Asymptotic stability of the Cauchy and Jensen functional equations

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid everywhere with a new error term which is a constant multiple of the original error term. As consequences, we also obtain results of hyperstability character for these two functional equations

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

NEW SECONDARY METABOLITES IN THE AMPHINOMID FIREWORM HERMODICE CARUNCULATA

Eight betaine-derived novel compounds were found in extracts of the Mediterranean stinging fireworm Hermodice carunculata. The identification of their structures relies on 1D and 2D NMR (Fig. 1-3) and HPLC-ESI/HRMS spectra. Two types of terminal ammonium portions A and B and a series of different alkyl chains were identified (Fig. 4a,b). Their matching provides the structures of uncharacterized secondary metabolites, named carunculines, and their related isomers. These molecules differ from already known trimethylammonium inflammatory compounds (i.e. complanines) isolated from another amphinomid species, for the structures of the terminal ammonium groups (Fig. 4c) [1]. Carunculine anatomical distribution within H. carunculata was assessed by screening through HPLC-ESI/HRMS (Fig. 5, Table 1): their occurrence was revealed in all the body parts analyzed, both involved in predator-prey interactions [2], and mainly in the digestive apparatus. The results achieved reveal an array of different novel compounds from a chemically unknown species, improving knowledge on Marine Animal Products with chemical and biological potential for bioprospection [3]. Overall, these data reinforce the necessity of studying poorly-investigated taxa to expand knowledge on animal venom biology, their mechanisms of action and exploitation as promising source of drug molecule

Synthesis and anticancer activity of CDDO and CDDO-me, two derivatives of natural triterpenoids

Triterpenoids are natural compounds synthesized by plants through cyclization of squalene, known for their weak anti-inflammatory activity. 2-cyano-3,12-dioxooleana-1,9(11)-dien-28-oic acid (CDDO), and its C28 modified derivative, methyl-ester (CDDO-Me, also known as bardoxolone methyl), are two synthetic derivatives of oleanolic acid, synthesized more than 20 years ago, in an attempt to enhance the anti-inflammatory behavior of the natural compound. These molecules have been extensively investigated for their strong ability to exert antiproliferative, antiangiogenic, and antimetastatic activities, and to induce apoptosis and differentiation in cancer cells. Here, we discuss the chemical properties of natural triterpenoids, the pathways of synthesis and the biological effects of CDDO and its derivative CDDO-Me. At nanomolar doses, CDDO and CDDO-Me have been shown to protect cells and tissues from oxidative stress by increasing the transcriptional activity of the nuclear factor (erythroid-derived 2)-like 2 (Nrf2). At doses higher than 100 nM, CDDO and CDDO-Me are able to modulate the differentiation of a variety of cell types, both tumor cell lines or primary culture cell, while at micromolar doses these compounds exert an anticancer effect in multiple manners; by inducing extrinsic or intrinsic apoptotic pathways, or autophagic cell death, by inhibiting telomerase activity, by disrupting mitochondrial functions through Lon protease inhibition, and by blocking the deubiquitylating enzyme USP7. CDDO-Me demonstrated its efficacy as anticancer drugs in different mouse models, and versus several types of cancer. Several clinical trials have been started in humans for evaluating CDDO-Me efficacy as anticancer and anti-inflammatory drug; despite promising results, significant increase in heart failure events represented an obstacle for the clinical use of CDDO-Me

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

The MAGIC Experiment and Its First Results

With its diameter of 17m, the MAGIC telescope is the largest Cherenkov detector for gamma ray astrophysics. It is sensitive to photons above an energy of 30 GeV. MAGIC started operations in October 2003 and is currently taking data. This report summarizes its main characteristics, its rst results and its potential for physics.Comment: 6 pages, 3 figures, to be published in the Proceedings of the 6th International Symposium ''Frontiers of Fundamental and Computational Physics'' (FFP6), Udine (Italy), Sep. 26-29, 200

The prognostic role of baseline CEA and CA 19-9 values and their time-dependent variations in advanced colorectal cancer patients submitted to first-line therapy.

Serum marker evaluation is an easily available prognostic indicator that may help clinicians to discriminate patients with an aggressive disease; there are few and small-sized studies exploring the prognostic role of baseline carcinoembryonic antigen (CEA) values and their variations during first-line therapy, and even fewer data are available for carbohydrate antigen 19-9 (CA 19-9). Our aim was to analyze the role of those prognostic markers to exploit them in daily clinical practice. Data of 892 patients with marker determination before and 3 and/or 6 months during therapy were extracted from two institutional databases. Patients were grouped according to single marker variation as always negative (G0), decreasing (G1), stable (G2), or increasing (G3). We evaluated the progression-free survival (PFS) and the overall survival (OS) of all the patents and correlated them with CEA and CA 19-9 values. A concordance between response to therapy and marker decrease was evident in 50.2% and in 34.4% of the patients for CEA and CA 19-9. Patients with low CEA or CA 19-9 baseline values had a longer PFS (15.1 vs. 10.5; 13.6 vs. 10.2 months) and OS (32.0 vs. 22.3; 30.5 vs. 20.1 months). The same results of PFS and OS were obtained by analyzing the data of the four different groups. Multivariate analyses confirmed the independent prognostic role of CEA and CA 19-9. Baseline CEA and CA 19-9 levels and their kinetics demonstrated to be independent prognostic factors. CA 19-9 dosage is not recommended; a possible role of CA 19-9 in patients with negative CEA could be worth further evaluation