This paper presents a method for predictive aggregation of the available flexibility at the residential unit level into a flexibility chart that represents the admissible active and reactive powers, along with the associated flexibility value. The method is also combined with centralized optimization to design a predictive privacy-preserving control scheme to manage low-voltage distribution systems in real-time. Similarly to hierarchical control strategies, this approach divides the optimization horizon into a real-time stage, responsible for decisions in the current market period, and an operational planning stage, which deals with decisions outside of this interval. First, a multiparametric optimization problem is solved offline at the residential unit level. Then, an operational planning problem, also formulated as a parametric optimization problem, is solved to account for the forecasts. The method generates the desired flexibility chart by combining the results of these two problems with measurements. The resulting approach is compatible with real-time control requirements, as heavy computations are performed offline in a decentralized manner. By linking real-time flexibility assessment with energy scheduling, our approach enables efficient and cost-effective management of low-voltage distribution systems. We validate this method on a low-voltage network of 43 buses by comparing it with a fully centralized optimization formulation with perfect foresight and a future-agnostic aggregation method.

We consider the quantitative description of a many-particle gas of interacting abelian anyons in the plane, confined in a trapping potential. If the anyons are modeled as bosons with a magnetic flux attachment, and if the total magnetic flux is small compared to the number of particles, then an average-field description becomes appropriate for the low-energy collective state of the gas. Namely, by means of a Hartree-Jastrow ansatz, we derive a two-parameter Chern-Simons-Schrödinger energy functional which extends the well-known Gross-Pitaevskii / nonlinear Schrödinger density functional theory to the magnetic (anyonic) self-interaction. One parameter determines the total number of self-generated magnetic flux units in the system, and the other the effective strength of spin-orbit self-interaction. This latter interaction can be either attractive/focusing or repulsive/defocusing, and depends both on the intrinsic spin-orbit interaction and the relative length scale of the flux profile of the anyons. Densities and energies of ground and excited states are studied analytically and numerically for a wide range of the parameters and align well with a sequence of exact nonlinear Landau levels describing Jackiw-Pi self-dual solitons. With increasing flux, counter-rotating vortices are formed, enhancing the stability of the gas against collapse. Apart from clarifying the relations between various different anyon models that have appeared in the literature, our analysis sheds new light on the many-anyon spectral problem, and also exemplifies a novel supersymmetry-breaking phenomenon.

We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral methods for partial differential equations. Mesh-based methods require a curved mesh for high-order convergence, which can be difficult to reliably obtain on many surfaces, and most meshfree methods require the ability to integrate a set of functions (such as radial basis functions) exactly on the domain of interest; these integrals are generally not known in closed form on most surfaces. We describe two methods for integrating on arbitrary, piecewise-smooth surfaces with or without boundary. Our approaches do not require a particular arrangement of points or an initial triangulation of the surface, making them completely meshfree. We also show how the methods can be extended to handle singular integrals while maintaining high accuracy without changing the point density near singularities.

As a fundamental metric for quantifying quantum advantage in non-local games, the quantum chromatic number reveals the power of entanglement in distributed tasks. In this paper, we investigate this parameter for $q$-ary Hamming graphs and a generalization of Hadamard graphs. Our main results establish an exponential separation between the quantum and classical chromatic numbers for both graph families, and determine the exact quantum chromatic numbers in several regimes. Our analysis builds on known upper and lower bounds via modulus-one orthogonal representations and minimum eigenvalues, respectively. Previous results for Hamming graphs $H(n,q,d)$ were restricted to specific cases: the minimum eigenvalue was only identified for $d > (q-1)n/q$, while modulus-one orthogonal representations had only been constructed for the binary case ($q=2$) with $d \ge n/2$. In this work, we fill several gaps in the existing literature by developing a linear programming approach to construct modulus-one orthogonal representations for arbitrary relative distances, and using the trace method to determine the minimum eigenvalues in the regime where $d$ lies slightly below the threshold $(q-1)n/q$. For generalized Hadamard graphs over cyclic groups and finite fields, by determining their minimum eigenvalues, we show that the spectral lower bound matches the natural upper bound on the quantum chromatic number. On the classical side, we apply the method of forbidden intersection pattern of Frankl and Rödl to obtain an exponential lower bound on the chromatic number, thereby quantifying the separation between the quantum and classical quantities.

In this note, we prove a 2-systolic inequality on compact positive scalar curvature Kähler surfaces admitting a nonconstant holomorphic map to a positive-genus compact Riemann surface. According to the classification of positive scalar curvature Kähler surfaces, any such surface must be a ruled surface fibred over a complex curve with positive genus.

Let S denote the family of all subspaces of the plane that are graphs of functions from the real line R to itself. We prove that S has two subfamilies G,H of spaces such that the cardinality of G is c (the cardinality of the continuum) and the cardinality of H is 2^c, every space in the family G is completely metrizable, each element of H is a dense subset of the plane and the elements of the union of G and H are pairwise non-embeddable (i.p. pairwise non-homeomorphic) subspaces of the plane. On the other hand, the family S contains precisely countably infinitely many locally connected spaces up to homeomorphism, and if X,Y are such spaces then X is embeddable into Y. Furthermore, if T is a topology on the set R finer than the Euclidean topology and the space (R,T) is separable and locally connected then the space is locally compact and homeomorphic to some space in S. In a very natural way we establish a complete classification of all these refinements T of the real line.

Freehand sketches exhibit unique sparsity and abstraction, necessitating learning pipelines distinct from those designed for images. For sketch learning methods, the central objective is to fully exploit the effective information embedded in sketches. However, there is limited research on what constitutes effective sketch information, which in turn constrains the performance of existing approaches. To tackle this issue, we first proposed the Multi-Level Sketch Representation Scheme to identify the effective information. The scheme organizes sketch representation into three levels: sketch-level, stroke-level, and point-level. This design is based on the granularity of analytical elements, from coarse (sketch-level) to fine (point-level), thereby ensuring more comprehensive coverage of the sketch information. For each level, we conducted theoretical analyses and experimental evaluations to identify and validate the effective information. Building on the above studies, we developed SDGraph, a deep learning architecture designed to exploit the identified effective information across the three levels. SDGraph comprises two complementary modules: a Sparse Graph that treats strokes as nodes for sketch-level and stroke-level representation learning, and a Dense Graph that treats points as nodes for sketch-level and point-level representation learning. Both modules employ graph convolution along with down-sampling and up-sampling operations, enabling them to function as both encoder and decoder. Besides that, an information fusion module bridges the two graphs to further enhance feature extraction. SDGraph supports a wide range of sketch-related downstream tasks, achieving accuracy improvements of 1.15\% and 2.30\% over the state-of-the-art in classification and retrieval, respectively, and 32.93\% improvement in vector sketch generation quality.

We study the problem of exact synthesis for the Clifford+R gate set and give the explicit structure of the underlying Bruhat-Tits building for this group. In this process, we also give an alternative proof of the arithmetic nature of the Clifford+R gate set.

Sub-Neptunes with planetary radii of $R_{p} \simeq 2-4 R_{\oplus}$ are the most common planets around solar-type stars in short-period ($P<100$ d) orbits. It is still unclear, however, what their most likely composition is, that is whether they are predominantly gas dwarfs or water worlds. The sub-Neptunes orbiting bright host stars are very valuable because they are suitable for atmospheric characterization, which can break the well-known degeneracy in planet composition from the planet bulk density, when combined with a precise and accurate mass measurement. Here we report on the characterization of the sub-Neptune TOI-5789 c, which transits in front of the bright ($V=7.3$ mag and $K_{s}=5.35$ mag) and magnetically inactive K1V dwarf HIP 99452 every 12.93 days, thanks to TESS photometry and 141 high-precision radial velocities obtained with the HARPS-N spectrograph. We find that its radius, mass, and bulk density are $R_{c}=2.86^{+0.18}_{-0.15} R_\oplus$, $M_{c}=5.00 \pm 0.50 M_\oplus$, and $ρ_{c}=1.16 \pm 0.23$ g cm$^{-3}$, and we show that TOI-5789 c is a promising target for atmospheric characterization with both JWST and, in the future, Ariel. By analyzing the HARPS-N radial velocities with different tools, we also detected three additional non-transiting planets, namely TOI-5789 b, d, and e, with orbital periods and minimum masses of $P_{b}=2.76$ d, $M_{b}\sin{i}=2.12 \pm 0.28 M_\oplus$, $P_{d}=29.6$ d, $M_{d}\sin{i}=4.29 \pm 0.68 M_\oplus$, and $P_{e}=63.0$ d, $M_{e}\sin{i}=11.61 \pm 0.97 M_\oplus$. TOI-5789 is a mutually inclined system as the difference between the orbital inclinations of planets b and c must be higher than $\sim4$ deg. Nevertheless, from sensitivity studies based on both the HARPS-N and archival HIRES radial-velocity measurements, we can exclude that these relatively high mutual inclinations are due to the perturbation by an outer gaseous giant planet.

This paper deals with the asymptotic behaviour of a widely used correlation characteristic in large quantum systems. The correlations are known as quantum entanglement, the characteristic is called entanglement entropy, and the system is an ideal gas of spinless lattice fermions. The system is determined by its one-body Hamiltonian. It is shown in EPS [18] that if the Hamiltonian is an ergodic finite difference operator with an exponentially decaying spectral projection, then the asymptotic form of the entanglement entropy is the so-called area law. However, the only class of one-body Hamiltonians for which this spectral condition was verified is that consisting of discrete Schrödinger operators with random potential. In this paper, we prove the validity of the area law for several classes of Schrödinger operators whose potentials are ergodic but not random. We begin with quasiperiodic and limit-periodic operators and then move on to the interesting and highly non-trivial case of potentials generated by subshifts of finite type. These arose in the theory of dynamical systems when studying non-random chaotic phenomena. The corresponding asymptotic study requires quite an involved spectral analysis. Consequently, the majority of the paper is devoted to the proof and application of a variety of spectral properties of the operators in question, in particular we prove uniform localisation of the ejgenfunctions for the Maryland model and the exponential decay of the eihgenfunction correlator for a variety of models . We believe that these properties are of considerable independent interest.

We consider hierarchical quantum Hall edge states with $N$ modes and a spatially local quantum point contact (QPC). In general, the field of an injected anyon does not directly acquire the universal statistical phase $θ$. Short-range inter-edge interactions split the universal anyon charge and phase into $N$ fractionalized charges associated with nonuniversal phases $πδ_m$. In contrast, their sum $δ=\sum_{m=1}^Nδ_m$, which defines the local scaling dimension at the QPC, remains protected and is tied to the statistical angle through $πδ=θ$. If the injected anyon is of the same species as the one dominating backscattering at the QPC, time-domain braiding with phase $θ$ is recovered either in the absence of inter-edge interactions with equal mode velocities, or by performing a spatially local anyon injection at the QPC. We then exploit a more robust \emph{local} anyonic time-exchange (ATE) link between anyons and quasiholes at the QPC, which is also a necessary ingredient for realizing such braiding. This allows us to propose minimal single-QPC protocols that do not rely on diluted anyon sources and that disentangle the role of $θ$ as a genuine statistical phase from that as a scaling dimension. From the ATE link we derive two novel nonequilibrium fluctuation--dissipation relations (FDRs) that isolate $θ$. They relate the DC backscattering noise either to an integral over the DC current or to the phase shift of the AC current with respect to an applied AC voltage (i.e., the phase of the admittance), accessible down to low frequencies. For thermalized edges, we show that in the quantum regime this admittance phase directly yields $θ$ whenever $δ>1/2$.

Anisotropic strain engineering in epitaxial oxide films provides new opportunities to control the antiferromagnetic and structural properties crucial for advancements of antiferromagnetic spintronics. Here we report on a (La0.7Sr0.3MnO3/LaFeO3)4 superlattice grown on (101)o DyScO3 substrate which imposes significant anisotropic in-plane strain. Reciprocal space mapping reveals selective strain relaxation along the tensile in-plane [010]o axis, while compression along the perpendicular in-plane [-101]o axis remains strained. Scanning precession electron diffraction and higher-order Laue zone analysis show that the relaxation is accommodated by structural domain formation in the LaFeO3 layers, initiating from the second bilayer and propagating out-of-plane. These domains minimise structural defects and correlate with the substrate step edges. X-ray magnetic dichroism measurements reveal bulk-like in-plane antiferromagnetic order with polydomain signature as previously reported. Our findings reveal the presence of structural domains coexisting with antiferromagnetic polydomain states, showing a strain-domain-magnetism relationship that provides insights for applications of strain engineering in spintronics applications.

Two-dimensional materials have attracted growing interest due to their unique electronic properties and potential applications in spintronics. Interfacing strongly spin-orbit-coupled chalcogenides with functional oxides such as perovskites has a particularly high potential. In this work, highly textured Bi2Te3 thin films were deposited on (111) oriented SrTiO3 by pulsed laser deposition. We show that, by careful selection of the temperature and pressure of growth, the film's stoichiometry can be manipulated between direct stoichiometry transfer from the target and tellurium-deficient phases. Optimized pulsed laser deposition enables the growth of films with coalesced, faceted grains with grain sizes reaching up to 430 nm, while preserving crystalline quality comparable to that of molecular-beam-epitaxy-grown films. We show striking differences arising from tuning the laser's pulsing frequency and fluence, which lead to changes in surface roughness, the film's porosity, and grain boundaries, as well as grain shape. Analysis of cross-sectional transmission electron microscopy images reveals a sharp substrate-film interface without atomic intermixing and without the formation of amorphous intermediate layers. The results demonstrate that pulsed laser deposition is a viable method for producing high-quality Bi2Te3 thin films and opens the door to the integration of chalcogenides with perovskites with this growth technique.

In experiments probing human vision at the few-photon level, precise alignment of the eye is necessary such that stimuli reach the most sensitive region of the retina. However, in literature there seems to be no consensus on the optimal eye alignment for such experiments. Typically, experiments are performed by presenting stimuli nasally or temporally, but the angle under which the few-photon pulses are presented varies between 7 deg and 23 deg. Here we combine a 3-dimensional eye model with retinal rod density measurements from literature in a ray tracing simulation to study the optimal eye alignment conditions and necessary alignment precision. We find that stimuli, directed at the eye's nodal point, may be best presented under an inferior angle of 12.6 deg with respect to the visual axis. Defining a target area on the retina with a radius of 0.5 mm around the optimum location, we find the horizontal and vertical angular precision should be better than 0.90 deg given a horizontal and vertical translational precision of $\pm$ 1 mm and a depth translational precision of $\pm$ 5 mm.

The conversion of gravitational potential to kinetic energy results in an intracluster medium (ICM) gas with a characteristic temperature near 10 keV in the most massive galaxy clusters. X-ray observations, primarily from Chandra and XMM-Newton, have revealed a wealth of information about the thermodynamics of this gas. However, two regimes remain difficult to study with current instruments: superheated gas well above 10 keV generated by shocks from major mergers, and distant systems strongly impacted by cosmological dimming. Relativistic corrections to the Sunyaev-Zel'dovich effect (rSZe) produce a fractional spectral distortion in the cosmic microwave background at submillimeter and millimeter wavelengths that could offer a complementary probe of both high-temperature and high-redshift ICM gas. Here we describe multiband measurements of the rSZe, including observations from the Fourier Transform Spectrometer on the Herschel-SPIRE instrument, that constrain the ICM thermodynamics of the major merger MACS J0717.5+3745. Within the seven observed lines of sight, we find an average temperature of $T_{\mathrm{rSZe}}=15.1^{+3.8}_{-3.3}$ keV which is consistent with the values obtained from X-ray measurements of the same regions, with $T_{\mathrm{Chandra}}=18.0^{+1.1}_{-1.1}$ keV and $T_{\mathrm{XMM}}=13.9^{+0.9}_{-0.9}$ keV. This work demonstrates that the rSZe signal can be detected with moderate spectral resolution submillimeter data, while also establishing the utility of such measurements for probing superheated regions of the ICM.

The final-parsec problem has long posed a central challenge in understanding the merger of supermassive black hole binaries. In this paper, we investigate a scenario in which a dark scalar or vector field is sourced by eccentric binaries, leading to accelerated mergers through additional dipole radiation, and thereby extending the range of masses for which the binary can merge within a Hubble time. The Newtonian-order radiation fluxes from an eccentric charged Keplerian binary are derived using general results for localized periodic sources in flat spacetime. We find that dipole radiation, although insufficient to fully resolve the final-parsec problem, can alter the low-frequency spectrum of the stochastic gravitational-wave background from supermassive black hole binary inspirals. We construct a simplified model for the spectrum and perform a Bayesian analysis using the current pulsar timing array data.

Near-surface turbulent flows beneath a free surface are reconstructed from sparse measurements of the surface height variation, by a novel neural network algorithm known as the {\em SHallow REcurrent Decoder} (SHRED). The reconstruction of turbulent flow fields from limited, partial, or indirect measurements remains a grand challenge in science and engineering. The central goal in such applications is to leverage easy-to-measure proxy variables in order to estimate quantities which have not been, and perhaps cannot in practice be, measured. Specifically, in the application considered here, the aim is to use a sparse number of surface height point measurements of a flow field, or drone video footage of surface features, in order to infer the turbulent flow field beneath the surface. SHRED is a deep learning architecture that learns a delay-coordinate embedding from a few surface height (point) sensors and maps it, via a shallow decoder trained in a compressed basis, to full subsurface fields, enabling fast, robust training from minimal data. We demonstrate the SHRED sensing architecture on two types of turbulent data from recent studies (Aarnes \emph{et al.} J.~Fluid Mech.\ \textbf{1007} A38, 2025 and Babiker \emph{et al.} arXiv:251003732, 2025, respectively): fully resolved DNS data and PIV laboratory data from a turbulent water tank. SHRED is capable of robustly mapping surface height fluctuations to full-state flow fields up to about two integral length scales deep, with as few as three surface measurements.

We initiate a systematic study of the computational complexity of property testing, focusing on the relationship between query and time complexity. While traditional work in property testing has emphasized query complexity, relatively little is known about the computational hardness of property testers. Our goal is to chart the landscape of time-query interplay and develop tools for proving time complexity lower bounds. Our first contribution is a pair of time-query hierarchy theorems for property testing. For all suitable nondecreasing functions $q(n)$ and $t(n)$ with $t(n)\geq q(n)$, we construct properties with query complexity $\tildeΘ(q(n))$ and time complexity $\tildeΩ(t(n))$. Our weak hierarchy holds unconditionally, whereas the strong version-assuming the Strong Exponential Time Hypothesis-provides better control over the time complexity of the constructed properties. We then turn to halfspaces in $\mathbb{R}^d$, a fundamental class in property testing and learning theory. We study the problem of approximating the distance from the input function to the nearest halfspace within additive error $ε$. For the distribution-free distance approximation problem, known algorithms achieve query complexity $O(d/ε^2)$, but take time $\tildeΘ(1/ε^d)$. We provide a fine-grained justification for this gap: assuming the $k$-SUM conjecture, any algorithm must have running time $Ω(1/ε^{d/2})$. This fine-grained lower bound yields a provable separation between query and time complexity for a natural and well-studied (tolerant) testing problem. We also prove that any Statistical Query (SQ) algorithm under the standard Gaussian distribution requires $(1/ε)^{Ω(d)}$ queries if the queries are answered with additive error up to $ε^{Ω(d)}$, revealing a fundamental barrier even in the distribution-specific setting.

The operations to be performed by a quantum computer are almost invariably given in the form of a quantum circuit. In the final stage of compilation, a quantum circuit must be translated into the input signals accepted by the quantum hardware itself. For a quantum computer based on superconducting qubits, this will be a sequence of microwave control pulses to be sent to the various input channels. A pulse schedule gives a full specification for which pulse should be applied to which channel at what time. There is as yet no language for these pulse schedules that is very amenable to formal semantics. In this paper, we propose such a language called GRAMPUS (GRAded Modal type theory for PUlse Schedules). It is a graded modal type theory, where the grades represent timing information: a variable $x :^{50} Q_1$ will represent a state of qubit $Q_1$ that will exist 50 nanoseconds in the future, and a variable $y :^{-75} Q_2$ will represent a state of qubit $Q_2$ that existed 75 nanoseconds in the past. We give the syntax for two type theories, one with grades (the annotated language) and one without (the plain language). We prove some metatheoretic properties, and describe the semantics in terms of category theory. We show that the input signals to a quantum chip forms a model of the annotated language. We also give a syntatic model, prove that it is initial, and hence prove soundness and completeness theorems.

We show that the three-point skewness of concentration fluctuations is non-vanishing in free liquid diffusion, even in the limit of vanishingly small mean concentration gradients. We exploit a high-Schmidt reduction of nonlinear Landau-Lifshitz hydrodynamics for a binary fluid, both analytically and by a massively parallel Lagrangian Monte Carlo simulation. Non-Gaussian statistics result from nonlinear coupling of concentration fluctuations to thermal velocity fluctuations, analogous to the turbulent advection of a passive scalar. Concentration fluctuations obey no central limit theorem, counter to the predictions of macroscopic fluctuation theory for generic diffusive systems.

The distribution of binary black hole (BBH) masses and its evolution with redshift provide key insights into the different formation channels of compact objects and their dependence on cosmic time and stellar properties such as metallicity and star formation history. We present a non-parametric framework of the redshift evolution of the BBH mass distribution using the gravitational-wave (GW) catalogs GWTC-3 and GWTC-4 of LIGO-Virgo-KAGRA (LVK). This method simultaneously searches for the signature of any linear and quadratic redshift evolution with respect to the low-redshift population in a Bayesian framework, taking into account the detector selection effects. We find tentative evidence for a linear redshift-dependent evolution of the mass distribution, consistent over a mass range ($m \gtrsim 50\,M_\odot$), while lower-mass systems show no significant evolution. The quadratic term remains consistent with zero, indicating that a simple linear dependence adequately describes the population up to redshift $z \sim 1$. With more GW sources in the future, this technique can reveal subtle evolutionary features in BBH populations and provide new insights into the cosmic history of black hole formation.

A massive vector field is a highly promising candidate for dark matter in the Universe. A salient property of dark matter is its negligible or null coupling to ordinary matter, with the exception of gravitational interaction. This poses a significant challenge in producing the requisite amount of dark particles through processes within the Standard Model. In this study, we examine the production of a vector field during inflation due to its direct interaction with the inflaton field through kinetic and axionlike couplings as well as the field-dependent mass. The gradient-expansion formalism, previously proposed for massless Abelian gauge fields, is extended to include the longitudinal polarization of a massive vector field. We derive a coupled system of equations of motion for a set of bilinear functions of the vector field. This enables us to address the nonlinear dynamics of inflationary vector field production, including backreaction on background evolution. To illustrate this point, we apply our general formalism to a low-mass vector field whose kinetic and mass terms are coupled to the inflaton via the Ratra-type exponential function. The present study investigates the production of its transverse and longitudinal polarization components in a benchmark inflationary model with a quadratic inflaton potential. It has been demonstrated that pure mass coupling is able to enhance only the longitudinal components. By turning on also the kinetic coupling, one can get different scenarios. As the coupling function decreases, the primary contribution to the energy density is derived from the transverse polarizations of the vector field. Conversely, for an increasing coupling function, the longitudinal component becomes increasingly significant and rapidly propels the system into the strong backreaction regime.

This paper presents a controller design framework aiming to balance control performance and actuation rate. Control performance is evaluated by an infinite-horizon average cost, and the number of control actions is penalized via sparsity-promoting regularization. Since the formulated optimal control problem has a combinatorial nature, we employ a rollout algorithm to obtain a tractable suboptimal solution. In the proposed scheme, actuation timings are determined through a multistage minimization procedure based on a receding-horizon approach, and the corresponding control inputs are computed online. We establish theoretical performance guarantees with respect to periodic control and prove the stability of the closed-loop system. The effectiveness of the proposed method is demonstrated through a numerical example.

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal delays influence feedback mechanisms. In the first case, we set one of the delays to zero and analyzed the resulting system. We then extended the study to a more general case where both delays are allowed to vary. We derive delay-independent stability conditions using linearization, characteristic equations, and bifurcation theory, along with complete theoretical proofs. The results are validated through numerical simulations and stability diagrams.

Beyond-diagonal reconfigurable intelligent surfaces (BD-RISs) are emerging as a transformative technology in wireless communications, enabling enhanced performance and quality of service (QoS) of wireless systems in harsh urban environments due to their relatively low cost and advanced signal processing capabilities. Generally, BD-RIS systems are employed to improve robustness, increase achievable rates, and enhance energy efficiency of wireless systems in both direct and indirect ways. The direct way is to produce a favorable propagation environment via the design of optimized scattering matrices, while the indirect way is to reap additional improvements via the design of multiple-input multiple-output (MIMO) beamformers that further exploit the latter "engineered" medium. In this article, the problem of sum-rate maximization via BD-RIS is examined, with a focus on feasibility, namely low-complexity physical implementation, by enforcing reciprocity in the BD-RIS design in a manner that adheres to the geometry of the manifold of symmetric matrices. To that end, the sum-rate objective is transformed into a quadratic function via fractional programming (FP), augmented via the also quadratic reciprocity constraint in the form of a regularization term, while the unitary constraint is dealt with via a manifold optimization framework. Simulation results demonstrate the effectiveness of the proposed method in outperforming current state-of-the-art (SotA) approaches in terms of sum-rate maximization.

We establish sharp extremal bounds on the Albertson and Sigma irregularity indices for trees with prescribed degree sequences, with emphasis on caterpillar trees as key extremal configurations. New lower and upper bounds are derived in terms of maximum degree, average degree, and auxiliary sequence parameters, highlighting the quadratic growth of the Sigma index relative to the linear Albertson index. Closed-form expressions, direct index relations, and empirical validation confirm the bounds' tightness. These findings extend prior work on linear irregularity measures and offer precise tools for analyzing degree-heterogeneous trees in graph theory and chemical graph applications.

In the heavy quarkonium decay process $ V \to ggg $ ($ V=J/ψ, Υ$), making a definite prediction including relativistic corrections has so far remained a significant challenge. In this work, we study this decay process by taking into account the relativistic corrections in the Bethe-Salpeter formalism, where the relativistic bound-state wave function of quarkonium is obtained by solving the Bethe-Salpeter equation under the covariant instantaneous ansatz. Through analytical calculation, we find that some polarized decay widths vanish due to the helicity selection rule, which suppresses the corresponding helicity amplitudes. Owing to helicity flip symmetry and phase space symmetry, the nonvanishing polarized decay widths are not all independent; they are related through a set of symmetry relations. Then we obtain the unpolarized decay width formula $Γ(V \to ggg)=\frac{80(π^{2}-9)α_{s}^{3}N_{V}^{2}β_{V}^{3}}{81π^{9/2} M } (1-κ\frac{β_{V}^{2}}{M^{2}})$, where the factor $κ\frac{β_{V}^{2}}{M^{2}}$ arises from the relativistic corrections with $κ\equiv\frac{3(112+25π^{2})}{16(π^{2}-9)}$. Furthermore, including both relativistic and QCD radiative corrections within the factorization assumption, our predictions of $\mathcal{B}(V \to ggg)$ and $\mathcal{B}(V \to e^{+}e^{-})$ agree well with their experimental data. As a crossing check, with the experimental value of the ratio $R_{V} = \frac{Γ(V \to ggg)}{Γ(V \to e^{+}e^{-})}$ and our result for $R_{V}$, we extract $α_{s}(M_{J/ψ}/2)=0.31$ and $α_{s}(M_Υ/2)=0.20$, respectively.

We are concerned with a Brezis-Nirenberg type problem for a critical Choquard equation, in the sense of Hardy-Littlewood-Sobolev inequality, and with the Hardy potential in a smooth bounded domain. By exploiting variational methods we obtain existence results, which extend to different perturbation terms. Some estimates of independent interest about a nonlocal minimization problem are also derived.

Electroencephalography (EEG) denoising methods typically depend on manual intervention or clean reference signals. This work introduces a task-oriented learning framework for automatic EEG denoising that uses only task labels without clean reference signals. EEG recordings are first decomposed into components based on blind source separation (BSS) techniques. Then, a learning-based selector assigns a retention probability to each component, and the denoised signal is reconstructed as a probability-weighted combination. A downstream proxy-task model evaluates the reconstructed signal, with its task loss supervising the selector in a collaborative optimization scheme that relies solely on task labels, eliminating the need for clean EEG references. Experiments on three datasets spanning two paradigms and multiple noise conditions show consistent gains in both task performance (accuracy: $2.56\%\uparrow$) and standard signal-quality metrics (signal-to-noise-ratio: $0.82$\,dB\,$\uparrow$). Further analyses demonstrate that the task-oriented learning framework is algorithm-agnostic, as it accommodates diverse decomposition techniques and network backbones for both the selector and the proxy model. These promising results indicate that the proposed task-oriented learning framework is a practical EEG denoising solution with potential implications for neuroscience research and EEG-based interaction systems.

The scaling limitations of conventional transistors demand alternative device concepts capable of dynamic reconfigurability at the atomic scale. Resistive switching (RS), a key mechanism for neuromorphic computing and non-volatile memory, has been widely demonstrated in oxides, semiconductors, and nanocomposites, but not in pure one-dimensional metallic systems. Here, we report the first electrical characterization of gold nanowires (AuNWs) synthesized within the lumen of functionalized microtubules. Structural analyses confirm continuous metallic wires with local compositional inhomogeneities. Electrical measurements reveal three distinct conduction behaviours and abrupt, reversible resistance transitions under applied bias, consistent with defect-driven electromigration. Voltage pulsing enables active and reproducible modulation of resistance states without loss of metallic conduction, establishing a new RS mechanism intrinsic to pure metallic nanowires. Owing to their high aspect ratio, lateral geometry, and CMOS-compatible processing, microtubule-templated AuNWs provide a versatile platform for reconfigurable interconnects and neuromorphic device architectures.