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We propose a class of locally Lipschitz functions with piecewise structure for use as Lyapunov functions for hybrid dynamical systems. Subject to some regularity of the dynamics, we show that Lyapunov inequalities can be checked only on a dense set and thus we avoid checking them at points of nondifferentiability of the Lyapunov function. Connections to other classes of locally Lipschitz or piecewise regular functions are also discussed and applications to hybrid dynamical systems are included., Mathematics of Control, Signals, and Systems, Springer Verlag, In press

Digital ulcers (DUs) represent one major burden for patients with systemic sclerosis (SSc). The objectives of our study were to evaluate blood flow in SSc-DUs with laser speckle contrast analysis (LASCA) and to correlate the skin perfusion to clinical and laboratory data.Forty DUs in 31 consecutive patients with SSc according to 2013 ACR/EULAR criteria (20 with limited cutaneous disease, 3 males) were prospectively examined with LASCA. Clinical and laboratory data were collected at the same time. DUs were classified according to clinical features and presence of infection.At LASCA analysis, patients with diffuse SSc had lower mean values of blood flow compared with those with limited disease at the finger affected by DUs (88.80 vs 44.40, p = 0.036) and at the periulcer area (p = 0.041). The presence of infection was associated to a higher flow at the finger with DU (103.02 vs 58.05 p = 0.04), at the level of ulcer (217.63 vs 67.15, p 0.001), and at the periulcer area (p = 0.001). The ratio between the blood flow at the ulcer area and the finger base (UA/FB) showed a bimodal trend in patients with infected DUs and in those without infections. Infection was positive correlated to the time of healing (HT) (r = 0.648, p = 0.023), while in DUs without infection a negative correlation to HT (r = - 0.46, p = 0.015) was identified.This study demonstrates for the first time that the UA/FB ratio may predict the healing time of DUs in SSc patients and may be crucial for the prognostic stratification of patients. Infection remains one of the main predictors of DU healing.Key Points• The prognostic value of laser speckle contrast analysis (LASCA) in patients with digital ulcers (DUs) in systemic sclerosis remains to be clarified.• LASCA may be able to predict the haling time of the digital ulcers.• The presence of infection of the wound bed may greatly influence the LASCA parameters and the healing time of the digital ulcer.

Uncertainty quantification for geomechanical and reservoir predictions is in general a computationally intensive problem, especially if a direct Monte Carlo approach with large numbers of full-physics simulations is used. A common solution to this problem, well-known for the fluid flow simulations, is the adoption of surrogate modeling approximating the physical behavior with respect to variations in uncertain parameters. The objective of this work is the quantification of such uncertainty both within geomechanical predictions and fluid-flow predictions using a specific surrogate modeling technique, which is based on a functional approach. The methodology realizes an approximation of full-physics simulated outputs that are varying in time and space when uncertainty parameters are changed, particularly important for the prediction of uncertainty in vertical displacement resulting from geomechanical modeling. The developed methodology has been applied both to a subsidence uncertainty quantification example and to a real reservoir forecast risk assessment. The surrogate quality obtained with these applications confirms that the proposed method makes it possible to perform reliable time–space varying dependent risk assessment with a low computational cost, provided the uncertainty space is low-dimensional.

We show that when selection is extreme-the fittest strategy always reproduces or is imitated-the unequivalence between the possible evolutionary game scenarios in finite and infinite populations resolves, in the sense that the three generic outcomes-dominance, coexistence, and mutual exclusion-emerge in well-mixed populations of any size. We consider the simplest setting of a 2-player-2-strategy symmetric game and the two most common microscopic definitions of strategy spreading-the frequency-dependent Moran process and the imitation process by pairwise comparison-both in the case allowing any intensity of selection. We show that of the seven different invasion and fixation scenarios that are generically possible in finite populations-fixation being more or less likely to occur and rapid compared to the neutral game-the three that are possible in large populations are the same three that occur for sufficiently strong selection: (1) invasion and fast fixation of one strategy; (2) mutual invasion and slow fixation of one strategy; (3) no invasion and no fixation. Moreover (and interestingly), in the limit of extreme selection 2 becomes mutual invasion and no fixation, a case not possible for finite intensity of selection that better corresponds to the deterministic case of coexistence. In the extreme selection limit, we also derive the large population deterministic limit of the two considered stochastic processes.

In this paper, we propose and analyze a new descriptive model of armed conflicts among N groups. The model is composed of $$N^2$$ ordinary differential equations, with $$3(N^2+N)$$ constant parameters that describe military characteristics and recruitment policies, ranging from pure defensivism to pure fanaticism. The results are only preliminary, but point out interesting (though not very surprising) properties: periodic coexistence is possible, and multiple attractors can exist; governmental groups cannot go extinct if they are highly defensivist, and rebels cannot be eradicated if they are highly fanatic. Shocks due to interventions of short duration of an external army can stabilize/destabilize the system and/or eradicate some group, and the same holds true for small structural changes. Other more subtle questions concerning, for example, the existence of chaotic regimes and the systematic evaluation of the role of strategic factors like power, intelligence, and fanaticism, remain open and require further research.

Since M. A. Nowak & R. May’s (1992) influential paper, limiting each agent’s interactions to a few neighbors in a network of contacts has been proposed as the simplest mechanism to support the evolution of cooperation in biological and socio-economic systems. The network allows cooperative agents to self-assort into clusters, within which they reciprocate cooperation. This (induced) network reciprocity has been observed in several theoreticalmodels and shown to predict the fixation of cooperation under a simple rule: the benefit produced by an act of cooperation must outweigh the cost of cooperating with all neighbors. However, the experimental evidence among humans is controversial: though the rule seems to be confirmed, the underlying modeling assumptions are not. Specifically, models assume that agents update their strategies by imitating better performing neighbors, even though imitation lacks rationality when interactions are far from all-to-all. Indeed, imitation did not emerge in experiments. What did emerge is that humans are conditioned by their own mood and that, when in a cooperative mood, they reciprocate cooperation. To help resolve the controversy, we design a model in which we rationally confront the two main behaviors emerging from experiments—reciprocal cooperation and unconditional defection—in a networked prisoner’s dilemma. Rationality is introduced by means of a predictive rule for strategy update and is bounded by the assumed model society. We show that both reciprocity and a multi-step predictive horizon are necessary to stabilize cooperation, and sufficient for its fixation, provided the game benefit-to-cost ratio is larger than a measure of network connectivity. We hence rediscover the rule of network reciprocity, underpinned however by a different evolutionary mechanism.

We present a methodology that allows conditioning the spatial distribution of geological and petrophysical properties of reservoir model realizations on available production data. The approach is fully consistent with modern concepts depicting natural reservoirs as composite media where the distribution of both lithological units (or facies) and associated attributes are modeled as stochastic processes of space. We represent the uncertain spatial distribution of the facies through a Markov mesh (MM) model, which allows describing complex and detailed facies geometries in a rigorous Bayesian framework. The latter is then embedded within a history matching workflow based on an iterative form of the ensemble Kalman filter (EnKF). We test the proposed methodology by way of a synthetic study characterized by the presence of two distinct facies. We analyze the accuracy and computational efficiency of our algorithm and its ability with respect to the standard EnKF to properly estimate model parameters and assess future reservoir production. We show the feasibility of integrating MM in a data assimilation scheme. Our methodology is conducive to a set of updated model realizations characterized by a realistic spatial distribution of facies and their log permeabilities. Model realizations updated through our proposed algorithm correctly capture the production dynamics.

Increasing evidence has been accumulated for treating rheumatoid arthritis (RA) with TNF-α blocking agents. The formulation and definition of an early indicator of patient's reactivity during therapy may be extremely simplified by a mathematical model of clinical response. We analyzed the most significant clinical and laboratory parameters of response of 35 homogeneous patients (30 women, 5 men mean age ± SD: 52.31 ± 12.30 years) treated with adalimumab 40 mg every 2 weeks associated with methotrexate (MTX) 10-15 mg/week and with a stable dosage of steroids for 30 weeks. The over time trend of the studied parameters showed a linear response, which has allowed the realization of a simple mathematical model. The formula derived from this mathematical model was then applied and therefore validated in a group of 121 patients previously treated with several anti-TNF-alpha agents for at least 6 months. We drafted a mathematical model (early response indicator, ERI) that, by using a simple calculation, allows us to identify a high percentage of responder patients after only 2 weeks of treatment. ERI identified a high percentage (88%) of patients responding after only 2 weeks, as was confirmed at weeks 30; the use of ERI calculation after 6 weeks increases the proportion of responding patients to 92% with a percentage of false negatives of only 12%. ERI could be a useful tool to early differentiate the responder from the non-responder patients.

In this paper we present an extension of the ensemble Kalman filter (EnKF) specifically designed for multimodal systems. EnKF data assimilation scheme is less accurate when it is used to approximate systems with multimodal distribution such as reservoir facies models. The algorithm is based on the assumption that both prior and posterior distribution can be approximated by Gaussian mixture and it is validated by the introduction of the concept of finite ensemble representation. The effectiveness of the approach is shown with two applications. The first example is based on Lorenz model. In the second example, the proposed methodology combined with a localization technique is used to update a 2D reservoir facies models. Both applications give evidence of an improved performance of the proposed method respect to the EnKF.

Mixed cryoglobulinemia remains a major challenge to the clinician, both in terms of diagnosis and treatment. The discovery of its association with the hepatitis C virus has helped to shed light on the mechanisms of its pathogenesis and on how this complex disease might be managed. In this respect, interferon represents the first attempt to take an etiological approach to the treatment of a virus-related, immune-mediated human disease. Its uneven results, however, have on the one hand raised hopes that a final solution to the problem may be near, and at the same time underlined the fact that we probably have a long way to go before our goal is actually reached.

Cement samples containing variable amounts of Cr(III) or Ni(II) or Cd(II) as chloride admixtures present in a MLW stream from reprocessing of spent fuel were prepared under established procedure. Due to the high pH generated in the cement clinker hydration, respective metal hydroxides are formed and improve the physical characteristics of the cement matrix. An increase in the value of the compressive strength was observed when about 7% of the above elements were blended in cement. The increase depends on the nature of the element in the sequence Cr >Ni >Cd.The leach tests confirm the formation of insoluble hydroxide presenting a low concentration in the leachate corresponding to 0.05, 0.004 and 0.052 mg.L−1 for Cr, Ni and Cd, respectively. On the other hand, the hydro-lyzed chloride ions seem to react with calcium with consequent increased degradation of the cement matrix.