Quasi-selective ultrafilters and asymptotic numerosities

We isolate a new class of ultrafilters on N, called “quasi-selective” because they are intermediate between selective ultrafilters and P-points. (Under the Continuum Hypothesis these three classes are distinct.) The existence of quasi-selective ultrafilters is equivalent to the existence of “asymptotic numerosities” for all sets of tuples A ⊆ N^k. Such numerosities are hypernatural numbers that generalize finite cardinalities to countable point sets. Most notably, they maintain the structure of ordered semiring, and, in a precise sense, they allow for a natural extension of asymptotic density to all sets of tuples of natural numbers

Convergence of Discrete-Time Cellular Neural Networks with Application to Image Processing

The paper considers a class of discrete-time cellular neural networks (DT-CNNs) obtained by applying Euler's discretization scheme to standard CNNs. Let T be the DT-CNN interconnection matrix which is defined by the feedback cloning template. The paper shows that a DT-CNN is convergent, i.e. each solution tends to an equilibrium point, when T is symmetric and, in the case where T + En is not positive-semidefinite, the step size of Euler's discretization scheme does not exceed a given bound (En is the n × n unit matrix). It is shown that two relevant properties hold as a consequence of the local and space-invariant interconnecting structure of a DT-CNN, namely: (1) the bound on the step size can be easily estimated via the elements of the DT-CNN feedback cloning template only; (2) the bound is independent of the DT-CNN dimension. These two properties make DT-CNNs very effective in view of computer simulations and for the practical applications to high-dimensional processing tasks. The obtained results are proved via Lyapunov approach and LaSalle's Invariance Principle in combination with some fundamental inequalities enjoyed by the projection operator on a convex set. The results are compared with previous ones in the literature on the convergence of DT-CNNs and also with those obtained for different neural network models as the Brain-State-in-a-Box model. Finally, the results on convergence are illustrated via the application to some relevant 2D and 1D DT-CNNs for image processing tasks

Drift of invariant manifolds and transient chaos in memristor Chua's circuit

The article shows that transient chaos phenomena can be observed in a generalized memristor Chua's circuit where a nonlinear resistor is introduced to better model the real memristor behaviour. The flux-charge analysis method is used to explain the origin of transient chaos, that is attributed to the drift of the index of the memristor circuit invariant manifolds caused by the charge flowing into the nonlinear resistor

Drug-Induced Psychosis: How to Avoid Star Gazing in Schizophrenia Research by Looking at More Obvious Sources of Light

The prevalent view today is that schizophrenia is a syndrome rather than a specific disease. Liability to schizophrenia is highly heritable. It appears that multiple genetic and environmental factors operate together to push individuals over a threshold into expressing the characteristic clinical picture. One environmental factor which has been curiously neglected is the evidence that certain drugs can induce schizophrenia-like psychosis. In the last 60 years, improved understanding of the relationship between drug abuse and psychosis has contributed substantially to our modern view of the disorder suggesting that liability to psychosis in general, and to schizophrenia in particular, is distributed trough the general population in a similar continuous way to liability to medical disorders such as hypertension and diabetes. In this review we examine the main hypotheses resulting from the link observed between the most common psychotomimetic drugs (lysergic acid diethylamide, amphetamines, cannabis, phencyclidine) and schizophrenia

A topological approach to non-Archimedean Mathematics

Non-Archimedean mathematics (in particular, nonstandard analysis) allows to construct some useful models to study certain phenomena arising in PDE's; for example, it allows to construct generalized solutions of differential equations and variational problems that have no classical solution. In this paper we introduce certain notions of non-Archimedean mathematics (in particular, of nonstandard analysis) by means of an elementary topological approach; in particular, we construct non-Archimedean extensions of the reals as appropriate topological completions of $\mathbb{R}$. Our approach is based on the notion of $\Lambda$-limit for real functions, and it is called $\Lambda$-theory. It can be seen as a topological generalization of the $\alpha$-theory presented in \cite{BDN2003}, and as an alternative topological presentation of the ultrapower construction of nonstandard extensions (in the sense of \cite{keisler}). To motivate the use of $\Lambda$-theory for applications we show how to use it to solve a minimization problem of calculus of variations (that does not have classical solutions) by means of a particular family of generalized functions, called ultrafunctions.Comment: 22 page

INCIDENCE OF PSYCHOTIC DISORDERS IN PALERMO: PRELIMINARY DATA

Background: The incidence of psychotic disorders varies in different geographical areas (McGrath 2004). Recent data suggest that the incidence is higher in males, migrant minorities and in urban areas. There aren\u2019t many available epidemiological data on the incidence of psychotic disorders in Italy. This is the first incidence study on psychotic disorders carried out in Palermo, the capital of Sicily. Methods: we screened all patients presenting with their first episode of psychosis to the mental health services of our catchment area (5 inpatient, 5 outpatient units and 3 private psychiatric hospitals) over a period of three years (2008-2011). The diagnosis of psychosis was defined using the Schedules for Clinical Assessment in Neuropsychiatry (SCAN Wing, J. K., et al., 1990).The main socio-demographic data were collected using the MRC Social Data Schedule. When subjects were not available (did not consent) for interview, information was collected from clinical notes. The population at risk referred to the people aged from 18-65 who were resident in the same catchment area (Palermo Municipality) in the period considered, according to the data of the Statistic Office of Palermo Municipality). Results: we identified 216 patients affected by a first episode of psychosis (FEP): 135 M (62.5%) and 81 F (37.5%), mean age 31.42 years (SD: 11.44). 77.1% of FEP had a diagnosis of non affective psychosis, 12.8% of affective psychosis and 10.1% received a diagnosis of other psychosis. 204 subjects were Caucasian, 12 non Caucasian belonging to various ethnicities and they were all first generation migrants (4 Indian, 3 African, 2 Bangladeshi, and 3 Mixed). Population at risk is 425.194 people. The mean age of onset was lower in men than women M: 29.98 years (SD: 10.41) vs. F: 34.28 (SD:12.64) (p=0.013)The incidence of psychotic disorders in our catchment area is 16,9 per 100.000 person years. It was higher in men 21,9 per 100.000 than women 12,2 per 100.000. Discussion: Our study is the first epidemiological study in Sicily investigating the incidence of psychotic disorders. In our population men have a higher incidence of psychotic disorders than women and an earlier age of onset

Overexpression of lpxT Gene in Escherichia coli Inhibits Cell Division and Causes Envelope Defects without Changing the Overall Phosphorylation Level of Lipid A

LpxT is an inner membrane protein that transfers a phosphate group from the essential lipid undecaprenyl pyrophosphate (C-55PP) to the lipid A moiety of lipopolysaccharide, generating a lipid A tris-phosphorylated species. The protein is encoded by the non-essential lpxT gene, which is conserved in distantly related Gram-negative bacteria. In this work, we investigated the phenotypic effect of lpxT ectopic expression from a plasmid in Escherichia coli. We found that lpxT induction inhibited cell division and led to the formation of elongated cells, mostly with absent or altered septa. Moreover, the cells became sensitive to detergents and to hypo-osmotic shock, indicating that they had cell envelope defects. These effects were not due to lipid A hyperphosphorylation or C-55PP sequestering, but most likely to defective lipopolysaccharide transport. Indeed, lpxT overexpression in mutants lacking the L,D-transpeptidase LdtD and LdtE, which protect cells with outer membrane defects from osmotic lysis, caused cell envelope defects. Moreover, we found that pyrophosphorylated lipid A was also produced in a lpxT deletion mutant, indicating that LpxT is not the only protein able to perform such lipid A modification in E. coli

Association Between Continued Cannabis Use and Risk of Relapse in First-Episode Psychosis: A Quasi-Experimental Investigation Within an Observational Study

IMPORTANCE: Cannabis use after first-episode psychosis is associated with poor outcomes, but the causal nature of this association is unclear. OBJECTIVE: To examine the precise nature of the association between continued cannabis use after the onset of psychosis and risk of relapse of psychosis. DESIGN, SETTING, AND PARTICIPANTS: This prospective cohort study followed up for at least 2 years after the onset of psychosis 220 patients who presented to psychiatric services in South London, England, from April 12, 2002, to July 26, 2013, with first-episode psychosis. Longitudinal modeling (fixed-effects analysis, cross-lagged path analysis) was used to examine whether the association between changes in cannabis use and risk of relapse over time is the result of shared vulnerability between psychosis and cannabis use, psychosis increasing the risk of cannabis use (reverse causation), or a causal effect of cannabis use on psychosis relapse. INTERVENTIONS: Exposure to cannabis within the first and second years after onset of psychosis. MAIN OUTCOMES AND MEASURES: The main outcome measure was relapse of psychosis, defined as subsequent hospitalization for psychosis. Effect of cannabis use status in the first year (Ct1) and second year (Ct2) and pattern of cannabis use continuation in the first year and second year were modeled for risk of relapse in the first year (Rt1) and risk of relapse in the second year (Rt2) after psychosis onset. RESULTS: A total of 220 patients with first-episode psychosis were included in the analysis (mean [SD] age, 28.62 [8.58] years; age range, 18-65 years; 90 women [40.9%] and 130 men [59.1%]). Fixed-effects models that adjusted for time-variant (other illicit drug use, antipsychotic medication adherence) and time-invariant (eg, genetic or premorbid environment) unobserved confounders revealed that there was an increase in the odds of experiencing a relapse of psychosis during periods of cannabis use relative to periods of no use (odds ratio, 1.13; 95% CI, 1.03-1.24). Change in the pattern of continuation significantly increased the risk (odds ratio, 1.07; 95% CI, 1.02-1.13), suggesting a dose-dependent association. Cross-lagged analysis confirmed that this association reflected an effect of cannabis use on subsequent risk of relapse (Ct1→Rt2: β = 0.44, P = .04) rather than an effect of relapse on subsequent cannabis use (Rt1→Ct2: β = -0.29, P = .59). CONCLUSIONS AND RELEVANCE: These results reveal a dose-dependent association between change in cannabis use and relapse of psychosis that is unlikely to be a result of self-medication or genetic and environmental confounding