We discuss some mathematical aspects of the Mori-Zwanzig projection operator formalism. The core of the Mori-Zwanzig formalism is the generalised Langevin equation, which is typically derived from the Dyson-Duhamel identity. We derive the projection operator formalism for Mori's projection by means of semigroup theory, and we illustrate where rigorous methods fail for the case of Zwanzig's projection. For bounded perturbations of the time-evolution operator (e.g. for Mori's projection), the Dyson-Duhamel identity coincides with the variation of constants formula. For unbounded perturbations (e.g. for Zwanzigs's projection), the Dyson-Duhamel identity should be considered an equation for the orthogonal dynamics, for which the existence of unique solutions has yet to be established. Then we recall that all properties of Mori's generalised Langevin equation follow directly from the well-posedness of Volterra equations, irrespective of the projection operator formalism. Further, we discuss the use of Mori's generalised Langevin equation as a coarse-grained model. Finally, we illustrate that the memory term is a coupling term that is not necessarily related to memory. To this end, we introduce projections onto subspaces of 'fast' and 'slow' variables that are associated with the spectral decomposition of skew-adjoint operators. For these projections, the memory term vanishes.

Fano resonances are sharp asymmetrical spectral peaks which are now ubiquitous in nanophotonics. The high sensitivity of these resonances to system parameter has been exploited to improve light matter interaction and in applications such as sensing, filters and on-chip processing. The ability to dynamically change the Fano slope and spectral phase would enable optimization of the device parameters post fabrication for various applications. Here we demonstrate such a control over the Fano resonance in a one-dimensional photonics crystal cavity integrated on a silicon waveguide -grating platform. In our device, Fano resonance arises due to interference between cavity mode and an oscillatory background due to grating coupler. The dynamics tuning of Fano asymmetric parameter is achieved using thermos-optic effect in silicon. We experimentally tune the Fano parameter from ~-3.2 to +1.7 achieving a highest extinction ratio of 21.6 dB and spectral slope of 108dB/nm. All the above is achieved in an ultra-compact design with simple fabrication and with multiple cavities or feedback elements. The steep slope offers distinct advantage over conventional cavity for sensing and modulation applications and the tunability enables dynamic control over gain, dynamic range, bandwidth and noise coupling.

We investigate the feasibility of the macrospin approximation to account for the actual shape of soft magnetic nanoparticles (MNPs) with realistic geometries. Specifically focusing on magnetite, we use the superellipsoidal parametrisation to account for a variety of shapes, with a continuous interpolation from spherical to cubic morphologies, as well as different elongations. Our procedure consists of the direct comparison between angular-dependent hysteresis loops obtained by full micromagnetic simulations, with those produced by an extended Stoner-Wohlfarth (SW) model that incorporates both the intrinsic cubic magnetocrystalline anisotropy, and an effective uniaxial contribution arising from the particle elongation. The limits of validity of the macrospin description are approximately 10-60 nm for axial ratios r>1.5, and 20-60 nm for 1.0<r<1.5. These results establish a direct connection between nanoparticle morphology and effective macrospin parameters, demonstrating the suitability of the generalized SW model for describing the magnetic response of realistically shaped MNPs.

We present recent results from the FASTSUM collaboration, using anisotropic lattice QCD to study spectral properties of heavy quarkonia and open heavy flavour systems at high temperature. For heavy quarkonium, our results using a number of different methods suggest a small but significant and robust negative mass shift as well as an increasing thermal width. We present the first lattice results for masses and spectral functions of B mesons at high temperature, and preliminary results for a high-precision calculation of the static quark potential.

Extreme weather events during peak winter periods drive resource adequacy risk in Great Britain (GB), with weather sensitivity of the supply-demand balance increasing through additional electric heating and wind generation. This work develops an approach of time-shifting weather within the peak season, through adjustment of the relevant terms in a statistical model for demand. This allows more complete consideration of the security of supply consequences of a weather series, as there will be relevant conditions where demand is suppressed due to weather occurring at a weekend or during the Christmas holiday. Results on a GB example show that consideration of this counterfactual is indeed important, and specifically that winter 2010-11 can either be the most severe in the dataset, or insignificant within the resource adequacy model, depending on the alignment of day-of-week with the weather series. Statistical interpretation of the shift model is discussed, which is straightforward for alignment of day-of-week with weather assuming that all seven alignments are equiprobable; but is more subtle for shifting weather in and out of Christmas, as there is no natural maximum on the realistic length of shift, but too large a shift may be physically unrealistic. It is likely that in all systems, assessment of a weather year's severity is incomplete without such consideration of the day-of-week effect; however, whether longer shifts of weather with respect to date need to be considered will depend on the presence of a major holiday (such as Christmas in GB) in the peak season.

We prove that if $X$ is a smooth Fano threefold and $L$ is an ample $\mathbb{Q}$-divisor such that $(X,L)$ is K-polystable, then the automorphism group $\operatorname{Aut}(X)$ is reductive. This verifies the reductivity statement predicted by the Yau--Tian--Donaldson conjecture in the setting of smooth Fano threefolds with arbitrary ample polarisation.

The nature of the recently observed $K(1690)$ state, reported by the COMPASS Collaboration as a candidate for a strange crypto-exotic meson with $J^P=0^-$, remains unclear. In this work, we investigate whether it can be described by local meson-meson currents within the framework of QCD sum rules. We construct a set of local meson-meson-type interpolating currents with $J^P=0^-$, covering the representative Dirac structures $0^- \otimes 0^+$, $0^+ \otimes 0^-$, $1^- \otimes 1^+$, $1^+ \otimes 1^-$, as well as tensor configurations. For all these currents, we perform a systematic operator product expansion up to dimension-eight condensates and carry out a detailed analysis of Borel stability, continuum threshold dependence, and pole contributions. We find that the extracted masses are consistently located around $2~\mathrm{GeV}$ or higher, significantly above the experimental mass of the $K(1690)$. This behavior is highly stable against variations of QCD parameters and the choice of interpolating currents, and is observed universally across all the considered configurations. The absence of any low-lying pole compatible with the COMPASS signal therefore disfavors interpreting the $K(1690)$ as a state predominantly coupled to these local meson-meson currents within the QCD sum rule framework. Our results thus make a compact multiquark configuration a more plausible explanation for this state.

Accurate state-of-health (SOH) estimation for lithium-ion batteries remains a challenging problem due to complex electrochemical degradation mechanisms and long-range temporal dependencies. In this work, we propose a quantum-enhanced recurrent framework, termed QLSTM, in which variational quantum circuits are directly embedded into the gating mechanisms of long short-term memory networks. By replacing classical affine transformations with parameterized unitary operations, the proposed model introduces structured nonlinear transformations into the recurrent state-transition process. Extensive experiments on multiple benchmark battery datasets demonstrate that QLSTM consistently outperforms classical sequence models in both predictive accuracy and robustness, achieving significant reductions in mean absolute error (MAE), with improvements on the order of 20% compared with classical LSTM baselines. Ablation studies further confirm that these improvements arise primarily from quantum-enhanced gating rather than input-level transformations. Additional analyses on qubit scaling and noise robustness reveal that model performance is governed by a balance between expressive capacity and trainability. These results provide empirical evidence that embedding quantum computational primitives within recurrent architectures offers a structurally grounded approach to improving sequence modeling capability. The proposed framework establishes a new design paradigm for integrating quantum operators into temporal learning models, with potential applications in complex dynamical system prediction tasks.

Soft composite solids, comprising discrete inclusions embedded within a compliant matrix, are emerging candidates for engineering synthetic tissues and soft robotic materials. Current strategies for controlling their nonlinear mechanics, such as strain-stiffening, have primarily relied on the nonlinear elasticity of polymer matrices. Although direct contacts between inclusions may enhance stiffening responses at high densities, the role of the non-equilibrium and history-dependent nature of disordered contact networks in composite mechanics remains unexplored. In this work, by applying a mechanical training protocol near a shear-jamming phase boundary, we demonstrate that the structural memory encoded in contact networks drives a crossover from granular-like to biopolymer-like strain stiffening. Simulations of a coarse-grained composite model reveal that this biopolymer-like mechanical response emerges from enhanced non-affine reconfigurations of nearly-jammed contact networks. Without relying on matrix nonlinearity, we establish a design strategy that leverages non-equilibrium memory effects intrinsic to granular systems to achieve highly programmable strain-stiffening in soft composites.

We study stochastic extinction for a class of Markov processes motivated by models in ecology and epidemiology. Extinction is often characterized by a boundedness condition and a condition on boundary Lyapunov exponents (invasion rates). While the latter is typically sharp, the former is often restrictive and can be improved. Building on the ideas initiated in \cite{benaim2018stochastic}, we develop a streamlined approach that relaxes this boundedness condition and yields concise and accessible criteria for extinction. In particular, we establish extinction criteria in two settings: with and without a linearly bounded quadratic variation condition. In the first case, our result is comparable to, and slightly improves upon, the main results in \cite{foldes2024stochastic}. In the second case, where the quadratic variation is not linearly bounded, we obtain new extinction results that fall outside the scope of existing frameworks. Several examples are provided to illustrate the applicability of our results and to highlight situations where previous conditions are not practically verifiable.

The emergence of generative models enables the creation of texts and images tailored to users' preferences. Existing personalized generative models have two critical limitations: lacking a dedicated paradigm for accurate preference modeling, and generating unimodal content despite real-world multimodal-driven user interactions. Therefore, we propose personalized multimodal generation, which captures modal-specific preferences via a dedicated preference model from multimodal interactions, and then feeds them into downstream generators for personalized multimodal content. However, this task presents two challenges: (1) Gap between continuous preferences from dedicated modeling and discrete token inputs intrinsic to generator architectures; (2) Potential inconsistency between generated images and texts. To tackle these, we present a two-stage framework called Discrete Preference learning for Personalized Multimodal Generation (DPPMG). In the first stage, to accurately learn discrete modal-specific preferences, we introduce a modal-specific graph neural network (a dedicated preference model) to learn users' modal-specific preferences, which preferences are then quantized into discrete preference tokens. In the second stage, the discrete modal-specific preference tokens are injected into downstream text and image generators. To further enhance cross-modal consistency while preserving personalization, we design a cross-modal consistent and personalized reward to fine-tune token-associated parameters. Extensive experiments on two real-world datasets demonstrate the effectiveness of our model in generating personalized and consistent multimodal content.

This paper investigates the so-called reward-balancing methods, a novel class of algorithms for solving discounted-return reinforcement learning (RL) problems. These methods consist of iteratively adjusting the reward function to transform the RL problem into an equivalent one in which the optimal policies are greedy. For this procedure, referred to as normalization process, we provide a theoretical analysis of the involved transformations, emphasizing their algebraic structure. Then, we introduce a control-theoretic reformulation, recasting the reward-balancing procedure into an optimal control framework. The approach is further extended to address model uncertainty through stochastic model sampling, yielding normalization guarantees and probabilistic bounds on stochastic fluctuations. Using the proposed optimal control framework within a scenario model predictive control (MPC) setting, we demonstrate, through simulation studies, performance improvements over the current state-of-the-art.

We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution. Certain special words, known as synchronizing words, drive the automaton into a predetermined state regardless of its initial configuration. Although such an apparently irreversible process seems incompatible with the unitarity of quantum mechanics, we present a resetting protocol based on quantum synchronizing words by incorporating auxiliary qubits whose states encode the rules of the automaton's alphabet. These qubits interact with the quantum automaton, whose state is encoded in a qudit, via a global unitary operation. When the qubit register is initially prepared in a state corresponding to a synchronizing word, the automaton evolves into a predetermined pure state independent of its initial state, while the qubit register is transformed into a complex, often entangled, state that encodes information about the automaton's original configuration. The resulting entanglement depends on both the rule set and the automaton's initial state, and we show how specific entangled states can be generated within this framework.

Reconfigurable distributed antennas and reflecting surface (RDARS) has emerged as a transformative solution to address the stringent requirements of future wireless networks. By combining distributed active antennas with reconfigurable passive reflecting surfaces, RDARS integrates the advantages of both active transmission and passive wave control in a cost-effective and energy-efficient manner. This hybrid architecture enables enhanced coverage, improved spectral efficiency, and seamless support for integrated communication and sensing. In this article, we first introduce the fundamental architecture and working principles of RDARS, followed by practical benefits and comparisons with recently proposed intelligent surface variants. We then highlight the signal-to-noise ratio (SNR) gains in representative applications of RDARS-aided communication and sensing scenarios, where RDARS demonstrates clear advantages over conventional reconfigurable intelligent surfaces. Finally, we outline key challenges related to practical implementation and resource allocation, and discuss potential research directions. With its unique hybrid mode synergy, RDARS is envisioned to play a pivotal role in shaping the evolution of next-generation intelligent communication systems.

In this paper, we consider a parabolic counterpart of Serrin's overdetermined problem, in which the overdetermined condition (constant flux condition) is imposed only on a discrete infinite set of time values. We show that, under suitable regularity assumptions on the domain, such a discrete-time overdetermined problem admits a solution if and only if the domain is a ball. Remarkably, depending on the temporal scale, the same overdetermined condition captures either geometric or spectral information, yet both mechanisms lead to the same rigidity conclusion. We study both the case in which the constant flux condition is imposed on the boundary and the case in which the constant flux condition is imposed on an interior surface. We remark that the methods employed in our analysis do not depend on the location of the overdetermined surface but only on whether the sequence of time instants accumulates away from zero. Finally, we will show how this problem generalizes to complete Riemannian manifolds.

In this paper, we study finite subgroups $G\subset\mathrm{Aut}(\mathbb{P}^n)$ such that $\mathbb{P}^n$ is $G$-birationally rigid. For each $n\geqslant 3$, we prove that $\mathrm{Aut}(\mathbb{P}^n)$ contains at most finitely many such subgroups up to conjugation. For $n=4$, we prove that $\mathbb{P}^4$ is $G$-birationally superrigid if $G\simeq\mathrm{PSp}_{4}(\mathbf{F}_3)$.

We classify pairs $(X,G)$ consisting of a (possibly singular) cubic threefold $X\subset\mathbb{P}^4$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally rigid, i.e., $X$ is a $G$-Mori fiber space (over a point), and $X$ is not $G$-birational to any $G$-Mori fibre space that is not $G$-biregular to $X$.

We complete the classification of regular generically free actions of finite groups on del Pezzo surfaces, up to birational equivalence. As a byproduct, we settle several open problems in equivariant birational geometry, e.g., we classify birationally rigid actions on del Pezzo surfaces.

Thermal runaway in lithium-ion batteries is governed by the poorly-understood initiation phase, where localised heating introduces instability. Here we identify the three key components that trigger thermal runaway, decreases in local conductivity, heat capacity changes, and intercalation heating, which significantly increase temperature gradients that accelerate battery degradation. Using a multiscale framework that links atomistic phonon calculations with grain-resolved thermal modelling, we identify large thermal gradients across grain boundaries arising from external heating events and intercalation-dependent thermal properties of Li$_x$ZrS$_2$. The observed changes in thermal conductivity are due to charge redistribution and bond-strength modulation of the host, in contrast to the existing theory of lithium rattler mechanics. Internal heating events driven by intercalation gives rise to local thermal gradients, finite-speed thermal wave interference, and internal thermal fluctuations that generate mechanical strain and sub-grain thermal breakdown. These results show that the trigger for thermal runaway is controlled by internal grain architecture and composition, as well as the external environment. Our findings establish materials and electrode design rules for suppressing hotspot formation and improving battery safety during fast charging.

We develop a likelihood-based inference for finite-state birth-death processes with composite birth rates, in which multiple distinct mechanisms contribute additively to the total birth intensity. Our main motivating example is an SIS epidemic model with pairwise and higher-order transmission. The process is observed through a single aggregate trajectory, and in the main setting of interest, birth events are unmarked. This creates a deconvolution problem in event space: the state is one-dimensional, but the mechanism underlying each birth is latent. We formulate the inference under a Doob $h$-transformed $Q$-process, which is time-homogeneous and ergodic and which provides a time-homogeneous asymptotic surrogate for the law of the original process conditioned on long survival. We derive the corresponding conditional likelihood and study both the conditional maximum likelihood estimator and a quasi-maximum likelihood estimator which is based on a simplified working score. Under the Doob-transform law, we prove consistency and asymptotic normality for both estimators, with asymptotic covariance determined by the inverse Fisher and inverse Godambe information matrices, respectively. We also showcase a practical one-dimensional test for the presence of a specific higher-order birth mechanism.

We study an Ising model with long-range interactions undergoing a time-periodic kicking. For different initial states we observe persistent period doubling. When there is period doubling we find that the initial state has relevant overlap with Floquet states showing time-translation symmetry breaking, organized in doublets displaying $π$-spectral pairing (as highlighted by the $π$-spectral gap) and long-range order (as shown by the eigenvalues of the magnetization in the doublet). We observe period doubling for initial states with domain walls and tilted spins, and for the latter ones a finite-size scaling of the relevant $π$-shifted gap and magnetization eigenvalues suggests period-doubling oscillations persisting for larger system sizes and lasting a time exponential in the system size. We find that just a minority of Floquet states displays time-translation symmetry breaking while the rest is thermal, a weak-ergodicity breaking situation typical of systems with quantum scars. Although the time-translation symmetry breaking eigenstates are the minority, their number is exponential in the system size and this motivates the period doubling observed for many different initial states.

Large families of confining holographic QFTs, described by Einstein-Dilaton gravity, are considered on constant-curvature manifolds in the presence of a $θ$-angle. The space of ground states of such theories is explored as a function of the UV parameters, namely the dimensionless curvature and the $θ$ angle. The free energy is computed, and the phase structure is determined. For constant negative curvature manifolds, we find solutions dual to single QFTs as well as solutions describing interfaces. The single QFTs exhibit an infinite family of saddle points, with the leading one dominating the gravitational path integral and no phase transitions present. For constant positive curvature manifolds, like de Sitter, the ($θ$-angle, curvature) phase diagram exhibits both first and second order phase transitions, as a function of the class of theories considered. We also show that when $θ=0$, a holographic Vafa-Witten-like theorem can be proven.

This report describes the SHARELIFE-MI project, which aims to generate multiple imputations for missing values in the life-course data collected in SHARELIFE Waves 3 and 7. The SHARELIFE study reconstructs individual life histories through retrospective questions covering key biographical domains such as partnerships, fertility, employment, and residence. As in the regular SHARE waves, item nonresponse represents an important source of nonsampling error - particularly for monetary variables, which require conversions across multiple currencies and long time periods. We document the preliminary data recoding and harmonization steps, as well as the design, specification, and implementation of an imputation model based on the fully conditional specification approach. Finally, we assess the internal and external validity of the resulting imputations through comparisons with the observed data, alternative nonresponse adjustments based on inverse propensity weighting, and external benchmarks from the regular SHARE waves.

We show that generic automorphisms of stable groups are supertight in a strong sense. In particular, we obtain the existence of supertight automorphisms. We also answer a question concerning the relationship between supertight automorphisms of $\mathrm{PGL}_2(K)$ and generic automorphisms of the underlying field $K$. Moreover, we provide partial evidence-already suggested by Hrushovski-toward the principle that ``fixed points are pseudofinite'' in the setting of generic automorphisms of simple groups of finite Morley rank.

Gaussian processes are widely used for accurate emulation of unknown surfaces in sequential design of expensive simulation experiments. Integrated mean squared error (IMSE) is an effective acquisition function for sequential designs based on Gaussian processes. However, existing approaches struggle with its implementation because the required integrals often lack closed-form expressions for most kernel functions. We propose a novel and computationally efficient Hilbert space Gaussian process approximation for the IMSE acquisition function, where a truncated eigenbasis representation of the integral enables closed-form evaluation. We establish sharp global non-asymptotic bounds for both the approximation error of isotropic kernels and the resulting error in the acquisition function. In a series of numerical experiments with $γ$-stabilizing, the proposed method achieves substantially lower prediction error and reduced computation time compared to existing benchmarks. These results demonstrate that the proposed Hilbert space Gaussian process framework provides an accurate and computationally efficient approach for Gaussian process based sequential design.

We construct a free Poisson algebra endowed with a Rota-Baxter operator. The same construction works for a free Poisson algebra endowed with a Nijenhuis operator.

High-performance computing often relies on parallel programming models such as MPI for distributed-memory systems. While powerful, these models are prone to subtle programming errors, leading to development of multiple correctness checking tools. However, these are often limited to C/C++ codes, tied to specific library implementations, or restricted to certain error classes. Building on our prior work with CoVer, a generic, contract-based verification framework for parallel programming models, we extend CoVer's applicability to Fortran, enabling static and dynamic analysis across multiple programming languages. We adapted language-specific contract definitions and modified the analyses to support both C/C++ and Fortran programs. Our evaluation demonstrates that the enhanced version preserves CoVer's analysis accuracy and even revealed a bug in the MPI-BugBench testing framework, underscoring the effectiveness of the approach. The Fortran port of CoVer turns out to be substantially more efficient than the state-of-the-art tool MUST, while maintaining generality across languages.

Releasing shell-shaped Bose-Einstein condensates from their confinement produces a spherically symmetric density distribution characterized by concentric ripples surrounding a central peak. Here we investigate how a vortex-antivortex dipole affects this dynamics, finding that increasing dipole separation progressively breaks the spherical symmetry and, correspondingly, the interplay of vortex physics and curvature produces a non-monotonic behavior of the cloud aspect ratio. These features can be used for preparing and detecting vortex dipoles in shell-shaped superfluids, as well as for analyzing their signatures in other thin superfluids with more general curved geometries.

We study OTC bond market making on a size ladder with quadratic inventory penalty and a running target on the dealer's size-weighted hit ratio within a stochastic optimal control approach. We demonstrate that the corresponding reduced Hamilton-Jacobi-Bellman (HJB) equation remains separable by dualizing the hit ratio target term and provides the exact optimal controls through the inverse of the fill-probability function and the Hamiltonian derivative. We then focus on the quadratic approximation á la Bergault et al., which yields a Riccati equation for the inventory curvature while retaining the exact quote map. In its linearized form, this approximation produces explicit quote decompositions into riskless spread, inventory-risk correction, and hit-ratio correction. The formulation is general and applies to multi-bond, multi-client-tier scenarios, with special cases obtained by restricting the targeted tiers, their bond coverage, and their associated targets.

We show that the $ L^2({\mathbb R}) $-unconditional well-posedness, that is well-known for the KdV equation, is shared by KdV type equations with weaker dispersion. This is despite the difference in the nature of these equations, which are quasilinear while KdV is semilinear. More precisely we prove that the low dispersion fractional KdV equation $$ \partial_t u -D_x^α\partial_x u +\partial_x(u^2)=0 $$ is unconditionally globally well-posed in $L^2({\mathbb R}) $ for $α\in ]\frac{55}{38},2] $. Our method of proof combined refined bilinear estimates with the energy method enhanced with Bourgain's type estimates developed in Molinet-Vento (2015).