Excitons in the weakly interacting regime can be well-described by many-body perturbation theories such as the Bethe-Salpeter equation formalism. However, for materials such as transition metal dichalcogenides moiré heterostructures under strong illumination, with the emergence of dense excitonic states, the strong correlation and entanglement between electrons and holes may cause the many-body perturbation method to fail, and excitons may not be treated in the bosonic picture, but exhibit fermionic behaviors. In our work, we investigate the phase space where excitons, and the electrons and holes which constitute them, are weakly or strongly entangled, as well as their binding for different interaction profiles and the degree of localization of the electrons and holes. We corroborate the validity of using many-body perturbation theory in the exciton with interactions. Our work provides a general way to analyze the correlation and entanglement of multi-particle excitations in many-body systems, and gives a more comprehensive understanding of different phases for exciton entanglement and interactions in 1D systems.

A photon linear collider, the two-photon collision mode of an $e^+e^-$ linear collider, uses high-energy laser photons backscattered off the incoming electrons and positrons. The colliding-photon polarization is fully controllable through the polarizations of the initial electron and positron beams and laser photons. We investigate the impact of colliding-photon polarization on the observability of quantum entanglement in top-quark pair production at a photon linear collider. Constructing the spin density matrix of the $t\bar{t}$ two-qubit system from the helicity amplitudes, we demonstrate that a photon linear collider is an ideal machine to probe quantum entanglement and Bell nonlocality across the broad phase space of the process.

Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry this embedding in the Lisa proof assistant. On top of this foundation, we implement a proof-producing bidirectional type-checking tactic to compute proofs for typing judgements, with partial support for subtyping. We present examples showing how our approach enables automated reasoning for dependent types that is fully verified from set-theoretic axioms and deduction rules for schematic first-order logic with equality. Because types are merely sets, the resulting formalism supports equality that applies to all types and values and permits the usual substitution rules.

In this article, we introduce and investigate polynomial curvelets on spheres, which form a class of Parseval frames for $L^2(\mathbb{S}^{d-1})$, $d \geq 3$. The proposed construction offers a directionally sensitive multiscale decomposition and provides a sparse representation of spherical data. As a main result, we derive a sharp pointwise localization bound which shows that the frame elements decay rapidly away from their center of mass, making them a powerful tool for position-based analyses. In contrast to previous constructions, polynomial curvelets are not limited in their directional resolution. Consequently, the frames established in this article are particularly powerful when it comes to the analysis of localized anisotropic features, such as edges. To illustrate this point, we show that, given a suitable test signal that exhibits (higher-order) discontinuities at the boundary $\partial A$ of a spherical cap $A\subset \mathbb{S}^{d-1}$, the corresponding curvelet coefficients peak precisely when the analysis function matches some segment of the boundary $\partial A$, both in terms of position and orientation. Otherwise, the coefficients decay rapidly.

Stars form in cold, dense clouds embedded in galactic discs, but whether their formation is primarily regulated by gravitational collapse, turbulence, or stellar feedback remains unclear. Using four high-resolution dwarf galaxy simulations with and without supernova (SN) feedback and magnetic fields, we test how feedback regulates the supply of dense gas and, consequently, the star formation rate (SFR). Although the SFR does increase when SNe are turned off, this increase is only by a factor of a few. Instead, across all models, the theoretical maximum SFR originally proposed by Zuckerman and Palmer, defined as the ratio of the total dense gas mass to its mean free-fall time (${M_{\rm dense}}/{\tff}$), always exceeds the measured SFR by nearly two orders of magnitude. Moreover, the increase of the SFR in the case without SNe is accompanied by a nearly corresponding increase of the total dense gas mass ($M_{\rm dense}$), such that the dense-gas depletion time, $τ\equiv {\rm SFR}/M_{\rm dense}$, decreases by only $\sim 33\%$ in the hydrodynamical case and by about 55\% in the magnetohydrodynamical models. This indicates that SN feedback does not primarily act by slowing the collapse of dense gas, but instead by limiting how much diffuse gas can be converted into dense gas. Our results suggest that the main contribution to the regulation of the SFR, at least in dwarf galaxies, may arise from stabilization by galactic rotation, rather than by SN feedback.

Structured meshes, composed of quadrilateral elements in 2D and hexahedral elements in 3D, are widely used in industrial applications and engineering simulations due to their regularity and superior accuracy in finite element analysis. Generating high-quality structured meshes, however, remains challenging, especially for complex geometries and singularities. Field-guided approaches, which construct cross fields in 2D and frame fields in 3D to encode element orientation, are promising but are typically defined on discrete meshes, limiting continuity and computational efficiency. To address these challenges, we introduce \emph{NeurFrame}, a neural framework that represents frame fields continuously over the domain, supporting infinite-resolution evaluation. Trained in a self-supervised manner on discrete mesh samples, NeurFrame produces smooth, high-quality frame fields without relying on dense tetrahedral discretizations. The resulting fields simultaneously guide high-quality quadrilateral surface meshes and hexahedral volumetric meshes, with fewer and better-distributed singularities. By using a single network, NeurFrame also achieves lower computational cost compared to prior self-supervised neural methods that jointly optimize multiple fields.

High-dimensional quantum key distribution (HD-QKD) offers a promising approach to enhance secret key rates beyond conventional binary-encoded QKD, addressing the growing demand for secure data transmission. However, the practical application of most HD-QKD systems has been hindered by their complexity, as they require the preparation and detection of quantum states in large Hilbert spaces. Here, we design and experimentally realize a directly modulated laser platform for HD-QKD. It operates at a repetition rate of 312.5 MHz, yielding a remarkably simple and scalable architecture. Through which, we achieve a record transmission distance of 250 km for HD-QKD, demonstrating its feasibility for long-distance quantum communication. Furthermore, we witness that the four-dimensional states outperform their two-dimensional counterpart in secret key rate, highlighting the practical advantage of high-dimensional encoding. This simple and scalable approach shows strong potential for chip-scale integration.

For given smooth functions $(f_1,\dots,f_n)$ on $M$, Fukaya and Oh showed that the moduli space of pseudoholomorphic disks in $T^*M$ which are bounded by Lagrangian sections $\{L_i^ε=\operatorname{graph}(εdf_i)\}$ is diffeomorphic to the moduli space of gradient trees in $M$ which consist of gradient curves of $\{f_i-f_j\}$. When the image of the pseudoholomorphic disk $w_ε$ is a polygon in $\mathbb{C}\simeq T^*\mathbb{R}$, we can describe $w_ε$ by a Schwarz-Christoffel map. In \cite{S25}, we proved that pseudoholomorphic disks $w_ε$ converge to the gradient tree in the limit $ε\to+0$ when the image of $w_ε$ is a generic convex quadrilateral. In this paper, we show such a convergence for any convex quadrilaterals by studying the non-generic case.

Movable antenna (MA) systems have emerged as a promising technology for future wireless communication systems. The movement of antennas gives rise to mutual coupling (MC) effects, which have been previously ignored and can be exploited to enhance the capacity of multiple-input multiple-output (MIMO) systems. To this end, we first model an MA-enabled point-to-point MIMO communication system with MC effects using a circuit-theoretic framework. The capacity maximization problem is then formulated as a non-concave optimization problem and solved via a block coordinate ascent (BCA)-based algorithm. The subproblem of optimizing MA positions is challenging due to the presence of the analytically intractable MC matrices. To overcome this difficulty, we develop a trust region method (TRM)-based algorithm to optimize MA positions, wherein Sylvester equations are employed to compute the derivatives of the inverse square roots of the MC matrices. Simulation results show significant capacity gains from leveraging MC effects, primarily due to customizable MC matrices and superdirectivity.

Realizing advanced functionalities with high efficiencies via reconfigurable intelligent surfaces (RISs) and reflectarrays requires configurations with strong electromagnetic non-local responses. The traditional approach to achieving strong non-locality has relied on modeling and synthesizing RISs with diagonal load impedance matrices composed of highly dense subwavelength structuring of arrays. In such designs, non-locality is not directly tunable, thereby limiting design flexibility and operational efficiency. This work proposes a rigorous co-simulation-based design and optimization framework for beyond-diagonal RISs with directly controllable non-locality. The co-simulation approach is based on non-local load and coupling networks, integrating electromagnetic antenna characterization with circuit-level modeling of cascaded load networks. The method benefits from additional degrees of freedom by generalizing the conventional diagonal load impedance matrix to a non-diagonal form through a non-local coupling network model. Wide-angle anomalous reflectors based on finite linear and infinite periodic arrays are designed and numerically validated, demonstrating that the proposed non-local loads embedded in realistic cascaded load networks with associated circuitry achieve significantly higher reflection efficiencies than diagonal load matrices at the given element density. Alternatively, for a fixed efficiency target, the required element density can be significantly reduced for efficient synthesis of beyond-diagonal RIS without compromising the performance of wave manipulations.

We present an efficient algorithm for least-squares constrained nuclear norm minimization, a computationally challenging problem with broad applications. Our approach combines a level set method with secant iterations and a proximal generation method. As a key theoretical contribution, we establish the nonsingularity of the Clarke generalized Jacobian for a general class of projection norm functions over closed convex sets. This property and the (strong) semismoothness of our value function yield fast local convergence of the secant method. For the resulting nuclear norm regularized subproblems, we develop a proximal generation method that exploits low-rank structures without compromising convergence. Extensive numerical experiments demonstrate the superior performance of our approach compared to state-of-the-art methods.

Determining the Hubble constant tension requires alternative strategies, and multiply imaged quasars, with their intermediate redshifts, can potentially be used in this regard. We provide a currently complete catalogue of spectroscopically confirmed lensed quasars with ESA/{\it Gaia} astrometry and photometry, as well as redshifts and time delays when available. In addition to the improved astrometry, the catalogue increases the number of lensed quasars by a factor of 1.5 (now 364, of which 277 are doubles and 87 are quads or triples) and significantly increases the number of lensing galaxies detected (now 218), which represents a major step forward. Redshifts are provided for 347 quasars and 188 deflectors. A completely new table of time delays, required for estimates of $H_0$, is presented, with 195 time delays from 73 systems. {\it Gaia} absolute astrometry is sub-milliarcsecond and covers the entire sky. Future {\it Gaia} data releases will provide long-term photometry, which should provide many more time delays. The catalogues as presented here enable machine-learning techniques to be trained and tested and subsequently applied to the {\it Gaia} data releases. Finally, we derive simple but homogeneous models of the 18 quadruply imaged quasars for which images of all four components are presented in {\it Gaia} DR3.}

A stochastic program typically involves several parameters, including deterministic first-stage parameters and stochastic second-stage elements that serve as input data. These programs are re-solved whenever any input parameter changes. However, in practical applications, quick decision-making is necessary, and solving a stochastic program from scratch for every change in input data can be computationally costly. This work addresses this challenge for two-stage stochastic linear programs (2-SLPs) with varying right-hand sides for the first-stage constraints. We construct a Piecewise Linear Difference-of-Convex (PLDC) policy by leveraging optimal bases from previous solves. This PLDC policy retains optimal solutions for previously encountered parameters and provides high-quality solutions for new right-hand-side vectors. Our proposed policy directly applies to the extensive form of the 2-SLP. When stage decomposition algorithms, such as the L-Shaped and Stochastic Decomposition, are applied to solve the 2-SLPs, we develop L-Shaped- and Stochastic-Decomposition-guided static procedures to train the policy. We also develop a sequential procedure that iteratively tracks the quality of the learned policy and incorporates new basis information to improve it. We assess the performance of our policy through analytical and numerical techniques. Our compelling experimental results show that the policy prescribes solutions that are feasible and optimal for a significant percentage of new instances.

We present a census of local active galactic nuclei (AGN) at a redshift of $z\leq0.025$ selected using the high-ionization [Ne v] $\lambda14.32\,μ$m emission line from the Infrared Database of Extragalactic Observables from Spitzer (IDEOS). We identify 103 sources with detected [Ne v] emission, which we regard as AGN within the volume. This sample represents $\sim18\%$ of the galaxy population within this redshift range, consistent with AGN fractions derived using other selection techniques. We investigate the biases and properties of this [Ne v]-selected AGN sample by comparing it with traditional AGN selection methods based on hard X-ray, optical, and mid-infrared colors. We find that our selection significantly misses AGN with underdeveloped narrow line regions (NLRs), which account for approximately half of the AGN identified by NLR-independent methods. However, approximately $\sim10\%$ of our sample are undetected in optical diagnostics, while $\sim40\%$ are missed by hard X-rays and $\sim70\%$ by infrared continuum. Notably, $\sim15\%$ of our AGN are missed by all classical methods, constituting a population of previously unidentified AGN revealed solely by the [Ne v] emission line. Based on our analysis, we show that this line can efficiently select heavily Compton-thick and host-dominated AGN systems. Our analysis also yields mean bolometric luminosities of $\log(L_{\rm bol}/{\rm erg~s^{-1}})=44.5\pm0.7$, black hole masses of $\log(M_{\rm BH}/M_{\odot})=7.3\pm0.6$, and Eddington ratio of $λ_{\rm Edd}=0.15\pm0.11$. Our sample harbors AGN with comparable luminosities but systematically lower-mass black holes accreting at higher Eddington ratios than those in the hard X-ray-selected sample. This suggests that our AGN may represent local analogs of the rapidly growing SMBH population prevalent at cosmic noon.

Equivariant Loday constructions are a means for providing geometric interpretations of equivariant homology theories. They are usually constructed for a simplicial $G$-set and a $G$-Tambara functor. We study situations where -- depending on the isotropy subgroups occurring in the simplicial $G$-set -- one can work with $H$-Tambara functors for a suitable subgroup $H$ of $G$. We apply this to give an interpretation of Real Hochschild homology of discrete $E_σ$-rings as equivariant Loday constructions where we consider $2m$-gons with a geometrically defined action of the dihedral groups $D_{2m}$ for all $m \geq 1$. The action of symmetric groups on $1$-skeleta of permutohedra also gives examples with isotropy groups $C_2$.

We study a nonlocal adhesion model for two interacting tumor cell phenotypes, combining diffusion, pairwise interactions, and random phenotypic switching. The system admits a microscopic diffusion--jump particle description whose mean-field limit is a nonlinear McKean--Vlasov equation on a product space encoding position and internal state. We first establish uniform-in-time propagation of chaos in the weak-interaction regime using a coupling approach that combines reflection coupling for the diffusion with an optimal coupling of the spin-flip dynamics. As a byproduct, we obtain exponential long-time contraction for the nonlinear McKean--Vlasov equation in the first-order Wasserstein distance, implying uniqueness of the stationary distribution. We also investigate the complementary regime of strong interactions, where the homogeneous equilibrium may lose stability through a bifurcation mechanism.

Neutrinos are the most abundant fermions in the Universe and influence the formation of large-scale structure through both their non-zero masses and a possible chemical potential which can be described by a single asymmetry parameter. While most previous studies have focused on the impact of the neutrino mass, the role of neutrino asymmetry remains comparatively unexplored. In this work, we investigate how massive neutrinos ($M_ν=0-0.24\,\mathrm{eV}$) with a non-zero asymmetry parameter ($η^{2}=0-0.8$) modify the halo mass function (HMF) and halo bias using cosmological N-body simulations with cosmological parameters consistently refitted to CMB observations. We find that at all redshifts, neutrino mass suppresses the abundance of massive halos, whereas neutrino asymmetry enhances the HMF over a broad mass range. At z=0, the abundance of the most massive halos is reduced by up to ~30% in the largest-mass case ($M_ν=0.24\,\mathrm{eV}$), while neutrino asymmetry ($η^{2}=0.8$) produces a maximum ~5% enhancement. These effects become increasingly pronounced at higher redshifts: by z=4 and z=9, the enhancement induced by neutrino asymmetry reaches ~25% and ~75%, respectively, while the corresponding suppression due to neutrino mass deepens to below ~40% and ~70% of the massless case. For halo bias, we find that halos with masses above $10^{13.4}\,\mathrm{M_\odot}$ exhibit an enhanced large-scale bias due to neutrino mass, reaching up to ~5% at z=0, while neutrino asymmetry reduces the bias by a few percent on linear scales. These trends strengthen with redshift, with the enhancement and suppression growing to ~15% and ~10% at z=2, respectively. Linear bias models provide an adequate, though not exact, description of halo bias in massive-neutrino cosmologies. Our results demonstrate that halo abundance and clustering offer sensitive probes of both neutrino mass and asymmetry.

Integrated sensing and communication (ISAC) is poised to redefine the landscape of wireless networks by seamlessly combining data transmission and environmental sensing. However, ISAC systems remain susceptible to eavesdropping, especially under uncertainty in eavesdroppers' channel state information, which can lead to secrecy outages. On the other hand, diverse and complex sensing performance requirements further complicate resource optimization, often requiring custom solutions for each scenario. To this end, this paper introduces a unified optimization framework that holistically addresses both the worst-case user secrecy rate and the sum secrecy rate across multiple users. Besides putting the two commonly used objectives into a single but flexible objective function, the framework accurately controls secrecy outage probabilities while accommodating a broad spectrum of sensing constraints. To solve such a general problem, we integrate the sensing requirements into the objective function through an auxiliary variable. This enables efficient alternating optimization and the proposed approach is theoretically guaranteed to converge to at least a stationary point of the original problem. Extensive simulation results show that the proposed framework consistently achieves higher optimized secrecy rates under various sensing constraints compared to existing methods. These results underscore the proposed unified framework's superiority and versatility in secure ISAC systems.

The rapid proliferation of unmanned aerial vehicle (UAV) applications imposes stringent requirements on continuous and reliable communication coverage in low-altitude airspace. Conventional cellular systems built upon fixed-position antennas (FPAs) are inherently constrained by static array geometries and limited mechanical degrees of freedom, which severely restrict their ability to adapt to highly dynamic three-dimensional (3D) propagation environments. Movable antenna (MA) technology has recently emerged as a promising paradigm to overcome these limitations by actively reconfiguring electromagnetic radiation characteristics through controllable antenna positioning and array orientation, thereby enabling flexible spatial coverage adaptation. To systematically quantify the airspace coverage capability of MA-enabled systems, this paper formulates a spatial coverage maximization problem over a discretized 3D voxel space. For each voxel, the received signal-to-noise ratio (SNR) is maximized via joint optimization of the MA's 3D positions and beamforming matrices. To efficiently solve the resulting non-convex problem, a hybrid particle swarm optimization and simulated annealing framework is developed to search for high-quality antenna configurations. Simulation results demonstrate that the proposed MA design framework substantially outperforms conventional FPA-based schemes in terms of spatial coverage, achieving coverage rates of 26.8% and 29.65% for airspace below 300m and 600m, respectively. Moreover, further coverage enhancement can be attained by incorporating mechanical tilt adjustment, highlighting the strong potential of MA technology for reliable low-altitude communication coverage.

We provide a rigorous mathematical analysis of a coupled system consisting of a floating platform in a fluid of finite depth, clamped to a flexible Euler-Bernoulli beam. The superstructure supports a rigid tip mass at its free end, resulting in a complex multi-physics interaction between potential flow, rigid-body dynamics, and elasticity. We derive the governing equations by coupling the linearised water-wave equations with the dynamics of the floating foundation and the tip-mass payload. The resulting system is formulated as an abstract Cauchy problem in an appropriate Hilbert space. By employing C0-semigroup theory, we establish its well-posedness. Finally, we derive the exact physical energy balance and prove the energy conservation of the system.

In this paper, we investigate the quantum gravity effects on the tunneling of particles and gravity's rainbow across the event horizon of Kerr-Newman black hole (KNBH) surrounded by the quintessence. The aspect of quantum gravity has been introduced by applying the Generalized Uncertainty Principle (GUP) to the Klein-Gordon equation and the Dirac equation of scalar and fermion particles. By solving the Generalized Klein-Gordon and Dirac equations obeyed by scalar and fermion particles, corrections to the Hawking temperature of the KNBH in the presence of quintessence is discussed. The tunneling of fermions is also examined using the modified Hamilton-Jacobi equation also known as modified Rarita-Schwinger equation, and the corrected Hawking temperature is determined. The corrected Hawking temperature of the KNBH surrounded by quintessence is found to be dependent not only on the properties of the black hole but also on the quantum numbers of the emitted particles and quintessence. Then, we explored the KNBH surrounded by quintessence within the framework of gravity rainbow using rainbow functions. In the context of rainbow functions in loop quantum gravity, we derive the Hawking temperature, heat capacity, equation of state parameters, and entropy for the KNBH surrounded by quintessence. It is found that these quantities are influenced by both the quintessence and the rainbow gravity.

During collaborative board games, cohesion represents a key aspect to define a well functionning group. From the success of the task to the developement of interpersonal relationship, this concept covers many aspects of group dynamics. The goal of our work is to investigate the factors that impact cohesion in a group, and specifically the relevant social skills that improve collaboration between multiple entities. In this article, we focus on the role of embodiement on different aspects of an interaction. We propose an experimental protocol, based on a collected corpus of humans playing a collaborative board game, to study how different agents' embodiment affect the perception of these agents and of the group as a whole. We conclude by presenting an outline of the problematics of the conception of the protocol and of multi-agent system related challenges.

We consider in this paper the problem of computing a nonnegative low-rank approximation of the rightmost eigenpair of a linear matrix-valued real operator. We propose an algorithm based on the time integration of a suitable differential system, whose solution is parametrized according to a nonnegative factorization. The conservation of the nonnegativity is theoretically motivated by the Perron-Frobenius theorem, while the computation of the rightmost eigenpair is motivated by two applications: (1) a new class of Markov chains, which we called Markov grids, whose transition matrices can be decomposed as the sum of Kronecker products, and (2) spatially structured systems in growth-diffusion operators arising for example in population and epidemic dynamics. Theoretical analysis and computational experiments show the effectiveness of the algorithm compared to standard approaches.

This paper studies the central limit theorems (CLTs) for linear spectral statistics (LSSs) of general sample covariance matrices, when the test functions belong to $C^3$, the class of functions with continuous third order derivatives. We consider matrices of the form $B_n=(1/n)T_p^{1/2}X_nX_n^{*}T_p^{1/2},$ where $X_n= (x_{i j} ) $ is a $p \times n$ matrix whose entries are independent and identically distributed (i.i.d.) real or complex random variables, and $T_p$ is a $p\times p$ nonrandom Hermitian nonnegative definite matrix with its spectral norm uniformly bounded in $p$. By using Bernstein polynomial approximation, we show that, under $\mathbb{E}|x_{ij}|^{8}<\infty$, the centered LSSs of $B_n$ have Gaussian limits. Under the stronger $\mathbb{E}|x_{ij}|^{10}<\infty$, we further establish convergence rates $O(n^{-1/2+κ})$ in Kolmogorov--Smirnov $O(n^{-1/2+κ})$, for any fixed $κ>0$.

The paper is concerned with the strict-feedback form of hyperbolic distributed-parameter systems. Such a system structure is well known to be the basis for the recursive backstepping control design for nonlinear ODEs and is also reflected in the Volterra integral transformation used in the backstepping-based stabilization of parabolic PDEs. Although such integral transformations also proved very helpful in deriving state feedback controllers for hyperbolic PDEs, they are not necessarily related to a strict-feedback form. Therefore, the paper looks at structural properties of hyperbolic systems in the context of controllability. By combining and extending existing backstepping results, exactly controllable heterodirectional hyperbolic PDEs as well as PDE-ODE systems are mapped into strict-feedback form. While stabilization is not the objective in this paper, the obtained system structure is the basis for a recursive backstepping design and provides new insights into coupling structures of distributed-parameter systems that allow for a simple control design. In that sense, the paper aims to take backstepping for PDEs back to its ODE origin.

Water mediates a broad range of chemical reactions, including proton transfer, bond rearrangement, and conventional radical processes, defining a continuously expanding repertoire of intrinsic reactivity. However, roaming, a fundamental reaction mechanism that a departing fragment bypasses the minimum energy path to recombine, has not been identified in water itself. Here, we report the discovery of hydrogen-atom roaming reactions in water clusters through high-precision ab initio calculations of first-principles. A neutral hydrogen atom departs as a radical, roams across the flat potential energy surface, and recombines along pathways that connect the same reactants and products as known hydrogen-bond network rearrangements. Interpretable machine learning analysis identifies the reactant dipole moment as the decisive switch governing whether roaming occurs, underpinned by exchange-repulsion and electrostatic interactions. Once roaming is initiated, polarizability and spin population determine barrier heights, while the charge distribution of the roaming hydrogen atom governs barrier widths, collectively shaped by electrostatic, orbital, and dispersion contributions. These findings establish hydrogen-atom roaming as a previously unrecognized intrinsic reaction class in water, complementing a fundamental dimension to the mechanistic picture of water reactivity.

We present a quantum code-division multiple-access (q-CDMA) framework for multiuser continuous-variable quantum key distribution (CV-QKD) over a shared quantum channel. The proposed architecture employs chaotic phase shifters to encode and decode quantum states, enabling efficient multiplexing and demultiplexing of signals generated by multiple transmitters. In this scheme, quantum states from different users are chaotically phase-encoded and combined through a beam splitter network before transmission. At the receiver, synchronized chaotic phase shifters are used for decoding, followed by an inverse beam splitter structure to recover the individual user signals. This chaotic synchronization allows reliable state recovery and secure key establishment between each sender-receiver pair. For an arbitrary number of users, we derive the input-output quadrature relations describing the multiuser q-CDMA CV-QKD system. Using this model, we evaluate the achievable secret key rate under collective attacks with reverse reconciliation. We further investigate the impact of key system parameters including the correction factor, multiuser interference noise, environmental noise, and channel transmittance. A comparison between the asymptotic and finite-size regimes is also presented to highlight the associated performance trade-offs. These results provide a theoretical framework for assessing the performance of q-CDMA-based CV-QKD and support the development of scalable and secure multiuser quantum communication networks.

It is well-known that Chvátal and Erdős stated that any graph of order at least three whose independence number is no greater than its connectivity is Hamiltonian; that any graph whose independence number is no greater than its connectivity minus one is Hamilton-connected; and that any graph whose independence number is no greater than its connectivity plus one is traceable. Kaneko and Yoshimoto [J. Graph Theory 43 (2003) 269--279] showed that every 4-connected graph of order at least six has a 2-factor with two components if its independence number is no greater than its connectivity. In this paper, we show that any connected graph of order at least three times its connectivity plus three has a 2-factor with at most two components, except for one exceptional class, if its independence number is no greater than its connectivity plus one. Our result is best possible.

We introduce the concept of Randomly Modulated Gaussian Processes as a unifying framework for modeling, analyzing and classifying anomalous diffusion models in heterogeneous media. This formulation incorporates correlations in the displacements together with correlated fluctuations of their amplitudes. Most known models of anomalous diffusion (including Continuous-Time Random Walk and fractional Brownian motion) and random diffusivity can be described and generalized within this framework. Moreover, the unified view identifies the main statistical properties to be probed experimentally for a reliable classification of diffusive dynamics. The proposed matrix formulation facilitates the computation of the first four moments and allows for a systematic statistical characterization of the considered processes. The necessary and sufficient conditions are provided for the emergence of anomalous diffusion. General expressions for the non-Gaussian parameter, ergodicity breaking parameter and covariance of squared increments are derived. Biological applications of this framework for systematic analysis and biophysical interpretations of experimental single-particle trajectories are discussed.

We investigate synchronization by noise for stochastic differential equations (SDEs) driven by a fractional Brownian motion (fbm) with Hurst index $H\in(0,1)$. Provided that the SDE has a negative top Lyapunov exponent, we show that a weak form of synchronization occurs. To this aim we use tools from stochastic dynamical systems, random dynamical systems and a support theorem for SDEs driven by fractional noise.~In particular, we characterize the support of an invariant measure of a random dynamical system in a non-Markovian setting.