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We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction that are applicable in level set methods. The most involved numerical scheme is third order accurate for the linear advection with a space dependent velocity and unconditionally stable in the sense of von Neumann stability analysis. We also present a simple high-resolution scheme that gives a TVD (Total Variation Diminishing) approximation of the spatial derivative for the advected level set function. In the case of nonlinear advection, the semi-implicit discretization is proposed to linearize the problem. The compact form of implicit stencil in numerical schemes containing unknowns only in the upwind direction allows applications of efficient algebraic solvers like fast sweeping methods. Numerical tests to evolve a smooth and non-smooth interface and an example with a large variation of velocity confirm the good accuracy of the methods and fast convergence of the algebraic solver even in the case of very large Courant numbers.

Population protocols form a well-established model of computation of passively mobile anonymous agents with constant-size memory. It is well known that population protocols compute Presburger-definable predicates, such as absolute majority and counting predicates. In this work, we initiate the study of population protocols operating over arbitrarily large data domains. More precisely, we introduce population protocols with unordered data as a formalism to reason about anonymous crowd computing over unordered sequences of data. We first show that it is possible to determine whether an unordered sequence from an infinite data domain has a datum with absolute majority. We then establish the expressive power of the immediate observation restriction of our model, namely where, in each interaction, an agent observes another agent who is unaware of the interaction.

The goal of this work is to study waves interacting with partially immersed objects allowed to move freely in the vertical direction, and in a regime in which the propagation of the waves is described by the one dimensional Boussinesq-Abbott system. The problem can be reduced to a transmission problem for this Boussinesq system, in which the transmission conditions between the components of the domain at the left and at the right of the object are determined through the resolution of coupled forced ODEs in time satisfied by the vertical displacement of the object and the average discharge in the portion of the fluid located under the object. We propose a new extended formulation in which these ODEs are complemented by two other forced ODEs satisfied by the trace of the surface elevation at the contact points. The interest of this new extended formulation is that the forcing terms are easy to compute numerically and that the surface elevation at the contact points is furnished for free. Based on this formulation, we propose a second order scheme that involves a generalization of the MacCormack scheme with nonlocal flux and a source term, which is coupled to a second order Heun scheme for the ODEs. In order to validate this scheme, several explicit solutions for this wave-structure interaction problem are derived and can serve as benchmark for future codes. As a byproduct, our method provides a second order scheme for the generation of waves at the entrance of the numerical domain for the Boussinesq-Abbott system.

One of the most important hyper-parameters in duration-dependent Markov-switching (DDMS) models is the duration of the hidden states. Because there is currently no procedure for estimating this duration or testing whether a given duration is appropriate for a given data set, an ad hoc duration choice must be heuristically justified. This is typically a difficult task and is likely the most delicate point of the modeling procedure, allowing for criticism and ultimately hindering the use of DDMS models. In this paper, we propose and examine a methodology that mitigates the choice of duration in DDMS models when forecasting is the goal. The idea is to use a parametric link instead of the usual fixed link when calculating transition probabilities. As a result, the model becomes more flexible and any potentially incorrect duration choice (i.e., misspecification) is compensated by the parameter in the link, yielding a likelihood and transition probabilities very close to the true ones while, at the same time, improving forecasting accuracy under misspecification. We evaluate the proposed approach in Monte Carlo simulations and using real data applications. Results indicate that the parametric link model outperforms the benchmark logit model, both in terms of in-sample estimation and out-of-sample forecasting, for both well-specified and misspecified duration values.

Nowadays, numerical models are widely used in most of engineering fields to simulate the behaviour of complex systems, such as for example power plants or wind turbine in the energy sector. Those models are nevertheless affected by uncertainty of different nature (numerical, epistemic) which can affect the reliability of their predictions. We develop here a new method for quantifying conditional parameter uncertainty within a chain of two numerical models in the context of multiphysics simulation. More precisely, we aim to calibrate the parameters $\theta$ of the second model of the chain conditionally on the value of parameters $\lambda$ of the first model, while assuming the probability distribution of $\lambda$ is known. This conditional calibration is carried out from the available experimental data of the second model. In doing so, we aim to quantify as well as possible the impact of the uncertainty of $\lambda$ on the uncertainty of $\theta$. To perform this conditional calibration, we set out a nonparametric Bayesian formalism to estimate the functional dependence between $\theta$ and $\lambda$, denoted $\theta(\lambda)$. First, each component of $\theta(\lambda)$ is assumed to be the realization of a Gaussian process prior. Then, if the second model is written as a linear function of $\theta(\lambda)$, the Bayesian machinery allows us to compute analytically the posterior predictive distribution of $\theta(\lambda)$ for any set of realizations $\lambda$. The effectiveness of the proposed method is illustrated on several analytical examples.

Hybrid working strategies have become, and will continue to be, the norm for many offices. This raises two considerations: newly unoccupied spaces needlessly consume energy, and the occupied spaces need to be effectively used to facilitate meaningful interactions and create a positive, sustainable work culture. This work aims to determine when spontaneous, collaborative interactions occur within the building and the environmental factors that facilitate such interactions. This study uses smartwatch-based micro-surveys using the Cozie platform to identify the occurrence of and spatially place interactions while categorizing them as a collaboration or distraction. This method uniquely circumvents pitfalls associated with surveying and qualitative data collection: occupant behaviors are identified in real-time in a non-intrusive manner, and survey data is corroborated with quantitative sensor data. A proof-of-concept study was deployed with nine hybrid-working participants providing 100 micro-survey cluster responses over approximately two weeks. The results show the spontaneous interactions occurring in hybrid mode are split evenly among the categories of collaboration, wanted socialization, and distraction and primarily occur with coworkers at one's desk. From these data, we can establish various correlations between the occurrence of positive spontaneous interactions and different factors, such as the time of day and the locations in the building. This framework and first deployment provide the foundation for future large-scale data collection experiments and human interaction modeling.

Purpose: The purpose of this article is to propose, based on a model of an interaction semantics, a certain understanding of the ''meaning'' of the exchanged characters within an interaction. Methodology: Based on a model of system interaction, I structure the model of interaction semantics similar to the semantics of a formal language: first, I identify adequate variables in my interaction model to assign values to, and second, I identify the interpretation function to provide meaning. Thereby I arrive at a model of interaction semantics which, in the sense of the late Ludwig Wittgenstein, can do without a 'mental' mapping from characters to concepts. Findings: The key findings are a better understanding of the tight relation between the informatical approach to model interactions and game theory; of the central 'chicken and egg' problem, any natural language has to solve, namely that to interact sensibly, we have to understand each other and to acquire a common understanding, we have to interact with each other, which I call the 'simultaneous interaction and understanding (SIAU)' problem; why ontologies are less 'semantic' then their proponents suggest; and how 'semantic' interoperability is to be achieved. Value: The main value of the proposed model of interaction semantics is that it could be applied in many different disciplines and therefore could serve as a basis for scientists of natural sciences and humanities as well as engineers to understand each other more easily talking about semantics, especially with the advent of cyber-physical systems.

We propose an accurate and energy-stable parametric finite element method for solving the sharp-interface continuum model of solid-state dewetting in three-dimensional space. The model describes the motion of the film\slash vapor interface with contact line migration and is governed by the surface diffusion equation with proper boundary conditions at the contact line. We present a new weak formulation for the problem, in which the interface and its contact line are evolved simultaneously. By using piecewise linear elements in space and backward Euler in time, we then discretize the weak formulation to obtain a fully discretized parametric finite element approximation. The resulting numerical method is shown to be well-posed and unconditionally energy-stable. Furthermore, the numerical method is extended for solving the sharp interface model of solid-state dewetting with anisotropic surface energies in the Riemmanian metric form. Numerical results are reported to show the convergence and efficiency of the proposed numerical method as well as the anisotropic effects on the morphological evolution of thin films in solid-state dewetting.

Foundational ontologies devoted to the effective representation of processes and procedures are not widely investigated at present, thereby limiting the practical adoption of semantic approaches in real scenarios where the precise instructions to follow must be considered. Also, the representation ought to include how agents should carry out the actions associated with the process, whether or not agents are able to perform those actions, the possible roles played as well as the related events. The OASIS ontology provides an established model to capture agents and their interactions but lacks means for representing processes and procedures carried out by agents. This motivates the research presented in this article, which delivers an extension of the OASIS 2 ontology to combine the capabilities for representing agents and their behaviours with the full conceptualization of processes and procedures. The overarching goal is to deliver a foundational OWL ontology that deals with agent planning, reaching a balance between generality and applicability, which is known to be an open challenge.

In the celebrated stable-matching problem, there are two sets of agents M and W, and the members of M only have preferences over the members of W and vice versa. It is usually assumed that each member of M and W is a single entity. However, there are many cases in which each member of M or W represents a team that consists of several individuals with common interests. For example, students may need to be matched to professors for their final projects, but each project is carried out by a team of students. Thus, the students first form teams, and the matching is between teams of students and professors. When a team is considered as an agent from M or W, it needs to have a preference order that represents it. A voting rule is a natural mechanism for aggregating the preferences of the team members into a single preference order. In this paper, we investigate the problem of strategic voting in the context of stable-matching of teams. Specifically, we assume that members of each team use the Borda rule for generating the preference order of the team. Then, the Gale-Shapley algorithm is used for finding a stable-matching, where the set M is the proposing side. We show that the single-voter manipulation problem can be solved in polynomial time, both when the team is from M and when it is from W. We show that the coalitional manipulation problem is computationally hard, but it can be solved approximately both when the team is from M and when it is from W.