This paper studies the economic role of persistent dispersion in allocations across agents. We develop a tractable model in which firms allocate resources under imperfect information and behavioral updating, generating sustained heterogeneity in beliefs and actions. While dispersion induces static misallocation, it also fosters decentralized experimentation, allowing the economy to explore a broader set of productive opportunities. We show that the economy converges to a stationary equilibrium with strictly positive dispersion and that, under plausible conditions, such disequilibrium can dominate the perfectly coordinated benchmark. The model provides a novel interpretation of observed dispersion in productivity and returns as reflecting both inefficiency and productive exploration. It also yields testable predictions linking dispersion to growth and innovation dynamics.

In 1972, J. S. Lew established a reasonable conjecture regarding an axiomatic characterization for the one-dimensional Riemann-Liouville integral. This conjecture was proved by Cartwright and McMullen in 1978. After that, little further work has been done on this topic, except some extensions for the Stieltjes case in one and several variables. In this paper, we prove the necessity of the axioms established in the conjecture of J. S. Lew using the Cauchy functional equation and Hamel bases. In addition, we give a proof for the characterization in several variables by employing Titchmarsh theorem, as a natural extension of the approach of Cartwright and McMullen. We also provide an alternative version and proof in one and several variables with Laplace transforms and the Cauchy functional equation, weakening parts of the continuity assumption. We show a similar result for the Riesz potential in terms of the Fourier transform. Finally, we illustrate how the theory can be used for characterization in the context of fractional calculus with respect to a non-smooth integrator, based on transmutation and measures.

We show that, for a principal ideal domain R, the homotopy category of Bousfield R-local spaces injects fully faithful into a homotopy category of simplicial pointed flat coalgebras.

We introduce a machine-learning approach for identifying hidden structural features of open quantum dynamics under restricted experimental access. Unlike most existing data-driven methods which focus on detection or prediction of dynamical behavior, our framework targets the inference of invariant algebraic structures underlying the effective Markovian evolution. Measurement limitations, symmetries, and superselection rules are incorporated through a $*$-algebraic description of accessible observables. The learning problem is formulated as maximum-likelihood estimation from multi-time measurement sequences, where the algebraic type of an invariant subalgebra - articularly a decoherence-free subalgebra - is treated as a discrete structural hypothesis. The feasibility of the approach is illustrated on multiple synthetic models and a waveguide quantum electrodynamics system, where nontrivial intermediate algebraic structures are identified directly from measurement data.

This paper proposes a new method for constructing multidimensional signal constellations (SC), referred to as SCOPT, for high-speed communication systems with enhanced energy efficiency (EE). In contrast to conventional approaches, the proposed method increases the minimum Euclidean distance (MED) between signals by increasing the normalized signal duration, without relying on coding or increasing transmit power. Analytical expressions for the demodulation error probability and the energy loss relative to the Shannon limit are derived. It is shown that, unlike classical Shannon-type constellations (SCSH), SCOPT enable reliable communication regimes in which the required signal-to-noise ratio may fall below the conventional Shannon limit within the adopted geometric framework. The proposed constellations retain a simple structure compatible with standard modulation schemes such as QAM and APSK,making them suitable for practical implementation in modern communication systems. Numerical analysis demonstrates that SCOPT significantly outperform SCSH in terms of energy efficiency while requiring substantially shorter signal duration.

Ultrafast light-driven chemical dynamics at surfaces are governed by energy transfer from excited electrons to vibrational degrees of freedom. When this nonadiabatic energy transfer is anisotropic, it can lead to dynamical steering effects that affect reaction probabilities or non-thermal final energy distributions in molecules. Here, we use a machine-learning-enabled simulation framework to compare isotropic and anisotropic models of electronic friction during laser-driven hydrogen evolution on the (111) facet of copper. While anisotropic friction strongly determines the rate of energy transfer into the adsorbate and the fluence dependence of reaction probabilities, it has little effect on final translational, vibrational and rotational energy distributions as these are mainly governed by the potential energy landscape at the barrier.

How do Dwarf Galaxies differ from spirals? Does star formation produce radio and far-infrared emission in the same way as in spiral galaxies? Radio, FarIR, and CO emission depend on gas density, temperature, magnetic field strength, and metallicity. The radio-FarIR correlation and Schmidt-Kennicutt relation characterize the links for Milky Way-like galaxies but do they hold for smaller objects, with different morphologies? Here we extend our previous work on the IR, line, and radio emission of local and high-z galaxies to local star-forming low-mass and dwarf galaxies. The calculation of the cosmic ray (CR) densities were improved compared to the previous version of the model. The CR ionization rate we found for the different galaxy samples is higher by a factor of three than for the solar neighborhood. This means that the mean yield of low-energy CR particles three times higher in external galaxies than was observed by Voyager I. The dependence of the N_H2/I_CO factor on the metallicity and stellar mass are calculated by the model. The weaker CO emission from low-metallicity galaxies is due to the large amount of (CO-dark) H_2 surrounding the regions where CO is not photo-dissociated. Within our model framework, star-forming low-mass and dwarf galaxies follow the radio-IR correlation.

An injection system for polymer particles, with diameters ranging from 1 to 6 $μ$m, has been developed for visualizing flows in superfluid $^4$He at temperatures down to 0.14 K. Using an ultrasound transducer, bursts of particles were launched into a sample of superfluid and allowed to descend under gravity. The particles were imaged using their fluorescence in the presence of a sheet of laser light. We report on the statistical behavior of particles during their descent, including descriptions of a mixture of smooth and erratic trajectories, indicative of the interactions with thermal excitations and quantized vortex lines. Temperature-dependent velocity distributions were measured and analyzed, yielding Gaussian distributions with power law tails persisting into the zero temperature limit. When sampled over increasing length scales, these distributions bifurcated into exponential for the smallest particles and bimodal Gaussian for the largest. We also report observations of long-lived suspensions of small particles at temperatures near 1 K, which appear to be associated with the trapping of large numbers of particles in a turbulent vortex tangle. A method was developed for identifying and quantifying the numbers of particles bound to vortex lines, allowing for a description of the temporal dynamics of their population by an analytical model.

We present a theoretical study of quantum magneto-transport and magneto-optical (M-O) properties in modified-Haldane model; which is applicable to diverse classes of two-dimensional (2D) quantum materials such as buckled Xene monolayers and transition metal dichalcogenide (TMDC) monolayers. By varying the staggered sublattice potential and intrinsic spin-orbit coupling, we identify distinct topological regimes and analyze their manifestations in the emergence of Landau levels, the evolution of the density of states, and the characteristics of M-O absorption spectra. Using the Kubo formalism, we compute the longitudinal and Hall M-O conductivities and show that inter-Landau-level (inter-LL) transitions produce characteristic resonance features that provide optical signatures of the underlying topological phases. Within this framework, we demonstrate electrically tunable topological phase transitions in buckled silicene. Extending our study to monolayer TMDCs, we show that inspite of large band gap, the spin-valley coupling provides a powerful tool for tailoring M-O absorption features across wide range of 2D materials. Collectively, these results underscore modified-Haldane-model materials as an ideal testbed for engineering quantum transport, with promising applications in topological photonics, valleytronic devices, and next-generation optoelectronics.

Neural Architecture Search (NAS) has become a pivotal technique in automated machine learning. Evolutionary Algorithm (EA)-based methods demonstrate superior search quality but suffer from prohibitive computational costs, while gradient-based approaches like DARTS offer high efficiency but are prone to premature convergence and performance collapse. To bridge this gap, we propose G-ICSO-NAS, a hybrid framework implementing a three-stage optimization strategy. The Warm-up Phase pre-trains supernet weights ($w$) via differentiable methods while architecture parameters ($α$) remain frozen. The Exploration Phase adopts a hybrid co-optimization mechanism: an Improved Competitive Swarm Optimizer (ICSO) with diversity-aware fitness navigates the architecture space to update $α$, while gradient descent concurrently updates $w$. The Stability Phase employs fine-grained gradient-based search with early stopping to converge to the optimal architecture. By synergizing ICSO's global navigation capability with differentiable methods' efficiency, G-ICSO-NAS achieves remarkable performance with minimal cost. In the context of the DARTS search space, an accuracy of 97.46\% is achieved on CIFAR-10 with a computational budget of just 0.15 GPU-Days. The method also exhibits strong transfer potential, recording accuracies of 83.1\% (CIFAR-100) and 75.02\% (ImageNet). Furthermore, regarding the NAS-Bench-201 benchmark, G-ICSO-NAS is shown to deliver state-of-the-art results across all evaluated datasets.

Due to their widespread use in industry, several techniques have been proposed in the literature to fuzz REST APIs. Existing fuzzers for REST APIs have been focusing on detecting crashes (e.g., 500 HTTP server error status code). However, security vulnerabilities can have major drastic consequences on existing cloud infrastructures. In this paper, we propose a series of novel automated oracles aimed at detecting violations of access policies in REST APIs, as well as executing traditional attacks such as SQL Injection and XSS. These novel automated oracles can be integrated into existing fuzzers, in which, once the fuzzing session is completed, a ``security testing'' phase is executed to verify these oracles. When a security fault is detected, as output our technique is able to general executable test cases in different formats, like Java, Kotlin, Python and JavaScript test suites. Our novel techniques are integrated as an extension of EvoMaster, a state-of-the-art open-source fuzzer for REST APIs. Experiments are carried out on 9 artificial examples, 8 vulnerable-by-design REST APIs with black-box testing, and 36 REST APIs from the WFD corpus with white-box testing, for a total of 52 distinct APIs. Results show that our novel oracles and their automated integration in a fuzzing process can lead to detect security issues in several of these APIs.

Vehicle-to-infrastructure collaborative perception (V2I-CP) leverages a high-vantage node to transmit supplementary information, i.e., bird's-eye-view (BEV) feature maps, to vehicles, effectively overcoming line-of-sight limitations. However, the downlink V2I transmission introduces a significant communication bottleneck. Moreover, vehicles in V2I-CP require \textit{heterogeneous yet overlapping} information tailored to their unique occlusions and locations, rendering standard unicast/broadcast protocols inefficient. To address this limitation, we propose \textit{Birdcast}, a novel multicasting framework for V2I-CP. By accounting for individual maps of interest, we formulate a joint feature selection and multicast grouping problem to maximize network-wide utility under communication constraints. Since this formulation is a mixed-integer nonlinear program and is NP-hard, we develop an accelerated greedy algorithm with a theoretical $(1 - 1/\sqrt{e})$ approximation guarantee. While motivated by CP, Birdcast provides a general framework applicable to a wide range of multicasting systems where users possess heterogeneous interests and varying channel conditions. Extensive simulations on the V2X-Sim dataset demonstrate that Birdcast significantly outperforms state-of-the-art baselines in both system utility and perception quality, achieving up to 27\% improvement in total utility and a 3.2\% increase in mean average precision (mAP).

The 15-minute city is a powerful planning concept to counter car-dependence by promoting active mobility to amenities and fostering inclusive urban environments. However, this policy has challenges in amenity-poor urban peripheries. Public transport remains underexplored in this discourse despite its role in distant access. Here, we propose a framework that incorporates public transport into the 15-minute city model using openly available data. By comparing Helsinki, Madrid, and Budapest, we demonstrate that multimodal mobility substantially increases access to amenities and enhances socio-spatial integration within a 15-minute reach. Although urban periphery benefit significantly from radial or high-speed public transport lines in their social mixing potential, such lines alone do not improve their access to amenities. These findings underscore the need to optimize polycentric public transport networks that can improve inclusive urban accessibility and complement active mobility in polycentric cities.

Magnetic refrigeration can provide an environmentally friendly technology to reduce significantly the energy consumption of cooling devices. To retain the sustainability of the device, all parts must be made from abundant materials, excluding e.g. rare earth elements. As such, materials based on Fe$_2$P have shown great potential for magnetocaloric devices. In this study, Fe$_2$P and FeMnP$_{0.55}$Si$_{0.45}$, have been studied using magnetometry, neutron scattering and theoretical modelling with the aim to understand the ferromagnetic transition, related to the magnetocaloric effect. Analysis of the diffraction data of Fe$_2$P showed that it is the Fe$_{3g}$-site that drives the magnetic transition as the Fe$_{3f}$ does not have any magnetic contribution at the magnetic transition temperature. For FeMnP$_{0.55}$Si$_{0.45}$, the magnetic transition is more gradual, on both sites, with coexistence of the para- and ferromagnetic phases close to the magnetic transition. The temperature dependent magnetic structure behaviour are well in agreement with our first principles calculations. Both Fe$_2$P and FeMnP$_{0.55}$Si$_{0.45}$ showed two distinct regions, at different length scales, in their S(\textbf{Q},$ω$) spectra. The two length scales can be modelled using a different set of magnetic spin states (S), using S$\rm _{Fe}$~=~2 and S$\rm _{Mn}$~=~2.5, consistent with the ground state of the magnetic atoms. QENS at low Q (Q~\textless{}~0.5~Å) shows similar magnetic processes in both compounds with uncorrelated magnetism below the magnetic transition temperature. The uncorrelated state highlights that the magnetic anisotropy does not play a major role in the formation of the magnetic state. Furthermore, this emphasises the existence of a two part system in FeMn(P,Si)-based compounds, that drives the magnetic transition and in turn the magnetocaloric effect.

In 2023, Li, Du, Yi proved a uniqueness theorem for L functions in the extended Selberg class under the assumptions of positive degree, a shared functional equation, and the sharing of three complex values. This was later strengthened by the present authors, who showed that sharing an arbitrary finite set of complex values, counted with multiplicities, still forces equality of the two L functions, again under the assumption that they satisfy the same functional equation. In this paper, we significantly improve all these results. We completely remove the requirement that the two L functions satisfy the same functional equation, yet we still obtain the same strong uniqueness conclusion under far weaker hypotheses. As a major consequence, we prove that every polynomial with distinct zeros is a strong uniqueness polynomial for L functions.

This paper establishes a quantitative, uniform-in-time diffusion approximation for the joint law of a broad class of fully coupled multiscale stochastic systems. We derive a precise characterization of the limiting joint distribution as a specific skew-product of the conditional equilibrium of the fast process and the homogenized law of the slow component, thereby providing a rigorous uniform-in-time formulation of the adiabatic elimination principle. The convergence rate explicitly separates the initial relaxation of the fast dynamics from the long-time homogenized evolution and depends only on the regularity of the coefficients in the slow variable. As a consequence, we obtain the first quantitative identification of the limiting stationary distribution of the original multiscale system and prove the commutativity of the limits $\eps\to0$ and $t\to\infty$ for a large class of observables. Our framework accommodates unbounded and irregular coefficients, degenerate structures, and weakly mixing dynamics. We illustrate its scope with three applications: {\it (i)} a uniform-in-time averaging principle for fast-slow systems; {\it (ii)} a uniform Smoluchowski--Kramers approximation for degenerate Langevin systems, yielding convergence of the joint position-scaled velocity law and global-in-time asymptotics of key thermodynamic functionals (e.g., total energy, entropy production, free energy); and {\it (iii)} the first uniform-in-time periodic homogenization result for SDEs with distributional drifts.

The Maximum (Minimum) Leaf Spanning Tree problem asks for a spanning tree with the largest (smallest) number of leaves. As spanning trees are often computed using graph search algorithms, it is natural to restrict this problem to the set of search trees of some particular graph search, e.g., find the Breadth-First Search (BFS) tree with the largest number of leaves. We study this problem for Generic Search (GS), BFS and Lexicographic Breadth-First Search (LBFS) using search trees that connect each vertex to its first neighbor in the search order (first-in trees) just like the classic BFS tree. In particular, we analyze the complexity of these problems, both in the classical and in the parameterized sense. Among other results, we show that the minimum and maximum leaf problems are in FPT for the first-in trees of GS, BFS and LBFS when parameterized by the number of leaves in the tree. However, when these problems are parameterized by the number of internal vertices of the tree, they are W[1]-hard for the first-in trees of GS, BFS and LBFS.

We investigate the coupled dynamics of symmetry breaking and phase separation during quenches across the critical point in a first-order phase transition. Based on the Einstein-Maxwell-scalar theory, we construct a holographic superfluid model with $\mathbb{Z}_2$ symmetry. By introducing higher-order nonlinear terms $λΨ^4$ and $τΨ^6$ into the scalar field potential, we realize a rich phase structure, which enables us to study the coupling effects between symmetry breaking and phase separation. Furthermore, by preparing initial conditions with well-defined spatial partitions, we discover a new triggering mechanism for the invasion phenomenon, namely that kinks serve as triggering sites for the phase separation process. This study reveals a novel coupling mechanism between topological defects and phase separation, enriches our understanding of nonequilibrium structure formation in strongly coupled systems.

Smart contract vulnerabilities can cause substantial financial losses due to the immutability of code after deployment. While existing tools detect vulnerabilities, they cannot effectively repair them. In this paper, we propose SCPatcher, a framework that combines retrieval-augmented generation with a knowledge graph for automated smart contract repair. We construct a knowledge graph from 5,000 verified Ethereum contracts, extracting function-level relationships to build a semantic network. This graph serves as an external knowledge base that enhances Large Language Model reasoning and enables precise vulnerability patching. We introduce a two-stage repair strategy, initial knowledge-guided repair followed by Chain-of-Thought reasoning for complex vulnerabilities. Evaluated on a diverse set of vulnerable contracts, SCPatcher achieves 81.5\% overall repair rate and 91.0\% compilation pass rate, substantially outperforming existing methods.

We develop a unified PDE-probabilistic framework for pointwise gradient and Hessian estimates of Markov semigroups associated with stochastic differential equations with singular and unbounded coefficients. Under mild local structural assumptions on the diffusion matrix and integrability/regularity conditions on the drift, we obtain quantitative sharp short-time regularization estimates as well as long-time decay bounds (including exponential and polynomial rates) for the first and second spatial derivatives of the semigroup. A distinctive feature of our results is the explicit dependence of these estimates on local norms of the coefficients (through scale-invariant quantities), without requiring any global smoothness, boundedness or uniform ellipticity. In particular, our approach allows for degenerate or highly irregular behavior at infinity, subject to suitable local ellipticity and Lyapunov/ergodicity controls. As applications, we establish solvability and regularity results for Poisson equations on the whole space with singular coefficients, and we derive pointwise gradient estimates for SDEs with distributional drifts via a Zvonkin-type transform.

Stochastic natural gradient variational inference (NGVI) is a popular and efficient algorithm for Bayesian inference. Despite empirical success, the convergence of this method is still not fully understood. In this work, we define and study a projected stochastic NGVI when variational distributions form an exponential family. Stochasticity arises when either gradients are intractable expectations or large sums. We prove new non-asymptotic convergence results for combinations of constant or decreasing step sizes and constant or increasing sample/batch sizes. When all hyperparameters are fixed, NGVI is shown to converge geometrically to a neighborhood of the optimum, while we establish convergence to the optimum with rates of the form $\mathcal{O}\left(\frac{1}{T^ρ} \right)$, possibly with $ρ\geq 1$, for all other combinations of step size and sample/batch size schedules. These rates apply when the target posterior distribution is close in some sense to the considered exponential family. Our theoretical results extend existing NGVI and stochastic optimization results and provide more flexibility to adjust, in a principled way, step sizes and sample/batch sizes in order to meet speed, resources, or accuracy constraints.

We extend the weak-strong uniqueness principle for mean-field game (MFG) systems to a broad class of second-order stationary and time-dependent problems. Under standard monotonicity, growth, and coercivity assumptions on the Hamiltonian, and relying strictly on the integrability exponents guaranteed by the existing theory for monotone MFG systems, we show that any weak solution must coincide with a given strong solution. Our analysis covers models with spatially dependent scalar diffusion coefficients, using monotonicity arguments and a coefficient-adapted mollification strategy to manage the variable diffusion terms. We extend this strategy to establish weak-strong uniqueness in the corresponding second-order, initial-terminal, time-dependent setting. Finally, to address the critical quadratic growth regime, we derive a new a priori second-order estimate for a stationary MFG system with logarithmic coupling. This estimate provides quantitative bounds on the solution in terms of the data, and yields weak-strong uniqueness in the range where the improved integrability yields $L^2$ control of the density. Since numerical and approximation methods for MFGs naturally yield weak solutions in the monotonicity sense, whereas strong solutions are known to exist in many settings, our results identify any weak limit produced by such methods with the strong solution whenever one exists.

This study is concerned with the problem of partial state estimation for linear time-invariant (LTI) distributed state-space systems. A necessary and sufficient condition is established in terms of a simple rank criterion involving the system coefficient matrices, provided the communication graph is either directed, balanced and strongly connected or undirected and connected. The estimator parameter matrices are obtained by simple matrix theory. Finally, a numerical example demonstrates the feasibility and effectiveness of the proposed theoretical results and design algorithm.

We investigate the heteroclinic connections between stable and unstable manifolds of unstable periodic orbits associated with the most important mean motion resonances (MMRs) in the Sun-Jupiter planar restricted three-body problem. We explicitly compute the stable and unstable manifolds of the unstable periodic orbits associated with the first order interior MMRs 2:1, 3:2, and the exterior MMR 2:3. We also compute short-time FLI maps showing the chaotic saddle structure created by the manifolds of several interior or exterior MMRs other than the 1:1 (co-orbital) resonance. Transits of particles from the exterior to the interior of Jupiter's orbit and vice versa are allowed for Tisserand parameter lesser than 3, and are shown to exist through a variety of heteroclinic channels. Besides the classical ones by Koon et al., we find heteroclinic connections between manifolds of short-period orbits around L3 and periodic orbits of interior or exterior first order MMRs, as well as direct connections between interior and exterior MMR manifolds not involving co-orbital periodic orbits. Through these manifolds and the corresponding FLI ridges, we explain the 'arches-of-chaos' in the asteroid orbital plane (a,e). Chaotic orbits shadowing heteroclinic trajectories exhibit resonance hopping, suggesting links to quasi-Hildas and Jupiter-family comets. Results are obtained in the circular RTBP but persist in the elliptic problem.

We study the impact of BN's phonons on the electrical resistivity of hBN-encapsulated graphene. While encapsulation yields high-mobility devices, the surrounding BN itself introduces remote scattering from polar optical phonons, whose role in standard resistivity measurements remains unclear. We combine high-quality transport experiments with ab initio calculations including a proper treatment of dynamically screened remote interactions. We demonstrate that hBN's out-of-plane phonons strongly influence resistivity between 150 K and room temperature, whereas higher-energy LO modes and intrinsic graphene phonons alone cannot explain the observed trends. The coupling between electrons and the BN's phonons becomes more pronounced at low carrier densities due to reduced screening. Our findings establish that remote phonon scattering fundamentally limits transport in encapsulated graphene, solving a longstanding debate.

High-Resolution three-dimensional (3D) radio maps (RMs) provide rich information about the radio landscape that is essential to a myriad of wireless applications in the future wireless networks. Although deep learning (DL) methods have shown their effectiveness in RM construction, existing approaches require massive high-resolution 3D RM samples in the training dataset, the acquisition of which is labor-intensive and time-consuming in practice. In this paper, our goal is to devise a data-friendly high-resolution 3D RM construction solution via training over a hybrid dataset, wherein the RMs associated with a small fraction of environment maps (EMs) are of high-resolution, while those corresponding to the majority of EMs are of low-resolution. To this end, we propose a Data-Friendly 3D Radio Map Estimator (DF-3DRME), which comprises two processing stages. Specifically, in the first stage, we leverage the abundant low-resolution 3D RM samples to train a neural network, termed the LR-Net, for predicting the low-resolution 3D RM from the input EM, which provides a coarse characterization of the spatial radio propagation. In the second stage, we employ an advanced super-resolution network, termed the SR-Net, to upscale the predicted low-resolution 3D RM to its high-resolution counterpart. Unlike the LR-Net, the SR-Net can be effectively trained with only the limited high-resolution 3D RM samples available in the hybrid dataset. Experimental results demonstrate that the proposed framework achieves compelling reconstruction performance with only 4% of the EMs in the dataset having high-resolution 3D RM labels, which significantly reduces data acquisition overhead and facilitates practical deployment.

A rapid expansion of system flexibility is essential to integrate increasing shares of renewable energy into future energy systems. However, flexibility needs and technology-specific contributions to flexibility remain poorly quantified in energy system modelling. Existing methods are not widely applied, leaving key questions unanswered: which flexibility technologies are critical for climate neutrality, and what are the cost implications of alternative deployment strategies? To address this gap, we apply a correlation-based flexibility metric to a high-resolution, sector-coupled model of the German energy system, covering its transformation towards climate neutrality. For our default scenario, we find that daily flexibility needs increase by a factor of 3.7 between 2025 and 2045, driven primarily by the expansion of solar PV. By 2045, stationary batteries provide 38% of daily flexibility, while flexible electric vehicle charging contributes 30%. Systems with constrained flexibility increase system costs by 6.9%, electricity prices by 14 EUR/MWh and trigger 47% higher hydrogen and e-fuel imports compared to an unconstrained system in 2045. In contrast, scenarios with high shares of flexible electric vehicle charging, vehicle-to-grid, and industrial demand-side management achieve system cost reductions of 3.3%, while also reducing import dependence. Higher flexibility also reduces electricity price ranges, decreases average electricity prices by 3 EUR/MWh, and reduces backup capacity by 22% (22 GW). Overall, our results highlight the decisive role of specific flexibility technologies in achieving cost-efficient and energy-secure climate-neutral energy systems, providing quantitative guidance for policy and investment decisions.

Probabilistic power flow (PPF) is essential for quantifying operational uncertainty in modern distribution systems with high penetration of renewable generation and flexible loads. Conventional PPF methods primarily rely on Monte Carlo (MC) based power flow (PF) simulations or simplified analytical approximations. While MC approaches are computationally intensive and demand substantial data storage, analytical approximations often compromise accuracy. In this paper, we propose a novel analytical PPF framework that eliminates the dependence on MC-based PF simulations and, in principle, enables an approximation of the analytical form of arbitrary voltage distributions. The core idea is to learn an explicit and invertible mapping between stochastic power injections and system voltages using invertible neural networks (INNs). By leveraging the Change of Variable Theorem, the proposed framework facilitates direct approximation of the analytical form of voltage probability distributions without repeated PF computations. Extensive numerical studies demonstrate that the proposed framework achieves state-of-the-art performance both as a high-accuracy PF solver and as an efficient analytical PPF estimator.

This paper applies a discrete adjoint gradient computation method for a multi-class traffic flow model on road networks. Vehicle classes are characterized by their specific velocity functions, which depend on the total traffic density, resulting in a coupled hyperbolic system of conservation laws. The system is discretized using a Godunov-type finite volume scheme based on demand and supply functions, extended to handle complex junction coupling conditions -- such as merges and diverges -- and boundary conditions with buffer lengths to account for congestion spillback. The optimization of different travel-related performance metrics, including total travel time and total travel distance, is formulated as a constrained minimization problem and is accomplished through the use of an adjoint gradient approach, allowing for an efficient computation of sensitivities with respect to the chosen time-dependent control variables. Numerical simulations on a sample network demonstrate the efficiency of the proposed framework, particularly as the number of control parameters increases. This approach provides a robust and computationally efficient solution, making it suitable for large-scale traffic network optimization.

A novel particle merging algorithm for rarefied gas dynamics simulations is proposed that can conserve arbitrary velocity and spatial moments of the particle distribution via solving a non-negative least squares problem. An extension that preserves both exact and approximate collision rates is also derived. The algorithm is applied to the simulation of several model rarefied gas dynamics problems, where it exhibits noticeably lower merging-induced error in key macroscopic quantities.