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This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between spatial and temporal variables for cases with anomalous diffusion phenomena. From a Lagrangian approach, we separate the corresponding stochastic differential equations (SDEs) into sub-problems and construct a one-step structure-preserving method to solve them. Then by modified equation systems, the convergence analysis in calculating the effective diffusivity is provided and compared between the structure-preserving scheme and the Euler-Maruyama scheme. Also, we provide the error estimate for the structure-preserving scheme in calculating the power law for a series of super-diffusive random flows. Finally, we calculate the effective diffusivity and anomalous diffusion phenomena for a series of 2D and 3D random fields.

The execution of Belief-Desire-Intention (BDI) agents in a Multi-Agent System (MAS) can be practically implemented on top of low-level concurrency mechanisms that impact on efficiency, determinism, and reproducibility. We argue that developers should specify the MAS behaviour independently of the execution model, and choose or configure the concurrency model later on, according to the specific needs of their target domain, leaving the MAS specification unaffected. We identify patterns for mapping the agent execution over the underlying concurrency abstractions, and investigate which concurrency models are supported by some of the most commonly used BDI platforms. Although most frameworks support multiple concurrency models, we find that they mostly hide them under the hood, making them opaque to the developer, and actually limiting the possibility of fine-tuning the MAS.

Topological Data Analysis (TDA) provides a pipeline to extract quantitative topological descriptors from structured objects. This enables the definition of topological loss functions, which assert to what extent a given object exhibits some topological properties. These losses can then be used to perform topological optimizationvia gradient descent routines. While theoretically sounded, topological optimization faces an important challenge: gradients tend to be extremely sparse, in the sense that the loss function typically depends on only very few coordinates of the input object, yielding dramatically slow optimization schemes in practice.Focusing on the central case of topological optimization for point clouds, we propose in this work to overcome this limitation using diffeomorphic interpolation, turning sparse gradients into smooth vector fields defined on the whole space, with quantifiable Lipschitz constants. In particular, we show that our approach combines efficiently with subsampling techniques routinely used in TDA, as the diffeomorphism derived from the gradient computed on a subsample can be used to update the coordinates of the full input object, allowing us to perform topological optimization on point clouds at an unprecedented scale. Finally, we also showcase the relevance of our approach for black-box autoencoder (AE) regularization, where we aim at enforcing topological priors on the latent spaces associated to fixed, pre-trained, black-box AE models, and where we show thatlearning a diffeomorphic flow can be done once and then re-applied to new data in linear time (while vanilla topological optimization has to be re-run from scratch). Moreover, reverting the flow allows us to generate data by sampling the topologically-optimized latent space directly, yielding better interpretability of the model.

This paper is devoted to the solution and stability of a one-dimensional model depicting Rao--Nakra sandwich beams, incorporating damping terms characterized by fractional derivative types within the domain, specifically a generalized Caputo derivative with exponential weight. To address existence, uniqueness, stability, and numerical results, fractional derivatives are substituted by diffusion equations relative to a new independent variable, $\xi$, resulting in an augmented model with a dissipative semigroup operator. Polynomial decay of energy is achieved, with a decay rate depending on the fractional derivative parameters. Both the polynomial decay and its dependency on the parameters of the generalized Caputo derivative are numerically validated. To this end, an energy-conserving finite difference numerical scheme is employed.

We consider the problem of sampling a high dimensional multimodal target probability measure. We assume that a good proposal kernel to move only a subset of the degrees of freedoms (also known as collective variables) is known a priori. This proposal kernel can for example be built using normalizing flows. We show how to extend the move from the collective variable space to the full space and how to implement an accept-reject step in order to get a reversible chain with respect to a target probability measure. The accept-reject step does not require to know the marginal of the original measure in the collective variable (namely to know the free energy). The obtained algorithm admits several variants, some of them being very close to methods which have been proposed previously in the literature. We show how the obtained acceptance ratio can be expressed in terms of the work which appears in the Jarzynski-Crooks equality, at least for some variants. Numerical illustrations demonstrate the efficiency of the approach on various simple test cases, and allow us to compare the variants of the algorithm.

Computability on uncountable sets has no standard formalization, unlike that on countable sets, which is given by Turing machines. Some of the approaches to define computability in these sets rely on order-theoretic structures to translate such notions from Turing machines to uncountable spaces. Since these machines are used as a baseline for computability in these approaches, countability restrictions on the ordered structures are fundamental. Here, we show several relations between the usual countability restrictions in order-theoretic theories of computability and some more common order-theoretic countability constraints, like order density properties and functional characterizations of the order structure in terms of multi-utilities. As a result, we show how computability can be introduced in some order structures via countability order density and multi-utility constraints.

Ising machines are dedicated hardware solvers of NP-hard optimization problems. However, they do not always find the most optimal solution. The probability of finding this optimal solution depends on the problem at hand. Using continuation methods, we show that this is closely linked to the bifurcation sequence of the optimal solution. From this bifurcation analysis, we can determine the effectiveness of solution schemes. Moreover, we find that the proper choice of implementation of the Ising machine can drastically change this bifurcation sequence and therefore vastly increase the probability of finding the optimal solution.

Three-dimensional effect of tunnel face and gravitational excavation generally occur in shallow tunnelling, which are nevertheless not adequately considered in present complex variable solutions. In this paper, a new time-dependent complex variable solution on quasi three-dimensional shallow tunnelling in gravitational geomaterial is derived, and the far-field displacement singularity is eliminated by fixed far-field ground surface in the whole excavation time span. With an equivalent coefficient of three-dimensional effect, the quasi three-dimensional shallow tunnelling is transformed into a plane strain problem with time-dependent virtual traction along tunnel periphery. The mixed boundaries of fixed far-field ground surface and nearby free segment form a homogenerous Riemann-Hilbert problem with extra constraints of the virtual traction along tunnel periphery, which is simultaneously solved using an iterative linear system with good numerical stability. The mixed boundary conditions along the ground surface in the whole excavation time span are well satisified in a numerical case, which is further examined by comparing with corresponding finite element solution. The results are in good agreements, and the proposed solution illustrates high efficiency. More discussions are made on excavation rate, viscosity, and solution convergence. A latent paradox is disclosed for objectivity.

Statistical modeling of high-dimensional matrix-valued data motivates the use of a low-rank representation that simultaneously summarizes key characteristics of the data and enables dimension reduction. Low-rank representations commonly factor the original data into the product of orthonormal basis functions and weights, where each basis function represents an independent feature of the data. However, the basis functions in these factorizations are typically computed using algorithmic methods that cannot quantify uncertainty or account for basis function correlation structure a priori. While there exist Bayesian methods that allow for a common correlation structure across basis functions, empirical examples motivate the need for basis function-specific dependence structure. We propose a prior distribution for orthonormal matrices that can explicitly model basis function-specific structure. The prior is used within a general probabilistic model for singular value decomposition to conduct posterior inference on the basis functions while accounting for measurement error and fixed effects. We discuss how the prior specification can be used for various scenarios and demonstrate favorable model properties through synthetic data examples. Finally, we apply our method to two-meter air temperature data from the Pacific Northwest, enhancing our understanding of the Earth system's internal variability.

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.