We study the concept of including the causality principle as regularizer into the solution of linear time-dependent inverse problems. This is achieved by combining transformer-based predictions with classical variational regularization, resulting in what we call transformer causality regularization (TCR). The causality principle states that an object at time $t'$ depends only on its previous states at $t < t'$ and is independent of future states at $t > t'$. Since the transformer architecture represents sequence-to-sequence functions and can be equipped with a causal attention mask, transformers are the natural choice for a learned causality function that predicts the state of an object at time $t'$ given the previous states at $t < t'$. We combine this with the inductive bias of convolutional neural networks (CNNs) for imaging tasks to treat the spatial variable. The output of the spatial-temporal transformer is then used as a prior for variational regularization, such that classical results on regularization and convergence for solution methods directly transfer to our case. Using the example of dynamic computerized tomography, we compare TCR to a static and dynamic version of the earlier introduced unrolled adversarial regularizer for simulated and measured data. The results show that using TCR within a variational framework improves reconstruction results and data-consistency.

Electroencephalography (EEG) - based air-writing recognition offers a human-computer interaction paradigm by decoding neural activity associated with handwriting movements. Despite its potential, reliable EEG-based air-writing recognition remains challenging due to low signal-to-noise ratio and pronounced inter-subject variability. In this study, we examine the use of supervised contrastive learning to improve representation learning for EEG-based air-writing recognition. The analysis is conducted on preprocessed EEG signals and independent component analysis (ICA)-derived neural components obtained from five participants, with trials segmented from -1 to 2 s relative to movement on-set. EEGNet and DeepConvNet architectures are evaluated under both conventional cross-entropy training and a supervised contrastive learning framework using a subject-dependent five-fold cross-validation scheme. The results indicate that supervised contrastive learning consistently improves classification accuracy across architectures and feature representations. For preprocessed EEG signals, the mean accuracy increases from 33.45% to 43.77% and from 29.14% to 38.06% with EEGNet and DeepConvNet, respectively. Using ICA components, higher mean accuracies of 49.21% and 43.32% are achieved with EEGNet and DeepConvNet, respectively. These results suggest that the supervised contrastive learning framework offers an efficient extension to existing EEG-based air-writing recognition approaches.

We investigate the vacuum distribution of a family of partial sums of nonsymmetric position operators, depending on a real parameter $λ$, and acting on the discrete Fock space in the framework of V-monotone independence. We analyze the combinatorics of the moments of this distribution, and using its Cauchy--Stieltjes transform, we determine its exact form, consisting of a unique atom and an absolutely continuous part. Finally, we present computer-generated graphs that illustrate the distribution for several values of the intensity parameter $λ$.

Variability is one of the classic features of active galactic nuclei (AGNs). The normalized structure function was applied to distinguish variability samples from OVRO, ASAS-SN and Fermi. A power-law function model was selected to fit the structure functions of samples of three bands. We present the available samples of three bands, and by integrating two parameters, we obtain ideal discrimination results for three bands. Meanwhile, the differences between BL Lacs and FSRQs of Fermi and non-Fermi samples are well verified. The results show that the improved structure function can effectively distinguish samples of radio, optical, and gamma-ray. Additionally, BL Lacs and FSRQs in both Fermi and non-Fermi samples can be distinguished. The conclusion obtained through the distinction of structural functions in different bands supports that the variability in the three bands are caused by different physical mechanisms respectively: the samples in the optical band are radio quiet AGNs, and their variability is mainly caused by the fluctuations of the accretion disk, and the samples of radio band and gamma-ray band are radio loud AGNs whose variability is mainly caused by relativistic jet radiation. This conclusion conforms to the unified standard interpretation of variability about AGNs. Using these two parameters, we verify that there is no fundamental difference between Fermi and non-Fermi BL Lacs, while significant differences exist between FSRQs. However, the power exponent of the two can well distinguish BL Lacs.

We consider the Voronoi diagram of lines in $\mathbb{R}^3$ under the Euclidean metric, and give a full classification of its structure in the base case of four lines in general position. We first show that the number of vertices in the Voronoi diagram of four lines in general position is always even, between 0 and 8, and all such numbers can be realized. We identify a key structure for the diagram formation, called a \emph{twist}, which is a pair of consecutive intersections among trisector branches; only two types of twists are possible, so-called \emph{full} and \emph{partial} twists. A full twist is a purely local structure, which can be inserted or removed without affecting the rest of the diagram. Assuming no full twists, the nearest and the farthest Voronoi diagrams of four lines, each have 15 distinct topologies, which are in one-to-one correspondence; the two-dimensional faces are all unbounded, and the total number of vertices is at most six. The unbounded features of the farthest diagram, encoded in a two-dimensional spherical map, are also in one-to-one correspondence. The identified topologies are all realizable. Any Voronoi diagram of four lines in general position in $\mathbb{R}^3$ can be obtained from one of these topologies by inserting full twists; each twist induces a bounded face of exactly two vertices in both the nearest and farthest diagrams. We obtain the classification by an exhaustive search algorithm using some new structural and combinatorial observations of line Voronoi diagrams.

We derive the factorization theorem for the quasi-transverse-momentum-dependent (quasi-TMD) correlator, including kinematic power corrections to all orders. The resulting expression involves only twist-two TMD distributions and is frame invariant. As in the leading-power approximation, the reduced soft factor factorizes multiplicatively; however, in contrast, the TMD evolution factor is not multiplicative but enters as a convolution with the nonperturbative TMD distribution. We present a numerical estimate of the difference between the derived expression and the leading-power approximation, finding it to be of the order of tens of percent for current lattice simulations. We also demonstrate that the inclusion of these corrections improves the agreement between phenomenological extractions of the Collins-Soper kernel and lattice results.

Intensity mapping (IM) represents an innovative and potent probe to cosmology. One of its prime applications is to measure the Baryonic Acoustic Oscillations (BAO) in the late universe. We study the BAO measurement by IM in configuration space using simulations, focusing on the impact of the telescope beam and foreground removal effects. Three types of correlation functions are applied to measure BAO, including the radial correlation function, multipole correlation function, and wedge correlation function. We check our pipeline against a set of IM mock catalogs, finding good agreement with the numerical results. We use the mock catalogs to look for the parameter choices that optimize the BAO constraint for the correlation function estimators. With the optimal settings, our pipeline is utilized to forecast the BAO constraint for the 21 cm IM experiments: BINGO, MeerKAT, and SKA-mid. We find that for the low redshift experiments BINGO and MeerKAT, the wedge correlation function achieves the tightest constraint for both the transverse and radial BAO. For SKA-mid, the radial correlation function and wedge correlation function deliver the tightest constraint for the radial and transverse BAO, respectively.

Alzheimer's disease is characterised by the spreading of misfolded proteins and progressive structural changes in the brain. Despite significant clinical research, understanding how microscopic protein dynamics translate into macroscopic tissue degeneration remains a major challenge. In this work, we present a three-dimensional, finite element-based computational framework to model disease progression by combining multi-protein transport and brain tissue deformation within anatomically realistic geometries. The propagation of toxic tau and amyloid-beta proteins is described using reaction-diffusion equations of the Fisher-Kolmogorov type, incorporating prion-like growth mechanisms and anisotropic transport along white matter fibre tracts. Brain atrophy is represented through a hyperelastic constitutive model driven by protein-dependent volume loss. Subject-specific simulations are achieved through an automated preprocessing pipeline that generates finite element meshes and reconstructs axonal orientation fields from medical imaging data. The model reproduces key morphological patterns observed in Alzheimer's disease and shows good quantitative agreement with longitudinal imaging measurements. Overall, the proposed framework offers an extensible computational platform for studying Alzheimer's disease progression across subject-specific brain geometries. The models developed, including the image processing framework (BrainImage2Mesh) and the coupled bio-chemo-mechanical COMSOL finite element implementation, are made freely available to download at https://mechmat.web.ox.ac.uk/codes.

We consider the incidence structure formed by the twelve pentagons given by the vertex neighborhoods of the icosahedron. Interpreting this structure purely in terms of coplanarity conditions, we show that -- up to projective equivalence -- it admits exactly two realizations. Both realizations coincide with the vertex set of the regular icosahedron and interpreted as cell complex they correspond to the great dodecahedron and the small stellated dodecahedron. The key step is to reinterpret the configuration via the pentagram map. We prove that any realization gives rise to a pentagon $X$ satisfying a homothety relation $P^2(X)\sim X$, and show that this condition forces $X$ to be an affine image of either a regular pentagon or a regular pentagram. This reduces the problem to a quadratic constraint and explains the rigidity of the configuration.

The restricted Delaunay triangulation of a closed surface $Σ$ and a finite point set $V \subset Σ$ is a subcomplex of the Delaunay tetrahedralization of $V$ whose triangles approximate $Σ$. It is well known that if $V$ is a sufficiently dense sample of a smooth $Σ$, then the union of the restricted Delaunay triangles is homeomorphic to $Σ$. We show that an $ε$-sample with $ε\leq 0.3245$ suffices. By comparison, Dey proves it for a $0.18$-sample; our improved sampling bound reduces the number of sample points required by a factor of $3.25$. More importantly, we improve a related sampling bound of Cheng et al. for Delaunay surface meshing, reducing the number of sample points required by a factor of $21$. The first step of our homeomorphism proof is particularly interesting: we show that for a $0.44$-sample, the restricted Voronoi cell of each site $v \in V$ is homeomorphic to a disk, and the orthogonal projection of the cell onto $T_vΣ$ (the plane tangent to $Σ$ at $v$) is star-shaped.

An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a potential $\hat{q}$ from a finite set of observed eigenvalues such that $\hat{q}$ yields an optimal approximation of the target potential $q_0$. Previous efforts have been confined to qualitative analysis, whereas the quantitative counterpart remains an open problem. This paper introduces a quantitative framework for the inverse spectral problem by using a phase plane analysis (planar dynamical system approach). We provide a quantitative characterization of the relationship between the reconstructed potential $\hat{q}$, its target potential $q_0$, and the observed eigenvalue $λ_*$. Remarkably, for ${q} \in \mathcal{L}^2$, our analysis yields a substantially stronger conclusion: an exact analytical expression for the reconstructed potential $\hat{q}$. In other words, our framework yields a complete resolution of the optimization inverse spectral problem in the $\mathcal{L}^2$ case. Moreover, we establish the uniqueness of $\hat{q}$ {\bf for any $q_0, λ_*\in \mathbb R$}, a key advance that eliminates the need for traditional constraints linking $λ_*$ and $q_0$. An additional finding is the construction of a homeomorphic mapping that reveals the dilation relation between the errors $\|\hat{q} - q_0\|_{\mathcal L^p}$ associated with the $m$-th eigenvalue and the principal eigenvalue. A summary of the main results, along with practical applications in engineering and mathematical physics, concludes this work.

Hydroxyapatite (HA) on a magnesium (Mg) surface is studied using density functional theory, to help understand the effect of HA coating and alloying in the surfaces of Mg-based biodegradable implants. We determine the adsorption energies and structural changes of a single layer of HA on pure Mg(0001) and on sparsely calcium (Ca) or zinc (Zn) doped Mg(0001) and find that both Zn and Ca doping improves the adsorption, except in a few positions of HA relative to the dopant position. All adsorption configurations, whether with pure or doped Mg surfaces, show deformation of the surface and HA layer. For Ca doping, we found that for a certain adsorption configuration, the dopant Ca atom moves out of the Mg surface and into the HA layer, leaving behind a Mg vacancy in the top layer of the Mg surface. Plots of electron density changes show that electrons accumulate around the Ca dopant and the neighboring Mg atoms, while in Zn doping this is less pronounced. Overall, our results demonstrate that the dopant choice and relative position of HA influence the interaction between HA and Mg-surfaces, and affect both adsorption energies and atomic and electronic structures.

Indoor positioning faces ongoing challenges due to complex propagation conditions, such as multipath propagation, signal blockages, and intrinsic target characteristics that substantially impact measurement reliability and positioning accuracy. Existing methods, in particular Least Squares (LS), frequently struggle to maintain robustness when confronted with unreliable observations caused by multipath interactions and extended targets. In this work, we propose an outlier-resistant algorithm designed to mitigate the impact of outlier measurements and accurately estimate the position of an extended target in multipath-rich environments. We develop a two-step algorithm in which an initial coarse position estimate is obtained using the angle-of-arrival (AoA) and subsequently refined using the Cauchy loss function to suppress outliers. The numerical results confirm that the proposed algorithm improves robustness and accuracy, outperforming existing benchmark methods, such as Iterative Reweighted Least Squares (IRLS), LS, and Huber loss function, and achieving a positioning error of less than $70$ cm in $90\%$ of cases. Its effectiveness in mitigating multipath effects is further assessed by comparing tracking performance in cluttered and empty room scenarios.

Range-Based Set Reconciliation (RBSR) synchronizes ordered sets by recursively comparing summaries of contiguous ranges and refining only the mismatching parts. While its communication complexity is well understood, its local computational cost fundamentally depends on the storage backend that must answer repeated range-summary, rank, and enumeration queries during refinement. We argue that a natural storage abstraction for RBSR implementations based on composable range aggregates is a \emph{range-summarizable order-statistics store} (RSOS): a dynamic ordered-set structure supporting composable summaries of contiguous ranges together with rank/select navigation. This identifies and formalizes the backend contract needed for efficient recursive refinement, combining range-summary support with order-statistics navigation for balanced partitioning. We then show that a specific augmentation of B\textsuperscript{+}-trees with subtree counts and composable summaries realizes a RSOS, and we derive corresponding bounds on local reconciliation work in this abstract storage model. Finally, we introduce AELMDB, an extension of LMDB that realizes this design inside a persistent memory-mapped engine, and evaluate it through an integration with Negentropy. The results show that placing the reconciliation oracle inside the storage tree substantially reduces local reconciliation cost on the evaluated reconciliation-heavy workloads compared with an open-source persistent baseline based on auxiliary tree caches, while the window-subrange ablation further confirms the usefulness of the systems optimizations built on top of the core aggregate representation.

We investigate a concrete realization of the Dark Dimension scenario, where a single large extra dimension is set at sub-millimeter scales. In this framework, the Casimir energy of bulk fields accounts for the observed dark energy. Working in a 5-dimensional setup with the Standard Model confined to a 4-dimensional brane, we derive the effective action for the radion. We demonstrate that a minimal model comprising only gravity and three right-handed bulk neutrinos typically yields a negative radion potential. To realize a positive vacuum energy, we consider some extensions with additional bulk degrees of freedom. These extensions generate a sufficiently flat positive potential that allows the radion to behave as a quintessence field, evolving slowly at the sub-eV scale. Finally, we analyze the evolution of the dark-energy equation-of-state parameter and show that our model is consistent with recent DESI BAO measurements, including the distance ratios $D_H/r_d$ and $D_M/r_d$.

We give the classification of thick representations and dense representations of the symmetric group over a field of characteristic zero.

Electron irradiation enables quantitative control over the plastic flow dynamics of silicate glasses, even far below the glass transition temperature. Through stress-relaxation experiments spanning ambient to near-glass-transition temperatures, we uncover a time-current equivalence that grants direct access to steady-state plastic flow over five decades in strain rate. This equivalence allows reconstruction of the intrinsic plastic-flow curve and quantitative assessment of the roles of network connectivity and temperature. Notably, the observed temperature dependence reveals a striking discrepancy with existing theoretical frameworks, highlighting the need for a comprehensive model of plastic flow dynamics in the glassy state.

Stochastic control barrier functions (SCBFs) provide a safety-critical control framework for systems subject to stochastic disturbances by bounding the probability of remaining within a safe set. However, synthesizing a valid SCBF that explicitly reflects the true safety probability of the system, which is the most natural measure of safety, remains a challenge. This paper addresses this issue by adopting a spectral perspective, utilizing the linear operator that governs the evolution of the closed-loop system's safety probability. We find that the dominant eigenpair of this Koopman-like operator encodes fundamental safety information of the stochastic system. The dominant eigenfunction is a natural and valid SCBF, with values that explicitly quantify the relative long-term safety of the state, while the dominant eigenvalue indicates the global rate at which the safety probability decays. A practical synthesis algorithm is proposed, termed power-policy iteration, which jointly computes the dominant eigenpair and an optimized backup policy. The method is validated using simulation experiments on safety-critical dynamics models.

Devices employing cryptographic approaches have to be resistant to physical attacks. Side-Channel Analysis (SCA) and Fault Injection (FI) attacks are frequently used to reveal cryptographic keys. In this paper, we present a combined SCA and laser illumination attack against an Elliptic Curve Scalar Multiplication accelerator using a differential probe from Teledyne LeCroy. Our experiments show that laser illumination increases the power consumption of the chip, especially its static power consumption but the success of the horizontal power analysis attacks was changed insignificantly. We assume that using a laser with a high laser beam power and concentrating on measuring and analysing only static current can improve the attack success significantly. The horizontal attacks against public key cryptosystems exploiting the Static Consumption under Laser Illumination (SCuLI attacks) are novel and their potential is not investigated yet. These attacks can be especially dangerous against cryptographic chips manufactured in scaled technologies. If such attacks are feasible, appropriate countermeasures have to be proposed in the future.

The generation of exciton valley coherence typically requires linearly polarized (LP) light as an external coherent drive, whereas circularly polarized (CP) light fails to induce coherence. Here, we develop a unified, microscopically-grounded open-quantum-system framework within a five-level model incorporating bright-dark exciton interactions in monolayer WSe2, and demonstrate that the polarization ellipticity of the excitation field provides selective control over distinct exciton species contributing to valley coherence. Specifically, LP and CP excitations generate bright and dark coherence, respectively, with continuous ellipticity tuning enabling controlled transitions between these states. We further reveal dual magnetic advantages for manipulating dark coherence even in the absence of initial coherence: (i) an out-of-plane magnetic field suppresses coherence decay and (ii) an in-plane field enables its optical readout, with quantitatively realistic field strengths. These findings provide a powerful mechanism for accessing hidden dark states via ellipticity-driven coherence transfer, and establish a new pathway for harnessing bright-dark valley-coherence transitions in future quantum control.

A widely held hypothesis for why generative recommendation (GR) models outperform conventional item ID-based models is that they generalize better. However, there is few systematic way to verify this hypothesis beyond a superficial comparison of overall performance. To address this gap, we categorize each data instance based on the specific capability required for a correct prediction: either memorization (reusing item transition patterns observed during training) or generalization (composing known patterns to predict unseen item transitions). Extensive experiments show that GR models perform better on instances that require generalization, whereas item ID-based models perform better when memorization is more important. To explain this divergence, we shift the analysis from the item level to the token level and show that what appears to be item-level generalization often reduces to token-level memorization for GR models. Finally, we show that the two paradigms are complementary. We propose a simple memorization-aware indicator that adaptively combines them on a per-instance basis, leading to improved overall recommendation performance.

Chains of co-Büchi automata (COCOA) have recently been introduced as a new canonical model for representing arbitrary omega-regular languages. They can be minimized in polynomial time and are hence an attractive language representation for applications in which normally, deterministic omega-automata are used. While it is known how to build COCOA from deterministic parity automata, little is currently known about their relationship to automaton models introduced earlier than COCOA. In this paper, we analyze the conciseness of chains of co-Büchi automata. We provide three main results and give an overview of the implications of these results. First of all, we show that even in the case that all automata in the chain are deterministic, chains of co-Büchi automata can be exponentially more concise than deterministic parity automata. We then present two main results that together negatively answer the question if this conciseness is retained when performing Boolean operations (such as disjunction, conjunction, and complementation) over COCOA. For the binary operations, we show that there exist families of languages for which their application leads to an exponential growth of the sizes of the automata. The families have the property that when representing them using deterministic parity automata, taking the disjunction or conjunction of the family elements only requires a polynomial blow-up. We finally show that an exponential blow-up is also unavoidable when complementing a COCOA, as this operation can require redistributing with which colors words need to be recognized.

We use the law of total variance to generate multiple expansions for the posterior predictive variance. These expansions are sums of terms involving conditional expectations and conditional variances and provide a quantification of the sources of predictive uncertainty. Since the posterior predictive variance is fixed given the model, it represents a constant quantity that is conserved over these expansions. The terms in the expansions can be assessed in absolute or relative sense to understand the main contributors to the length of prediction intervals. We quantify the term-wise uncertainty across expansions varying in the number of terms and the order of conditionates. In particular, given that a specific term in one expansion is small or zero, we identify the other terms in other expansions that must also be small or zero. We illustrate this approach to predictive model assessment in several well-known models.

Recent transmission spectra of the temperate sub-Neptune K2-18 b obtained with JWST have attracted significant attention. Debates have quickly arisen over the interpretation of the spectral data, particularly the recent MIRI observation where dimethyl sulfide (DMS) and dimethyl disulfide (DMDS) are claimed. Here we revisit K2-18 b as a case study to examine several key questions that are also broadly relevant to the temperate sub-Neptune population: i) Can the low water abundance be reconciled with water clouds driven by orbital eccentricity? ii) Are the observed and non-observed atmospheric compositions mutually consistent? iii) Is it kinetically possible to produce DMS under sub-Neptune conditions? To address these questions, we couple climate and photochemical models to obtain self-consistent climate-photochemistry states for K2-18 b with a moderate orbital eccentricity of 0.2, as suggested by radial-velocity measurements. In addition, we present new laboratory measurements of DMS and DMDS infrared opacities by HFML-FELIX and compile updated C$_2$H$_6$ (ethane) opacities that include weak overtone bands. Our results support the interpretation of a sub-Neptune scenario without invoking DMS, and we do not find strong evidence for a water-rich interior.

Let $\mathbf{R}$ be the sample correlation matrix constructed from $\mathbf{X}\in \mathbb{R}^{p\times n}$, whose entries are independent and identically distributed random variables with mean zero and tail probability condition $\lim_{x\rightarrow \infty}x^3\mathbb{P}(|ξ|>x)=0$. We derive the universal logarithmic law for $\log \det \mathbf{R}$, \begin{equation*} \frac{\log \det \mathbf{R}-(p-n+1/2)\log (1-\frac{p-1}{n})+p-\frac{p}{n}}{\sqrt{-2\log (1-\frac{p-1}{n})-2\frac{p}{n}}}\stackrel{d}{\rightarrow} {N}(0,1), \end{equation*} if $p\le n$ as $p,n\rightarrow \infty$. Moreover, under the near-singularity case $0\le n-p\le n^{1-w}$ for any $w\in (0,1)$, it is shown that the tail probability condition can be weakened to $\lim_{x\rightarrow \infty}x^3(\log x)^{-1/4+\mathfrak{c}}\mathbb{P}(|ξ|>x)<\infty$ for any constant $0<\mathfrak{c}<1/4$.

Traditional Functional Principal Component Analysis typically focuses on densely observed univariate functional data, yet many applications, particularly in longitudinal studies, involve multivariate functional data observed sparsely and irregularly across subjects. A common approach for extracting multivariate functional principal components in such settings relies on an eigen decomposition of univariate functional principal component scores to capture cross-component correlations. We propose a new approach for the estimation of multivariate functional principal components by improving the univariate eigenanalysis through maximum likelihood estimation combined with a modified Gram-Schmidt orthonormalization. The performance of the proposed approach is evaluated against two established methods, and its practical utility is demonstrated through an application to longitudinal cognitive biomarker data from an Alzheimer's disease study and a collection of data on dairy milk yield and milk compositions from research dairy farms in Ireland.

In this paper, we show that in weak field limit Schwarzschild Bertotti-Robinson black hole (Schwarzschild-BR BH) turns into Schwarzschild black hole immersed in external uniform magnetic field which is given in 1. The dynamics of both magnetized and electrically charged particles in the vicinity of a Schwarzschild-BR black hole are investigated. The innermost stable circular orbits (ISCOs) for both magnetized and electrically charged particles are examined in detail, revealing that the magnetic field parameter B exerts a considerable influence, leading to an increase in the ISCO radius. The orbital and epicyclic motion of test particles in Schwarzschild-BR black hole spacetime was analyzed, including both circular orbits and their oscillatory perturbations. Additionally, the trajectories of both magnetized and electrically charged particles are analyzed for various configurations of the magnetic parameter B. We also demonstrate how the magnetic field B, electric charge q, and magnetic moment μ influence the dynamics of charged particles, specifically affecting the chaotic behavior, Poincare' sections, oscillatory frequencies and power spectral density.

The Majorana Double Charge Exchange (MDCE) provides a suitable environment for studying the dynamics of the neutrinoless double beta ($0νββ$) decay, particularly short-range correlations among nucleons. The study of the pion potential is essential in this respect, as it represents the strong interaction counterpart of the neutrino potential, driving nucleon correlations in $0νββ$ decay. Numerical studies on pion potential have revealed an effective range of about 1 fm with slight dispersion around this value, confirming the short-range character of the MDCE process.

We introduce a distribution-free lattice Boltzmann formulation for general compartmental reaction--diffusion systems arising in mathematical epidemiology. The proposed scheme, termed a single-step simplified lattice Boltzmann method (SSLBM), evolves directly macroscopic compartment densities, eliminating the need for particle distribution functions and explicit streaming operations. This yields a compact and computationally efficient framework while retaining the kinetic consistency of lattice Boltzmann methodologies. The approach is applied to a SEIRD (Susceptible-Exposed-Infected-Recovered-Deceased) reaction-diffusion model as a representative case. The resulting discrete evolution equations are derived and shown to recover the target macroscopic dynamics. The method is systematically validated against a fourth-order finite difference reference solution and compared with a standard BGK lattice Boltzmann formulation. Numerical results demonstrate that the SSLBM consistently improves accuracy across all compartments and norms. The error reduction is robust with respect to both the basic reproduction number and diffusion strength, typically ranging between factors of approximately two and five depending on the regime. In particular, the method shows enhanced control of localised errors in regimes characterised by strong nonlinear coupling and steep spatial gradients. Our findings indicate that the proposed formulation provides an accurate and efficient alternative to classical lattice Boltzmann approaches for reaction-diffusion systems, with particular advantages in stiff and nonlinear epidemic dynamics.

Serverless computing abstracts infrastructure management but also obscures system-level behaviors that can introduce security risks. Prior work has shown that serverless platforms are vulnerable to attacks exploiting shared execution environments, including attacker--victim co-location and denial-of-service through resource contention, yet analyzing these risks on production platforms is difficult due to limited observability, high cost, and lack of experimental control, while existing simulators primarily focus on performance and cost rather than security. We present Kumo, a security-focused simulator for serverless platforms that enables controlled, reproducible analysis of security risks arising from scheduling and resource sharing decisions. Kumo models invocation arrivals, scheduler placement, container reuse, resource contention, and queuing within a discrete-event framework, explicitly representing attackers and victims as first-class entities and providing metrics such as co-location probability, time to first co-location, invocation drop rate, and tail latency. Through two case studies, we show that scheduler choice is a first-order factor for co-location attacks, inducing orders-of-magnitude differences under identical workloads, while Denial-of-Service behavior is largely governed by system-level factors such as service time, queuing policy, and cluster capacity once contention dominates. These results highlight the need to distinguish scheduler-driven isolation risks from broader resource exhaustion vulnerabilities and position Kumo as a flexible foundation for systematic, security-aware exploration of serverless platforms.