Papers

Error-correcting codes enable reliable communication, yet practical soft decoding remains challenging across code families and block lengths. We propose SB-ECC, a score-based decoder that casts decoding as continuous-time denoising. A neural denoiser defines a probability-flow ordinary differential equation (ODE) that iteratively updates the noisy channel observation toward a valid codeword, guided by parity constraints. The model is trained across noise levels without time/SNR conditioning, enabling inference without SNR estimation and supporting a direct latency accuracy trade off controlled by the ODE solver budget. We use the raw signed channel observation as input for learning a continuous denoising field. Across 42 code/SNR settings, SB-ECC achieves the best BER in 39/42 entries, with an average SNR gain of 0.17dB and a maximum gain of 0.46dB over the strongest competing baseline, we showed that swapping the solver from Euler to DPM preserves -ln(BER) while reducing end-to-end decoding time by 8.86% on average (up to 12.82%).

This paper investigates a generation expansion planning (GEP) problem encompassing renewable, thermal, and storage technologies while simultaneously optimizing market participation, operational expenditures, and capital investment. To alleviate the computational burden of the GEP model, we propose a novel iterative time series aggregation (TSA) method that constructs a temporally aggregated counterpart of the original full-scale GEP model. Unlike traditional TSA methods, which are purely heuristic, our method enables the assessment of the optimality gap between the aggregated and full-scale models. Moreover, by leveraging machine learning-based estimates of the GEP model marginal costs, the algorithm guides TSA to construct an aggregated model that preserves the active constraints of its full-scale counterpart, which has been shown to yield exact temporal aggregation. Numerical results show that incorporating estimated marginal costs as clustering features substantially improves the quality of temporal aggregation compared with traditional TSA methods that rely solely on input data analysis.

Parametric Hamiltonians often exhibit point-like spectral degeneracies, called diabolic points (DPs) or conical intersections, which can lead to singularities in the Provost-Vallee metric of eigenstate manifolds. We regularise the metric by a transformation to polar coordinates and develop a formalism in which DPs act as bridges between adjacent eigenstate manifolds, glueing them into a single connected state manifold (CSM). We characterise the topology of this structure and extend the local rules for nodal lines governing the Berry phase to global ones. On the CSM, the class of geodesics can be enlarged by those passing through the DPs. They can be stable with respect to their initial direction, and can be shorter than those constrained to a single eigenstate manifold, providing new geodesic shortcuts. Further, the CSM provides a new mechanism for Berry phase computation along paths traversing the DPs.

We study causal inference for time-to-event outcomes under right censoring in the presence of unmeasured confounding. Focusing on structural accelerated failure time models, we develop an identification and inference framework that exploits interactions among instrumental variables. The proposed approach does not rely on classical instrumental variable validity and yields valid causal inference under both valid and invalid instruments, provided that the interaction-based identification condition holds. To accommodate right censoring, we construct a censoring-adjusted observed data moment function using an augmented inverse probability censoring weighting approach. The resulting moment function is Neyman orthogonal with respect to nuisance functions and enjoys a double robustness property, enabling valid inference under flexible nuisance estimation. Estimation and inference are conducted using generalized empirical likelihood, which is well suited to settings with many potentially weak interaction-based moment conditions. We establish consistency, and asymptotic normality under many weak moment asymptotics, and develop diagnostic tools to assess interaction-based identification strength and overidentifying restrictions. Simulation studies demonstrate favorable finite sample performance across a range of censoring rates and instrument configurations. An application to UK Biobank data illustrates the practical relevance of the proposed method for causal survival analysis in large-scale observational studies.

We study the asymptotic behaviour of different statistics for time series exhibiting long memory and nonstationarity. For processes with memory parameter $d\in(-1/2,3/2)$, we derive the joint limiting distribution of discrete Fourier transforms at a fixed number of Fourier frequencies, with a unified normalization. The resulting limits are Gaussian with an explicit covariance structure. Particular attention is given to the boundary case $d=1/2$, also known as $1/f$ noise. We show that logarithmic corrections yield nondegenerate limits for sample mean and sample variance leading to explicit asymptotic distributions of $\chi^2$ type. We construct a statistic that combines the sample mean, the sample variance, and low-frequency periodogram ordinates, designed so that, at the boundary case $(d=1/2)$, it admits a tractable limit distribution. These results are applied to construct a consistent parameter-free test of nonstationarity against long memory stationarity.

We propose a practical computational framework for detecting structural changes in parameter-dependent topological data. In many applications, such as time-series data analysis, anomaly detection, and monitoring of systems under changing control parameters, persistence diagrams describe the birth and death of topological features at each parameter value, but they do not fully capture how these features are reorganized over time. To address this limitation, we represent homological features by zero modes of the ordinary combinatorial Hodge Laplacian and track the corresponding feature spaces in a common ambient chain space. This allows us to compute curvature and holonomy as descriptors of local reorganization and accumulated memory in evolving topological structures. Curvature highlights parameter regions where homological features mix or change rapidly, while holonomy summarizes the net effect of such changes after a closed cycle. We also establish stability estimates showing that these descriptors are robust under perturbations of the Hodge Laplacian on regular regions. Numerical experiments on controlled time-dependent point-cloud data show that the proposed method detects tracking instability, distinguishes systems with nearly identical persistence diagrams, and captures cycle-level memory invisible to pointwise feature matching. These results suggest that zero-mode transport geometry can serve as a useful computational tool for analyzing dynamic topological data.

Integrated sensing and communication (ISAC) is a promising feature of future communication networks. While spatial sensing can improve network performance and enable external services, it also creates privacy challenges that go beyond the confidentiality of communication content. Future networks using millimeter-wave (mmWave) and sub-terahertz (THz) frequencies may collect or infer detailed information about people, devices, bystanders, passive objects, and environments in a sixth-generation (6G) deployment area. Such sensing can reveal location and environment data, support behavioral profiling such as movement or activity recognition, and, in advanced cases, expose physiological information such as breathing frequency or heart-rate-related data. Thus, the capabilities of spatial sensing must be controlled to satisfy privacy requirements. In this work, we organize privacy-sensitive ISAC data into three sensing levels: location and environment data, behavioral data, and physiological data, and use this classification as the organizing principle throughout the paper. Based on this classification, we discuss internal and external ISAC applications, identify privacy challenges related to consent, transparency, data ownership, profiling, bystander exposure, and sensitive sensing data, review representative solution directions, and outline future research directions for privacy-preserving ISAC.

We study the dissipative spectral form factor (DSFF) at complex time $T e^{i\theta}$ for the complex elliptic Ginibre ensemble with non-Hermiticity parameter $\tau \in [0,1)$. As the matrix dimension $N \to \infty$, we consider the natural scalings in both the time variable and the non-Hermiticity parameter, namely $T = O(N^\gamma)$ and $1 - \tau = O(N^{-\alpha})$. For all regimes $\gamma \ge 0$ and $\alpha \ge 0$, we derive the precise asymptotic behaviour of both the disconnected and connected components of the DSFF. In particular, we explicitly characterise the dip–ramp–plateau structure, including the dip time and the Heisenberg time. In addition, we identify the mesoscopic regime $\alpha \in (0,1)$, which interpolates between the behaviour of the DSFF of non-Hermitian random matrices and the spectral form factor (SFF) of Hermitian ensembles. We further provide an explicit description of the phase diagram, in which the ramp exhibits quadratic, linear, or intermediate behaviour depending on the scaling parameters.

This paper proposes a novel fluid antenna system (FAS)-enabled architecture to improve energy efficiency (EE) without sacrificing capacity. Specifically, we integrate FAS into cell-free massive MIMO systems to counteract low-resolution ADCs. We establish a comprehensive uplink transmission model and derive analytical expressions for SE and EE. These expressions explicitly capture the quantization error under slow fluid antenna multiple access and quantify the benefits of low-resolution ADCs on EE. Furthermore, we formulate a joint optimization problem to maximize EE performance. To solve this, we develop an efficient alternating optimization framework. This framework leverages the Dinkelbach algorithm-based fractional programming for power control, alongside novel accelerated projected gradient ascent (APGA) algorithms to optimize both continuous FAS positions and discrete ADC bit allocations. Numerical results reveal that low-resolution ADCs aggressively compress signals to save hardware power, which inevitably degrades SE but maintains EE. However, FASs can recover this SE loss thanks to their spatial flexibility and significantly boost EE by improving the received signal prior to destructive quantization. Furthermore, optimized power control can prevent quantization-induced multi-user interference, while efficient bit allocation can reduce exponential hardware power. Ultimately, our proposed FAS-enabled system, coupled with efficient power control and bit allocation, effectively improves system performance and outperforms traditional fixed-position antennas. It establishes a highly robust and energy-efficient paradigm for 6G networks.

Neural surrogates promise large speedups over classical solvers for physical dynamics but fail silently at sharp dynamical events such as shocks, fronts, and contact. We present hybrid neural world models for physical dynamics: a recipe for training and deploying multi-horizon surrogates in physical state space, where a single network with continuous horizon conditioning is trained with direct supervision against textbook reference solvers to predict any future state at horizon T in one forward pass. Although no part of the training data, loss function, or architecture supervises discontinuity location, the trained surrogate encodes it implicitly, recoverable from its forward passes alone as a per-trajectory error map that concentrates on shocks, fronts, and contacts, and stays small elsewhere. The map is competitive with or better than standard label-free baselines including deep ensembles, learned error heads, gradient-magnitude indicators, and locally-adaptive conformal prediction, while using only a single trained network and requiring no calibration set or governing-equation knowledge. The recipe supports two operating points. Mode 1 runs the surrogate alone for maximum throughput, with same-hardware CPU speedups of 26x to 72x against textbook solvers on the PDE environments. Mode 2 uses the error map to gate a reference-solver fallback, deferring uncertain trajectories and roughly halving the surrogate's residual error at the default operating point. The recipe applies without modification across reaction-diffusion, compressible Euler, and rigid-body collision dynamics.

In this article we study devlop some fundaments for a function theory in the 16-dimensional complexified octonions.

We introduce two ordinal indices that are linear invariants for Banach spaces: the dyadic tree index and the sprawling tree index. We show that they are also bi-Lipschitz invariants. In fact, we characterize their values in terms of sub-Lipschitz embeddability of dyadic or countably branching diamond graphs of ordinal height. We derive applications for separable Banach spaces that are universal for complete countable metric spaces and bi-Lipschitz embeddings. We also discuss the links of these tree indices with classical fragmentability indices of Banach spaces such as the dentabilty, weak fragmentability and Szlenk indices.

The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem for the class of virtually polycyclic groups.

We analyze a construction of Cherlin, van den Dries, and Macintyre to code graphs in PAC fields. We show that, in many cases, model-theoretic properties of the graph are preserved in the passage from the graph to the field. As a corollary, we show that the SOP$_{n}$ hierarchy is strict in the class of fields. The main ingredient is a detailed treatment of the model theory of inverse systems of certain profinite groups that code graphs and can be realized as the absolute Galois groups of PAC fields.

The purpose of this paper is to constructively develop a Galois theory on irreducible shifts of finite type (SFTs) and to analyze the automorphism groups of SFTs using this framework. Let $X$ and $Y$ be irreducible SFTs. We demonstrate that a factor map $Y \to X$ satisfying algebraic conditions exhibits Galois-theoretic behavior. Specifically, we prove that a Galois correspondence, analogous to those known in the Galois theory of fields and covering spaces in topology, holds for irreducible SFTs. Furthermore, we introduce the absolute Galois group and its cohomology as conjugacy invariants for irreducible SFTs. Finally, we construct a representation of the automorphism group of an irreducible SFT into this cohomology to extract information from the automorphism group, whose structure is not yet fully understood.

We obtain estimates in simultaneous approximation for a summation-integral type genuine hybrid operator. The convergence of derivatives of operator to the corresponding derivatives of the functions is proved and estimates for rate of approximation are obtained.

The reliable and accurate numerical approximation of the $p$-Laplacian is particularly challenging in the extreme regimes $p \to 1^{+}$ and $p \gg 1$, where the operator becomes either highly singular or strongly degenerate, often causing severe instability in standard numerical methods. To address these difficulties, we propose a novel deep learning based framework, termed the dual variational neural network, for $p$-Laplace problems. The approach is based on a mixed formulation and an $L^q$-based Helmholtz decomposition, which decouples the original problem into two convex subproblems: a linear Poisson problem for the irrotational component and an unconstrained minimization problem over divergence-free fields for the solenoidal component. Following the decomposition, we employ two neural networks using a gradient–curl representation to approximate the flux, and further establish an error analysis of the neural approximation. The analysis relies on fundamental vector inequalities together with tools from statistical learning theory. Numerical experiments demonstrate robust convergence of the proposed method in challenging settings, including the extreme cases $p \to 1^{+}$ and $p \gg 1$, as well as the $p(x)$-Laplace equation.

A sequence D=(d1, d2, ..., dn) of positive integers is graphic if it is the degree sequence of a simple graph, called in this case a realization of D. In this paper, we introduce the operation of 2-reduction, that subtracts 1 from two integers of D such that the resulting sequence D' is graphic if and only if D is graphic. We show that 2-reductions allow us to simply generate all the realizations of D, to prove existing characterizations of graphic sequences, as well as to propose new characterizations that highlight connections between mathematical and algorithmic aspects of graphic sequences.

We study the Brauer-Manin set of smooth projective surfaces over global fields of positive characteristic for which Kodaira vanishing fails. Our results apply in particular to Raynaud surfaces.

Krylov subspace methods, such as the Conjugate Gradient (CG) and BiCGSTAB methods, are widely used in scientific computing for solving linear systems. In this study, we propose a new framework for solving large Sylvester equations in a low-rank format by reconstructing matrix-oriented Krylov subspace methods. The framework realizes efficient algorithms that are mathematically equivalent to the matrix-oriented Krylov subspace methods by exploiting the mathematical properties of the Sylvester operator and the low-rank structure of the right-hand side. Specifically, by leveraging these properties, approximate solutions can be expressed in a low-rank factorized form, enabling efficient computation and reduced memory requirements. The effectiveness of our algorithms is demonstrated through numerical experiments.

We initiate the study of inflection curves of rational vector fields on the Riemann sphere. For a rational vector field $v_R=-R(z)\frac{\partial}{\partial z}, \qquad R(z)=\frac{Q(z)}{P(z)} $ we define its affine regular inflection locus by $ \{z\in \mathbb{C}: R(z)\ne0,\ P(z)\neq 0,\ \text{Im} R'(z)=0\} $ and its algebraic inflection curve by the closure of this locus, equivalently by $ \mathfrak{I}_R=(R')^{-1}(\mathbb{RP}^1). $ We prove an explicit defining equation, degree bounds, local normal forms near poles, the asymptotic directions at infinity, and a maximum-principle obstruction excluding compact components without poles. We also explain that these curves are precisely the real dessins associated with exact rational differentials, i.e. rational differentials with zero residues. Finally, we give a reducibility criterion for the complexification, prove a generic irreducibility statement in the usual separated-variable sense, and classify the exact dessins of degree at most two. The degree-three problem is reduced to three explicit normal forms.

This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$ estimates for the $L_p$ dual Minkowski problem without symmetric assumptions, thereby resolving a related problem proposed by Böröczky-Chen-Liu-Saroglou in the smooth sense. We further prove the uniqueness of smooth solutions under appropriate conditions, provided the density function is sufficiently close to a constant in the Hölder norm. Finally, exploiting the fact that the uniqueness of the Minkowski type problem is equivalent to the validity of the Brunn-Minkowski inequality in a certain sense, we study the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals for origin-symmetric convex bodies with $p<q$.

In a nonautonomous nonlinear dynamical system, generic critical transitions (tipping points) are not limited to slow passage through fold bifurcations. They can also correspond to slow passage through other generic bifurcations, such as subcritical Hopf or even (in the multiscale setting) singular Hopf bifurcation. In systems such as these, generic early warning signals associated with critical slowing down, such as observing an increase in variance and lag-1 autocorrelation, can be obscured by oscillatory behaviour. Here, we present a method using vector autoregression (VAR) that aims to identify multiple eigenvalues of the system from multiple time series. With this, we are not only able to deduce the system's stability but also identify the type of bifurcation we are approaching and, therefore, the underlying dynamics, which gives us insight into the system's future state post-tipping. In practice, this can be beneficial for estimation and mitigation of risk. We look at three bifurcations in particular: the fold, the subcritical Hopf bifurcation, and the singular Hopf bifurcation in the presence of an extra time-scale separation. We hope to show that VAR is potentially a powerful tool in an EWS toolkit and can be more enlightening than simply looking at AR(1) of individual time series, especially if there is more than one timescale present in the system.

Take a holomorphic Lie algebroid $(V,\phi)$ over a rationally connected smooth complex projective variety $X$. We show that, under certain conditions, a vector bundle $E$ over $X$ admits a $(V,\phi)$-connection if and only if $E$ is trivial. Moreover, we prove that under the same conditions, any $(V,\phi)$-connection over $X$ is flat.

Robotic locomotion can become efficient when mechanisms exploit passive dynamics, compliance, and resonance rather than track prescribed trajectories. This paper formulates natural locomotion as an exchange principle for systems whose motion is mediated by environmental constraints or interactions. A motion is natural when an internal oscillator returns periodically, the body pose drifts, and the mean Propulsion–Oscillator Exchange power (POE power) vanishes over one cycle. The selected family is a Natural Locomotion Manifold (NLM). We develop the conservative realization of this principle for continuous ideal environmental constraints: the constraints do no external work, total mechanical energy is conserved, and zero mean POE power is an internal exchange with the environment-mediated propulsive channel, not external energy input. The method is a closed/open construction. The propulsive channel is first closed to reveal an effective internal oscillator, organized by scalar action-angle structure in one effective degree of freedom or by nonlinear modal sectors in several degrees of freedom. The channel is then reopened, pose is reconstructed, and accepted cycles must preserve internal recurrence and zero mean POE power. We demonstrate the principle on two ideal nonholonomic no-slip systems: a Chaplygin-sleigh / pendulum-driven car and a three-body extension. In the scalar case, POE closure is equivalent to the missing internal return condition, giving a theorem-backed computation of the NLM family. In the multi-degree case, POE closure remains necessary but must be completed by modal identity, internal return, dynamics consistency, same fixed passive architecture, and nonzero displacement. Natural locomotion becomes a design question: which passive architectures support no, one, or several certified NLM families?

We investigate the gravitational collapse of a massive scalar field in a conformally flat, spherically symmetric spacetime within general relativity. The collapsing matter distribution is modeled using a minimally coupled homogeneous scalar field together with both perfect fluid and dissipative matter sectors. Imposing conformal flatness through the vanishing of the Weyl tensor considerably constrains the geometry and enables the construction of exact analytical solutions. In the non-dissipative case, the field equations admit a separable conformal factor leading to a continuously collapsing configuration smoothly matched to an exterior Schwarzschild spacetime. The collapse proceeds asymptotically and does not develop a shell-focusing singularity within finite proper time. We further examine the possibility of self-similar evolution associated with homothetic symmetry. It is shown that self-similar solutions are incompatible with a perfect-fluid configuration alone, but become consistent when dissipative effects in the form of a radial heat flux are included. The resulting self-similar collapse must be matched to an exterior Vaidya spacetime and exhibits a monotonically decreasing Misner-Sharp mass due to outward energy transport. For both classes of solutions, the proper radius remains finite throughout the evolution, preventing the formation of shell-focusing singularities within the considered domain. The scalar field sector satisfies the null energy condition for the potentials studied, while the effective fluid sector exhibits violations of the null and strong energy conditions, indicating the emergence of effective exotic matter behavior.

We introduce the notion of $k$-regular factorizations for contractions into $k$ factors, generalizing the classical notion of regular factorization due to Sz.-Nagy and Foiaş, and develop a systematic framework for their analysis. Using this concept, a one-to-one correspondence is established between chains of invariant subspaces \[ \mathcal{M}_1 \subseteq \cdots \subseteq \mathcal{M}_{k-1}, \] associated with a completely non-unitary contraction and the class of all $k$-regular factorizations of its characteristic function. An explicit functional model for the corresponding completely non-unitary contraction is constructed, and the associated functional model representations of the chain of invariant subspaces are obtained. Finally, examples illustrating the applicability of these results are provided. Furthermore, we introduce symmetric $k$-regular tuples for commuting $k$-contractions, proving this property holds when the product of contractions has a finite-dimensional defect space and is $k$-regular under at least one permutation. Importantly, we demonstrate that the classical counterexamples for commuting $3$-tuples provided by Parrott, Crabb-Davie, and Kaijser-Varopoulos fail to be symmetric $3$-regular tuples. This structural failure highlights the significance of symmetric $k$-regularity and offers a promising framework that encourages further research into this property and the commutative dilation theory of commuting $k$-contractions.

We study the geodesic flow on the unit cotangent bundle $M=S^{*}\mathcal{N}$ of a closed hyperbolic surface $\mathcal{N}$, using the representation theory of $SL_{2}(\mathbb{R})$. We construct explicit $X$-adapted Hilbert spaces, obtained by completing propagated dense domains of $L^{2}(M)$, which are tailored to the spectral analysis of the geodesic generator $X$. In these spaces, $X$ becomes a normal operator with discrete spectrum, except at the threshold $\mu=1/4$, where Jordan blocks of size two may occur. In this Hilbert model, the propagator $e^{tX}$ factorizes into a damped harmonic oscillator with eigenvalues $e^{-t(n+1/2)}$, $n\in\mathbb{N}$, and a transverse part involving the shifted wave group $e^{\pm it\sqrt{\Delta-1/4}}$ on $\mathcal{N}$, together with the holomorphic and anti-holomorphic discrete series. The model clarifies two classical links between geodesic dynamics and the Laplace spectrum. Comparing the spectral trace of the propagator in the $X$-adapted Hilbert model with the Atiyah–Bott–Guillemin flat trace gives a dynamical form of the Selberg trace formula: closed geodesics arise from the flat trace, while the spectral side comes from the explicit $SL_{2}(\mathbb{R})$-decomposition. The same factorization also explains the large-time structure of spherical mean operators on $\mathcal{N}$: after the natural $e^{t/2}$-renormalization and the removal of a finite-rank low-energy part, the shifted wave equation on $\mathcal{N}$ emerges as the leading effective dynamics. Thus the construction provides an explicit Hilbert-space structure relating classical geodesic dynamics, Ruelle resonances, and the spectral theory of the surface.

This paper develops sharp Hautus-type criteria, stochastic counterparts of the classical Popov-Belevitch-Hautus test, for exact controllability and stabilizability of backwardstructured stochastic linear systems. The main finding is that the stochastic Hautus obstruction is not a left eigenvector, as in deterministic linear systems, nor an arbitrary symmetric eigenmatrix, but a positive semidefinite eigenmatrix of a Lyapunov-type operator. We prove that exact controllability is equivalent to the absence of such nonzero positive semidefinite eigenmatrices that are orthogonal to the control directions. This cone restriction is sharp: excluding all symmetric eigenmatrices with the same orthogonality property is sufficient but not necessary. We further show that stabilizability is characterized by the same cone-restricted Hautus condition imposed only on the nonstable spectral part of the Lyapunov-type operator. Thus the stochastic Hautus theory developed here is governed by a simultaneous spectral restriction and cone restriction. In addition to these criteria, we provide finite-rank and Gramian characterizations underlying exact controllability, establish the corresponding controllability decomposition, and show that exact controllability implies stabilizability.

We develop a cutting-plane methodology that adjusts solutions to optimization problems so as to reduce features that bring about exposure to risk, such as concentration of assets or resources. The methodology is agnostic to the representation of risk. Our procedure aims to reduce the appropriate risk metric without accruing a significant increase in nominal cost, rapidly, or proves that such an adjustment is not possible. The underlying approach borrows from techniques used in first-order methods for optimization.