Ground-based solar observations enable unprecedented spatial, spectral, and temporal resolution of the lower solar atmosphere, yet Earths turbulent atmosphere imposes significant limitations, requiring advanced post-facto image reconstruction. State-of-the-art reconstruction methods are based on restoring a burst of short exposure frames to a single observation. Limitations of these techniques arise due to the sparse information about the atmospheric point spread function (PSF) that degrade the observations and consequently the quality of reconstructions. We develop a novel image reconstruction method to achieve unprecedented spatial resolution from short exposure image bursts. This can provide high-quality reconstructions and therefore advance the study of the smallest spatial scales from the solar photosphere to the chromosphere. In this study, we present a novel approach for high-resolution solar image reconstruction based on physics-informed neural networks. In the training process, the neural network maps coordinate points directly to their corresponding intensity values while simultaneously updating the PSF parameters. The method convolves the true object from the neural network with the estimated PSFs and optimizes the network by minimizing the loss between the synthesized and real short-exposure image burst. This approach enables the simultaneous estimation of both the degrading PSF and the real high-resolution intensity distribution. We demonstrate the method on synthetic intensity data derived from a radiative MHD simulation and apply it to high-resolution observations from GREGOR and DKIST. Our results demonstrate the ability to reconstruct small-scale solar features that exceed the reconstruction performance of state-of-the-art reconstruction methods. With this approach we lay the foundation for future spatially varying PSFs.

Atomically thin materials exhibit electronic and optical properties distinct from their three-dimensional counterparts. For metals, particularly gold, monolayer studies remain largely unexplored due to fabrication and characterisation challenges. Here we report the first optical study of a stable quasi-freestanding gold monolayer formed by Au intercalation between graphene and SiC. Mid-infrared nanoimaging reveals plasmon-polaritons with wavelengths nearly an order of magnitude shorter than free-space light. Analysis of their dispersion using a Drude model yields a relaxation time of $τ= 18\,$fs, comparable to bulk gold, and a Drude weight of $D = 1.3\,$mS$\cdot$eV, nearly twice the bulk expectation. These results establish monolayer gold as a two-dimensional metal, opening opportunities for nanoscale photonics, plasmonics and ultra-thin electronics.

We propose a computationally efficient nonlinear Model Predictive Control (NMPC) algorithm for safe, learning-based control. The system model is represented as an affine combination of basis functions with unknown parameters, and is subject to additive set-bounded disturbances. Our algorithm employs successive linearization around nominal predicted trajectories and accounts for uncertainties in predicted states due to linearization, model errors, and disturbances using ellipsoidal sets. The ellipsoidal tube-based approach ensures that constraints on control inputs and system states are satisfied. Robustness to uncertainty is ensured using bounds on linearization errors and a backtracking line search. We show that the ellipsoidal embedding of model uncertainty scales favourably with system dimensions in numerical simulations. The algorithm incorporates set membership parameter estimation, and provides guarantees of recursive feasibility and input-to-state practical stability.

The topological magnetoelectric effect (TME) in three-dimensional topological insulators (TIs), described by $ΔP = \frac{e^2}{2h} N_{\rm Ch}^{(2)} ΔB$, serves as a condensed-matter realization of the four-dimensional quantum Hall effect (4D QHE). In dual-gate axion-insulator devices, the TME-induced polarization yields a current $I_{\rm TME} \propto (C_{\rm total}/C_{\rm S})\,Q_{\rm 4D\text{-}QHE}$, where the signal is suppressed by the capacitance ratio $C_{\rm total}/C_{\rm S}$. Here we propose an active compensation scheme that introduces a tunable negative capacitance $C_{\rm comp} \approx -C_{\rm gate}$ into the gate line, effectively canceling the gate dielectric capacitance and driving $C_{\rm total}/C_{\rm S} \to 1$. We validate the method using a quantum anomalous Hall (QAH) device, which shares the same surface-state physics with the axion insulator but permits direct charge measurement via a single gate, recovering over $95\%$ of the quantized charge signal from an initially half-attenuated state. This compensation method provides a robust means of resolving minute TME signals, offering a promising pathway toward direct measurements of the 4D QHE.

Distributed multi-target tracking (DMTT) in limited field-of-view (FoV) sensor networks commonly suffers from label inconsistency, whereby different nodes disagree on the identity of the same target. Recent track-consensus DMTT (TC-DMTT) strategies mitigate this issue by enforcing kinematic and label agreement through metric-based track matching. Nevertheless, their behavior under adversarial conditions remains largely unexplored. In this paper, we reveal identity-level vulnerabilities in TC-DMTT and introduce the concept of label hijacking: an attack in which an adversary injects spoofed tracks to corrupt target identities across the network. Drawing on an analogy to classical pull-off deception in radar, we formalize a notion of attack stealthiness and derive an optimization-based strategy for crafting such attacks. A three-sensor network case study demonstrates the impact of the proposed attack on label consistency and tracking accuracy, showing successful target impersonation. Overall, this work highlights the need to rethink robustness at the consensus layer in DMTT frameworks.

Analyzing and controlling system entropy is a powerful tool for regulating predictability of control systems. Applications benefiting from such approaches range from reinforcement learning and data security to human-robot collaboration. In continuous-state stochastic systems, accurate entropy analysis and control remains a challenge. In recent years, finite-state abstractions of continuous systems have enabled control synthesis with formal performance guarantees on objectives such as stage costs. However, these results do not extend to entropy-based performance measures. We solve this problem by first obtaining bounds on the entropy of system discretizations using traditional formal-abstractions results, and then obtaining an additional bound on the difference between the entropy of a continuous distribution and that of its discretization. The resulting theory enables formal entropy-aware controller synthesis that trades predictability against control performance while preserving formal guarantees for the original continuous system. More specifically, we focus on minimizing the linear combination of the KL divergence of the system trajectory distribution to uniform -- our system entropy metric -- and a generic cumulative cost. We note that the bound we derive on the difference between the KL divergence to uniform of a given continuous distribution and its discretization can also be relevant in more general information-theoretic contexts. A set of case studies illustrates the effectiveness of the method.

The indirect determination of the total width of the detected Higgs boson that is carried out by the experimental collaborations at the LHC relies on the assumption that the coupling modifiers for the on-shell and off-shell couplings are the same. However, physics beyond the Standard Model affecting the on-shell and off-shell regions differently could invalidate this assumption, so that the actual width of the detected Higgs boson could be larger than the bounds obtained under this assumption. Relaxing the assumption and investigating different types of extensions of the Standard Model, we analyse under which conditions a larger total width of the detected Higgs boson is compatible with all experimental and theoretical constraints. For the considered scenarios of scalar extensions with an additional state contributing as a resonance or at the loop level, we find that the indirect bounds obtained by ATLAS and CMS remain valid over large parts of the parameter space, with the exception of parameter regions where the additional particles have relatively small masses. We discuss the potential of experimental searches for new particles to further constrain such scenarios. Based on the existing experimental and theoretical constraints we conclude that relaxing the assumption of equal on-shell and off-shell coupling modifiers that is used in the experimental analyses at the LHC yields an upper bound on the total width of the detected Higgs boson in realistic extensions of the Standard Model that is only weakened by up to a factor of about two compared to the case where this assumption is valid.

This exploratory pilot study investigates the impact of haptic perception --specifically tactile sensitivity (touch) and kinaesthetic intensity (movement)-- on learning, operationalized as information retention (immediate recall) through handwriting. Participants (N=20) were randomly assigned to one of four experimental groups in a 2x2 factorial design, manipulating touch (via glove use) and movement (via increased writing pressure). Information retention was measured using an immediate recall test, while mental effort (reaction time in a secondary task) and perceived workload (NASA-TLX) were examined as mediating variables. Bayesian binomial regression revealed moderate evidence that increased writing pressure negatively influenced recall (85-88% probability of negative effect), whereas glove use alone demonstrated no clear effect. Bayesian mediation analysis found no strong evidence that mental effort or perceived workload mediated these effects, as all 95% credible intervals included zero, indicating substantial uncertainty. These findings suggest that increased Kinaesthetic demands may slightly impair immediate recall, independent of perceived workload or mental effort. Importantly, the manipulation of touch alone does not appear to influence information retention. The study contributes to understanding the nuanced relationship between embodied interactions and cognitive outcomes, with implications for designing sensor-based multimodal learning environments.

The Rayleigh expansion is widely used as a formal radiation condition in the analysis and numerical treatment of grating diffraction problems for incoming plane waves. However, the Rayleigh expansion does not always lead to uniqueness of open waveguide scattering problems, due to the existence of surface/guided waves (in other words, Bound States in the Continuum (BICs)) which exponentially decay in the direction perpendicular to the periodicity. In this paper we suppose that a bi-periodic inhomogeneous medium supports BICs at some real-valued incident wavenumber. Based on singular perturbation arguments, we justify the Limiting Absorption Principle (LAP) for both time-harmonic acoustic and electromagnetic scattering of plane waves from bi-periodic structures. Replacing the wavenumber $k$ with $k+iε$, we prove that the unique solution with $ε>0$ converges to a solution of the original diffraction problem that additionally satisfies an orthogonal identity. This constraint condition together with the classical Rayleigh expansion leads to a sharp radiation condition to ensure uniqueness of time-harmonic scattering of plane waves by BIC-supporting bi-periodic materials.

We examine the observational viability and physical implications of the Gong-Zhang (GZ) dark--energy equation-of-state parametrizations using exclusively late-time cosmological probes. Two one-dimensional parametrization models, GZ-Type~I and GZ-Type~II, are constrained with Type~Ia supernovae (Union3, Pantheon+SH0ES, and DES-SN5YR), DESI baryon acoustic oscillations, and cosmic chronometer measurements of $H(z)$. Bayesian inference combined with information-criteria diagnostics shows that both parametrizations provide competitive alternatives to $Λ$CDM, while the GZ-Type~II model is consistently favored, exhibiting reduced parameter degeneracy and stronger Jeffreys-scale support. Beyond background expansion tests, we employ configuration entropy as a thermodynamically motivated probe of structure formation. We demonstrate that the entropy-production rate sensitively traces the impact of dynamical dark energy on late-time gravitational clustering while preserving standard early-time behavior. Our results establish the Gong-Zhang framework as a physically transparent and observationally consistent extension of $Λ$CDM, with configuration entropy providing a complementary diagnostic of late-time cosmic acceleration.

We introduce a general framework for positional games in which players score points by claiming a prescribed portion of each winning set, extending the notion of scoring Maker-Breaker games. In the scoring variant, Maker gains a point by fully claiming a winning set, while Breaker aims to minimize Maker's total score. In this paper, we generalize these models for all k-uniform positional games by fixing an integer threshold s in {1,2,..., k} so that a player scores a point whenever she claims at least s elements of a winning set of size k. We refer to this class as s-of-k games. Such formulation allows for a flexible description of scoring objectives that appear in both theoretical models and real-life board games. We further investigate the impact of strategy restrictions on the achievable score. In particular, we analyze s-of-k games both under optimal play, where the score is denoted by SC, and under the additional constraint that Maker is restricted to a pairing strategy. The corresponding score in this setting is denoted by SC_2. While the unrestricted score captures the standard notion of optimal play in scoring positional games, the pairing-restricted score allows us to observe Maker's loss incurred by limiting her to these standard strategies. We comprehensively study s-of-k games played on regular grids, which provide a natural and uniform setting for illustrating the general framework. After developing several general tools for the analysis of both scores, we complement them by a number of ad-hoc strategies tailored for particular cases of these games, to obtain both upper and lower bounds for the two scores on triangular, square, rhombus and hexagonal grids.

We present a method to determine the sensitivity of a closed dielectric haloscope to axion dark matter. Dielectric haloscopes aim to probe the theoretically well-motivated axion mass range of ~26 $\mathrmμ$eV to ~500 $\mathrmμ$eV by utilizing a stack of dielectric disks and a mirror to enhance the axion-photon conversion within an external magnetic field. Their conversion volume is nearly axion-mass independent, thereby favoring large-scale designs to increase sensitivity. The large volume causes simulations to be computationally expensive and time-consuming. This paper presents a simple model that can be used to determine the sensitivity of the experiment with minimal computational resources. The model is able to describe the electromagnetic response of a closed dielectric haloscope, accounting for realistic geometric imperfections, as well as the noise introduced by the receiver system. It is applied to data taken with a MAgnetized Disk and Mirror Axion Experiment (MADMAX) prototype within the 1.6 T Morpurgo magnet at CERN. This work underpins the first axion dark matter search using a dielectric haloscope and provides the foundation for future dark matter searches with MADMAX.

Traditional financial institutions face inefficiencies that can be addressed by distributed ledger technology. However, a primary barrier to adoption is the privacy concerns surrounding publicly available transaction data. Existing private protocols for distributed ledger that focus on the Ring-CT model are not suitable for adoption for financial institutions. We propose a post-quantum, lattice-based transaction scheme for encrypted ledgers which better aligns with institutions' requirements for confidentiality and audit-ability. The construction leverages various zero-knowledge proof techniques, and introduces a new method for equating two commitment messages, without the capability to open one of the commitment during the re-commitment. Subsequently, we build a publicly verifiable transaction scheme that is efficient for single or multi-assets, by introducing a new compact range-proof. We then provide a security analysis of it. The techniques used and the proofs constructed could be of independent interest.

Turbulent transport near the X-point of a large tokamak is examined using local, gradient-driven simulations that determine the saturated plasma profiles. The distribution of a representative set of particle tracers evolving within these profiles is then analyzed. The study demonstrates that the resulting transport is diffusive, characterized by a coefficient that depends on the spectral properties of the turbulent energy and attains anomalous high values under broad conditions. These findings suggest that anomalous transport is an inherent outcome of the fundamental non-linear drift dynamics of plasmas. The scaling of transport with turbulent energy is also addressed, with implications for future progress toward a mean-field framework for turbulent transport.

The spatial public goods game has been used to examine factors that promote cooperation. Owing to the complexity of the dynamics of this game, previous studies on this model neglected analytical approaches and relied entirely on numerical calculations using the Monte Carlo (MC) simulations. In this paper, we present the approximate master equations (AMEs) for this model. We report that the results obtained by the AMEs are mostly qualitatively consistent with those obtained by the MC simulations. Furthermore, we show that it is possible to obtain phase boundaries analytically in certain parameter regions. In the region where the noise in strategy decisions is very large, the phase boundary can be obtained analytically by considering perturbations from the steady state of the voter model. In the noiseless region, discontinuous phase transitions occur because of the characteristics of the function that represents strategy updating. Our approach is useful for clarifying the details of the mechanisms that promote cooperation and can be easily applied to other group interaction models.

Structural break identification methods are an important tool for evaluating the effectiveness of climate change mitigation policies. In this paper, we introduce a unified probabilistic framework for detecting structural breaks with unknown timing and arbitrary sequence in longitudinal data. The proposed Bayesian setup uses indicator-saturated regression and a spike-and-slab prior with an inverse-moment density as the slab component to ensure model selection consistency. Simulation results show that the method outperforms comparable frequentist approaches, particularly in environments with a high probability of structural breaks. We apply the framework to identify and evaluate the effects of climate policies in the European road transport sector.

We present a loop quantization of the marginally bound Lemaître-Tolman-Bondi (LTB) model, describing the gravitational collapse of pressureless dust in spherical symmetry. The full quantum LTB model is constructed as a collection of non-interacting shells, each governed by an individual single-shell loop quantum dynamics. We show that the single-shell evolution is non-singular and that wave packets initially peaked on a collapsing trajectory undergo a bounce at Planckian energy densities and subsequently follow an expanding classical trajectory, resolving the classical central curvature singularity. We also compare the loop quantum theory with the Wheeler-DeWitt quantization of the same model and assess the accuracy of the loop quantum gravity effective theory in reproducing the full quantum dynamics. Specifically, we find that initially collapsing wave packets generically develop an interference pattern at the bounce, which suppresses the accuracy of the effective theory near the center of the dust cloud.

Robust control of complex engineered and biological systems hinges on the integration of feedforward and feedback mechanisms. This is exemplified in neural motor control, where feedforward muscle co-contraction complements sensory-driven feedback corrections to ensure stable behaviors. However, deriving a general continuous-time framework to determine such optimal control policies for partially observable, stochastic, nonlinear, and high-dimensional systems remains a formidable computational challenge. Here, we introduce a framework that extends neighboring optimal control by enabling the feedforward plan to explicitly account for feedback uncertainties and latencies. Using statistical linearization, we transform the stochastic problem into an approximately equivalent deterministic optimization within a tractable, augmented state space that retains critical nonlinearities, offering both mechanistic interpretability and theoretical guarantees on approximation fidelity. We apply this framework to human neuromechanics, demonstrating that muscle co-contraction emerges as an optimal adaptation to task demands, given the characteristics of our sensorimotor system. Our results provide a computational foundation for neuromotor control and a generalizable tool for the control of nonlinear stochastic systems.

Belief propagation (BP) decoding of quantum low density parity check (QLDPC) codes is often implemented using overcomplete stabilizer (OS) representations, where redundant parity checks are introduced to improve finite length performance. Decoder behavior for such representations is governed primarily by finite iteration dynamics rather than asymptotic code properties. These dynamics are known to critically depend on the initialization of the decoder. In this paper, we investigate the impact of mismatched log likelihood ratios (LLRs) used for BP initialization on the performance of QLDPC codes with OS representations. Our results demonstrate that initial LLR mismatch has a strong influence on the frame error rate (FER), particularly in the low noise regime. We also show that the optimal performance is not sharply localized: the FER remains largely insensitive over an extended region of mismatched LLRs. This behavior motivates an interpretation of LLR mismatch as a regularization control parameter rather than a quantity that must be precisely matched to the quantum channel.

Perovskite based nanocomposites provide a versatile platform for tailoring light matter coupling and carrier injection in low dimensional optoelectronics. In particular hybrid structures incorporating transition metal dichalcogenides (TMDCs) enable tunable band alignment and excitonic dynamics. However, the central challenge lies in the scalable synthesis of defect controlled layered TMDCs suitable for coherent interfacial coupling. Here we demonstrate geometry dependent femtosecond (fs) laser ablation in liquid as a scalable strategy for defect controlled exfoliation of WS2 and in situ formation of WS2/CsPbBr3 nanocomposite. Using 50 fs pulses at identical fluence, we directly compare Gaussian and Bessel beam profiles to elucidate how spatial energy distribution governs nonlinear carrier generation, Coulomb stress and electron-lattice energy transfer. Multiphysics modeling combining nonlinear absorption, Coulomb instability criteria and two temperature dynamics reveals that the axially extended, weakly diffracting Bessel profile excites carrier densities above the electronic destabilization threshold while reducing the peak lattice heating. In contrast, Gaussian excitation concentrates energy within the focal volume, promoting rapid thermalization and defect formation. Spectroscopic analysis reveals reduced trap assisted recombination and enhanced excitonic stability in Bessel processed samples. Transient absorption spectroscopy (TAS) further demonstrates prolonged carrier lifetime. Extending this approach, single step ablation yields WS2/CsPbBr3 hybrids exhibiting Type-I band alignment and geometry dependent interfacial carrier injection, evidenced by photoluminescence quenching and modified ultrafast decay dynamics.

Multi-degree-of-freedom (DOF) robotic manipulators exhibit strongly nonlinear, high-dimensional, and coupled dynamics, posing significant challenges for controller design. To address these issues, this work proposes a unified hybrid control architecture that integrates model predictive control (MPC) with feedback regulation, together with a stability analysis of the proposed scheme. The proposed approach mitigates the optimization difficulty associated with high-dimensional nonlinear systems and enhances overall control performance. Furthermore, a hardware implementation scheme based on machine learning (ML) is proposed to achieve high computational efficiency while maintaining control accuracy. Finally, simulation and hardware experiments under external disturbances validate the proposed architecture, demonstrating its superior performance, hardware feasibility, and generalization capability for multi-DOF manipulation tasks.

Phases that go beyond dipolar ordering and into multipolar ordering have recently been observed in magneto-electric materials. The resulting phase diagram is commonly explained using the concept of competing orders and exact microscopic interactions. In contrast, we propose an approach based on composite order emerging from a parent phase to explain quadrupoling above magnetic or electric dipolar orders. We include thermal fluctuations and symmetry and show their influence on the emergence of quadrupolar order. We find an analytical expression for the quadrupolar transition temperature, the critical anisotropy and explain the coupling of the quadrupolar order to mechanical strain, in agreement with experiments. The shift in perspective on quadrupolar ordering from competing to composite order is universal and can be extended to other types of multipolar ordering. This offers the possibility of understanding tunability and material-specific predictions of the related phase transitions without explicit knowledge of the microscopic mechanisms.

Personas are a valuable tool for discussing accessibility requirements in software design and development practices. However, the use of personas for accessibility-focused requirements elicitation in VR projects remains limited and is accompanied by several challenges. To fill this gap, we developed an auto-generated persona system in a VR course, where the personas were used to facilitate discussions on accessibility requirements and to guide VR design and development. Our findings indicate that the auto-generated persona system enabled students to develop empathy more efficiently. This study demonstrates the use of automatically generated personas in VR course settings as a means of eliciting latent accessibility requirements.

We study the time-splitting scheme for approximating solutions to the Cauchy problem of the nonlinear Dirac equation in 1+1 dimensions. Under the assumption that the initial data for the scheme are convergent in $\mathrm{L}^{2}(\mathbb{R})$, we prove that the approximate solutions constructed by the corresponding time-splitting scheme are strongly convergent in $\mathrm{C}([0,\infty);\mathrm{L}^{2}(\mathbb{R}))$ to the global strong solution of the nonlinear Dirac equation. To achieve this, we first establish the pointwise estimates for time-splitting solutions. Based on these estimates, a modified Glimm-type functional is carefully designed to show that it is uniformly bounded in time, which yields $\mathrm{L}^2$ stability estimates for the scheme. Furthermore, we prove that the set of time-splitting solutions is precompact in $\mathrm{C}([0,T];\mathrm{L}^{2}(\mathbb{R}))$ for any $T>0$. Finally, we show that the limit of any subsequence of the time-splitting solutions is the unique strong solution to the Cauchy problem of the nonlinear Dirac equation.

Given a compact oriented manifold of dimension $n$ with a conically smooth stratification, we show that the moduli of $\mathcal{D}(k)$-valued constructible sheaves and the moduli of perverse sheaves are $(2-n)$-shifted Lagrangian. The former statement follows from the construction of a relative left $n$-Calabi--Yau structure on the stable $\infty$-category of $\mathcal{D}(k)$-valued constructible sheaves. This is achieved via a lax gluing result for categorical cubes equipped with cubical Calabi--Yau structures. Given a codimension $2$ submanifold, we further identify symplectic leaves corresponding to perverse sheaves with prescribed monodromy.

Compared to the first generation of deep neural networks, dominated by regular, compute-intensive kernels such as matrix multiplications (MatMuls) and convolutions, modern decoder-based transformers interleave attention, normalization, and data-dependent control flow. This demands flexible accelerators, a requirement met by scalable, highly energy-efficient shared-L1-memory vector processing element (VPE) clusters. Meanwhile, the ever-growing size and bandwidth needs of state-of-the-art models make reduced-precision formats increasingly attractive. Microscaling (MX) data formats, based on block floating-point (BFP) representations, have emerged as a promising solution to reduce data volumes while preserving accuracy. However, MX semantics are poorly aligned with vector execution: block scaling and multi-step mixed-precision operations break the regularity of vector pipelines, leading to underutilized compute resources and performance degradation. To address these challenges, we propose VMXDOTP, a RISC-V Vector (RVV) 1.0 instruction set architecture (ISA) extension for efficient MX dot product execution, supporting MXFP8 and MXFP4 inputs, FP32 and BF16 accumulation, and software-defined block sizes. A VMXDOTP-enhanced VPE cluster achieves up to 97 % utilization on MX-MatMul. Implemented in 12 nm FinFET, it achieves up to 125 MXFP8-GFLOPS and 250 MXFP4-GFLOPS, with 843/1632 MXFP8/MXFP4-GFLOPS/W at 1 GHz, 0.8 V, and only 7.2 % area overhead. Our design yields up to 7.0x speedup and 4.9x energy efficiency with respect to software-emulated MXFP8-MatMul. Compared with prior MX engines, VMXDOTP supports variable block sizes, is up to 1.4x more area-efficient, and delivers up to 2.1x higher energy efficiency.

We present a systematic investigation of superconductivity in a topological superconductor candidate $T_{\rm d}$-MoTe$_2$ in the few-layer limit. By examining multiple mechanically exfoliated samples with different thicknesses, substrates and crystal qualities, we quantitatively correlate superconducting temperature ($T_c$) with disorder, carrier density, carrier type and mobility. By integrating these experimental findings with first-principles calculations, we reveal the relationship between the band structure and superconductivity in this material. Notably, in 2 L samples we access a highly hole-doped regime that has not been systematically explored in previous experiments, providing a complementary perspective to earlier studies. In this regime, we demonstrate that superconductivity can be realized in a manner consistent with a conventional phonon-mediated $s_{(++)}$-wave pairing.

In order to describe the nonisothermal dynamics of two-phase flows or binary mixtures such as colloidal suspensions consisting of colloidal particles and solvent on a microscopic level, we derive a new extended dynamical density functional theory (EDDFT) that includes the total mass density, the local concentration of one species, the total momentum density, and the energy density as variables using the Mori-Zwanzig-Forster projection operator technique. Through the incorporation of the momentum density into EDDFT, not only the diffusive but also the convective dynamics is taken into account. We derive an exact entropy and free-energy functional for the case of hard spheres. The hydrodynamic limit of our new EDDFT and its relation to the mode-coupling theory of the glass transition are discussed. It is shown that EDDFT allows to obtain the correct value for the speed of sound.

Let $G^{w}=(V,E,w)$ be a positive-weighted graph with the weight $w(e)>0$ for all $e\in E$. The weighted graph $G^{\widetilde{w}}=(V,E,\widetilde{w})$ is called a hyper-dual number weighted graph, where the weight $\widetilde{w}(e)=w(e)+Δw(e)(\varepsilon+\varepsilon^{*})$ is a hyper dual number, $Δw(e)$ is a real number, $\varepsilon$ and $\varepsilon^{*}$ are two dual units, $e\in E$. In this paper, we give a representation for the Moore-Penrose inverse of the Laplacian matrix, and calculation formulas for the resistance distance and Kirchhoff index of $G^{\widetilde{w}}$, respectively. We establish quadratic forms of the Hessian matrices for the resistance distance and Kirchhoff index of $G^{w}$ via generalized matrix inverses. We further derive explicit bounds on the eigenvalues of the Hessian matrices for the resistance distance and the Kirchhoff index of $G^{w}$ in terms of graph parameters. We also prove that the Kirchhoff index of a positive-weighted graph with bounded edge weights is strongly convex on its edge weight vector.

As the penetration level of distributed energy resources (DERs) continues to rise, traditional frequency and voltage support from synchronous machines declines. This weakens grid stability and increases the need for fast and adaptive control in a dynamic manner, especially in weak grids. However, most virtual power plants (VPPs) rely on static aggregation and plan based resource allocation strategies. These methods overlook differences in device response times and limit flexibility for ancillary services. To address this issue, we propose a dynamic virtual power plant (DVPP) that coordinates heterogeneous resources across multiple time scales using grid forming control. We first contrast grid following and grid forming converters: grid following designs rely on a phase locked loop which can undermine stability in weak grids, whereas our DVPP applies virtual synchronous generator control at the aggregate level to provide effective inertia and damping. Then, we introduce a dynamic participation factor framework that measures each device s contribution through the frequency active power and voltage reactive power loops. Exploiting device heterogeneity, we adopt a banded allocation strategy: slow resources manage steady state and low frequency regulation; intermediate resources smooth transitions; and fast resources deliver rapid response and high frequency damping. Comparative simulations demonstrate that this coordinated, timescale aware approach enhances stability and ancillary service performance compared to conventional VPPs.