We characterize monitored quantum dynamics in a solvable model exhibiting a phase transition between a measurement apparatus and a scrambler. We show that approximate decoherent histories emerge in both phases with respect to a coarse-grained extensive observable. However, the apparatus phase, where quantum Darwinism emerges, is distinguished by the non-ergodicity of the histories and their correlation with the measured qubit, which selects an ensemble of preferred pointer states. Our results demonstrate a clear distinction between two notions of classicality, decoherent histories and environment-induced decoherence.

This paper addresses the single-assignment, uncapacitated, multi-level facility location (MFL) problem, a strategic decision-making process critical to the design of long-term supply chain networks. Specifically, we examine four- and five-level facility location structures (k-LFL), modeled as a location-allocation problem where demand nodes must be assigned to open facilities across hierarchical levels. Although the MFL has been addressed in the literature, solutions to large-scale, realistic problems involving thousands of nodes are lacking. This paper proposes a heuristic framework based on the Variable Neighborhood Descent (VND) metaheuristic with a multi-start strategy. We develop and compare four variants: Basic Variable Neighborhood Descent (BVND), Pipe Variable Neighborhood Descent (PVND), Cyclic Variable Neighborhood Descent (CVND), and Union Variable Neighborhood Descent (UVND). In each case, a multi-start strategy with strong diversification components is employed. Extensive computational experiments compare the methods on large-scale instances involving up to 10,000 customers, 150 distribution centers, 50 warehouses, and 30 plants. Each algorithm settled into a unique, statistically significant computational time when solving these problems. Sensitivity analyses, supported by non-parametric statistical methods, validate the effectiveness of the proposed heuristic framework.

The residual cutting (RC) method has been proposed as an outer-inner loop iteration for efficiently solving large and sparse linear systems of equations arising in solving numerically problems of elliptic partial differential equations. Then based on RC the generalized residual cutting (GRC) method has been introduced, which can be applied to more general sparse linear systems problems. In this paper, we show that GRC can stabilize the BiCGSTAB, which is also an iterative algorithm for solving large, sparse, and nonsymmetric linear systems, and widely used in scientific computing and engineering simulations, due to its robustness. BiCGSTAB converges faster and more smoothly than the original BiCG method, by reducing irregular convergence behavior by stabilizing residuals. However, it sometimes fails to converge due to stagnation or breakdown. We attempt to emphasize its robustness by further stabililizing it by GRC, avoiding such failures.

We present SPARCS, which combines the moment-based radiative transfer method SPH-M1RT with the non-equilibrium metal chemistry solver CHIMES in the modern highly-parallel astrophysical code SWIFT. SPARCS enables on-the-fly radiation hydrodynamics simulations, with multi-frequency ultraviolet radiative transfer coupled with all ionisation states of 11 major elements, in the presence of dust, cosmic ray ionization and heating, and self-gravity. Direct radiation pressure on gas and dust is also accounted for. We validate SPARCS against analytic solutions and standard photo-ionization codes such as CLOUDY in idealized tests. As an example application, we simulate an ionization front propagating through an inhomogeneous interstellar medium with solar metallicity. We produce mock optical emission line observations with the level population calculation code HyLight and the diagnostic radiative transfer code RADMC3D. We find that non-equilibrium effects and inhomogeneities can boost the low ion fractions by up to an order of magnitude. Possible applications of SPARCS include studying the dynamical impact of radiation on gas in star-forming regions, and in the interstellar and circumgalactic medium, as well as interpreting line diagnostics in such environments, and galactic or AGN outflows.

We devise and analyse a novel $\boldsymbol{H}(\textbf{curl})$-reconstruction operator for piecewise polynomial fields on shape-regular simplicial meshes. The (non-polynomial) reconstruction is devised over the mesh vertex patches using the partition of unity induced by hat basis functions in combination with local Helmholtz decompositions. Our main focus is on homogeneous tangential boundary conditions. We prove that the difference between the reconstructed $\boldsymbol{H}_0(\textbf{curl})$-field and the original, piecewise polynomial field, measured in the broken curl norm and in the $\boldsymbol{L}^2$-norm, can be bounded in terms of suitable jump norms of the original field. The bounds are always $h$-optimal, and $p$-suboptimal by $\frac12$-order for the broken curl norm and by $\frac32$-order for the $\boldsymbol{L}^2$-norm. An auxiliary result of independent interest is a novel broken-curl, divergence-preserving Poincaré inequality on vertex patches. Moreover, the $\boldsymbol{L}^2$-norm estimate can be improved to $\frac12$-order suboptimality under a (reasonable) assumption on the uniform elliptic regularity pickup for a Poisson problem with Neumann conditions over the vertex patches. We also discuss extensions of the $\boldsymbol{H}_0(\textbf{curl})$-reconstruction operator to the prescription of mixed boundary conditions, to agglomerated polytopal meshes, and to convex domains. Finally, we showcase an important application of the $\boldsymbol{H}(\textbf{curl})$-reconstruction operator to the $hp$-a posteriori nonconforming error analysis of Maxwell's equations. We focus on the (symmetric) interior penalty discontinuous Galerkin (dG) approximation of some simplified forms of Maxwell's equations.

Integrated Sensing and Communication (ISAC) technology plays a critical role in future intelligent transportation systems, by enabling vehicles to perceive and reconstruct the surrounding environment through reuse of wireless signals, thereby reducing or even eliminating the need for additional sensors such as LiDAR or radar. However, existing ISAC based reconstruction methods often lack the ability to track dynamic scenes with sufficient accuracy and temporal consistency, limiting the real world applicability. To address this limitation, we propose a deep learning based framework for vehicular environment reconstruction by using ISAC channels. We first establish a joint channel environment dataset based on multi modal measurements from real world urban street scenarios. Then, a multistage deep learning network is developed to reconstruct the environment. Specifically, a scene decoder identifies the environmental context such as buildings, trees and so on; a cluster center decoder predicts coarse spatial layouts by localizing dominant scattering centers; a point cloud decoder recovers fine grained geometry and structure of surrounding environments. Experimental results demonstrate that the proposed method achieves high-quality dynamic environment reconstruction with a Chamfer Distance of 0.29 and F Score@1% of 0.87. In addition, complexity analysis demonstrates the efficiency and practical applicability of the method in real time scenarios. This work provides a pathway toward low cost environment reconstruction based on ISAC for future intelligent transportation.

The present work investigates the causal parameter space of the Mueller-Israel-Stewart second-order theory for heat-conducting fluids in the Eckart frame for one-dimensional fluid flow in systems with finite baryon density. It is shown that this parameter space is highly constrained and particularly sensitive to the equation of state and second-order transport coefficients. Through numerical analysis of the characteristic equations, the present analysis identifies regions of strong hyperbolicity, weak hyperbolicity, and non-hyperbolicity, mapping the boundaries of causality violation as functions of the heat flux to energy density ratio $q/\varepsilon$ and relaxation parameters. The present work also explores the causality conditions using a realistic lattice QCD-based equation of state. Using the Navier-Stokes approximation, an estimate is made of the heat flow magnitude to assess causality criteria for one-dimensional heat conduction in heavy-ion collisions. The present calculations reveal unrealistically large heat flux values ($|{\bf{q}}|/\varepsilon \approx 330$--$811$) for typical RHIC conditions when using thermal conductivity estimates from kinetic theory models, suggesting either significant overestimation of transport coefficients or breakdown of the fluid approximation in these extreme conditions. The pressure gradient corrections reduce the heat flow by approximately 15\% but do not resolve the causality concerns.

We introduce a unified framework for analyzing utility regions of wireless networks, with a focus on signal-to-interference-plus-noise-ratio (SINR) and achievable rate regions. The framework provides valuable insights into interference patterns of modern network architectures, including extremely large MIMO and cell-less networks. A central contribution is a simple characterization of feasible utility regions using the concept of spectral radius of nonlinear mappings. This characterization provides a powerful mathematical tool for wireless system design and analysis. For example, it allows us to generalize existing characterizations of the weak Pareto boundary using compact notation. It also allows us to derive tractable sufficient conditions for the identification of convex utility regions. This property is particularly important because, on the weak Pareto boundary, it guarantees that time sharing (or user grouping) cannot simultaneously improve the utilities of all users. Beyond geometrical insights, these sufficient conditions have two key implications. First, they identify a family of (weighted) sum-rate maximization problems that are inherently convex, thus paving the way for the development of efficient, provably optimal solvers for this family. Second, they provide justification for formulating sum-rate maximization problems directly in terms of achievable rates, rather than SINR levels. Our theoretical insights also motivate an alternative to the concept of favorable propagation in the massive MIMO literature -- one that explicitly accounts for self-interference and the beamforming strategy.

We consider the first positive Steklov eigenvalue on planar domains. First, we provide an example of a planar domain for which a first eigenfunction has a closed nodal line. Second, we establish a lower bound for the first positive eigenvalue on certain symmetric domains and show that this eigenvalue is simple for all ellipses. These results complement two statements contained in a work by Kuttler and Sigillito (Proc. Amer. Math. Soc. 20, 1969).

We first obtain explicit upper bounds for the proportion of elements in a finite classical group G with a given characteristic polynomial. We use this to complete the proof that the proportion of elements of a finite classical group G which lie in a proper irreducible subgroup tends to 0 as the dimension of the natural module goes to infinity. This result is analogous to the result of Luczak and Pyber [15] that the proportion of elements of the symmetric group S_n which are contained in a proper transitive subgroup other than the alternating group goes to 0 as n goes to infinity. We also show that the probability that 3 random elements of SL(n,q) invariably generate goes to 0 as n goes to infinity.

Imaging of the human body at ultra-high fields (static magnetic field B0>7 Tesla) is challenging due to the radio-frequency field inhomogeneities in the human body tissues caused by the short wavelength. These effects could be partially mitigated using an array of antennas and by parallel transmission allowing for control of the radio-frequency field distribution in the region of interest. All commonly-used radio-frequency arrays for ultra-high field MRI consist of resonant elements: dipoles, TEM-resonators, loops and individual slots. All these elements rely on standing wave excitation, in the sense that they are resonant devices that produce a field pattern with a constant phase distribution along the commensurable conductor elements. However, it was shown previously, that a non-uniform phase of surface current is required to reach the ultimate intrinsic signal-to-noise ratio or a maximized signal in the desired region of interest. In our work we propose to use a previously demonstrated non-resonant leaky-wave approach to control the phase of currents in radio-frequency coil conductors to increase the B1+ field in the center or in the region of interest. Using this approach, we developed a radio-frequency coil based on a leaky-wave antenna approach with optimized surface current distribution resulting in stronger B1+ in the desired region compared to e.g. a fractionated dipole.

This work studies certain notions of entropy that can be associated to (i) a representation of a separable, unital C*-algebra $\mathfrak{A}$ and (ii) an auxiliary random sequence $(π_n)_{n\ge 1}$ of finite-dimensional representations of $\mathfrak{A}$. This continues a previous research program into the properties of these entropy notions when each $π_n$ is deterministic, which uncovered a range of analogies with entropy in ergodic theory and also with non-commutative generalizations of Szegő's limit theorems. We associate two new notions of entropy to data as in (i) and (ii) above: `annealed' AP entropy, which is roughly a kind of first-moment average of deterministic AP entropies; and `zeroth-order' AP entropy, which controls the large deviations probabilities that certain positive definite functions appear in the representations $π_n$ at all. After developing some of this general theory, we then focus on the special case in which $\mathfrak{A}$ is the group C*-algebra of a finitely-generated free group and each $π_n$ is generated by choosing a tuple of $n$-by-$n$ unitary matrices independently at random from Haar measure. In that case, explicit formulas can be derived for some of our notions of entropy, and new large deviations principles in random matrix theory are obtained as a consequence.

We expand in instanton charge sectors the representation content of the infinite coupling chiral ring of the Higgs branch of 5d $\mathcal{N}=1$ $Sp(k)$ theories with $N_f$ flavours. The entire chiral ring can be expressed as the product of bare instantons, one for each topological sector, times a common dressing factor depending on the mesons and the instanton-anti instanton bound state. The dressing factor, which is independent of the instanton number, encodes the chiral ring of the theory at finite coupling with one additional colour.

Understanding the interplay between topology and correlated electron states is central to the study of quantum materials. TaTe$_4$ is a quasi-one-dimensional charge density wave (CDW) compound predicted to host topological phases, which makes it a model platform to explore this interplay. Here, we combine high-field magnetotransport measurements with density functional theory calculations to provide a comprehensive mapping of the Fermi surface (FS) of TaTe$_4$ in its CDW phase. Using multiple current-field geometries, we resolve the four largest of six pockets of the FS predicted by theory and find no evidence of non-CDW bands, highlighting the full reconstruction of the FS in the bulk. We identify a previously unobserved quasi-cylindrical pocket and uncover a large size orbit consistent with magnetic breakdown between reconstructed FS sheets, from which we estimate a CDW gap of $\sim$0.29~eV. Moreover, we observe a robust linear magnetoresistance that persists across all field directions when current flows perpendicular to the 1D chains along which the CDW is formed, with a distinct high-field linear regime emerging when field is along the chains. These findings establish TaTe$_4$ as a prototypical material to study the coexistence of correlation-driven reconstruction and topological electronic states.

Quantum electrodynamics lies at the heart of hybrid quantum systems essential for future technologies. The thermodynamic limit of the Dicke model, a fundamental model describing these systems, predicts exotic quantum phenomena, such as equilibrium superradiant phase transitions and ground-state two-mode squeezing. However, the experimental realization of genuine Dicke systems has remained elusive due to the inevitable existence of gauge-invariant self-interaction terms that hinder such phenomena. Here, we report on the on-chip realization of a Dicke-type system utilizing ultrastrong magnetic-dipole interactions between collective excitations in a spatially separated ferromagnetic array and a superconducting resonator, resulting in creation of magnon polaritons. Crucially, this spatially separated architecture allows the cooperative enhancement of the coupling strength without increasing the self-interaction energy. We experimentally confirm the Bloch-Siegert shift, originating from the counter-rotating terms, alongside the suppression of self-excitation terms required to observe critical Dicke physics. Our results establish a versatile platform, which provides the playground to explore quantum collective coupling physics and open pathways towards integrated quantum devices harnessing Dicke physics.

The TRIUMF Ultracold Advanced Neutron (TUCAN) collaboration has been developing a high-intensity ultracold neutron (UCN) source aimed at searching for the neutron electric dipole moment (EDM) with a sensitivity goal of $10^{-27}\ e{\rm cm}$. This article reports on recent progress in commissioning of the UCN source and in the development of the neutron EDM spectrometer. In its final configuration, the accelerator-driven super-thermal UCN source will enable a neutron EDM experiment with two orders of magnitude improved statistics compared to the current best experiment. Substantial progress in 2024 allowed the collaboration to operate the complete source system, with the exception of the liquid deuterium cold moderator, resulting in the first production of UCNs. The status of the EDM spectrometer is also presented, with emphasis on UCN handling components and magnetic subsystems relevant to field control, shielding, and magnetometry.

Challenges in last-mile delivery have encouraged innovative solutions like crowdsourced delivery, where online platforms leverage the services of drivers who occasionally perform delivery tasks for compensation. A key challenge is that occasional drivers' acceptance behavior towards offered tasks is uncertain and influenced by task properties and compensation. The current literature lacks formulations that fully address this challenge. Hence, we formulate an integrated problem that maximizes total expected cost savings by offering task bundles to occasional drivers. To this end, we simultaneously determine the optimal bundle set, their assignment to occasional drivers, and compensations for each pair while considering acceptance probabilities, which are captured via generic logistic functions. The vast number of potential bundles, combined with incorporating acceptance probabilities leads to a mixed-integer nonlinear program (MINLP) with exponentially many variables. Using mild assumptions, we address these complexities by exploiting properties of the problem, leading to an exact linearization of the MINLP which we solve via a tailored exact column generation algorithm. Our algorithm uses a variant of the elementary shortest path problem with resource constraints (ESPPRC) that features a non-linear and non-additive objective function as its subproblem, for which we develop tailored dominance and pruning strategies. We introduce several heuristic and exact variants and perform an extensive set of experiments evaluating the algorithm performances and solution structures. The results demonstrate the efficiency of the algorithms for instances with up to 120 tasks and 60 drivers and highlight the advantages of integrated decision-making over sequential approaches. The sensitivity analysis indicates that compensation is the most influential factor in shaping the bundle structure.

Half a century ago, Bollobás and Erdős [Bull. London Math. Soc. 5 (1973)] proved that every $n$-vertex graph $G$ with $e(G)\ge (1- \frac{1}{k} + \varepsilon )\frac{n^2}{2}$ edges contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\varepsilon}(\log n)$. A well-known theorem of Nikiforov [Combin. Probab. Comput. 18 (3) (2009)] asserts that if $G$ is an $n$-vertex graph with adjacency spectral radius $λ(G)\ge (1- \frac{1}{k} + \varepsilon)n$, then $G$ contains a blowup $K_{k+1}[t]$ with $t=Ω_{k,\varepsilon}(\log n)$. This gives a spectral version of the Bollobás--Erdős theorem. In this paper, we systematically explore variants of Nikiforov's result in terms of the signless Laplacian spectral radius, extending the supersaturation, blowup of cliques and the stability results.

Metaheuristic algorithms are powerful tools for global optimization, particularly for non-convex and non-differentiable problems where exact methods are often impractical. Particle-based optimization methods, inspired by swarm intelligence principles, have shown effectiveness due to their ability to balance exploration and exploitation within the search space. In this work, we introduce a novel particle-based optimization algorithm where velocities are updated via random jumps, a strategy commonly used to enhance stochastic exploration. We formalize this approach by describing the dynamics through a kinetic modelling of BGK type, offering a unified framework that accommodates general noise distributions, including heavy-tailed ones like Cauchy. Under suitable parameter scaling, the model reduces to the Consensus-Based Optimization (CBO) dynamics. For non-degenerate Gaussian noise in bounded domains, we prove propagation of chaos and convergence towards minimizers. Numerical results on benchmark problems validate the approach and highlight its connection to CBO.

Evolving phenomena, often complex, can be represented using knowledge graphs, which have the capability to model heterogeneous data from multiple sources. Nowadays, a considerable amount of sources delivering periodic updates to knowledge graphs in various domains is openly available. The evolution of data is of interest to knowledge graph management systems, and therefore it is crucial to organize these constantly evolving data to make them easily accessible and exploitable for analysis. In this article, we will present and formalize the condensed representation of these evolving graphs and propose a new solution called QuaQue that allows querying across multiple versions of graphs and we also present the results of our benchmark comparing our solution against existing approaches.

We theoretically demonstrate via numerical modeling that fully degenerate triple-photon states generated by three-mode spontaneous parametric down-conversion can be categorized into four distinct states: 0-phase, $π$/2-phase, $π$-phase, and 3$π$/2-phase squeezed states. Using quantum relative entropy and Wigner negativity as quantitative measures, we show that the nonGaussianity and nonclassicality of these squeezed states increase with the increase of interaction strength. Analogous to Gaussian scenarios, these squeezed states serve as basic building blocks for deterministic preparation of two-mode non-Gaussian states. We study the correlation properties of two-mode state generated by interfering 0-phase and $π$-phase squeezed states on a beam splitter, and reveal its entanglement at 3rd and 6th-order moments using the positive partial transposition criterion based on higher-order covariance matrices. In particular, by adjusting the intensities of the two input beams, the entanglement of the two output modes at the 3rd- and 6th-order moments can be dynamically modulated. Our results highlight the nonclassical nature of fully degenerate triple-photon states and establish a pathway for preparing non-Gaussian entanglement based on such states.

The one-dimensional (1D) $J_1-J_2$ quantum spin model can be viewed as a strong-coupling analogue of the Schrieffer-Su-Heeger model with two inequivalent alternating Ising couplings along the wire, associated to the physics of resonating valence bonds. Similar to the quantum Ising model, which differently presents a long-range N\' eel ordered phase, this model also maps onto a p-wave superconducting wire which shows a topological phase transition with the emergence of low-energy Majorana fermions. We show how signatures of the topological phase transition for the p-wave superconducting wire, i.e. a half Skyrmion, are revealed through local (short-range) spin observables and their derivatives related to the capacitance of the pairing fermion model. Then, we present an edge correspondence through the edge spin susceptibility in the $J_1-J_2$ model revealing that the topological phase transition is a metal of Majorana fermions. We justify that the spin magnetization at an edge at very small transverse magnetic field is a good marker of the topological invariant and of Majorana zero modes. We identify a correspondence between the quantum information of resonating valence bonds and the charge fluctuations in a p-wave superconductor through our method "the bipartite fluctuations". Physical properties of this 1D model are in fact robust when including additional interactions, which is optimistic for practical applications e.g. in quantum circuits.

Many resources are provided by an ecological system that is vulnerable to tipping when exceeding a certain level of pollution, with a sudden big loss of ecosystem services. An ecological system is usually also a common-pool resource and therefore vulnerable to suboptimal use resulting from non-cooperative behavior. An analysis requires methods to derive cooperative and non-cooperative solutions for managing a dynamical system with tipping points. Such a game is a differential game which has two well-defined non-cooperative solutions, the open-loop and feedback Nash equilibria. This paper provides new numerical methods for deriving open-loop and feedback Nash equilibria, for one-dimensional and two-dimensional dynamical systems. The methods are applied to the lake game, which is the classical example for these types of problems. Especially, two-dimensional feedback Nash equilibria are a novelty of this paper. This Nash equilibrium is close to the cooperative solution which has important policy implications.

The properties of satellite halos provide a promising probe for dark matter (DM) physics. Observations have motivated current efforts to explain surprisingly compact DM halos. If DM is not collisionless, but has strong self-interactions, halos can undergo gravothermal collapse, leading to higher densities in the central region of the halo. However, it is challenging to model this collapse phase from first principles. To improve on this, we sought to better understand the numerical challenges and convergence properties of self-interacting dark matter (SIDM) N-body simulations in the collapse phase. Especially, our aim was to better understand the evolution of satellite halos. To do so, we ran SIDM N-body simulations of a low-mass halo in isolation and within an external gravitational potential. The simulation set-up was motivated by the perturber of the stellar stream GD-1. We find that the halo evolution is very sensitive to energy conservation errors, and a SIDM kernel size that is too large can artificially speed up the collapse. Moreover, we demonstrate that the King model can describe the density profile at small radii for the late stages that we have simulated. Furthermore, for our most highly resolved simulation (N = 5x10^7) we have made the data public. It can serve as a benchmark. Overall, we find that the current numerical methods do not suffer from convergence problems in the late collapse phase and provide guidance on how to choose numerical parameters, for example that the energy conservation error is better kept well below 1%. This allows simulations to be run of halos that become concentrated enough to explain observations of GD-1-like stellar streams or strong gravitational lensing systems.

We prove an analogue of the Gabriel--Quillen embedding theorem for exact $\infty$-categories, giving rise to a presentable version of Klemenc's stable envelope of an exact $\infty$-category. Moreover, we construct a symmetric monoidal structure on the $\infty$-category of small exact $\infty$-categories and discuss the multiplicative properties of the Gabriel--Quillen embedding. For $E$ an Adams-type homotopy associative ring spectrum, this allows us to identify the symmetric monoidal $\infty$-category of $E$-based synthetic spectra with the presentable stable envelope of the exact $\infty$-category of compact spectra with finite projective $E$-homology. In addition, we show that algebraic K-theory, considered as a functor on exact $\infty$-categories, admits a unique delooping as a localising invariant.

In this article, we combine V. Arnold's celebrated approach via the Euler-Arnold equation -- describing the geodesic flow on a Lie group equipped with a right-invariant metric \cite{Arnold66} -- with his formulation of the motion of a charged particle in a magnetic field \cite{ar61}. We introduce the \emph{magnetic Euler-Arnold equation}, which is the Eulerian form of the magnetic geodesic flow for an infinite-dimensional magnetic system on a Lie group endowed with a right-invariant metric and a right-invariant closed two-form serving as the magnetic field. As an illustration, we demonstrate that the Korteweg-de Vries equation, the generalized Camassa-Holm equation, the infinite conductivity equation, and the global quasi-geostrophic equations can all be interpreted as magnetic Euler-Arnold equations. In particular, we obtain both local and global well-posedness results for the magnetic Euler-Arnold equation associated with the global quasi-geostrophic equations.

In this paper, we introduce \emph{$\ell^p$-information geometry}, an infinite dimensional framework that shares key features with the geometry of the space of probability densities \( \mathrm{Dens}(M) \) on a closed manifold, while also incorporating aspects of measure-valued information geometry. We define the \emph{$\ell^2$-probability simplex} with a noncanonical differentiable structure induced via the \emph{$q$-root transform} from an open subset of the $\ell^p$-sphere. This structure renders the $q$-root map an \emph{isometry}, enabling the definition of \emph{Amari--Čencov $α$-connections} in this setting. We further construct \emph{gradient flows} with respect to the $\ell^2$ Fisher--Rao metric, which solve an infinite-dimensional linear optimization problem. These flows are intimately linked to an \emph{integrable Hamiltonian system} via a \emph{momentum map} arising from a Hamiltonian group action on the infinite-dimensional complex projective space.

This paper establishes sharp concentration inequalities for simple random tensors. Our theory unveils a phenomenon that arises only for asymmetric tensors of order $p \ge 3:$ when the effective ranks of the covariances of the component random variables lie on both sides of a critical threshold, an additional logarithmic factor emerges that is not present in sharp bounds for symmetric tensors. To establish our results, we develop empirical process theory for products of $p$ different function classes evaluated at $p$ different random variables, extending generic chaining techniques for quadratic and product empirical processes to higher-order settings.

Wind turbines operating in the atmospheric boundary layer are constantly exposed to time-varying flow conditions. These disturbances often occur on similar time scales to wind-turbine controllers, which may interfere with wind-farm control strategies that operate under steady-flow assumptions. This study aims to investigate the significance of such time variations on wind-turbine wake dynamics, focusing on slow time scales representative of quasi-steady processes in large wind farms. Experiments are conducted at near utility-scale Reynolds numbers ($Re_D=4\times10^6$) in a pressurized-air wind tunnel, with a wind turbine forced in periodic rotation-rate oscillations by means of a time-varying generator torque at low Strouhal numbers ($St=0.04$). Flow measurements in the wake of the turbine demonstrate that disturbances propagate through the wake as traveling waves, which are advected nonlinearly at the velocity of the wake rather than that of the free stream. The wake behavior can be described in a quasi-steady manner, but only after wake advection is accounted for by a Lagrangian transformation. Even in the quasi-steady regime, the spatiotemporal evolution of the wake can be controlled by independently varying the turbine thrust and tip-speed ratio. The results suggest that wake advection is important to consider for wind-farm modeling and control, and that time-varying control may allow wind-turbine wake interactions to be tuned even in nominally quasi-steady conditions for optimal wind-farm performance.

Temporal metamaterials are artificially manufactured materials with time-dependent material properties that exhibit interesting phenomena when waves propagate through them. The propagation of electromagnetic waves in such time-varying dielectric media is governed by Maxwell's equations, which lead to wave equations with temporal highly oscillatory coefficients for the electric and magnetic fields. In this study, we analyze the effective behavior of electromagnetic fields in time-varying metamaterials using a formal two-scale asymptotic expansion. We provide a mathematical derivation of the effective equations for the leading-order homogenized solution, as well as for the first- and second-order corrections of the effective solution. While the effective solution and the first-order correction are governed by local material laws, we reveal a nonlocal constitutive relation for the second-order corrections. Special attention is also paid to temporal interface conditions through initial values of the homogenized equations. The results provide a mathematically justified framework for the effective description of wave-type equations of time-varying media, applicable to models in optics, elasticity, and acoustics.