We establish new examples and non-examples of pro-p limit groups among the class of Demushkin groups, that is, pro-p Poincaré duality groups of dimension 2.

We investigate analytically and numerically correlation functions of the phase of light waves that propagate through turbulent media. We examine the case of strong scintillations that occur at large values of the Rytov dispersion, $σ^2_R$. Then, it is possible to relate the pair correlation function of phase gradients to the known pair correlation function of the envelope dependent on the distance $r$ assuming Gaussianity of the envelope of the beam. Our direct numerical simulations show that the profile of the pair correlation function for phase gradients gradually approaches the theoretical expression as the value of $σ_R^2$ increases, if $r<r_0$ where $r_0$ is the Fried length. For larger $r$ the behavior of the computed correlation function is quite different because of destroying the Gaussianity.

We theoretically investigate how phase modulation alters the dynamics of temporal localized structures (TLSs) in vertically emitting Kerr micro-cavities under detuned optical injection operating in the normal dispersion regime. We show that the emergence of TLSs in general is governed by a synchronization between the imposed modulation and the intrinsic pulse dynamics. We perform a multi-parameter bifurcation analysis of the underlying delay-algebraic equation model in the uniform field limit and demonstrate that weakly nonlinear and dissipative Hermite-Gauss modes shape the dynamics of dark TLSs, leading to a complex hybrid bifurcation structure. Beyond the uniform field limit, both bright and dark modulated TLSs are shown to exist and to occupy distinct equilibrium positions within the cavity. An effective equation of motion for the TLS positions is derived, showing a good agreement with the full model.

Suspensions of attractive particles form space-spanning networks that endow the suspension with solid-like behavior at rest. The microstructure of these colloidal gels depends sensitively on the shear history and on the path followed across the sol-gel transition, resulting in viscoelastic properties that can be tuned by shear. Here, we report in situ X-ray tomo-rheoscopy experiments on carbon black gels whose elastic properties exhibit a non-monotonic dependence on the shear intensity applied prior to flow cessation. By directly imaging the gel microstructure under a well-controlled rheological protocol, we reveal the emergence of pronounced structural heterogeneities extending from tens to hundreds of microns -- length scales far larger than those accessible by conventional scattering techniques such as Ultra-Small Angle X-ray Scattering. In particular, we show that only the low-shear reinforcement of elasticity correlates with a growing mesoscale correlation length, while high-shear strengthening occurs without detectable mesoscale reorganization. These observations demonstrate that flow memory in colloidal gels is not solely governed by local particle rearrangements, but is also encoded in a mesoscale structural organization extending up to 100 times the particle size. More broadly, this work highlights the power of X-ray tomo-rheoscopy to uncover large-scale structural signatures of flow history in soft materials, opening new perspectives to tailor their mechanical properties.

Computational properties of the Hahn-Banach theorem have been studied in computable, constructive and reverse mathematics and in all these approaches the theorem is equivalent to weak Kőnig's lemma. Gherardi and Marcone proved that this is also true in the uniform sense of Weihrauch complexity. However, their result requires the underlying space to be variable. We prove that the Hahn-Banach theorem attains its full complexity already for the Banach space $\ell^1$. We also prove that the one-step Hahn-Banach theorem for this space is Weihrauch equivalent to the intermediate value theorem. This also yields a new and very simple proof of the reduction of the Hahn-Banach theorem to weak Kőnig's lemma using infinite products. Finally, we show that the Hahn-Banach theorem for $\ell^1$ in the two-dimensional case is Weihrauch equivalent to the lesser limited principle of omniscience.

We present multi-frequency polarimetric observations of 3C 84 obtained with the Korean VLBI Network at 43-141 GHz, the Very Long Baseline Array at 43 GHz, and the High Sensitivity Array at 8 GHz from 2015 to 2024. We find that the Faraday rotation measure (RM) decreases systematically with distance from the black hole over 1-8 pc, following a single power-law trend of RM proportional to r^{-2.7+/-0.2}. Notably, RM measurements from earlier studies across the same distance range follow the same relation. This consistency across epochs, frequencies, and independent datasets indicates a common and stable external Faraday screen. These results naturally identify the circumnuclear ambient medium within the parsec-scale Bondi radius of the host galaxy NGC 1275 as the origin of the Faraday rotation, thereby resolving a long-standing question about its physical origin. From the RM profile, we derive radial distributions of the electron density and magnetic-field strength in the circumnuclear ambient medium that are consistent with independent constraints. The derived density lies below that of the free-free absorption disk and, when extrapolated inward, remains below the density of the broad-line region. The magnetic-field strength gradually increases from 0.1-1.5 microgauss at the Bondi radius to milligauss-to-gauss levels toward the black hole, providing the first spatially resolved constraint on the magnetic-field strength at parsec-scale distances in an elliptical galaxy. Together, these results present a spatially resolved and physically consistent picture of the circumnuclear environment in NGC 1275.

Any quantum state of the radiation field, sliced in small non-overlapping space-time bins is a collection of single-rail qubits, each spanning the vacuum and single-photon Fock state of a mode. Quantum logic on these qubits would enable arbitrary measurements on information-bearing light, but is hard due to the lack of strong nonlinearities. With unentangled ancilla single-rail qubits, an $8$-port interferometer and photon detection, we show any single-rail qubit measurement in the $XY$ Bloch plane is realizable with success probability $147/256$, which beats the prior-known $1/2$ limit.

In his approach to Jones theorem on the interpolation of Hardy spaces on the torus, Pisier introduced an original method allowing the computation of complex interpolation spaces by means of real interpolation techniques. This approach has been successfully extended to noncommutative analytic Hardy spaces arising from subdiagonal algebras. In this paper, we formulate and prove an abstract version of Pisier s method in a more general setting. The method is then applied in the study of noncommutative martingale transforms.

Forecasting permafrost thaw from aerial lidar requires projecting 3D point cloud features onto 2D prediction grids, yet naive aggregation methods destroy the vertical structure critical in forest environments where ground, understory, and canopy carry distinct information about subsurface conditions. We propose a projection decoder with learned height embeddings that enable height-dependent feature transformations, allowing the network to differentiate ground-level signals from canopy returns. Combined with stratified sampling that ensures all forest strata remain represented, our approach preserves the vertical information critical for predicting subsurface conditions. Our approach pairs this decoder with a Point Transformer V3 encoder to predict dense thaw depth maps from drone-collected lidar over boreal forest in interior Alaska. Experiments demonstrate that z-stratified projection outperforms standard averaging-based methods, particularly in areas with complex vertical vegetation structure. Our method enables scalable, high-resolution monitoring of permafrost degradation from readily deployable UAV platforms.

We show stabilisation of solutions to one-dimensional advective Cahn-Hilliard equation modeling the Langmuir-Blodgett thin films. This problem has the structure of a gradient flow perturbed by a linear term $βu_x$. Through application of an abstract result by Carvalho-Langa-Robinson, we show that for small $β$ the equation has the structure of gradient flow in a weak sense. Combining this with the finite number of steady states implies stabilization of solutions.

This paper consider the LAN property for the mixed O-U process under high-frequency observation when H>3/4. As considered in mixed fractional Brownian motion, we will also use the projection step to get the non-diagonal rate matrix.

Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to nonequilibrium control in integrable many-body systems, enabling the realization of nonequilibrium dynamics with greater flexibility than Floquet engineering. However, extending QSP to nonintegrable systems faces fundamental obstacles arising from the limited number of conserved quantities and thermalization. In this work, we propose a protocol that leverages QSP in systems exhibiting Hilbert space fragmentation (HSF). Specifically, we consider a pair-hopping model with four-fold periodic potentials that exhibits an HSF structure, thereby providing integrable and nonintegrable sectors within a single system. We analytically show that nonequilibrium dynamics can be flexibly designed through QSP engineered by these potentials in the integrable sectors. In contrast, we numerically identify signatures of thermalization in the nonintegrable sectors. Remarkably, by inserting domain walls, we achieve parallel control of multiple quantum dynamics within a single system. This approach sheds light on the control of nonequilibrium dynamics from the perspective of quantum computation by extending the scope of QSP to nonintegrable systems.

We investigate the response of the Rashba spin-orbit system to a time-periodic scalar potential, in order to determine whether an induced magnetization exists. We approach this by employing the Floquet-Green function method within the Keldysh formalism, computing the non-equilibrium steady state of the system. We find that, even in the absence of an external magnetic field, the system evolves into a state with an oscillating magnetization density that is remarkably rich in structure. We provide a detailed physical interpretation of the results by performing a Fourier decomposition in non-local momentum-space, which helps to uncover the physical origin of the induced magnetic field in terms of Fermi surface spin polarization and the system's dynamical character.

Quantum computing has been regarded as a promising approach to accelerate power system optimization. However, challenges such as limited qubits and inherent noise hinder their widespread adoption in power systems. In this paper, we propose a qubit-efficient framework for solving a crucial power system optimization problem, the probabilistic optimal power flow (POPF). We demonstrate that quantum noise, traditionally viewed as a drawback, can in fact be leveraged to provide a built-in differential privacy (DP) guarantee. Specifically, we first linearize POPF into a multi-parametric linear program (MP-LP) with renewable uncertainties being the parameters. This decomposes the parameter space into critical regions with precomputed solution maps. Second, a variational quantum circuit (VQC) classifies the critical region based on each uncertainty realization and then recovers the final solution. In this way, the required qubits scale with the uncertain parameters instead of the network size, with only 5 qubits versus 600+ for direct quantum OPF in a 69-bus system. Moreover, we prove the depolarizing noise of VQC provides DP guarantees and characterize the privacy-cost tradeoff. Case studies validate the proposed VQC achieves 2.1$\times$ smaller privacy budgets compared to its classical counterpart. At matched privacy levels, the VQC also maintains lower infeasibility and prediction error.

A procedure for the algebraization of a $CR$-manifold and its holomorphic automorphisms is described. Examples of the application of algebraization are considered. Questions arising in connection with the algebraization of a $CR$-manifold are formulated. The possibilities of extending this procedure to other branches of geometry and analysis are discussed.

The realization of efficient micro-machines built from active matter requires precise thermodynamic control far from equilibrium. Despite theoretical progress, the focus on single-parameter driving, coupled with strict theoretical assumptions, limits efforts to capture modern multi-parameter control experiments. Here, guided by careful theoretical considerations, we develop a transparent computational framework based on exact-gradient descent via automatic differentiation. We derive optimal protocols for a wide range of multi-parameter problems -- involving trap stiffness, trap center, and particle activity -- to minimize the thermodynamic work or heat. We demonstrate that smoothed, experimentally plausible protocols -- obtained by assigning kinetic costs to the controls -- achieve near-optimal efficiencies comparable to discontinuous ``bang-bang'' solutions. By exploring both open- and closed-loop control, we find the dynamical coupling between parameters leads to genuinely new strategies, including symmetry breaking in optimal activity cycles and non-monotonic trap stiffness controls. Further, we identify regimes where initial measurement and multi-parameter flexibility combine to improve efficiency. Finally, we reveal that the naive simultaneous execution of independently optimized controls incurs only slightly more work than the full multi-parameter solutions. Taken together, our work elucidates the non-equilibrium physics of multi-parameter control and provides robust, scalable strategies for controlling active matter.

Zero modes, understood here as degrees of freedom with vanishing confining frequency, play a central role in the nonequilibrium dynamics of bosonic systems. In Gaussian models, however, they lead to an unbounded, logarithmic growth of entanglement entropy. We show that this divergence is not an intrinsic property of zero modes themselves, but arises specifically for non-compact zero modes. Their non-compact configuration space allows unbounded spreading in position space, while their continuous spectra enable indefinite dephasing in momentum space. By contrast, compact zero modes in compact bosonic systems behave fundamentally differently: Spreading and dephasing are eventually halted, so that compactness caps the entanglement entropy at a finite value, making its dynamical role most transparent in the presence of a zero mode. We demonstrate this mechanism in a minimal setting by comparing two coupled harmonic oscillators with two coupled quantum rotors. We then show that the same physics persists in many-body systems by contrasting an N-site compact rotor chain with the non-compact harmonic chain. Finally, we relate these insights to ultra-cold-atom realizations of compact quantum field theories. In particular, we clarify when a compact free-boson (Tomonaga-Luttinger liquid) description is required and when the commonly used non-compact massless Klein-Gordon model breaks down. Even when the initial state is accurately captured by a non-compact Gaussian description, compactness ultimately governs the late-time quench dynamics, curbing entanglement growth rather than allowing a dynamical divergence.

The notions of tree-like loop and Lipschitz tree-like loop were introduced by Hambly and Lyons in their 2010 Annals of Mathematics paper. They showed that the Lipschitz tree-like property determines an equivalence relation on the set of paths of bounded variation in a given metric space and then asked if this notion could be extended to paths without the Lipschitz requirement. We show that after eliminating the Lipschitz requirement, the resulting relation is no longer transitive and thus is not an equivalence relation. The counterexample is obtained by analyzing an explicit fractal construction in the plane.

OBJECTIVE: To propose a new approach to analyze the age-distribution of reported cases for vector-transmitted infections. METHODS: Using officially reported number of cases of dengue, Zika, chikungunya, malaria and leishmaniasis for distinct geographical areas, in different periods. Data were treated in special but well-known procedure, transforming the raw data into a density age-dependent distribution and fitting a special continuous function to it. RESULTS: We found that the proportion of age-dependent cases with respect to the total number of cases in a given year (or any transmission season) is probably determined by the ecological interactions between vectors and hosts. The age-distribution of the proportion of cases for the three Aedes-related infections are essentially the same independently of the magnitude of the outbreak and the geographical region considered. On the other hand, for the infections transmitted by other vectors, the age-distributions of the proportion of cases are entirely different. CONCLUSIONS: During specific outbreaks, the ratio between the age distribution of the proportion of officially reported cases and the total number of cases for Aedes transmitted infections such as dengue, chikungunya and zika is independent of the size of the outbreak, the size of the studied population, the period when the outbreak occurs; and the geographical region considered. Our results also suggest that the age-distribution of cases is mainly due to the interaction between vectors and their hosts.

We introduce a concept of the commuting probability of a skew left brace analogous to group theory. We establish upper and lower bounds for the commuting probability and prove that, for finite non-trivial skew left braces, it is always at most $\frac{3}{4}$. Interestingly, there is no skew left brace with commuting probability in the open interval $(5/8, 1)$, except $\frac{3}{4}$, for which we construct an explicit example. A characterization of skew left braces having commuting probability $\frac{3}{4}$ or $\frac{5}{8}$ is presented. We further show that the finite skew left braces with commuting probability larger than $\frac{65}{128}$ are necessarily nilpotent. We prove that the commuting probability remains invariant under isoclinism of skew braces. We introduce a concept of a compact Hausdorff topological skew left brace $B$, where we prove that the set of all elements of $B$ having finite centraliser index in $B$ is a Borel subgroup. For such infinite non-trivial skew left braces too $\frac{3}{4}$ is the upper bound for the commuting probability, and $\frac{3}{4}$ is the only rational number which occurs as commuting probability in the open interval $(5/8, 1)$.

Force fields for molecular dynamics are usually developed manually, limiting their transferability and making systematic exploration of functional forms challenging. We developed a graph neural network that assigns all force field parameters for diverse molecules using continuous atom typing. The freely-available model, called Garnet, was trained on quantum mechanical, condensed phase and protein nuclear magnetic resonance data without the use of existing parameters. The resulting force field shows comparable performance to current force fields on small molecules, folded proteins, protein complexes and disordered proteins. It shows similar results to popular approaches for relative binding free energy predictions across a range of targets. Assessing different functional forms shows that the double exponential potential is a flexible and accurate alternative to the Lennard-Jones potential. Garnet provides a platform for automated, reproducible force field discovery that brings the benefits of machine learning to classical force fields.

Emerging large-scale engineering systems rely on distributed fusion for situational awareness, where agents combine noisy local sensor measurements with exchanged information to obtain fused estimates. However, at the sheer scale of these systems, tracking cross-correlations becomes infeasible, preventing the use of optimal filters. Covariance intersection (CI) methods address fusion problems with unknown correlations by minimizing worst-case uncertainty based on available information. Existing CI extensions exploit limited correlation knowledge but cannot incorporate structural knowledge of correlation from multiple sources, which naturally arises in distributed fusion problems. This paper introduces Overlapping Covariance Intersection (OCI), a generalized CI framework that accommodates this novel information structure. We formalize the OCI problem and establish necessary and sufficient conditions for feasibility. We show that a family-optimal solution can be computed efficiently via semidefinite programming, enabling real-time implementation. The proposed tools enable improved fusion performance for large-scale systems while retaining robustness to unknown correlations.

Motivated by the recent development of noncommutative Novikov algebras and multi-Novikov algebras from the study of regularity structures of stochastic PDEs, this paper gives a general approach to study various multi-Novikov algebras and multi-differential algebras, with close connection with Poisson algebras. The construction of S. Gelfand of Novikov algebras from differential commutative algebras is generalized to this context. Free noncommuting multi-Novikov algebras are constructed from typed decorated rooted trees and from noncommuting multi-differential polynomials with populated conditions.

We prove that a finitely generated virtually RFRS group of cohomological dimension at most $2$ is coherent if and only if its second $L^{2}$-Betti number vanishes if and only if it is virtually free-by-cyclic. The non-vanishing of the second $L^{2}$-Betti number provides the first known global obstruction to coherence in any reasonably wide class of groups, allowing for proofs of incoherence without needing to exhibit explicit witnesses to incoherence. As applications of this result, we completely characterise coherence among two-dimensional Coxeter groups, confirming conjectures of Jankiewicz and Wise, and show that incoherence is generic in groups of nonpositive deficiency, confirming a conjecture of Wise. We also find that, among virtually compact special groups of virtual cohomological dimension two, coherence is algorithmically decidable and is a quasi-isometry, measure equivalence, and profinite invariant. In an appendix, Marco Linton applies one of the main results to prove that cubulated locally quasi-convex hyperbolic groups are virtually free-by-cyclic, solving problems of Abdenbi--Wise and Wise in the cubulated case.

Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

Inspired by numerous lab on a chip, biomedical and bioengineering applications such as cell sorting, focusing, trapping, and filtering of particles, manipulation of micron sized particle trajectories has been of significant interest in the context of microfluidics. Systematic deflection of microparticles away from their initial streamlines is a central objective in microfluidic particle manipulation. In many widely used microfluidic platforms including deterministic lateral displacement (DLD) devices, density matched, force free particles suspended in low Reynolds number flows encounter arrays of obstacles that potentially breaks the flow symmetry and alter their trajectories. Despite the prevalence of these devices, the physical mechanism responsible for particle deflection from encountering obstacle wall in strictly non inertial flows (Stokes flows) remains incompletely understood and is often attributed to short range contact interactions rather than hydrodynamic effects.

We show that the Dirac dressing of the fermion is equivalent to a shift of the gauge parameter. For every gauge, the gauge-dependent part is projected out of physical observables. After renormalization, the physical mass is the same for every dressing. The non-locality, compositeness and path dependence associated with the dressing are therefore not physical obstructions.

This note serves as an attempt towards the Jiang conjecture on the upper bound nilpotent orbits in the wavefront sets of representations in local Arthur packets of classical groups, which is a natural generalization of the well-known Shahidi conjecture, reflecting the relation between the structure of wavefront sets and the local Arthur parameters. Applying the character identities of local Arthur packets and the matching method of endoscopic liftings, we reduce the study of the upper bound to certain properties of the wavefront sets of the corresponding bi-torsor representations of general linear groups.

The primary analysis for longitudinal randomized controlled trials (RCTs) often compares treatment groups at the last timepoint, referred to as the landmark time. Assuming data are normally distributed and missing at random, the mixed model for repeated measures (MMRM) is widely used to conduct inference in terms of a mean difference. When outcomes violate normality assumption and/or the mean difference lacks a clear interpretation, we may quantify treatment effects using the probability that a treated participant would have a better outcome than (or win over) a control participant. For RCTs with missing data, one may apply the generalized pairwise comparison (GPC) procedure, which carries forward the results of a pairwise comparison from a previous timepoint. We propose first using ranks to converts each observation at a timepoint into a win fraction, reflecting the proportion of times that the observation is better than every observation in the comparison group. Then, we conduct inference for the win probability based on the win fractions using the MMRM to obtain the point and variance estimates. Simulation results suggest that our method performed much better than the GPC procedure. We illustrate our proposed procedure in SAS and R using data from two published trials.

We develop a tractable identification approach for strategic network formation models with both strategic link interdependence and individual unobserved heterogeneity (fixed effects). The key challenge is that endogenous network statistics (e.g. number of common friends) enter the link formation equation, while the mapping from model primitives to equilibrium network structure is generally intractable. Our approach sidesteps this difficulty using a ``bounding-by-$c$'' technique that treats endogenous covariates as random variables and exploits monotonicity restrictions to obtain identifying information. A central contribution is to develop a spectrum of fixed-effects handling strategies based on subnetwork configurations: tetrad-based restrictions that difference out all individual fixed effects, triad-based and weighted restrictions that combine ``difference-out'' and ``integrate-out'' steps by differencing out some fixed effects and profiling over the remainder conditional on observed characteristics, and general weighted cycle-based restrictions that unify these cases. We also provide point identification results. Preliminary simulations show that the approach can deliver informative bounds on the structural parameters.