We classify projective terminalizations of quotients of Fano varieties of lines on smooth cubic fourfolds by finite groups of symplectic automorphisms of the underlying cubic. We compute the second Betti number and the fundamental group of the regular locus. As a consequence, we identify two new deformation classes of four-dimensional irreducible holomorphic symplectic varieties with second Betti number equal to four and simply connected regular locus.

We classify Riemannian foliations of manifolds homeomorphic to CROSSes.

With the rise of artificial intelligence and machine learning, a new wave of private information is being flushed into applications. This development raises privacy concerns, as private datasets can be stolen or abused for non-authorized purposes. Secure function computation aims to solve such problems by allowing a service provider to compute functions of datasets in the possession of a a data provider without reading the data itself. A foundational primitive for such tasks is Bit Commitment (BC), which is known to be impossible to realize without added assumptions. Given the pressing nature of the topic, it is thus important to develop BC systems and prove their security under reasonable assumptions. In this work, we provide a novel quantum optical BC protocol that uses the added assumption that the network provider will secure transmission lines against eavesdropping. Under this added assumption, we prove security of our protocol in the honest but curious setting and discuss the hardness of Mayer's attack in the context of our protocol.

Thermal fluctuations play a central role in fluid dynamics at mesoscopic scales and must be incorporated into numerical schemes in a manner consistent with statistical mechanics. In this work, we develop a fluctuating lattice Boltzmann formulation based on an orthogonal central-moments-based representation. Stochastic forcing is introduced directly in the space of central moments (CMs) and consistently paired with mode-dependent relaxation, yielding a discrete kinetic model that satisfies the fluctuation-dissipation theorem exactly at the lattice level. Owing to the orthogonality of the basis, the equilibrium covariance matrix of the central moments is diagonal, and each non-conserved mode can be interpreted as an independent discrete Ornstein-Uhlenbeck process with variance fixed by equilibrium thermodynamics. The resulting formulation guarantees exact equipartition of kinetic energy at equilibrium, preserves Galilean invariance, and retains the enhanced numerical stability characteristic of CMs-based collision operators. Explicit fluctuating schemes are constructed for the D2Q9 and D3Q27 lattices. The extension to reduced-velocity discretisation is discussed too. A comprehensive set of numerical tests verifies correct thermalisation, isotropy of equilibrium statistics, and the expected scaling of velocity fluctuations with thermal energy, density, and relaxation time. In contrast to fluctuating BGK formulations, the present method remains stable and well posed in the over-relaxation regime, including in the immediate vicinity of the stability limit. These results demonstrate that CMs-based lattice Boltzmann methods provide a natural and robust framework for fluctuating hydrodynamics, in which dissipation, noise, and kinetic mode structure are consistently aligned at the discrete level.

We introduce the non-self OU sequence and the OU number for link diagrams. Using these, we give a lower bound for the number of necessary Reidemeister moves of type III between two diagrams of the same link.

The Casimir-Polder force is analyzed when an atom is moving at a constant velocity relative to a collection of translationally invariant macroscopic bodies with generic shapes and compositions. The interaction is described within an approach that accurately treats the atom-field coupling and accounts for the backaction from the environment onto the moving particle. Previously overlooked aspects are uncovered and linked to the nonequilibrium and nonconservative nature of the interaction. Specifically, we examine a behavior that can be understood by characterizing the underlying physical processes in terms of a motional-induced effective temperature. This phenomenon shares similarities with the Fulling-Davies-Unruh effect, opening new perspectives for the understanding of nonequilibrium physics at work in the system.

Federated Learning (FL) enables collaborative model training without exposing clients' private data, and has been widely adopted in privacy-sensitive scenarios. However, FL faces two critical security threats: curious servers that may launch inference attacks to reconstruct clients' private data, and compromised clients that can launch poisoning attacks to disrupt model aggregation. Existing solutions mitigate these attacks by combining mainstream privacy-preserving techniques with defensive aggregation strategies. However, they either incur high computation and communication overhead or perform poorly under non-independent and identically distributed (Non-IID) data settings. To tackle these challenges, we propose SRFed, an efficient Byzantine-robust and privacy-preserving FL framework for Non-IID scenarios. First, we design a decentralized efficient functional encryption (DEFE) scheme to support efficient model encryption and non-interactive decryption. DEFE also eliminates third-party reliance and defends against server-side inference attacks. Second, we develop a privacy-preserving defensive model aggregation mechanism based on DEFE. This mechanism filters poisonous models under Non-IID data by layer-wise projection and clustering-based analysis. Theoretical analysis and extensive experiments show that SRFed outperforms state-of-the-art baselines in privacy protection, Byzantine robustness, and efficiency.

This paper enhances the result of the work [G. Kozma, B. Tóth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free (or, doubly stochastic) random environment, with substantially relaxed ellipticity assumptions. Integrability of the reciprocal of the symmetric part of the jump rates is only assumed (rather than their boundedness, as in previous works on this type of RWRE). Relaxing ellipticity involves substantial changes in the proof, making it conceptually elementary in the sense that it does not rely on Nash's inequality in any disguise.

In this paper, we build a procedure that allows to establish regularity and controls in time for probabilistic solutions to PDEs. Probabilistic approaches to global wellposedness problems usually provide ensemble bounds on the solutions. These bounds are the main tools to ensure convergence procedures yielding the existence and uniqueness of global solutions. A question of interest consists in transforming such ensemble bounds into individual controls on the flow ; this, among other uses, gives valuable information on the long-time behavior of the solutions. Toward such question of bounds transformation, Bourgain initiated a successful procedure that exploited the local wellposedness of the PDE, with an estimate of the time of size-doubling. In this note, we construct an estimation procedure which relies on a different local requirement. It turns out that this substitute is flexible enough to be possible to fulfill with the help of the ensemble bound itself. For applications of the procedure, we are able to provide new pathwise controls on solutions to NLS equations.

In this work, we revisit several thin-crust approximations presented in the literature and compare them with the exact solutions of the Tolman--Oppenheimer--Volkoff (TOV) equations. In addition, we employ three different equations of state (EoSs), including one with a pasta phase, each based on a distinct theoretical framework: the variational method, relativistic Brueckner--Hartree--Fock theory, and relativistic mean-field theory. We emphasize that these approximations require only the TOV solutions for the core and the EoS properties at the core--crust interface; in our approach, only the energy density is needed. Finally, the relativistic approximation, as well as the Newtonian approximation with corrections, shows good agreement with the exact solutions. This indicates that a simple treatment of the crust is sufficient for structural purposes, independently of the uncertainties in the sub-nuclear equation of state, which are not very large. The unified EoS SINPA (relativistic mean-field theory), including the pasta phase, was used to study the thin-crust approximation, while degeneracy in the $M$--$R$ relation is demonstrated through: (i) anisotropic pressure in the modified TOV equations, (ii) the $f(R, L_m, T)$ gravity model, and (iii) dark matter admixture. As demonstrated, modifications to the description of gravitation introduce degeneracies in the mass--radius relation that are challenging to disentangle or quantify precisely.

We present a framework to \emph{certify} Hamilton--Jacobi (HJ) reachability learned by reinforcement learning (RL). Building on a discounted initial time \emph{travel-cost} formulation that makes small-step RL value iteration provably equivalent to a forward Hamilton--Jacobi (HJ) equation with damping, we convert certified learning errors into calibrated inner/outer enclosures of strict backward reachable tube. The core device is an additive-offset identity: if $W_λ$ solves the discounted travel-cost Hamilton--Jacobi--Bellman (HJB) equation, then $W_\varepsilon:=W_λ+ \varepsilon$ solves the same PDE with a constant offset $λ\varepsilon$. This means that a uniform value error is \emph{exactly} equal to a constant HJB offset. We establish this uniform value error via two routes: (A) a Bellman operator-residual bound, and (B) a HJB PDE-slack bound. Our framework preserves HJ-level safety semantics and is compatible with deep RL. We demonstrate the approach on a double-integrator system by formally certifying, via satisfiability modulo theories (SMT), a value function learned through reinforcement learning to induce provably correct inner and outer backward-reachable set enclosures over a compact region of interest.

Using molecular dynamics simulations of an incommensurate Au(111)/graphite interface, we investigate the conditions under which structural lubricity produces load-independent friction. We show that strict load independence occurs only in laterally infinite, area-filling contacts, where dissipation is governed by phonon-mediated viscous coupling and the shear stress scales linearly with sliding velocity. Finite contacts with explicit boundary terminations exhibit substantially higher friction yet remain load independent up to a critical load. Load dependence arises only when elastic out-of-plane deformation near the contact line exceeds a critical amplitude, activating additional dissipation channels. These results demonstrate that contact geometry and local elastic compliance, rather than normal load itself, determine the onset and breakdown of load-independent structural lubricity.

A systolic complex/bridged graph is fit when its (metric) intervals are "not too large". We prove that uniformly locally finite fit systolic complexes have Yu's Property A. In particular, groups acting properly on such complexes have Property A, (equivalently) they are exact, and (equivalently) they are boundary amenable. As applications we show that groups from a class containing all large-type Artin groups, as well as all finitely presented graphical $C(3)$--$T(6)$ small cancellation groups, and finitely presented classical $C(6)$ small cancellation groups are exact. We also provide further examples. Our proof relies on a combinatorial criterion for Property~A due to Špakula and Wright.

Refracton of particles (nucleons, nuclei, $γ$-quanta) in matter with polarized protons (nuclei) results in revealing coherent quasi-optical phenomenon of nuclear spin precession of particles (nuclei) in the pseudomagnetic field of matter with polarized spins and the phenomenon of birefringence of particles (nuclei) with spin $S \ge 1$. These phenomena can be observed and studied at complex NuclotronM-NICA. The similar effects for $γ$-quanta could be observed at LINAC accelerator. Quasi-optical coherent phenomena of spin rotation and dichroism are not caused by strong interactions only, the T-odd P-odd, T-odd P-even, T-even P-odd interactions also contribute. Limits for the value of these contributions at energies available at complex NuclotronM-NICA can be obtained by investigating all these phenomena. When studying polarized particles collisions, it is necessary to consider possible influences of quasi-optical phenomena of spin rotation and spin dichroism caused by nuclear precession and birefringence.

We study deformations of the geodesic distances on a domain of R N induced by a function called conformal factor. We show that under a positive reach assumption on the domain (not necessarily a submanifold) and mild assumptions on the conformal factor, geodesics for the conformal metric have good regularity properties in the form of a lower bounded reach. This regularity allows for efficient estimation of the conformal metric from a random point cloud with a relative error proportional to the Hausdorff distance between the point cloud and the original domain. We then establish convergence rates of order n^(-1/d) that are close to sharp when the intrinsic dimension d of the domain is large, for an estimator that can be computed in O(n^2 ) time. Finally, this paper includes a useful equivalence result between ball graphs and nearest-neighbors graphs when assuming Ahlfors regularity of the sampling measure, allowing to transpose results from one setting to another.

A standard type of uncertainty set in robust optimization is budgeted uncertainty, where an interval of possible values for each parameter is given and the total deviation from their lower bounds is bounded. In the two-stage setting, discrete and continuous budgeted uncertainty have to be distinguished. The complexity of such problems is largely unexplored, in particular if the underlying nominal optimization problem is simple, such as for selection problems. In this paper, we give a comprehensive answer to long-standing open complexity questions for three types of selection problems and three types of budgeted uncertainty sets. In particular, we demonstrate that the two-stage selection problem with continuous budgeted uncertainty is NP-hard, while the corresponding two-stage representative selection problem is solvable in polynomial time. Our hardness result implies that also the two-stage assignment problem with continuous budgeted uncertainty is NP-hard.

Sources of quantum correlated photons pairs bridging the 3um-4um Mid-infrared (MIR) band and Telecom/Near-Infrared/Visible band are of high importance for quantum technologies. Spontaneous Parametric Down Conversion is generally used for realizing such sources, but requires costly implementation platforms with reduced versatility. Here, we explore the potentialities of Spontaneous Four-Wave Mixing (SFWM) in all-solid Silicon On Insulator (SOI) waveguides thanks to an experimentally validated model and propose designs ensuring the production of correlated photon pairs bridging the 3um-4um Mid-infrared band and Telecom C-band. Choosing a pump with a wavelength in the range 2100nm-2210nm and a pulse duration of 5ps, we quantitatively performed simulations targeting a probability of photon pair generation per pulse of 0.05, and we found realistic conditions of utilization (2cm-length straight waveguides, intra-modal Four Wave Mixing with the fundamental TE00 mode) with a pump peak power in between 9.2mW and 32mW. A first design (wCOM) reaches a signal wavelength as high as 3.905um, which is situated in an atmospheric transparency window, while maintaining an idler in the Telecom C-band, making it of high interest for atmospheric Quantum Key Distribution. Two other designs wCH4 and wNO2 aim precise CH4 and NO2 gas sensing with a signal wavelength of 3265nm and 3461nm respectively. In terms of signal/idler wavelength separation, wCOM attains the value of 2364nm which is well above the current record of ~1125nm obtained in quantum regime with SFWM in all-solid SOI waveguides.

This paper motivates and develops a novel and focused approach to variable selection in linear regression models. For estimating the regression mean $μ=\E\,(Y\midd x_0)$, for the covariate vector of a given individual, there is a list of competing estimators, say $\hattμ_S$ for each submodel $S$. Exact expressions are found for the relative mean squared error risks, when compared to the widest model available, say $\mse_S/\mse_\wide$. The theory of confidence distributions is used for accurate assessments of these relative risks. This leads to certain Focused Relative Risk Information Criterion scores, and associated FRIC plots and FRIC tables, as well as to Confidence plots to exhibit the confidence the data give in the submodels. The machinery is extended to handle many focus parameters at the same time, with appropriate averaged FRIC scores. The particular case where all available covariate vectors have equal importance yields a new overall criterion for variable selection, balancing complexity and fit in a natural fashion. A connection to the Mallows criterion is demonstrated, leading also to natural modifications of the latter. The FRIC and AFRIC strategies are illustrated for real data.

Photonic integration offers the potential to bring complex high-performance optical systems to the form factor of a compact semiconductor chip. However, the range of system functions accessible critically depends on the extent to which free-space and fiber components can be made integrable. The ultralow-expansion cavity-stabilized laser$-$often used in precision metrology, high-resolution sensors, and advanced systems in atomic physics$-$is one component that currently has no direct parallel on chip. Lasers stabilized to photonically-integrated resonators exist, but exhibit considerably higher frequency noise and are accompanied by large levels of frequency drift. We demonstrate here a new architecture for an ultranarrow linewidth integrated laser based on stabilization to a sinusoidal fringe of an interferometer having a long 25-m unbalanced delay line. Our interferometric laser not only advances the state-of-the-art for on-chip lasers, but we in addition introduce an amplitude locking scheme that greatly suppresses the laser's long-term frequency wander. We achieve a record on-chip fractional frequency noise of $5.6 \times 10^{-14}$, corresponding to a linewidth of 12 Hz centered at 1348 nm. To showcase the utility of this laser, we divide the optical carrier to microwave frequencies, demonstrating the ability to outperform state-of-the-art quartz crystal oscillators by 15 dB or more.

We establish uniqueness and structural stability of a class of parallel flows in a 2D straight, infinite channel, under perturbations with either globally or locally bounded Dirichlet integrals. The significant feature of our result is that it does not require any restriction on the size of the flux characterizing the flow. Precisely, by extending and refining an approach initially introduced by J.B. McLeod, we demonstrate the continuous invertibility of the linearized operator at a generic Couette-Poiseuille solution that does not exhibit flow reversal. We then deduce local uniqueness of these solutions as well as their nonlinear structural stability under small external forces. Moreover, we prove the uniqueness of certain class of Couette-Poiseuille solutions ``in the large," within the set of solutions possessing natural symmetry. Finally, we bring an example showing that, in general, if the flow reversal assumption is violated, the linearized operator is no longer invertible.

In this letter, we develop a continuous fluid antenna (FA) framework for uplink channel estimation in cell-free massive multiple-input and multiple-output (CF-mMIMO) systems. By modeling the wireless channel as a spatially correlated Gaussian random field, channel estimation is formulated as a Gaussian process (GP) regression problem with motion-constrained spatial sampling. Closed-form expressions for the linear minimum mean squared error (LMMSE) estimator and the corresponding estimation error are derived. A fundamental comparison with discrete port-based architectures is established under identical position constraints, showing that continuous FA sampling achieves equal or lower estimation error for any finite pilot budget, with strict improvement for non-degenerate spatial correlation models. Numerical results validate the analysis and show the performance gains of continuous FA sampling over discrete baselines.

In this paper, we consider the action of the Goeritz group $\mathcal G_p$ for the genus two Heegaard splitting of the lens space $L(p,1)$ with $p\ge 2$ on the homology of the Heegaard surface. We describe the action in terms of matrices in $GL(4, \mathbb Z)$, and provide homology and homotopy obstructions for when two curves in the Heegaard surface are Goeritz equivalent.

The strong-field process of high-harmonic generation (HHG) has, in recent years, been treated from a quantum optical perspective in the emerging research area of strong-field quantum optics. These investigations show that HHG radiation is, in general, in a nonclassical state of light. However, the quantum optical treatment of HHG from topological nontrivial materials is missing. Here, we aim to address this gap in current knowledge and consider the quantum optical HHG response from the Su-Schrieffer-Heeger model, a finite chain of atoms with both a topologically trivial and nontrivial insulating phase, the latter supporting edge states. We find that HHG from both topological phases is squeezed at the band-gap frequency. Interestingly, while the harmonic spectrum discriminates the two topological phases of the system, the degree of squeezing only discriminates the phases for smaller chain lengths. We attribute this difference to a relative increase in overlap between bulk and edge states in the topological nontrivial phase for smaller systems. Our findings reveal how the strength of dipole couplings governs the nonclassical HHG response and define new research questions on topologically protected generation of quantum light in strong-field physics.

Using the Socrates photolysis scheme, we present newly calculated photolysis rates under modern Earth atmospheric conditions for species directly relevant to Earth and species relevant to different atmospheric compositions. We compare to a previous photolysis comparison exercise, namely PhotoComp 2011. Overall, we find good agreement between our results and previous work, with discrepancies usually caused by the implementation of temperature or pressure dependent quantum yields and updated cross-section data. We provide a new set of benchmark photolysis rates for additional species both for Solar irradiance and when irradiated by an M dwarf host star. In general, the higher actinic flux at far-UV and shorter wavelengths of the M dwarf compared to the Sun drives increased photolysis rates for reactions with high threshold energies. This work provides an updated set of benchmark results for further studies of photolysis in the Earth's atmosphere and that of other planets.

Let $\{ρ_λ:G_K\rightarrow GL_n(\overline E_λ)\}$ be a semisimple E-rational compatible system of a number field K. In a first step, building upon the theory of pseudocharacters [Ro96],[Ch14], we attach to each $ρ_λ$ an algebraic monodromy group $G_λ$ defined over $E_λ$ and also prove that the compatible system can be descended to a strongly E'-rational compatible system $\{ρ_{λ'}: G_K\rightarrow GL_n(E'_{λ'})\}$ for some finite extension E'/E. Secondly, we demonstrate that the maximal potentially abelian quotient of $G_λ$ is independent of $λ$ in a strong sense. Finally, as an application, we generalize a result of Patrikis--Snowden--Wiles on residual irreducibility of compatible systems.

Confinement epitaxy beneath graphene stabilizes exotic material phases by restricting vertical growth and altering lateral diffusion, conditions unattainable on bare substrates. However, achieving long-range interfacial order while maintaining high-quality graphene remains a significant challenge. Here, we demonstrate the synthesis of large-area quasi-free-standing monolayer graphene (QFMLG) via the intercalation of a two-dimensional (2D) Sn. While the triangular Sn(1x1) interface exhibits a robust metallic band structure, the decoupled QFMLG maintains charge neutrality, confirmed by photoemission spectroscopy. Using high-resolution Raman spectroscopy and microscopy, we distinguish between direct intercalation and diffusion-driven expansion, identifying the latter as the critical pathway to superior QFMLG crystalline quality. Temperature-dependent analysis reveals dynamical structural coupling between the decoupled QFMLG and the Sn interface, providing a novel degree of freedom for strain engineering. Beyond uncovering the diffusion-driven mechanism, this work establishes metal intercalation as an effective strategy for tailoring durable graphene-metal heterostructures with tunable properties for next-generation quantum materials platforms.

We present a detailed study of momentum broadening for high-energy partons traversing the Quark-Gluon Plasma (QGP), extending the Gyulassy-Levai-Vitev (GLV) formalism to include both all-path-length (APL) and sub-eikonal corrections. Traditional GLV calculations rely on the large separation distance and large formation time approximations, which are valid for large systems, but whose applicability in small systems such as pp and p/dA may fail. We derive analytic expressions for the momentum broadening distributions to first order in the opacity expansion, and perform a numerical investigation to quantify their impact. Our results show that the APL result reduces the low-momentum broadening and the sub-eikonal correction enhances the high-momentum broadening. The combined APL and sub eikonal correction show that the sub-eikonal correction mitigates the effect of the APL correction.

Diversity-Generating Retroelements (DGRs) create rapid, targeted variation within specific genomic regions in phages and bacteria. They operate through stochastic retro-transcription of a template region (TR) into a variable region (VR), which typically encodes ligand-binding proteins. Despite their prevalence, the evolutionary conditions that maintain such hypermutating systems remain unclear. Here we introduce a two-timescale framework separating fast VR diversification from slow TR evolution, allowing the dynamics of DGR-controlled loci to be analytically understood from the TR design point of view. We quantity the fitness gain provided by the diversification mechanism of DGR in the presence of environmental switching with respect to standard mutagenesis. Our framework accounts for observed patterns of DGR activity in human-gut \textit{Bacteroides} and clarifies when constitutive DGR activation is evolutionarily favored.

Ambient backscatter communication (AmBC) enables ultra-low-power connectivity by allowing passive backscatter devices (BDs) to convey information through reflection of ambient signals. However, the cascaded AmBC channel suffers from severe double path loss and multiplicative fading, while accurate channel state information (CSI) acquisition is highly challenging due to the weak backscattered signal and the resource-limited nature of BDs. To address these challenges, this paper considers an AmBC system in which the reader is equipped with a pixel-based fluid antenna system (FAS). By dynamically selecting one antenna position from a dense set of pixels within a compact aperture, the FAS-enabled reader exploits spatial diversity through measurement-driven port selection, without requiring explicit CSI acquisition or multiple RF chains. The intrinsic rate-energy tradeoff at the BD is also incorporated by jointly optimizing the backscatter modulation coefficient under an energy harvesting (EH) neutrality constraint. To efficiently solve this problem, a particle swarm optimization (PSO)-based framework is developed to jointly determine the FAS port selection and modulation coefficient on an optimize-then-average (OTA) basis. Simulation results show that the proposed scheme significantly improves the achievable rate compared with conventional single-antenna readers, with gains preserved under imperfect observations, stringent EH constraints, and different pixel spacings.

Channel measurements in MIMO systems hinge on precise synchronization. While methods for time and frequency synchronization are well established, maintaining real-time phase coherence remains an open requirement for many MIMO systems. Phase coherence in MIMO systems is crucial for beamforming in digital arrays and enables precise parameter estimates such as Angle-of-Arrival/Departure. This work presents and validates a simple local real-time phase calibration method for a digital array. We compare two different approaches, instantaneous and smoothed calibration, to determine the optimal interval between synchronization procedures. To quantitatively assess calibration performance, we use two metrics: the average beamforming power loss and the RMS cycle-to-cycle jitter. Our results indicate that both approaches for phase calibration are effective and yield RMS of jitter in the 2.1 ps to 124 fs range for different SDR models. This level of precision enables coherent transmission on commonly available SDR platforms, allowing investigation on advanced MIMO techniques and transmit beamforming in practical testbeds.