On the effects of firing memory in the dynamics of conjunctive networks

Boolean networks are one of the most studied discrete models in the context of the study of gene expression. In order to define the dynamics associated to a Boolean network, there are several \emph{update schemes} that range from parallel or \emph{synchronous} to \emph{asynchronous.} However, studying each possible dynamics defined by different update schemes might not be efficient. In this context, considering some type of temporal delay in the dynamics of Boolean networks emerges as an alternative approach. In this paper, we focus in studying the effect of a particular type of delay called \emph{firing memory} in the dynamics of Boolean networks. Particularly, we focus in symmetric (non-directed) conjunctive networks and we show that there exist examples that exhibit attractors of non-polynomial period. In addition, we study the prediction problem consisting in determinate if some vertex will eventually change its state, given an initial condition. We prove that this problem is {\bf PSPACE}-complete

Dynamical Stability of Threshold Networks over Undirected Signed Graphs

In this paper we study the dynamic behavior of threshold networks on undirected signed graphs. While much attention has been given to the convergence and long-term behavior of this model, an open question remains: How does the underlying graph structure influence network dynamics? While similar papers have been carried out for threshold networks (as well as for other networks) these have largely focused on unsigned networks. However, the signed graph model finds applications in various real-world domains like gene regulation and social networks. By studying a graph parameter that we call "stability index," we search to establish a connection between the structure and the dynamics of threshold network. Interestingly, this parameter is related to the concepts of frustration and balance in signed graphs. We show that graphs that present negative stability index exhibit stable dynamics, meaning that the dynamics converges to fixed points regardless of threshold parameters. Conversely, if at least one subgraph has positive stability index, oscillations in long term behavior may appear. Finally, we generalize the analysis to network dynamics under periodic update schemes and we explore the case in which the stability index is positive for some subgraph finding that attractors with superpolynomial period on the size of the network may appear

On the impact of treewidth in the computational complexity of freezing dynamics

An automata network is a network of entities, each holding a state from a finite set and evolving according to a local update rule which depends only on its neighbors in the network's graph. It is freezing if there is an order on states such that the state evolution of any node is non-decreasing in any orbit. They are commonly used to model epidemic propagation, diffusion phenomena like bootstrap percolation or cristal growth. In this paper we establish how treewidth and maximum degree of the underlying graph are key parameters which influence the overall computational complexity of finite freezing automata networks. First, we define a general model checking formalism that captures many classical decision problems: prediction, nilpotency, predecessor, asynchronous reachability. Then, on one hand, we present an efficient parallel algorithm that solves the general model checking problem in NC for any graph with bounded degree and bounded treewidth. On the other hand, we show that these problems are hard in their respective classes when restricted to families of graph with polynomially growing treewidth. For prediction, predecessor and asynchronous reachability, we establish the hardness result with a fixed set-defiend update rule that is universally hard on any input graph of such families

Local Certification of Majority Dynamics

In majority voting dynamics, a group of $n$ agents in a social network are asked for their preferred candidate in a future election between two possible choices. At each time step, a new poll is taken, and each agent adjusts their vote according to the majority opinion of their network neighbors. After $T$ time steps, the candidate with the majority of votes is the leading contender in the election. In general, it is very hard to predict who will be the leading candidate after a large number of time-steps. We study, from the perspective of local certification, the problem of predicting the leading candidate after a certain number of time-steps, which we call Election-Prediction. We show that in graphs with sub-exponential growth Election-Prediction admits a proof labeling scheme of size $\mathcal{O}(\log n)$. We also find non-trivial upper bounds for graphs with a bounded degree, in which the size of the certificates are sub-linear in $n$. Furthermore, we explore lower bounds for the unrestricted case, showing that locally checkable proofs for Election-Prediction on arbitrary $n$-node graphs have certificates on $\Omega(n)$ bits. Finally, we show that our upper bounds are tight even for graphs of constant growth

Exploring the Dynamics of Fungal Cellular Automata

Cells in a fungal hyphae are separated by internal walls (septa). The septa have tiny pores that allow cytoplasm flowing between cells. Cells can close their septa blocking the flow if they are injured, preventing fluid loss from the rest of filament. This action is achieved by special organelles called Woronin bodies. Using the controllable pores as an inspiration we advance one and two-dimensional cellular automata into Elementary fungal cellular automata (EFCA) and Majority fungal automata (MFA) by adding a concept of Woronin bodies to the cell state transition rules. EFCA is a cellular automaton where the communications between neighboring cells can be blocked by the activation of the Woronin bodies (Wb), allowing or blocking the flow of information (represented by a cytoplasm and chemical elements it carries) between them. We explore a novel version of the fungal automata where the evolution of the system is only affected by the activation of the Wb. We explore two case studies: the Elementary Fungal Cellular Automata (EFCA), which is a direct application of this variant for elementary cellular automata rules, and the Majority Fungal Automata (MFA), which correspond to an application of the Wb to two dimensional automaton with majority rule with Von Neumann neighborhood. By studying the EFCA model, we analyze how the 256 elementary cellular automata rules are affected by the activation of Wb in different modes, increasing the complexity on applied rule in some cases. Also we explore how a consensus over MFA is affected when the continuous flow of information is interrupted due to the activation of Woronin bodies.Comment: 31 pages, 30 figure

Computing Power of Hybrid Models in Synchronous Networks

During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable. The separation results are obtained by approaching communication complexity through an original angle, which may be of independent interest. The two players are not bounded to compute the value of a binary function, but the combined outputs of the two players are constrained by this value. In particular, we introduce the XOR-Index problem, in which Alice is given a binary vector $x\in\{0,1\}^n$ together with an index $i\in[n]$, Bob is given a binary vector $y\in\{0,1\}^n$ together with an index $j\in[n]$, and, after a single round of 2-way communication, Alice must output a boolean $\textrm{out}_A$, and Bob must output a boolean $\textrm{out}_B$, such that \mbox{out}_A\land\mbox{out}_B = x_j\oplus y_i. We show that the communication complexity of XOR-Index is $\Omega(n)$ bits

Atypical fibroxanthoma with lymphomatoid reaction

Background: Atypical fibroxanthoma (AFX) represents an uncommon skin tumor typically occurring on sun-damaged skin of the elderly. Histopathologic variants include spindled, clear cell, osteoid, osteoclastic, chondroid, pigmented, granular cell and myxoid lesions. To date, an atypical lymphoid infiltrate, including CD30-positive large cells mimicking lymphomatoid papulosis, has not been described in association with AFX. Methods: The clinical and histopathological characteristics of two AFX cases inciting an atypical lymphoid infiltrate, along with immunohistochemical profiles and T-cell receptor gamma ( TCR γ) gene rearrangement results, were reviewed. Results: Lesions in both cases occurred as solitary nodules in elderly patients. Microscopically, both lesions showed a cellular proliferation composed of pleomorphic spindle cells, associated with a prominent intralesional atypical lymphoid infiltrate. The spindle cells expressed CD10 but lacked the expression of S-100, cytokeratins and muscle markers, thereby confirming the diagnosis of AFX. CD30 highlighted a significant subset of large mononuclear cells in the lymphoid infiltrate of one case. TCR γ gene rearrangement analyses were negative for both cases. Conclusion: An atypical lymphoid infiltrate, including the one resembling lymphomatoid papulosis, associated with AFX has not been previously described. It is important to recognize the reactive nature of the infiltrate to avoid a misdiagnosis of lymphoma.Zheng R, Ma L, Bichakjian CK, Lowe L, Fullen DR. Atypical fibroxanthoma with lymphomatoid reaction.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/79152/1/j.1600-0560.2010.01622.x.pd

Infected pancreatic necrosis: outcomes and clinical predictors of mortality. A post hoc analysis of the MANCTRA-1 international study

: The identification of high-risk patients in the early stages of infected pancreatic necrosis (IPN) is critical, because it could help the clinicians to adopt more effective management strategies. We conducted a post hoc analysis of the MANCTRA-1 international study to assess the association between clinical risk factors and mortality among adult patients with IPN. Univariable and multivariable logistic regression models were used to identify prognostic factors of mortality. We identified 247 consecutive patients with IPN hospitalised between January 2019 and December 2020. History of uncontrolled arterial hypertension (p = 0.032; 95% CI 1.135-15.882; aOR 4.245), qSOFA (p = 0.005; 95% CI 1.359-5.879; aOR 2.828), renal failure (p = 0.022; 95% CI 1.138-5.442; aOR 2.489), and haemodynamic failure (p = 0.018; 95% CI 1.184-5.978; aOR 2.661), were identified as independent predictors of mortality in IPN patients. Cholangitis (p = 0.003; 95% CI 1.598-9.930; aOR 3.983), abdominal compartment syndrome (p = 0.032; 95% CI 1.090-6.967; aOR 2.735), and gastrointestinal/intra-abdominal bleeding (p = 0.009; 95% CI 1.286-5.712; aOR 2.710) were independently associated with the risk of mortality. Upfront open surgical necrosectomy was strongly associated with the risk of mortality (p < 0.001; 95% CI 1.912-7.442; aOR 3.772), whereas endoscopic drainage of pancreatic necrosis (p = 0.018; 95% CI 0.138-0.834; aOR 0.339) and enteral nutrition (p = 0.003; 95% CI 0.143-0.716; aOR 0.320) were found as protective factors. Organ failure, acute cholangitis, and upfront open surgical necrosectomy were the most significant predictors of mortality. Our study confirmed that, even in a subgroup of particularly ill patients such as those with IPN, upfront open surgery should be avoided as much as possible. Study protocol registered in ClinicalTrials.Gov (I.D. Number NCT04747990)

Sur la dynamique des réseaux d'automates: une approche basée sur la théorie de la complexité informatique

An automata network (AN) is a network of entities, each holding a state from a finite set and related by a graph structure called an interaction graph. Each node evolves according to the states of its neighbors in the interaction graph, defining a discrete dynamical system. This thesis work explores two main questions : a) what is the link between dynamical and computational properties of an AN ? and b) what is the impact of the interaction graph topology on the global dynamics of an AN ?.In order to tackle the first question a notion of computational complexity of an AN family is defined in terms of the computational complexity of decision problems related to the dynamics of the network. On the other hand, dynamical complexity of a particular AN family is defined in terms of the existence of attractors of exponential period. A strong link between these two last definitions is presented in terms of the notion of simulation between AN families. In this context, complexity is characterized from a localized standpoint by studying the existence of structures called coherent gadgets which satisfy two properties : i) they can locally interact in a coherent way as dynamical systems and ii) they are capable of simulating a finite set of functions defined over a fixed finite set.Finally, the second question is addressed in the context of a well-known family called freezing automata networks. An AN is freezing if there is an order on states such that the state evolution of any node is non-decreasing in any orbit. A general model checking problem capturing many classical decision problems is presented. In addition, when three graph parameters, the maximum degree, the treewidth and the alphabet size are bounded, a fast-parallel algorithm that solves general model checking problem is presented. Moreover, it is shown that the latter problem is unlikely to be fixed-parameter tractable on the treewidth parameter as well as on the alphabet size when considered as single parameters.Un réseau d’automates (RA) est un réseau d’entités (les automates) en interaction. Ces automates ont un nombre fini d’états possibles et sont reliés les uns aux autres par une structure de graphe appelée graphe d’interaction. Chaque automate évolue au cours du temps discret en fonction des états de ses voisins dans le graphe d’interaction, ce qui définit un système dynamique. Ce travail de thèse explore deux questions principales : a) quel est le lien entre les propriétés dynamiques et calculatoires d’un RA ? et b) quel est l’impact de la topologie du graphe d’interaction sur la dynamique globale d’un RA ?.Pour aborder la première question, une notion de complexité calculatoire est définie au regard de problèmes de décision liés à la dynamique des RA. De même, une notion de complexité dynamique est définie en termes de l’existence d’attracteurs de période exponentielle. Un lien fort entre ces deux définitions est présenté qui met en exergue le concept de simulation entre familles de RA. Dans ce contexte, la complexité se caractérise d’un point de vue localisé en étudiant l’existence de structures appelées gadgets qui satisfont deux propriétés : i) ils peuvent interagir localement de manière cohérente comme des systèmes dynamiques et ii) ils sont capables de simuler un ensemble fini de fonctions définies sur un ensemble fini.La deuxième question est quant à elle abordée dans le contexte des RA “freezing”. Un RA est “freezing” s’il y a un ordre sur les états de telle sorte que l’évolution de l’état de n’importe quel automate ne diminue pas quelle que soit l’orbite. Un problème général de model-checking capturant de nombreux problèmes de décision classiques est présenté. De plus, lorsque trois paramètres de graphe, le degré maximum, la largeur arborescente et la taille de l’alphabet sont bornés, un algorithme parallèle efficace résolvant le problème mentionné est donné. De plus, il est montré que ce problème est peu susceptible d’être FPT (fixed-parameter tractable) lorsque le paramètre de largeur arborescente ou celui de taille de l’alphabet sont considérés comme unique paramètre