Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones. Part I

Ultra low frequency, kHz and MHz electromagnetic anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on April 6, 2009. The main aims of this contribution are: (i) To suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be possible to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we attempt, through a multidisciplinary analysis, to provide elements of a definition. (ii) To link the detected MHz and kHz EM anomalies with equivalent last stages of the L'Aquila earthquake preparation process. (iii) To put forward physically meaningful arguments to support a way of quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. The whole effort is unfolded in two consecutive parts. We clarify we try to specify not only whether or not a single EM anomaly is pre-seismic in itself, but mainly whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic one

Stability of Simple Periodic Orbits and Chaos in a Fermi -- Pasta -- Ulam Lattice

We investigate the connection between local and global dynamics in the Fermi -- Pasta -- Ulam (FPU) $\beta$ -- model from the point of view of stability of its simplest periodic orbits (SPOs). In particular, we show that there is a relatively high $q$ mode $(q=2(N+1)/{3})$ of the linear lattice, having one particle fixed every two oppositely moving ones (called SPO2 here), which can be exactly continued to the nonlinear case for $N=5+3m, m=0,1,2,...$ and whose first destabilization, $E_{2u}$, as the energy (or $\beta$) increases for {\it any} fixed $N$, practically {\it coincides} with the onset of a ``weak'' form of chaos preceding the break down of FPU recurrences, as predicted recently in a similar study of the continuation of a very low ($q=3$) mode of the corresponding linear chain. This energy threshold per particle behaves like $\frac{E_{2u}}{N}\propto N^{-2}$. We also follow exactly the properties of another SPO (with $q=(N+1)/{2}$) in which fixed and moving particles are interchanged (called SPO1 here) and which destabilizes at higher energies than SPO2, since $\frac{E_{1u}}{N}\propto N^{-1}$. We find that, immediately after their first destabilization, these SPOs have different (positive) Lyapunov spectra in their vicinity. However, as the energy increases further (at fixed $N$), these spectra converge to {\it the same} exponentially decreasing function, thus providing strong evidence that the chaotic regions around SPO1 and SPO2 have ``merged'' and large scale chaos has spread throughout the lattice.Comment: Physical Review E, 18 pages, 6 figure

Decision Procedure for Entailment of Symbolic Heaps with Arrays

This paper gives a decision procedure for the validity of en- tailment of symbolic heaps in separation logic with Presburger arithmetic and arrays. The correctness of the decision procedure is proved under the condition that sizes of arrays in the succedent are not existentially bound. This condition is independent of the condition proposed by the CADE-2017 paper by Brotherston et al, namely, one of them does not imply the other. For improving efficiency of the decision procedure, some techniques are also presented. The main idea of the decision procedure is a novel translation of an entailment of symbolic heaps into a formula in Presburger arithmetic, and to combine it with an external SMT solver. This paper also gives experimental results by an implementation, which shows that the decision procedure works efficiently enough to use

Chaotic Dynamics of N-degree of Freedom Hamiltonian Systems

We investigate the connection between local and global dynamics of two N-degree of freedom Hamiltonian systems with different origins describing one-dimensional nonlinear lattices: The Fermi-Pasta-Ulam (FPU) model and a discretized version of the nonlinear Schrodinger equation related to Bose-Einstein Condensation (BEC). We study solutions starting in the vicinity of simple periodic orbits (SPOs) representing in-phase (IPM) and out-of-phase motion (OPM), which are known in closed form and whose linear stability can be analyzed exactly. Our results verify that as the energy E increases for fixed N, beyond the destabilization threshold of these orbits, all positive Lyapunov exponents exhibit a transition between two power laws, occurring at the same value of E. The destabilization energy E_c per particle goes to zero as N goes to infinity following a simple power-law. However, using SALI, a very efficient indicator we have recently introduced for distinguishing order from chaos, we find that the two Hamiltonians have very different dynamics near their stable SPOs: For example, in the case of the FPU system, as the energy increases for fixed N, the islands of stability around the OPM decrease in size, the orbit destabilizes through period-doubling bifurcation and its eigenvalues move steadily away from -1, while for the BEC model the OPM has islands around it which grow in size before it bifurcates through symmetry breaking, while its real eigenvalues return to +1 at very high energies. Still, when calculating Lyapunov spectra, we find for the OPMs of both Hamiltonians that the Lyapunov exponents decrease following an exponential law and yield extensive Kolmogorov--Sinai entropies per particle, in the thermodynamic limit of fixed energy density E/N with E and N arbitrarily large.Comment: 29 pages, 10 figures, published at International Journal of Bifurcation and Chaos (IJBC

Model checking for symbolic-heap separation logic with inductive predicates

We investigate the model checking problem for symbolic-heap separation logic with user-defined inductive predicates, i.e., the problem of checking that a given stack-heap memory state satisfies a given formula in this language, as arises e.g. in software testing or runtime verification. First, we show that the problem is decidable; specifically, we present a bottom-up fixed point algorithm that decides the problem and runs in exponential time in the size of the problem instance. Second, we show that, while model checking for the full language is EXPTIME-complete, the problem becomes NP-complete or PTIME-solvable when we impose natural syntactic restrictions on the schemata defining the inductive predicates. We additionally present NP and PTIME algorithms for these restricted fragments. Finally, we report on the experimental performance of our procedures on a variety of specifications extracted from programs, exercising multiple combinations of syntactic restrictions

Neutrophil gelatinase-associated lipocalin in dehydrated patients: a preliminary report

<p>Abstract</p> <p>Background</p> <p>Acute kidney injury has been recognized as a major contributor to end stage renal disease. Although neutrophil gelatinase-associated lipocalin (Ngal) has been reported as a promising biomarker for early detection of acute kidney injury, no study has yet examined its potential clinical impact in patients with normal renal function. The purpose of current study is to investigate possible difference in serum Ngal levels between dehydrated and control patients.</p> <p>Findings</p> <p>A total of twelve patients presented with symptoms of mild dehydration defined by history of diarrheas or vomiting and orthostatic (postural) hypotension and an age and sex matched group of twelve control patients were included. The two groups of patients did not seem to differ in basic clinical and laboratory parameters. Serum Ngal was higher in dehydrated patients when compared to control group (Ngal = 129.4 ± 25.7 ng/mL vs 60.6 ± 0.4 ng/mL, p = 0.02). Ngal was not correlated with age, hemoglobin, white blood cell count, red blood cell count, urea or creatinine.</p> <p>Conclusions</p> <p>The presence of elevated Ngal levels in dehydrated patients may suggest its role as a very sensitive biomarker in even minimal and "silent" prerenal kidney dysfunction</p