Constraint-based reachability

Iterative imperative programs can be considered as infinite-state systems computing over possibly unbounded domains. Studying reachability in these systems is challenging as it requires to deal with an infinite number of states with standard backward or forward exploration strategies. An approach that we call Constraint-based reachability, is proposed to address reachability problems by exploring program states using a constraint model of the whole program. The keypoint of the approach is to interpret imperative constructions such as conditionals, loops, array and memory manipulations with the fundamental notion of constraint over a computational domain. By combining constraint filtering and abstraction techniques, Constraint-based reachability is able to solve reachability problems which are usually outside the scope of backward or forward exploration strategies. This paper proposes an interpretation of classical filtering consistencies used in Constraint Programming as abstract domain computations, and shows how this approach can be used to produce a constraint solver that efficiently generates solutions for reachability problems that are unsolvable by other approaches.Comment: In Proceedings Infinity 2012, arXiv:1302.310

A random walk approach to Stochastic Calculus

L’objectiu d’aquest treball és presentar una introducció al càlcul estocàstic. En la primera part parlem del moviment brownià, el qual veurem que es pot pensar com a límit de passeigs aleatoris amb l’ajut del principi d’invariància de Donsker. A continuació, presentem de manera heurística les equacions diferencials estocàstiques i veiem com es poden definir de manera rigorosa amb l’ajut de la integral estocàstica. Finalment, parlem d’existència i unicitat de solucions d’aquestes equacions i tractem un cas senzill com és el de l’equació de Langevin.The aim of this work is to provide an introduction to the subject of Stochastic Calculus. In the first part we talk about the Brownian motion, which we will see that it can be thought as a limit of random walks via Donsker’s Invariance Principle. Next, we heuristically present the stochastic differential equations and see how they can be rigorously defined with the help of the stochastic integral. Finally, we discuss the matter of existence and uniqueness of solutions to such equations and solve a rather simple case like the Langevin equation

An introduction to stochastic integration

L’objectiu d’aquest treball és el d’estudiar integrals estocàstiques que no són necessàriament respecte del moviment brownià. Primer de tot es revisa la construcció d’aquesta darrera integral per motivar les possibles extensions a altres integradors com són les martingales. A continuació, estudiem les integrals respecte de camps aleatoris, on comencem per estudiar aquestes integrals respecte del soroll blanc gaussià per, un cop més, estendre la classe d’integradors. Alhora que es van estudiant aquests objectes, també presentem alguns resultats referents a l’aproximació en llei d’aquests

An introduction to stochastic integration

Treballs finals del Màster en Matemàtica Avançada, Facultat de Matemàtiques, Universitat de Barcelona: Curs: 2023-2024. Director: Xavier Bardina i Simorra i David Márquez[en] The main purpose of this master’s thesis is to continue and extend the study of the stochastic integral seen in the subject of Stochastic Calculus, providing (hopefully) an introductory text that will allow the average student of the subject (and to anyone who is already familiar with the stochastic integral with respect to the Brownian motion) to expand his knowledge. To do so, in the second chapter we briefly review the construction of the Itô integral to then see how we exploit these ideas to generalize the construction to other processes, this is done following the construction provided in the third chapter [7]. Many of the presented results and notions of this part (and the following ones) have been completed with additional explanations and comparisons with the already seen objects in order to make the understanding of these clearer. In the third chapter, we discuss the topic of stochastic integration with respect to random fields. We first treat the integral with respect to the space-time Gaussian white noise, following the construction presented in the first two chapters of [6], since it deals with objects which might be a bit more familiar to the intended audience as its construction uses the already studied Itô integral with respect to the Brownian motion. Before doing so, we introduce two crucial Gaussian processes (the isonormal process and the white noise), which generalize the Brownian motion and are crucial when it comes to define the stochastic integral with respect to the space-time white noise. Next, and following the second chapter of [11], we introduce a wider class of random fields (which contains the ones already seen) that can be used as integrators and show how one constructs integrals with respect to such objects. During this process, we use the already studied Gaussian white noise as a canonical example that will serve us as a model to compare the new construction. Finally, and to keep the reader entertained, in the Introduction and in Section 2.1 we pose a problem regarding the validity of the models that use the Brownian motion and the space-time Gaussian white noise as driving noises which is treated in Sections 2.3.4 and 3.2.4, providing results regarding the approximation in law of the stochastic integral with respect to the Brownian motion (Theorem 2.3.11, of which we could not find a statement nor a proof elsewhere) and the one with respect to the Brownian sheet (Theorem 3.2.2, which is a simplification of one of the results in [2]), respectively

Weak convergence of the Lazy Random Walk to the Brownian motion

En aquest article considerem una modificació del passeig aleatori simple, el Lazy Random Walk, i construïm una família de processos estocàstics a partir d’aquest procés que convergeix feblement cap a un moviment Brownia estàndard en una dimensió.In this paper we consider a modification of the simple random walk, the Lazy Random Walk, and construct a family of stochastic processes from the latter that converges weakly to a standard one-dimensional Brownian motion

Plasma sTNFR1 and IL8 for prognostic enrichment in sepsis trials: a prospective cohort study.

BackgroundEnrichment strategies improve therapeutic targeting and trial efficiency, but enrichment factors for sepsis trials are lacking. We determined whether concentrations of soluble tumor necrosis factor receptor-1 (sTNFR1), interleukin-8 (IL8), and angiopoietin-2 (Ang2) could identify sepsis patients at higher mortality risk and serve as prognostic enrichment factors.MethodsIn a multicenter prospective cohort study of 400 critically ill septic patients, we derived and validated thresholds for each marker and expressed prognostic enrichment using risk differences (RD) of 30-day mortality as predictive values. We then used decision curve analysis to simulate the prognostic enrichment of each marker and compare different prognostic enrichment strategies.Measurements and main resultsAn admission sTNFR1 concentration > 8861 pg/ml identified patients with increased mortality in both the derivation (RD 21.6%) and validation (RD 17.8%) populations. Among immunocompetent patients, an IL8 concentration > 94 pg/ml identified patients with increased mortality in both the derivation (RD 17.7%) and validation (RD 27.0%) populations. An Ang2 level > 9761 pg/ml identified patients at 21.3% and 12.3% increased risk of mortality in the derivation and validation populations, respectively. Using sTNFR1 or IL8 to select high-risk patients improved clinical trial power and efficiency compared to selecting patients with septic shock. Ang2 did not outperform septic shock as an enrichment factor.ConclusionsThresholds for sTNFR1 and IL8 consistently identified sepsis patients with higher mortality risk and may have utility for prognostic enrichment in sepsis trials

Bifurcation Analysis for Prey-Predator Model with Holling Type III Functional Response Incorporating Prey Refuge

In this paper, we carried out the bifurcation analysis for a Lotka-Volterra prey-predator model with Holling type III functional response incorporating prey refuge protecting a constant proportion of the preys. We study the local bifurcation considering the refuge constant as a parameter. From the center manifold equation, we establish a transcritical bifurcation for the boundary equilibrium. In addition, we prove the occurrence of Hopf bifurcation for the homogeneous equilibrium. Moreover, we give the radius and period of the unique limit cycle for our syste

L’Intelligence Stratégique et l’innovation dans une entreprise publique : une analyse par l’approche holistique

In a context marked by a diversity of reforms, unpredictability of crisis and an intensity of ecosystem requirements, public enterprises meet challenges qualified as complex and multi-dimensional. In addition, there is an increasing need to innovate products, services, and managerial practices. Meeting these challenges requires switching the mode of management to a more proactive one based on Strategic Intelligence. In our knowledge, the previous studies analyzed the impact of Strategic Intelligence on innovation from different angles and without articulating the functions of Strategic Intelligence which generate ambiguities involved in practical application. For this purpose, our study aims to investigate how to articulate Strategic Intelligence with innovation in a public enterprise. Our study was based on the qualitative method by conducting interviews in a public enterprise. The main results of our study pointed out that Strategic Intelligence could support innovation through its triptych, highlighting the importance of adopting a holistic approach to analyze Strategic Intelligence and innovation.Dans un contexte marqué par la diversité des réformes, l’imprévisibilité des crises et l’intensité des besoins de l’écosystème, les entreprises publiques relèvent des défis complexes et multidimensionnels. Aussi, il est nécessaire  d’innover les produits, les services et les pratiques managériales. Relever ces défis revient à adopter un mode de gestion proactif, fondé sur l’Intelligence Stratégique. À notre connaissance, les études précédentes ont analysé l’impact de l’Intelligence Stratégique sur l’innovation sous différents angles sans articuler les différentes fonctions de l’Intelligence Stratégique générant ainsi des ambiguïtés quant à son application pratique. À cette fin, notre étude vise à étudier comment articuler l’Intelligence Stratégique et l’innovation dans une entreprise publique. Notre étude a adopté la méthode  qualitative à travers le guide d’entretien. Les résultats de notre étude montrent que l’Intelligence Stratégique soutient l’innovation grâce à son triptyque ce qui interpelle l’importance de l’adoption d’une approche holistique pour l’analyse de l’Intelligence Stratégique et de l’innovation