Despite longstanding interest, controller synthesis remains challenging for networks of heterogeneous, nonlinear agents. Moreover, the requirements for computational scalability and information privacy have become increasingly critical. This paper introduces a dissipativity-based distributed controller synthesis framework for networks with heterogeneous agents and diverse performance objectives, leveraging the Network Dissipativity Theorem and iterative convex overbounding. Our approach enables the synthesis of controllers in a distributed way by achieving a network-wide consensus on agents' dissipativity variables while keeping sensitive subsystem information locally. The proposed framework is applied to full-state feedback controller synthesis.

The extension problem asks whether positive semi-definite functions on a symmetric unital subset of a discrete group can be extended to positive semi-definite functions on the whole group. It has been known at least since the work of Rudin in the 1960s that this is closely related to the problem of finding sums of squares factorisations of positive elements in the group C*-algebra. We give an operator system perspective at these two problems explaining their equivalence: the extension property is characterised by a certain quotient map on the Fourier--Stieltjes algebra, and the factorisation property by a certain complete order embedding into the group C*-algebra. These properties are linked to the duality of the operator systems which have recently emerged from spectral and Fourier truncations in noncommutative geometry. We exemplify how one can relate certain extension problems to operator system techniques such as nuclearity and the C*-envelope.

The system identification capabilities of a novel information-theoretic method are examined here. Specifically, this work uses information-theoretic metrics and vibration-based measurements to enhance damping estimation accuracy in mechanical systems. The method refers to a key limitation in system identification, signal processing, monitoring, and alert systems. These systems integrate various components, including sensors, data acquisition devices, and alert mechanisms. They are designed to operate in an environment to calculate key parameters such as peak accelerations and duration of high acceleration values. The current operational modal identification methods, though, suffer from limitations related to obtaining poor damping estimates due to their empirical nature. This has a significant impact on alert warning systems. This occurs when their duration is misestimated; specifically, when using the vibration amplitudes as an indicator of danger alerts for monitoring systems in damage or anomaly detection scenarios. To this end, approaches based on the Shannon entropy and the Kullback-Leibler divergence concept are proposed. The primary objective is to monitor the vibration levels in near real-time and provide immediate alerts when predefined thresholds are exceeded. In considering the proposed approach, both new real-world data from the multi-axis simulation table at the University of Bath, as well as the benchmark International Association for Structural Control-American Society of Civil Engineers (IASC-ASCE) structural health monitoring problem are considered. Importantly, the approach is shown to select the optimal model, which accurately captures the correct alert duration, providing a powerful tool for system identification and monitoring.

The Hadamard rank of a point with respect to a projective variety is, if it exists, the minimum number of points of the variety whose coordinate-wise product is the given point. We classify the projective varieties for which the Hadamard rank is finite for any point. As a by-product we obtain the finiteness of the Hadamard rank with respect to varieties of tensors, such as Grassmannians, Chow varieties, varieties of reducible forms and their secant varieties, complementing previous known results on secant varieties of Segre-Veronese varieties. We prove sharp upper bounds on the maximum Hadamard rank for certain families of algebraic varieties: this is a consequence of a result on the lower semi-continuity of the Hadamard rank for curves that do not contain points with at least two zero coordinates.

The addition of Kounterterms to Einstein gravity leads to a finite action for asymptotically anti-de Sitter (AdS) spaces with a conformally flat boundary. In that sense, it provides a partial renormalization for AdS gravity when compared to standard holographic techniques, where the mismatch is given in terms of nontrivial conformal properties of the boundary. On the other hand, this method has the clear advantage that the variation of the action has a closed form in an arbitrary dimension. In this work, it is shown how to extract holographic information on conformal anomalies from the variation in $(2n+1)$-dimensional Einstein-AdS plus Kounterterms. Remarkably enough, a considerable part of the Weyl anomaly can be worked out for any odd dimension.

We present a stochastic approach to calculate the full statistics of classical voltage fluctuations across an arbitrary, nonlinear, dissipative device embedded in a circuit in the presence of a bias. We show how the feedback resulting from the circuit, made of an ohmic resistor and a capacitor, affects the cumulants of the voltage, and in particular resolves Brillouin's paradox to satisfy thermodynamics. We apply our results to the case of a tunnel junction and a diode.

We present a new general method for performing basic arithmetic in the finite field~$\mathbb{F}_p$ for any prime $p>2$ by using traditional binary operations over~$\mathbb{F}_2$. Our new approach is efficient and competitive with current state-of-art methods. We apply our new arithmetic method to the computation of the minimum Hamming distance of random linear codes for the fields $\mathbb{F}_3$ and $\mathbb{F}_7$. Our new arithmetic method allows to apply new techniques such as the isometric addition that accelerate the computation of the Hamming distance. We have developed implementations in the C programming language for computing the Hamming distance that clearly outperform both state-of-art licensed software and open-source software such as \textsc{Magma} and \textsc{GAP}/\textsc{Guava} on single-core processors, multicore processors, and shared-memory multiprocessors.

We address the problem of localizing multiple sources in 3D by combining sensor array measurements with camera observations. We propose a fusion framework extending the covariance matrix fitting method with an unbalanced optimal transport regularization term that softly aligns sensor array responses with visual priors while allowing flexibility in mass allocation. To solve the resulting largescale problem, we adopt a greedy coordinate descent algorithm that efficiently updates the transport plan. Its computational efficiency makes full 3D localization feasible in practice. The proposed framework is modular and does not rely on labeled data or training, in contrast with deep learning-based fusion approaches. Although validated here on acoustic arrays, the method is general to arbitrary sensor arrays. Experiments on real data show that the proposed approach improves localization accuracy compared to sensor-only baselines.

The term XR is currently widely used as an expression encompassing Virtual Reality (VR), Augmented Reality (AR), and Mixed Reality (MR). However, there is no clear consensus regarding its origin or meaning. XR is sometimes explained as an abbreviation for Extended Reality, but multiple interpretations exist regarding its etymology and formation process. This paper organizes the historical formation of terminology related to VR, AR, MR, and XR, and reexamines the context in which the term XR emerged and how it has spread. In particular, by presenting a timeline that distinguishes between the coinage of terms and the drivers of their adoption, we suggest that XR, as an umbrella term, functions not as an abbreviation of Extended Reality, but rather as a neutral symbolic label that encompasses multiple "reality"-related terms. Furthermore, we argue that stable usage of terminology, including XR, requires governance through collaboration among academia, industry, and standardization organizations.

Yes.................

We report a scalable molecular beam epitaxy strategy to achieve a low density of O-band electrically tunable InAs/InGaAs quantum dots (QDs) on GaAs(001) substrates. Our approach is based on a gradient deposition of InAs in the sub-ML regime and subsequent capping with an InGaA strain-reducing layer to redshift the emission wavelength. For different growth conditions, we investigate the optical properties of the dots using photoluminescence mapping and correlate with structural properties determined by scanning transmission electron microscopy. Using a surface roughness modulation technique and synchronizing InAs sub-monolayer deposition cycles with substrate rotation, we control the dot density and position low-density regions (< 1 QD per um^2) on the substrate. Hyperspectral imaging is used to map the spatial and spectral characteristics of many individual dots in the low-density region, confirming that our approach is universally applicable to conventional MBE growth on (001) surfaces. Finally, we tune the QD emission wavelength within the O-band using electric fields and demonstrate single-photon emission with g(2)(0) = 0.020(14).

As software in industry grows in size and complexity, so does the volume of engineering data that companies generate and use. Ideally, this data could be used for many purposes, including informing decisions on engineering priorities. However, without a structured representation of the links between different aspects of software development, companies can struggle to identify the root causes of deficiencies or anticipate the effects of changes. In this paper, we report on our experience at Bloomberg in developing a novel tool, dubbed BayesInsights, which provides an interactive interface for visualising causal dependencies across various aspects of the software engineering (SE) process using Bayesian Networks (BNs). We describe our journey from defining network structures using a combination of established literature, expert insight, and structure learning algorithms, to integrating BayesInsights into existing data analytics solutions, and conclude with a mixed-methods evaluation of performance benchmarking and survey responses from 24 senior practitioners at Bloomberg. Our results revealed 95.8% of participants found the tool useful for identifying software delivery challenges at the team and organisational levels, cementing its value as a proof of concept for modelling software delivery and developer experience. BayesInsights is currently in preview, with access granted to seven engineering teams and a wider deployment roadmap in place for the future.

We investigate lower bounds for the number of ideal and finite vertices of right-angled hyperbolic polyhedra of finite volume. We use a geometric method of orthogonal gluings to establish new bounds in low dimensions, specifically $v_\infty(P^5) \ge 3$ and $v_{fin}(P^7) \ge 4$. By combining these initial bounds with double counting arguments and recurrence relations, we obtain improved lower bounds for both types of vertices in all higher dimensions up to $n=12$, the maximal dimension where polyhedra of this class exist.

Monotone co-design enables compositional engineering design by modeling components through feasibility relations between required resources and provided functionalities. However, its standard boolean formulation cannot natively represent quantitative criteria such as cost, confidence, or implementation choice. In practice, these quantities are often introduced through ad hoc scalarization or by augmenting the resource space, which obscures system structure and increases computational burden. We address this limitation by developing a quantale-enriched theory of co-design. We model resources and functionalities as quantale-enriched categories and design problems as quantale-enriched profunctors, thereby lifting co-design from boolean feasibility to general quantitative evaluation. We show that the fundamental operations of series, parallel, and feedback composition remain valid over arbitrary commutative quantales. We further introduce heterogeneous composition through change-of-base maps between quantales, enabling different subsystems to be evaluated in different local semantics and then composed in a common framework. The resulting theory unifies feasibility-, cost-, confidence-, and implementation-aware co-design within one compositional formalism. Numerical examples on a target-tracking system and a UAV delivery problem demonstrate the framework and highlight how native quantitative enrichment can avoid the architectural and computational drawbacks of boolean-only formulations.

In the analysis of real-world data, extracting meaningful features from signals is a crucial task. This is particularly challenging when signals contain non-stationary frequency components. The Iterative Filtering (IF) method has proven to be an effective tool for decomposing such signals. However, such a technique cannot handle directly data that have been sampled non-uniformly. On the other hand, graph signal processing has gained increasing attention due to its versatility and wide range of applications, and it can handle data sampled both uniformly and non-uniformly. In this work, we propose two algorithms that extend the IF method to signals defined on graphs. In addition, we provide a unified convergence analysis for the different IF variants. Finally, numerical experiments on a variety of graphs, including real-world data, confirm the effectiveness of the proposed methods. In particular, we test our algorithms on seismic data and the total electron content of the ionosphere. Those data are by their nature non-uniformly sampled, and, therefore, they cannot be directly analyzed by the standard IF method.

LLM-based coding agents rely on \emph{skills}, pre-packaged instruction sets that extend agent capabilities, yet every token of skill content injected into the context window incurs both monetary cost and attention dilution. To understand the severity of this problem, we conduct a large-scale empirical study of 55,315 publicly available skills and find systemic inefficiencies: 26.4\% lack routing descriptions entirely, over 60\% of body content is non-actionable, and reference files can inject tens of thousands of tokens per invocation. Motivated by these findings, we present \textsc{SkillReducer}, a two-stage optimization framework. Stage~1 optimizes the routing layer by compressing verbose descriptions and generating missing ones via adversarial delta debugging. Stage~2 restructures skill bodies through taxonomy-driven classification and progressive disclosure, separating actionable core rules from supplementary content loaded on demand, validated by faithfulness checks and a self-correcting feedback loop. Evaluated on 600 skills and the SkillsBench benchmark, \textsc{SkillReducer} achieves 48\% description compression and 39\% body compression while improving functional quality by 2.8\%, revealing a \emph{less-is-more} effect where removing non-essential content reduces distraction in the context window. These benefits transfer across five models from four families with a mean retention of 0.965, and generalize to an independent agent framework.

We propose new analytical tools for describing growth-rate distributions generated by stationary time-series. Our analysis shows how deviations from normality are not pathological behaviour, as suggested by some traditional views, but instead can be accounted for by clean and general statistical considerations. In contrast, strict normality is the effect of specific modelling choices. Systems characterized by stationary Gamma or heavy-tailed abundance distributions produce log-growth-rate distributions well described by a generalized logistic distribution, which can describe tent-shaped or nearly normal datasets and serves as a useful null model for these observables. These results prove that, for large enough time lags, in practice, growth-rate distributions cease to be time-dependent and exhibit finite variance. Based on this analysis, we identify some key stylized macroecological patterns and specific stochastic differential equations capable of reproducing them. A pragmatic workflow for heuristic selection between these models is then introduced. This approach is particularly useful for systems with limited data-tracking quality, where applying sophisticated inference methods is challenging.

We present galactic constellations: charming shapes in large cosmological surveys. By exploring a dense subset of DESI's first data release, we discover distinctive constellations including "Pisces Grandis", "The DESI Stick Woman", and "W". We additionally develop a public website for anyone to explore DESI data, find their own constellations, and share their creations: see cmlamman.github.io/galactic-constellations. Early users of the site discovered 93 constellations. We analyze the size of these constellations as an unconventional probe of homogeneity, finding consistency with the cosmological principle and Lambda-CDM.

We prove that for any smooth polarized complex $n$-dimensional manifold $(X, L_X)$ which admits an extremal Kähler metric in $c_1(L_X)$, and for any integer $k$ large enough (in terms of a bound depending on $(X, L_X)$), the $(n+k+1)$-dimensional complex cone $\mathcal{Y}:= \overline{(L_X \otimes \mathcal{O}_{\mathbb{P}^k}(1))^{\times}}$ with section $X \times \mathbb{P}^k$ admits a scalar-flat Kähler cone metric. Equivalently, the unweighted Sasaki join of a smooth compact quasi-regular extremal Sasaki manifold with a regular Sasaki sphere $\mathbb{S}^{2k+1}$ of sufficiently large dimension $(2k+1)$ admits a Sasaki metric of constant (positive) scalar curvature. This gives an affirmative answer to an asymptotic version of a question raised by Boyer--Huang--Legendre--Tønnesen-Friedman in arXiv:1906.04827.

The classical bar-cobar adjunction between dg algebras and dg coalgebras goes back to the origins of differential homological algebra as developed by Cartan, Eilenberg, Moore, and many others, and is part of the broader framework of Koszul duality. In recent years, several $\infty$-categorical analogues of this adjunction have been developed, notably by Lurie, Francis--Gaitsgory, and Heuts. However, there is no comparison in the literature between the classical chain-level constructions and their higher-categorical counterparts, and in fact the two constructions are not quite compatible. In this paper we provide a unified framework relating these different forms of Koszul duality in the differential graded setting. We construct a commutative square of adjunctions, called the inclusion-restriction square, intertwining the classical operadic bar-cobar adjunction with its completed variant due to Le Grignou--Lejay. We show that this square induces an $\infty$-categorical adjunction between algebras and their Koszul dual coalgebras, recovering in particular the differential graded case of Lurie's bar-cobar adjunction, and explain precisely how our constructions relate to those of Francis--Gaitsgory and Heuts.

In his quest to disprove a claim by Peirce that all lattices are distributive, Ernst Schröder considered 135 years ago a list of 990 equational laws on quasigroups, analogous to associativity, such as $(x // y) * z = (y // x) \backslash\backslash z$. A quasigroup is a non-associative analogue of groups, specifically a set equipped with multiplication and right/left conjugate-division operations that are compatible. Each equation of interest identifies two three-variable expressions built from these operations. I determine all $114$ equivalence classes of their conjunctions, and all implications between them. This includes as a small corner the five-element non-distributive lattice identified by Schröder.

This article provides a naturel sequel of previous works [6, 4] regarding the stability of travelling waves for a general one-dimensional Schrödinger equation (N LS) with non-zero condition at infinity. The aim of this article is twofold. First, we prove the asymptotic stability of well-prepared chains of dark solitons and secondly, we construct an asymptotic N -soliton-like solution, which is an exact solution of (N LS), the large-time dynamics of which is similar to a decoupled chain of solitons.

Macroscopic dark matter with dominating strong interactions, supposed to be composites, represents an alternative to the most popular WIMP particles. Predicted in various models as strangelets, nuclearites, nuggets, having different internal structures and properties, but not yet observed experimentally, these forms of dark matter are associated with the existence of a large number of still unexplained observations. Nuggets, initially predicted by Witten, were reconsidered from the point of view of their internal structure and further theorized in 2003 by Zhitnitsky as axion quark nuggets and axion antiquark nuggets, as being made of quarks in a superconducting colour state, in the core, an electrosphere of electrons or positrons and a domain wall that maintain the stability of the macros with an incredible density, mass in the gram range and radius on the order of micrometers. If the existence of $\rm{AQNs}$ and $\rm{A\bar{Q}Ns}$ is demonstrated, two major open problems in physics could be addressed simultaneously: they would constitute viable dark matter candidates and, at the same time, provide a natural mechanism for restoring matter-antimatter symmetry in the Universe. The experimental evidence of the $\rm{AQNs}$ and $\rm{A\bar{Q}Ns}$ is a challenge for current and future experiments. The present study demonstrates that if these macroscopic systems exist, axions produced by $\rm{A\bar{Q}N}$s could be detected by the next generation of neutrino physics experiments using liquid noble gases, due to their huge active volumes.

Brain connectomics is still largely dominated by pairwise-based models, such as graphs, which cannot represent circulatory or higher-order functional interactions. In this paper, we propose a multimodal framework based on Topological Signal Processing (TSP) that models the brain as a higher-order topological domain and treats functional interactions as discrete vector fields. We integrate diffusion MRI and resting-state fMRI to learn subject-specific brain cell complexes, where statistically validated structural connectivity defines a sparse scaffold and phase-coupling functional edge signals drive the inference of higher-order interactions (HOIs). Using Hodge-theoretic tools, spectral filtering, and sparse signal representations, our framework disentangles brain connectivity into divergence (source-sink organization), gradient (potential-driven coordination), and curl (circulatory HOIs), enabling the characterization of temporal dynamics through the lens of discrete vector calculus. Across 100 healthy young adults from Human Connectome Project, node-based HOIs are highly individualized, yet robust mesoscale structure emerges under functional-system aggregation. We identify a distributed default mode network-centered gradient backbone and limbic-centered rotational flows; divergence polarization and curl profiles defining circulation regimes with insightful occupancy and dwell-time statistics. These topological signatures yield significant brain-behavior associations, revealing a relevant higher-order organization intrinsic to edge-based models. By making divergence, circulation, and recurrent mesoscale coordination directly measurable, this work enables a principled and interpretable topological phenotyping of brain function.

The $1+1$ dimensional $Z_2$ gauge theory is the simplest model that allows for quantum computation or quantum simulation to probe the fundamental aspects of a gauge theory coupled with dynamical fermions. To reliably benchmark such a system, it is crucial to understand the non-unitary quantum dynamics arising from the underlying non-Hermitian evolution and to model the effects of quantum measurements. This work focuses on monitoring ultra-local physical observables for a $\mathbb Z_2$ gauge theory. Tensor network calculations are performed to dynamically probe entanglement entropy at larger lattice sizes. In this work, we report that continuously monitoring local and diagonal observables (electric and mass energy densities) in the computational basis demonstrates the absence of any measurement-induced phase transition, as indicated by the system-size independence of the late-time saturation value of the bipartite entanglement entropy.

The Large Magellanic Cloud (LMC) exhibits vigorous high-mass star formation, including the HII regions 30~Dor that is the most active site of star formation in the local group. The present paper focuses on the Giant Molecular Cloud (GMC) in the HII region N113 in the central part of the LMC. Based on the $^{12}$CO($J$ =1-0) and $^{13}$CO($J$ = 1-0) data at a resolution of approximately 0.2 pc taken with ALMA+APEX, we reveal that the GMC consists of two filamentary structures each of approximately 10 pc in length, forming a V-shape pattern with a vertex angle of 90 degrees. The filamentary structures host high-mass young stellar objects in gravitationally bound dense gas. Large-scale HI gas data covering 100 pc reveal two distinct velocity components separated by more than 40 km s$^{-1}$, that correspond to the low velocity (L-) and disk (D-) HI components of the LMC. The L-component appears to be located in a cavity-like distribution of the D-component, and the CO filaments are positioned at the cavity's edge. We find evidence for the L-component to fit the cavity by a 53 pc displacement, and suggest that collisional compression of the HI gas during the last 1.3 Myr triggered the GMC formation and the high-mass star formation. This lends support for the large scale collision driven by the tidal interaction is playing a role in evolution of interstellar medium in N113.

We consider discrete Schrödinger operators $H_{μQ}=Δ+μQ$ with real periodic potentials $Q$ on periodic graphs, where $Δ$ is the adjacency operator and $μ\in\mathbb R$ is a coupling constant. The spectra of the operators consist of a finite number of closed intervals (bands). In the large coupling regime, we obtain an asymptotic upper bound for the measure of the spectrum of $H_{μQ}$ which depends essentially on a "degeneracy degree" of the potential $Q$. This result extends the result of Y. Last obtained for the one-dimensional lattice $\mathbb Z$ to the case of general periodic graphs. It also may serve as a certain quantitative complement to the recent criterion of J. Fillman for the measure of the spectrum of $H_{μQ}$ to go to zero as $μ\to\infty$.

We study the stabiliser formalism for qudits of arbitrary dimension $d$. In the free case, we show that the basic theorem of the stabiliser formalism remains valid: if the stabiliser subgroup $H$ is free as a $Z/dZ$-module and contains no non-trivial scalars, then the protected space $V^H$ is naturally identified with the state space of a smaller number of qudits of the same dimension, and the quotient $N(H)/H$ is identified with the Pauli group on a smaller number of qudits. We then remove the freeness assumption and describe the resulting structure in general. In this case, the protected space is identified with a tensor product of qudit spaces of possibly smaller dimensions, and the quotient $N(H)/H$ is described by a corresponding product of qudit Pauli groups, possibly of smaller dimensions, over a common center. We also characterise the shifted free case, which is exactly the situation in which $N(H)/H$ is again an ordinary qudit Pauli group. Our approach is algebraic and uniform, and applies in particular to the qudit Kitaev model and to its shifted and twisted variants.

Reducing the non-Clifford cost of fault-tolerant quantum circuits is a central challenge in quantum compilation, since T gates are typically far more expensive than Clifford operations in error-corrected architectures. For Clifford+T circuits, minimizing T-count remains a difficult combinatorial problem even for highly structured algebraic optimizers. We introduce VarTODD, a policy-parameterized variant of FastTODD in which the correctness-preserving algebraic transformations are left unchanged while candidate generation, pooling, and action selection are exposed as tunable heuristic components. This separates the quality of the algebraic rewrite system from the quality of the search policy. On standard arithmetic benchmarks, fixed hand-designed VarTODD policies already match or improve strong FastTODD baselines, including reductions from 147 to 139 for GF(2^9) and from 173 to 163 for GF(2^10) in the corresponding benchmark branches. As a proof of principle for automated tuning, we then optimize VarTODD policies with GigaEvo, an LLM-guided evolutionary framework, and obtain additional gains on harder instances, reaching 157 for GF(2^10) and 385 for GF(2^16). These results identify policy optimization as an independent and practical lever for improving algebraic T-count reduction, while LLM-guided evolution provides one viable way to exploit it.

Disorder masks much of the rich physics in two-dimensional electronic systems, with charged impurities often the limiting factor. In graphene, progress in reducing disorder has largely stagnated since boron nitride encapsulation was introduced a decade ago. Here we show that a brief deep-UV exposure enhances the electronic quality of encapsulated graphene - typically by two orders of magnitude - by neutralizing charged impurities within boron nitride. Following illumination, standard graphene devices exhibit numerous evendenominator fractional quantum Hall states, including non-Abelian candidates, and frequently reveal hidden superlattice minibands. Even macroscopically inhomogeneous devices, seemingly unusable for transport studies, recover after deep-UV illumination and display Landau quantization in millitesla fields. This finding provides a straightforward route to exceptional-quality graphene, enabling further exploration of interaction-driven, topological and other quantum phenomena.