Complexity of ITL model checking: some well-behaved fragments of the interval logic HS

Model checking has been successfully used in many computer science fields, including artificial intelligence, theoretical computer science, and databases. Most of the proposed solutions make use of classical, point-based temporal logics, while little work has been done in the interval temporal logic setting. Recently, a non-elementary model checking algorithm for Halpern and Shoham's modal logic of time intervals HS over finite Kripke structures (under the homogeneity assumption) and an EXPSPACE model checking procedure for two meaningful fragments of it have been proposed. In this paper, we show that more efficient model checking procedures can be developed for some expressive enough fragments of HS

Checking Interval Properties of Computations

Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by checking the formula against the model. Classically, system behaviour is expressed by a formula of a temporal logic, such as LTL and the like. These logics are "point-wise" interpreted, as they describe how the system evolves state-by-state. However, there are relevant properties, such as those constraining the temporal relations between pairs of temporally extended events or involving temporal aggregations, which are inherently "interval-based", and thus asking for an interval temporal logic. In this paper, we give a formalization of the model checking problem in an interval logic setting. First, we provide an interpretation of formulas of Halpern and Shoham's interval temporal logic HS over finite Kripke structures, which allows one to check interval properties of computations. Then, we prove that the model checking problem for HS against finite Kripke structures is decidable by a suitable small model theorem, and we provide a lower bound to its computational complexity.Comment: In Journal: Acta Informatica, Springer Berlin Heidelber, 201

An extension of a theorem of Schoenberg to products of spheres

We present a characterization for the continuous, isotropic and positive definite kernels on a product of spheres along the lines of a classical result of I. J. Schoenberg on positive definiteness on a single sphere. We also discuss a few issues regarding the characterization, including topics for future investigation

Effect of assortative mixing in the second-order Kuramoto model

In this paper we analyze the second-order Kuramoto model presenting a positive correlation between the heterogeneity of the connections and the natural frequencies in scale-free networks. We numerically show that discontinuous transitions emerge not just in disassortative but also in assortative networks, in contrast with the first-order model. We also find that the effect of assortativity on network synchronization can be compensated by adjusting the phase damping. Our results show that it is possible to control collective behavior of damped Kuramoto oscillators by tuning the network structure or by adjusting the dissipation related to the phases movement.Comment: 7 pages, 6 figures. In press in Physical Review

On the onset of synchronization of Kuramoto oscillators in scale-free networks

Despite the great attention devoted to the study of phase oscillators on complex networks in the last two decades, it remains unclear whether scale-free networks exhibit a nonzero critical coupling strength for the onset of synchronization in the thermodynamic limit. Here, we systematically compare predictions from the heterogeneous degree mean-field (HMF) and the quenched mean-field (QMF) approaches to extensive numerical simulations on large networks. We provide compelling evidence that the critical coupling vanishes as the number of oscillators increases for scale-free networks characterized by a power-law degree distribution with an exponent $2 < \gamma \leq 3$, in line with what has been observed for other dynamical processes in such networks. For $\gamma > 3$, we show that the critical coupling remains finite, in agreement with HMF calculations and highlight phenomenological differences between critical properties of phase oscillators and epidemic models on scale-free networks. Finally, we also discuss at length a key choice when studying synchronization phenomena in complex networks, namely, how to normalize the coupling between oscillators

Circulating anions usually associated with the Krebs cycle in patients with metabolic acidosis

Introduction: Acute metabolic acidosis of non-renal origin is usually a result of either lactic or ketoacidosis, both of which are associated with a high anion gap. There is increasing recognition, however, of a group of acidotic patients who have a large anion gap that is not explained by either keto- or lactic acidosis nor, in most cases, is inappropriate fluid resuscitation or ingestion of exogenous agents the cause. Methods: Plasma ultrafiltrate from patients with diabetic ketoacidosis, lactic acidosis, acidosis of unknown cause, normal anion gap metabolic acidosis, or acidosis as a result of base loss were examined enzymatically for the presence of low molecular weight anions including citrate, isocitrate, α-ketoglutarate, succinate, malate and d-lactate. The results obtained from the study groups were compared with those obtained from control plasma from normal volunteers. Results: In five patients with lactic acidosis, a significant increase in isocitrate (0.71 ± 0.35 mEq l-1), α-ketoglutarate (0.55 ± 0.35 mEq l-1), malate (0.59 ± 0.27 mEq l-1), and d-lactate (0.40 ± 0.51 mEq l-1) was observed. In 13 patients with diabetic ketoacidosis, significant increases in isocitrate (0.42 ± 0.35 mEq l-1), α-ketoglutarate (0.41 ± 0.16 mEq l-1), malate (0.23 ± 0.18 mEq l-1) and d-lactate (0.16 ± 0.07 mEq l-1) were seen. Neither citrate nor succinate levels were increased. Similar findings were also observed in a further five patients with high anion gap acidosis of unknown origin with increases in isocitrate (0.95 ± 0.88 mEq l-1), α-ketoglutarate (0.65 ± 0.20 mEq l-1), succinate (0.34 ± 0.13 mEq l-1), malate (0.49 ± 0.19 mEq l-1) and d-lactate (0.18 ± 0.14 mEq l-1) being observed but not in citrate concentration. In five patients with a normal anion gap acidosis, no increases were observed except a modest rise in d-lactate (0.17 ± 0.14 mEq l-1). Conclusion: The levels of certain low molecular weight anions usually associated with intermediary metabolism were found to be significantly elevated in the plasma ultrafiltrate obtained from patients with metabolic acidosis. Our results suggest that these hitherto unmeasured anions may significantly contribute to the generation of the anion gap in patients with lactic acidosis and acidosis of unknown aetiology and may be underestimated in diabetic ketoacidosis. These anions are not significantly elevated in patients with normal anion gap acidosis