification, short-horizon trajectory and RSRP forecasting, and a PPO Actor--Critic policy, runs entirely inside an rApp in the non-RT RIC. The rApp generates per-UE ranked neighbour-cell recommendations and delivers them to the existing handover xApp through the A1 interface. The xApp combines these rankings with instantaneous E2 measurements and performs the final standards-compliant handover decision. This hierarchical design preserves low-latency execution in the xApp while enabling the rApp to supply richer and mode-specific predictive guidance. Evaluation using mobility traces demonstrates that the proposed approach reduces ping-pong handover events and improves handover reliability compared to conventional 3GPP A3-based and ML-based baselines.

We study strategic interaction in linear-quadratic network games where agents act on subjective, misspecified models of their environment. Agents observe noisy aggregate signals generated by local network externalities and interpret them through simplified conjectures, such as constant or mean-field representations. We characterize the long-run behavior using the Berk-Nash equilibrium (BNE) concept, establishing conditions under which BNE diverges from the Nash equilibrium of the perfectly specified game. We quantify this divergence using a Value of Misspecification (VoM) metric. Building on this framework, we introduce "cognitive arbitrage" -- a design paradigm where a system designer strategically shapes agents' conjectures via minimal observation distortions to steer equilibrium outcomes. We formulate the cognitive arbitrage problem as a Stackelberg optimization with closed-form solutions and prove the convergence of a two-time-scale learning algorithm to the optimal BNE. Our results provide a principled framework for influencing behavior in networked systems with bounded rationality, offering a new perspective on mechanism design that operates on agents' representations rather than their incentives.

Networked multi-agent dynamical systems have been used to model how individual opinions evolve over time due to the opinions of other agents in the network. Particularly, such a model has been used to study how a planning agent can be used to steer opinions in a desired direction through repeated, budgeted interventions. In this paper, we consider the problem where individuals' susceptibilities to external influences are unknown. We propose an online algorithm that alternates between estimating this susceptibility parameter, and using the current estimate to drive the opinion to a desired target. We provide conditions that guarantee stability and convergence to the desired target opinion when the planning agent faces budgetary or temporal constraints. Our analysis shows that the key advantage of estimating the susceptibility parameter is that it helps achieve near-optimal convergence to the target opinion given a finite amount of intervention rounds, and, for a given intervention budget, quantifies how close the opinion can get to the desired target.

We study the problem of coded information retrieval for block-structured data, motivated by DNA-based storage systems where a database is partitioned into multiple files that must each be recoverable as an atomic unit. We initiate and formalize the block-structured retrieval problem, wherein $k$ information symbols are partitioned into two files $F_1$ and $F_2$ of sizes $s_1$ and $s_2 = k - s_1$. The objective is to characterize the set of achievable expected retrieval time pairs $\bigl(E_1(G), E_2(G)\bigr)$ over all $[n,k]$ linear codes with generator matrix $G$. We derive a family of linear lower bounds via mutual exclusivity of recovery sets, and develop a nonlinear geometric bound via column projection. For codes with no mixed columns, this yields the hyperbolic constraint $s_1/E_1 + s_2/E_2 \le 1$, which we conjecture to hold universally whenever $\max\{s_1,s_2\} \ge 2$. We analyze explicit codes, such as the identity code, file-dedicated MDS codes, and the systematic global MDS code, and compute their exact expected retrieval times. For file-dedicated codes we prove MDS optimality within the family and verify the hyperbolic constraint. For global MDS codes, we establish dominance by the proportional local MDS allocation via a combinatorial subset-counting argument, providing a significantly simpler proof compared to recent literature and formally extending the result to the asymmetric case. Finally, we characterize the limiting achievability region as $n \to \infty$: the hyperbolic boundary is asymptotically achieved by file-dedicated MDS codes, and is conjectured to be the exact boundary of the limiting achievability region.

Coalition formation is often modeled as a static equilibrium problem, neglecting the dynamic processes governing how agents self-organize. This paper proposes a dynamic split-and-merge framework that balances two conflicting economic forces: individual fairness and collective efficiency. We introduce a control-theoretic mechanism where topological operations are driven by distinct signals: splits are triggered by fairness violations (specifically, negative Shapley values representing "agent-responsible inefficiency"), while merges are driven by strict surplus improvements (superadditivity). We prove that these dynamics converge in finite time to a specific class of steady states termed Shapley-Fair and Merge-Stable (SFMS) partitions. Convergence is established via a vector Lyapunov function tracking aggregate fairness deficits and system surplus, leveraging a discrete-time LaSalle invariance principle. Numerical case studies on a 10-player game demonstrate the algorithm's ability to resolve fairness tensions and reach stable configurations, providing a rigorous foundation for endogenous coalition formation in dynamic environments.

Option prices encode the market's collective outlook through implied density and implied volatility. An explicit link between implied density and implied volatility translates the risk-neutrality of the former into conditions on the latter to rule out static arbitrage. Despite earlier recognition of their parity, the two had been studied in isolation for decades until the recent demand in implied volatility modeling rejuvenated such parity. This paper provides a systematic approach to build neural representations of option implied information. As a preliminary, we first revisit the explicit link between implied density and implied volatility through an alternative and minimalist lens, where implied volatility is viewed not as volatility but as a pointwise corrector mapping the Black-Scholes quasi-density into the implied risk-neutral density. Building on this perspective, we propose the neural representation that incorporates arbitrage constraints through the differentiable corrector. With an additive logistic model as the synthetic benchmark, extensive experiments reveal that deeper or wider network structures do not necessarily improve the model performance due to the nonlinearity of both arbitrage constraints and neural derivatives. By contrast, a shallow feedforward network with a single hidden layer and a specific activation effectively approximates implied density and implied volatility.

Secure communication is the cornerstone of modern infrastructures, yet achieving unconditional security -resistant to any computational attack- remains a fundamental challenge. The One-Time Pad (OTP), proven by Shannon to offer perfect secrecy, requires a shared random key as long as the message, used only once. However, distributing large keys over long distances has been impractical due to the lack of secure and scalable sharing options. Here, we introduce a DNA-based cryptographic primitive that leverages random pools of synthetic DNA to install a synchronized entropy source between distant parties. Our approach uses duplicated DNA molecules -comprising random index-payload pairs- as a shared secret. These molecules are locally sequenced and digitized to generate a common binary mask for OTP encryption, achieving unconditional security without relying on computational assumptions. We experimentally demonstrate this protocol between Tokyo and Paris, using in-house sequencing, generating a shared secret mask of $\sim$ 400 Mb with a residual error rate to achieve the usual overall decryption failure rate of $2^{-128}$. The min-entropy of the binary mask meets the most recent National Institute of Standards and Technology requirements (SP 800-90B), and is comparable to that of approved cryptographic random number generators. Critically, our system can resist two types of adversarial interference through molecular copy-number statistics, providing an additional layer of security reminiscent of Quantum Key Distribution, but without distance limitations. This work establishes DNA as a scalable entropy source for long-distance OTP, enabling high-throughput and secure communications in sensitive contexts. By bridging molecular biology and cryptography, DNA-based key distribution opens a promising new route toward unconditional security in global communication networks.

We completely characterize the range of $L^p$-boundedness of certain multilinear Radon-like transforms involving vertical projections in the Heisenberg group.

In this paper, we study the homogenization of elliptic equations that combine a local part, given by the Laplacian with Neumann boundary conditions, and its nonlocal version, defined through an integral operator with a smooth kernel. These two components are coupled through an additional nonlocal operator also given by a smooth kernel. We consider a sequence of partitions of a fixed spatial domain into two regions - local and nonlocal - which are periodically distributed in space (with one of the regions consisting of small, periodically arranged holes). Depending on the relative location of the local and nonlocal regions, we obtain qualitatively different limit behaviors. When the local part of the equation is confined to the small periodic holes, the sequence of solutions converges to the unique solution of a limit system in which the local component vanishes, while the nonlocal part persists and splits into two distinct components. On the other hand, when the local part of the problem lies outside the holes, the limit system exhibits a homogenized local diffusion operator coupled with a nonlocal equation. Finally, we analyze an intermediate regime in which only part of the local diffusion survives in the limit, by considering configurations consisting of parallel thin strips instead of holes.

The purpose of this paper is to study the influence of relaxation and acceleration techniques on the convergence behavior of the non-overlapping Schwarz algorithm with alternating Dirichlet-Neumann transmission conditions in the context of domain decomposition- (DD-) based coupling. After demonstrating that the multiplicative Schwarz scheme can be formulated as a fixed-point iteration, we explore, both theoretically and numerically, two promising techniques for speeding up the method: (i) Aitken acceleration and (ii) Anderson acceleration. In the process, we derive a robust and efficient adaptive variant of Anderson acceleration, termed "Anderson with memory adaptation". We compare the proposed acceleration strategies to the well-known classical relaxed Dirichlet-Neumann Schwarz alternating method. Our results suggest that, while Aitken-accelerated Schwarz is the best approach in terms efficiency and robustness when considering two sub-domain DDs, Anderson-accelerated Schwarz is the method of choice in larger multi-domain setting.

Cross-sectional observations from a dynamical system can be modeled via steady-state distributions of Markov processes. The major challenge is then to determine whether the process parameters can be identified and estimated from the steady-state distributions. We study this problem for continuous Lyapunov models that arise as steady-state distributions of the solution to a multivariate stochastic differential equation, whose linear drift matrix is parametrized by a directed graph. We derive equations for the cumulant tensors of any order for this distribution, which generalize the well-known covariance Lyapunov equation. Under a non-Gaussianity assumption we prove generic identifiability of the drift matrix for any connected graph using the equations for the higher-order cumulants. Based on the identifiability result, we propose a new semiparametric estimator of the drift matrix, and we derive its asymptotic distribution. A simulation study demonstrates the asymptotic validity of the estimator but shows that it is only accurate for relatively large sample sizes, illustrating the hardness of the unconstrained estimation problem.

We construct a Grothendieck site whose objects are Mealy machines over definable sets in an o-minimal structure and whose coverings are jointly surjective families of definable open immersions. On this site, we define presheaves of explanations -- systems equipped with an interpretable interface, parameterised by a ``judge.'' We prove that the behavioral presheaf (quotienting by observable output equivalence) is separated: a global explanation is determined by its local restrictions. We show that gluing fails in general -- locally consistent explanations need not assemble globally -- and give, for stateless explanatory systems of the restricted-interface presheaf, a necessary and sufficient topological condition for the sheaf property in terms of robust disconnection of fibers of the judge.