We demonstrate that the functorial properties of the symplectic field theory under strong cobordisms and surgery cobordisms can produce finite algebraic (planar) torsions from simple examples, which gives a unified treatment of most of the known computations of algebraic (planar) torsions. In addition, we obtain many families of new examples, notably including (1) stably fillable examples in all dimensions $\ge 5$ with algebraic (planar) torsion precisely $k$ for any given $k\in \mathbb{N}_+$, confirming a conjecture of Latschev and Wendl; (2) contact structures on spheres of all dimensions at least $5$ with finite algebraic planar torsion at least $1$, which implies that tight not weakly fillable contact structures are ubiquitous in higher dimensions. We also explain that all known examples of contact manifolds without strong/weak fillings in dimension $\ge 5$ have algebraic planar torsion.

Advances in generative AI, speech synthesis, and embodied avatars enable systems that not only assist communication, but can act as proxies on users' behalf. Prior work in HCI has largely focused on systems as external tools, with less attention paid to the experiential consequences of users' speech and actions becoming assimilated with AI-generated output. We introduce the design and implementation of ProxyMe, a work-in-progress VR prototype that allows users to embody an avatar whose voice and spoken content are modified by an AI system. By combining avatar-based embodiment, voice cloning, and AI-mediated speech augmentation, ProxyMe invites the exploration of avatar self-extension: situations in which AI-modified communication is experienced as part of one's own expressive behavior. We chart out research challenges and envisioned scenarios, with a focus on how varying degrees of delegation and steerability can influence perceived agency, authorship, and self-identification.

We study the propagation of coherent states in self-interacting bosonic quantum field theories in the semi-classical (mean-field) regime. Relying on Hepp's method and a detailed analysis of the associated classical and quantum field dynamics, non-linear and linear respectively, we construct an asymptotic expansion of arbitrary order for the quantum evolution of coherent states. The results are first established for the spatially cutoff $P(ϕ)_2$ model, under standard assumptions ensuring essential self-adjointness of the Hamiltonian and well-posedness of the classical flow, and are then extended to a class of non-polynomial analytic interactions. This work refines and generalizes earlier results, which identified only the leading-order term of the expansion.

This paper develops a physically consistent signal model with hardware constraints for a simultaneous transmitting and reflecting beyond-diagonal RIS (STAR BD-RIS) endowed with per-element amplification and lossless power splitting. We explicitly decouple (i) amplification via a diagonal gain matrix, (ii) element-wise reflection/transmission splitting, and (iii) passive beyond-diagonal coupling on each branch, while enforcing practical feasibility through per-element emission caps and an aggregate RIS power budget under the operating covariance. Building on this model, we cast downlink sum-rate maximization as an equivalent weighted minimum mean-square error (WMMSE) problem and propose an alternating optimization framework with provable monotonic descent. The method admits closed-form updates for MMSE combiners and weights, waterfilling-like beamformer updates via a single dual variable, a per-element amplification update that satisfies emission constraints, and a STAR power-splitting update based on cyclic coordinate descent with a global acceptance test. For the beyond-diagonal coupling matrices, we derive Riemannian gradient steps on the complex Stiefel manifold with QR/polar retraction method, preserving passivity at every iterate. Furthermore, the proposed approach decouples the optimization of the reflective and transmissive responses of the BD-RIS, enabling efficient distributed implementation. Numerical results demonstrate substantial sum-rate gains compared to the conventional passive BD-RIS.

In this paper we study the maximization of the sum of the first two Dirichlet eigenvalues for Sturm-Liouville operators with potentials in the noncompact space $L^1$. We prove that there exists a unique potential function achieving the maximum, which is non-negative, piecewise smooth, and symmetric. Using measure differential equations and weak$^*$ convergence, we show that the nonzero part of the maximizer can be determined by the solution to the pendulum equation $θ'' + \ell \sinθ= 0 $.

The strong-interaction functionals $W_\infty[n]$ and ${W'}_\infty[n]$ play an important role in the adiabatic-connection method of Density Functional Theory. The strictly-correlated electron approach can be used to exactly compute these functionals, yet calculations are computationally very expensive even for small electronic systems, and thus semilocal approximations have been proposed. In this work we develop a meta-generalized gradient approximation (meta-GGA) model for the strong-interaction functionals, enhanced point-and-charge (ePC), constructed from exact constraints. In particular, the ePC restores the second-order gradient expansion of the PC model, that is relevant for the equilibrium properties of Wigner crystals, and ensures the non-negativity of ${W'}_\infty[n]$. We assess the ePC model for atoms and various model systems: Hooke's atoms, two-electron exponential densities, s- and p-hydrogenic shells, quasi-two-dimensional infinite barrier model, perturbed uniform electron gas and H$_2$ dissociation. We prove a good overall accuracy of the ePC model, that achieves a broader applicability than any previous semilocal models.

The upper mid-band (UMB) spectrum is a key enabler for 6G systems, yet reconfigurable intelligent surface (RIS)-assisted UMB communications face severe channel estimation challenges due to near-field propagation and transitional scattering, which induce strong spatial correlation and ill-conditioned least-squares (LS) formulations. To overcome this limitation, we propose a conditioning-aware channel estimation framework that transforms the inherently ill-conditioned high-dimensional problem into multiple well-conditioned subproblems via greedy column grouping. By systematically separating highly correlated RIS elements into distinct sub-blocks via piecewise RIS phase design, the proposed method directly improves Gram matrix conditioning and stabilizes piecewise LS reconstruction without relying on sparsity assumptions. Simulation results demonstrate that the proposed method significantly outperforms conventional LS and OMP-based estimators in pilot-limited and transitional UMB regimes, achieving robust performance with low computational complexity.

In this paper we describe the spectrum of values of weak uniform Diophantine exponents of lattices in arbitrary dimension.

In this paper, we construct a class of simple weight modules over the twisted Heisenberg-Virasoro algebra and gap-$p$ Virasoro algebras from restricted modules over some positive part subalgebra of the twisted Heisenberg-Virasoro algebra. These modules are new. In particular, when $p=2$, the gap-$p$ Virasoro algebra is the mirror Heisenberg-Virasoro algebra and we obtain many new simple weight modules for the mirror Heisenberg-Virasoro algebra.

Implementing time-evolution operators in shallow quantum circuits is important for quantum simulations. The standard method of Trotterization requires a large number of gates to achieve practical accuracy. Variational Quantum Simulation (VQS) is an algorithm that calculates the time evolution of a quantum state and can be executed with shallower circuits than Trotterization. However, the operator obtained by VQS evolves only a fixed initial state and is not the time evolution operator itself. In this paper, we propose Variational Quantum Operator Simulation (VQOS), a method to realize time evolution operators in shallow quantum circuits. This method is based on the variational principle for operators and does not require the implementation of the desired Trotter decomposition of the time evolution operator. We performed numerical simulations of the VQOS algorithm and successfully implemented the time evolution operator for closed systems in a quantum circuit that is up to 5 times shallower than the Trotterization. By providing a more practical way to implement time evolution operators, VQOS increases the applicability of near-term quantum computers.

Bounded self-certification in Turing machines fails because self-simulation necessarily incurs a strictly positive temporal overhead. We translate this operational constraint into a domain-theoretic framework, defining an operator that advances a finite halting observation from time bound $i$ to $i+1$. While no bounded machine can achieve a fixed point under this operator, the iterative process forms an ascending $ω$-chain. The Scott limit of this chain resolves to the least fixed point of the operator, representing an unbounded computation that fully captures the machine's halting behavior. Our construction provides a novel perspective on the halting problem, framing the transition from finite observability to the least fixed point as the continuous deferral of the diagonal.

Reading is a pervasive and cognitively demanding activity that underpins modern human culture. It is a prime instance of a class of tasks where eye movements are coordinated for the purpose of comprehension. Existing theories explain either eye movements or comprehension during reading, but the critical link between the two remains unclear. Here, we propose resource-rational optimization as a unifying principle governing adaptive reading behavior. Eye movements are selected to maximize expected comprehension while minimizing cognitive and temporal costs, organized hierarchically across nested time scales: fixation decisions support word recognition; sentence-level integration guides skipping and regression; and text-level comprehension goals shape memory construction and rereading. A computational implementation successfully replicates an unprecedented range of findings in human reading, from lexical effects to comprehension outcomes. Together, these results suggest that resource rationality provides a general mechanism for coordinating perception, memory, and action in knowledge-intensive human behaviors, offering a principled account of how complex cognitive skills adapt to limited resources.

We determine all $δ$-biderivations for the Witt algebra, the Virasoro algebra, the $W$-algebras $W(a,b)$ and their universal central extensions $\widetilde W(a,b)$, and then give some applications.

We investigate slices of the Sierpiński tetrahedron from a topological viewpoint. For each $c\in[0,1]$, we study the Čech (co)homology group of the slice at height $c$. We show that the topology of the slice exhibits a sharp dichotomy. If $c$ is a dyadic rational, then the slice has finitely many connected components, infinite first Čech homology, and trivial higher homology. If $c$ is not a dyadic rational, then the slice is totally disconnected and all positive-degree Čech homology groups vanish.

In this article, we propose a Newton-based method for solving multiobjective interval optimization problems (MIOPs). We first provide a connection between weakly Pareto optimal points and Pareto critical points in the context of MIOPs. Introducing this relationship, we develop an algorithm aimed at computing a Pareto critical point. The algorithm incorporates the computation of a descent direction at a non-Pareto critical point and employs an Armijo-like line search strategy to ensure sufficient decrease. Under suitable assumptions, we prove that the sequence generated by our proposed algorithm converges to a Pareto critical point. The effectiveness and performance of the proposed method are demonstrated through a series of numerical experiments on some test problems. Finally, we apply our proposed algorithm in a portfolio optimization problem with interval uncertainty.

We study outer length billiards; our main results are as follows. We prove 3- and 4-periodic versions of the Ivrii conjecture. We show that, for every period $n\ge 3$, there exists a functional space of billiard tables that possess invariant curves consisting of $n$-periodic points. For $n=4$, we explicitly parameterize such centrally symmetric billiard tables by functions of one variable and describe how to construct these tables geometrically, similarly to the known construction of Radon curves.

The emergence and decline of democratic systems worldwide raises fundamental questions about the dynamics of political change. Contrary to the idea of a stable endpoint of liberal democracy, recent backsliding towards less democratic regimes highlights the non-stationary nature of regime evolution. Here, we analyse the historical trajectories of countries within a two-dimensional regime space derived from the principal components of the Varieties of Democracy dataset. We observe weakly non-ergodic dynamics unfolding in an effective landscape characterised by sparse and shifting basins of stability. Step sizes and sojourn times characterising this dynamics follow heavy-tailed distributions near the critical regime, in which mean values appear to diverge. These facts point to the intermittent and heterogeneous nature of the regime change dynamics. A continuous time random walk model reproduces the dynamics of the three most recent decades with remarkable accuracy. Together, these results suggest that some aspects of political regime evolution follow universal stochastic principles, while remaining punctuated by unique historical pathways.

We develop numerical methods for elliptic systems governed by partial segregation constraints, in which three nonnegative components are required to have a vanishing pointwise product throughout the domain. This constraint enforces that at least one component must be zero at every spatial location, leading to a highly nonconvex admissible set that prevents the use of standard convex optimization techniques. We propose two complementary computational frameworks. The first is a strong-competition penalty method, solved via damped Gauss-Seidel/Picard iterations with a continuation strategy on the penalty parameter, for which we establish compactness results, Lipschitz estimates, and interior exponential improvement in the strong-competition regime. The second is a projected gradient method, together with an accelerated variant, that exploits an explicit pointwise projection onto the three-phase segregation set. Numerical experiments on a suite of benchmark boundary configurations confirm that both algorithms resolve segregated phase patterns.

In this paper, we show that methanol (CH3OH) torsional-rotational transitions, which have increased sensitivity to small variations of mu - the electron-to-proton mass ratio, are shifted relative to less sensitive transitions in the spectrum of the SgrB2(N) molecular cloud located at the Galactic center. At the same time, an identical set of methanol lines in the spectrum of the Orion-KL molecular cloud, located far from the center, shows no shifts. Interpreting this behavior of molecular frequencies in terms of Delta mu/mu = (mu_obs - mu_lab)/mu_lab leads to the following weighted mean values: <Delta mu/mu> = (-3.4 +/- 0.4)*10^(-7) for SgrB2 and <Delta mu/mu> = (-1.1 +/- 0.8)*10^(-7) for Orion-KL (indicated are the total +/-1sigma errors of the weighted means <Delta mu/mu> including both statistical and systematic uncertainties). A possible correlation between <Delta mu/mu> values measured in various molecular clouds of the Galactic disk and the distribution of dark matter along the Galactic radius is discussed, which may suggest a hypothetical modulation of the Higgs scalar field by dark matter, resulting in a change of mu.

Network protocols are the foundation of modern communication, yet their implementations often contain semantic vulnerabilities stemming from inadequate understanding of specification semantics. Existing gray-box and black-box testing approaches lack semantic modeling of protocols, making it difficult to precisely express testing intent and cover boundary conditions. Moreover, they typically rely on coarse-grained oracles such as crashes, which are inadequate for identifying deep semantic vulnerabilities. To address these limitations, we present a semantics-aware fuzzing framework, SemFuzz. The framework leverages large language models to extract structured semantic rules from RFC documents and generates test cases that intentionally violate these rules to encode specific testing intents. It then detects deep semantic vulnerabilities by comparing the observed responses with the expected ones. Evaluation on seven widely deployed protocol implementations shows that SemFuzz identified sixteen potential vulnerabilities, ten of which have been confirmed. Among the confirmed vulnerabilities, five were previously unknown and four have been assigned CVEs. These results demonstrate the effectiveness of SemFuzz in detecting semantic vulnerabilities.

Parameter estimation for the truncated skew-normal distribution is challenging, as truncation introduces additional nonlinearity into the likelihood function and often leads to numerical instability in existing estimation procedures. In this paper, we propose a grid-based estimation method, referred to as GRID-MOM, for parameter estimation in the truncated skew-normal distribution. The proposed approach fixes the shape parameter on a pre-specified grid and, for each grid point, estimates the location and scale parameters using the method of moments. The optimal value of the shape parameter is then selected via likelihood-based comparison, yielding the final parameter estimates. By decoupling the estimation of the shape parameter from that of the location and scale parameters, the proposed method reduces the complexity of the optimization problem and improves numerical stability. We evaluate the finite-sample performance of the proposed estimator through an extensive numerical study, comparing it with existing methods under a variety of scenarios. The results demonstrate that the proposed method provides stable and accurate estimation, particularly for the shape parameter, suggesting that the proposed method offers a practical alternative for inference in truncated skew-normal models. We further demonstrate the practical applicability of the proposed method using phosphoproteomics data and hospital admission data.

Let $\{X_n= e^{2πi θ_n}\}$ be a sequence of Steinhaus random variables, where $θ_n$ are independent and uniformly distributed on $[0,1]$. We compute the almost sure Hausdorff dimension of the images and graphs of the random complex series $S(x)=\sum_{n=1}^{\infty}a_n X_nϕ_n(λ_nx)$, where $λ_n$ is an increasing sequence with $\sup_nλ_{n+1}/λ_n<\infty$ and $ϕ_n$ satisfies some uniform Lipschitz and boundedness conditions. This class of series includes the famous Weierstrass and Riemann functions as well as others appeared in literature. These results help predict the exact values of the deterministic cases.

Knowledge infrastructures are defined as robust networks of people, artifacts, and institutions that generate, share and maintain specific knowledge. Yet, many domains are fragmented and far from robustly networked, such as science communication or aerospace engineering. While FAIR (Findable, Accessible, Interoperable, Reusable) data management tools exist, their adoption in these domains is limited. Several challenges inhibit this adoption, from complex heterogeneous data formats to lack of structured support to outright incentives against collaboration or legal barriers. This doctoral work outlines how to foster underdeveloped knowledge infrastructures with the use-cases of science communication and aerospace engineering. By analyzing these problems and identifying available solutions, tool-supported workflows towards collaborative infrastructure can be implemented and evaluated. These include human-in-the-loop artificial intelligence (AI)-supported workflows for information extraction and processing, wiki- and knowledge-graph-based digital libraries, and stakeholder-requirement-driven interfaces. While these developed tools for workflow automation and knowledge representation show promise, significant challenges remain. Future work will have to go beyond technical problem-solving and address the societal and legal barriers to unlock the particular domains. Beyond that, advocates of emerging knowledge infrastructures in any domain are welcome to apply the findings of this work to foster the networking of available knowledge.

This article addresses the planar Coleman--Gurtin heat equation with memory on a bounded domain, with rough anisotropic diffusion $A_μ$, typical of heterogeneous or composite media and encoded by a Beltrami coefficient $μ\in L^\infty(Ω)$ satisfying $\|μ\|_{\infty}<1$. First, under no additional smoothness assumptions on $μ$, solutions with $H^1_0(Ω)$-based initial data enter a time-averaged $L^\infty(Ω)$ regime, and instantaneously regularize into the second-order graph space $D(A_μ)$. Assuming in addition $μ\in W^{1,2}(Ω)$, this regularization upgrades to $W^{2,p}(Ω)$ for every $1<p<2$, and we construct regular global and exponential attractors of finite fractal dimension, for both the $L^2(Ω)$ and $H^1_0(Ω)$-based dynamics. The proof combines the instantaneous smoothing method of Chekroun, Di Plinio, Glatt-Holtz and Pata with maximal parabolic regularity for divergence-form operators with measurable coefficients, and with planar quasiconformal Beltrami estimates recently obtained in work by Green, Wick and the author.

Gauss's Lemma is revised by showing that the point set association of the double tangential space with the tangential space of a Riemannian manifold is not the identity. The latter point set association is called a metrical distortion, an isometry that actually induces the geometry. The defnition of the exterior differential, which linearizes a mapping that points on the top of a Riemannian manifold, is worked out concretely by covariant gradient transport, what includes a differential slip in contrast to inner differentials. A differential slip is a scalar gauge theory that considers the reparametrization of different length scales. The metrical distortion is determined by geodesically radial volume preservation, whereas the Riemannian exponential mapping is determined by geodesically radial length preservation. The theory is exemplifed by the exterior geometry of the 2-sphere.

We consider bounded open connected sets $Ω_1, Ω_2 \subset \mathbb{R}^n$ and Sobolev maps $f: Ω_1 \times Ω_2 \subset \mathbb{R}^n \times \mathbb{R}^n$, such that for almost every $x \in Ω_1 \times Ω_2$ the weak differential $\nabla f(x)$ is invertible and preserves or swaps the spaces $\mathbb{R}^n \times \{0\}$ and $\{0\} \times \mathbb{R}^n$. We show that if $n \ge 2$ and $f \in W^{1,2}$ then $f$ is split, i.e., $f(x_1, x_2) = (f_1(x_1), f_2(x_2))$ or $f(x_1, x_2) = (f_2(x_2), f_1(x_1))$. We also show that this conclusion fails in general for $n=1$, even if we assume in addition that $f$ is bi-Lipschitz and area preserving. These results complement our previous work https://arxiv.org/abs/2403.20265, where we showed that the conclusion fails for $n \ge 2$ if the Sobolev space $W^{1,2}$ is replaced by $W^{1,p}$ for any $p < 2$. We also discuss results for approximately split maps, i.e. for sequences of maps $f_k$ such that $\nabla f_k$ approaches the set of linear invertible split maps in suitable $L^p$ spaces. This work is partly motivated by the question whether Sobolev maps defined on products of Carnot groups are split.

In the current information age, asymmetrical cryptography is widely used to protect information and financial transactions such as cryptocurrencies. The loss of private keys can have catastrophic consequences; therefore, effective MFA schemes are needed. In this paper, we focus on generating ephemeral keys to protect private keys. We propose a novel bit-truncation method in which the most significant bits (MSBs) of response values derived from facial features in a template-less biometric scheme are removed, significantly improving both accuracy and security. A statistical analysis is presented to optimize an MFA comprising at least three factors: template-less biometrics, an SRAM PUF-based token, and passwords. The results show a reduction in both false-reject and false-acceptance rates, and the generation of error-free ephemeral keys.

Zero-shot Text-to-Speech (TTS) models can generate speech that captures both the voice timbre and accent of a reference speaker. However, disentangling these attributes remains challenging, as the output often inherits both the accent and timbre from the reference. In this study, we introduce a novel, post-hoc, and training-free approach to neutralize accent while preserving the speaker's original timbre, utilizing inference-time activation steering. We first extract layer-specific "steering vectors" offline, which are derived from the internal activation differences within the TTS model between accented and native speech. During inference, the steering vectors are applied to guide the model to produce accent-neutralized, timbre-preserving speech. Empirical results demonstrate that the proposed steering vectors effectively mitigate the output accent and exhibit strong generalizability to unseen accented speakers, offering a practical solution for accent-free voice cloning.

We focus on the sensitivity of the Higgs-gauge boson couplings at $HγZ$ and $HZZ$ vertices through the process $\ell^- \ell^+ \rightarrow HZZ$ at CLIC and Muon Collider. Signal and relevant backgrounds events are generated in MadGraph within Standard Model Effective Field Theory (SMEFT) framework. These events are passed through Pythia for parton showering, and realistic detector effects are simulated by Delphes. The limits at 95% C.L. on the coefficients $\overline{c}_{HB}$ and $\overline{c}_{HW}$ are obtained at three b-tagging working points; loose, medium, and tight containing the Delphes card from CLIC and Muon Collider, corresponding to b-tagging efficiencies of 90%, 70%, and 50%, respectively. We report that our best 95% C.L. limits on $\overline{c}_{HB}$ and $\overline{c}_{HW}$ coefficients are $[-0.00098; 0.00047]$ and $[-0.00158; 0.00008]$, respectively, at 3 TeV CLIC with an integrated luminosity of 5 ab$^{-1}$, and $[-0.00021; 0.00019]$ and $[-0.00019; 0.00007]$, respectively, at 10 TeV Muon Collider with an integrated luminosity of 10 ab$^{-1}$. These limits are compared with the present experimental and various phenomenological limits.

For integers $1\le \ell<k$, the $\ell$-degree Turán density $π_\ell(F)$ measures the minimum $\ell$-degree threshold that forces a copy of a fixed $k$-uniform hypergraph $F$, generalizing both the classical Turán density $π_1$ and the codegree Turán density $π_{k-1}$. Motivated by Erdős' characterization of $k$-graphs with zero Turán density, we study the structural implications of vanishing $\ell$-degree Turán density. We prove for every uniformity $k\ge 3$ that if $π_2(F)=0$, then $F$ admits a $2$-vanishing order-a global vertex ordering under which all edges align canonically. This provides a higher-degree analogue of the classical fact that $π_1(F)=0$ forces $k$-partiteness, and identifies a structural obstruction to vanishing $2$-degree Turán density. As an application, we show that, unlike $π_1$, $π_2$ accumulates at $0$. For $3\le \ell\le k-1$, we also obtain weaker necessary conditions for $π_\ell(F)=0$. The proof combines random geometric building blocks, a design-theoretic gluing scheme, and random sparsification to reconcile positive $2$-degree with local vanishing structure.