Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intended in some generalized sense: in our analysis, we consider both Carath'eodory and Krasovskii solutions. We first prove existence and completeness of Carath'e-o-dory solutions from every initial condition and we highlight a pathological behavior of Carath'eo-do-ry solutions, which can converge to points that are not (Carath'eodory) equilibria. Notably, such points can be arbitrarily far from consensus and indeed simulations show that convergence to non-consensus configurations is very common. In order to cope with these pathological attractors, we then study Krasovskii solutions. We give an estimate of the asymptotic distance of all Krasovskii solutions from consensus and we prove its tightness by an example of equilibrium such that this distance is quadratic in the number of agents. This fact implies that quantization can drastically destroy consensus. However, consensus is guaranteed in some special cases, namely when the communication among the individuals is described by either a complete or a complete bipartite graph

FlhF, a signal recognition particle-like GTPase, is involved in the regulation of flagellar arrangement, motility behaviour and protein secretion in Bacillus cereus

Flagellar arrangement is a highly conserved feature within bacterial species. However, only a few genes regulating cell flagellation have been described in polar flagellate bacteria. This report demonstrates that the arrangement of flagella in the peritrichous flagellate Bacillus cereus is controlled by flhF. Disruption of flhF in B. cereus led to a reduction in the number of flagella from 10-12 to 1-3 filaments per cell in the insertion mutant MP06. Moreover, compared to the parental strain, MP06 exhibited: (i) shorter smooth swimming phases, causing reduced swimming motility but not affecting chemotaxis; (ii) complete inhibition of swarming motility, as differentiated swarm cells were never detected; (iii) an increased amount of extracellular proteins; and (iv) differential export of virulence determinants, such as haemolysin BL (HBL), phosphatidylcholine-preferring phospholipase C (PC-PLC) and non-haemolytic enterotoxin (NHE). Introduction of a plasmid harbouring flhF (pDGflhF) into MP06 completely restored the wild-type phenotype in the trans-complemented strain MP07. B. cereus flhF was found to constitute a monocistronic transcriptional unit and its overexpression did not produce abnormal features in the wild-type background. Characterization of a B. cereus mutant (MP05) carrying a partial flhF deletion indicated that the last C-terminal domain of FlhF is involved in protein export while not required for flagellar arrangement and motility behaviour. Taken together, these data suggest that B. cereus FlhF is a promising candidate for connecting diverse cellular functions, such as flagellar arrangement, motility behaviour, pattern of protein secretion and virulence phenotype

Contribution of Surfactin and SwrA to Flagellin Expression, Swimming, and Surface Motility in Bacillus subtilis.

Multicellular communities produced by Bacillus subtilis can adopt sliding or swarming to translocate over surfaces. While sliding is a flagellum-independent motility produced by the expansive forces in a growing colony, swarming requires flagellar functionality and is characterized by the appearance of hyperflagellated swarm cells that associate in bundles or rafts during movement. Previous work has shown that swarming by undomesticated B. subtilis strains requires swrA, a gene that upregulates the expression of flagellar genes and increases swimming motility, and surfactin, a lipopeptide biosurfactant that also facilitates sliding. Through an analysis of swrA(+) and swrA mutant laboratory strains with or without a mutation in sfp (a gene involved in surfactin production), we show that both swrA and surfactin upregulate the transcription of the flagellin gene and increase bacterial swimming. Surfactin also allows the nonswarming swrA mutant strain to efficiently colonize moist surfaces by sliding. Finally, we reconfirm the essential role of swrA in swarming and show that surfactin, which increases surface wettability, allows swrA(+) strains to produce swarm cells on media at low humidity

Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach

Lyapunov-Krasowskii functionals are used to design quantized control laws for nonlinear continuous-time systems in the presence of constant delays in the input. The quantized control law is implemented via hysteresis to prevent chattering. Under appropriate conditions, our analysis applies to stabilizable nonlinear systems for any value of the quantization density. The resulting quantized feedback is parametrized with respect to the quantization density. Moreover, the maximal allowable delay tolerated by the system is characterized as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals, and System

b-Gamma-glutamyltransferase activity in human vulnerable carotid plaques.

Objective: The atherosclerotic plaque that is vulnerable to rupture and to superimposed thrombosis is mainly represented by a thin-cap fibroatheroma with or without ulceration/thrombosis and inflammatory infiltrates. Total serum gamma-glutamyltransferase (GGT) activity is an independent predictor for cardiovascular events. Four GGT fractions have been identified in plasma and only one of them (b-GGT) in atherosclerotic plaques, but the possible role of GGT in plaque pathophysiology has not been assessed yet. We investigated the relationships between plaque b-GGT activity and the histological features of plaque vulnerability. Methods and results: Plaque GGT activity was investigated in 65 patients undergoing carotid endarterectomy; plaques were histologically characterized and immunostained for GGT. Intra-plaque total and fractional GGT activity was determined by a cost-effective test of molecular size exclusion chromatography, and compared with histological markers of plaque vulnerability. Plaque cholesterol content was also measured by chromatography. b-GGT was the only fraction detected within the atherosclerotic plaques and intra-plaque b-GGT activity correlated to plaque cholesterol content (r = 0.667, P < 0.0001), plasma b-GGT and f-GGT fractions (r = 0.249; r ¼ 0.298, both P < 0.05). Higher b- GGT activity was found in thin-cap fibroatheromas and it was associated to histological markers of vulnerable plaques, i.e., larger necrotic areas, greater macrophage infiltration and higher cholesterol content (P < 0.05). Conclusions: intra-plaque b-GGT activity correlates with the histological markers of vulnerable plaque and with plasma b-GGT in human carotid atherosclerosis; these data support the possible role of b-GGT in clinically significant atherosclerotic disease

Towards Physical Hybrid Systems

Some hybrid systems models are unsafe for mathematically correct but physically unrealistic reasons. For example, mathematical models can classify a system as being unsafe on a set that is too small to have physical importance. In particular, differences in measure zero sets in models of cyber-physical systems (CPS) have significant mathematical impact on the mathematical safety of these models even though differences on measure zero sets have no tangible physical effect in a real system. We develop the concept of "physical hybrid systems" (PHS) to help reunite mathematical models with physical reality. We modify a hybrid systems logic (differential temporal dynamic logic) by adding a first-class operator to elide distinctions on measure zero sets of time within CPS models. This approach facilitates modeling since it admits the verification of a wider class of models, including some physically realistic models that would otherwise be classified as mathematically unsafe. We also develop a proof calculus to help with the verification of PHS.Comment: CADE 201

Hepatic steatosis in a school population of overweight and obese adolescents

OBJECTIVE: To assess hepatic steatosis by ultrasound method as a concomitant risk factor among overweight adolescents. METHODS: A case-control study including 83 cases (47 overweight and 36 obese) and 89 controls (normal weight), frequency matched by gender, year of birth, pubertal stage (Tanner 4/5), and income. Cases and controls were selected from 1,420 students enrolled in a Vila Mariana public high school, in São Paulo, Brazil. Must et al. criteria were used for nutritional status classification. Nonalcoholic fatty liver disease was diagnosed through hepatic ultrasonography performed and analyzed by one radiologist. Hepatic enzymatic activities (alanine and aspartate transaminases, alkaline phosphatase, gamma-glutamyl transpeptidase) and direct bilirubin were measured. Eight covariables were fitted into logistic regression models; criterion for inclusion of variables was the association with overweight in the bivariate analyses (p 24 U/L were 10.77 (2.45-47.22) and 4.18 (1.46-11.94), respectively. CONCLUSIONS: This is the first population-based study showing that hepatic steatosis is strongly associated with overweight/obesity among adolescents attending a Brazilian public school. The diagnostic tool used in this investigation is a non-invasive method that might be applied to monitor overweight and obese adolescents and to propose actions for preventing more severe hepatic diseases in adulthood.OBJETIVO: Avaliar esteatose hepática pelo método de ultrassom como fator de risco concomitante entre adolescentes com sobrepeso. MÉTODOS: Estudo de caso-controle incluindo 83 casos (47 com sobrepeso e 36 obesos) e 89 controles (peso normal), frequência pareada por gênero, ano de nascimento, estágio pubertário (Tanner 4/5) e renda. Casos e controles foram selecionados de 1.420 alunos matriculados em uma escola pública de ensino médio na Vila Mariana, São Paulo. Os critérios de Must et al. foram usados para classificação do estado nutricional. A doença hepática gordurosa não-alcoólica foi diagnosticada por meio de ultrassonografia realizada e analisada por um radiologista. Foram medidas atividades enzimáticas hepáticas (alanina e aspartato transaminases, fosfatase alcalina, gama-glutamil transpeptidase) e bilirrubina direta. Oito co-variáveis foram inseridas em modelos de regressão logística; o critério de inclusão de variáveis foi a associação com sobrepeso nas análises bivariadas (p 24 U/L foram 10,77 (2,45-47,22) e 4,18 (1,46-11,94), respectivamente. CONCLUSÕES: Este é o primeiro estudo populacional mostrando que a esteatose hepática tem forte associação com sobrepeso/obesidade entre adolescentes matriculados em uma escola pública brasileira. A ferramenta de diagnóstico usada nesta investigação é um método não-invasivo que poderia ser aplicado para monitorar adolescentes com sobrepeso e obesos e propor ações para prevenir doenças hepáticas mais graves na fase adulta.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Universidade Federal de São Paulo (UNIFESP) Escola Paulista de MedicinaUNIFESP-EPM Department of PediatricsUNIFESP, EPM, Department of PediatricsFAPESP: 03/00415-4SciEL

Hypervirulent Clostridium difficile PCR-Ribotypes Exhibit Resistance to Widely Used Disinfectants

The increased prevalence of Clostridium difficile infection (CDI) has coincided with enhanced transmissibility and severity of disease, which is often linked to two distinct clonal lineages designated PCR-ribotype 027 and 017 responsible for CDI outbreaks in the USA, Europe and Asia. We assessed sporulation and susceptibility of three PCR-ribotypes; 012, 017 and 027 to four classes of disinfectants; chlorine releasing agents (CRAs), peroxygens, quaternary ammonium compounds (QAC) and biguanides. The 017 PCR-ribotype, showed the highest sporulation frequency under these test conditions. The oxidizing biocides and CRAs were the most efficacious in decontamination of C. difficile vegetative cells and spores, the efficacy of the CRAs were concentration dependent irrespective of PCR-ribotype. However, there were differences observed in the susceptibility of the PCR-ribotypes, independent of the concentrations tested for Virkon®, Newgenn®, Proceine 40® and Hibiscrub®. Whereas, for Steri7® and Biocleanse® the difference observed between the disinfectants were dependent on both PCR-ribotype and concentration. The oxidizing agent Perasafe® was consistently efficacious across all three PCR ribotypes at varying concentrations; with a consistent five Log10 reduction in spore titre. The PCR-ribotype and concentration dependent differences in the efficacy of the disinfectants in this study indicate that disinfectant choice is a factor for llimiting the survival and transmission of C. difficile spores in healthcare settings

Short- and Long-Term Biomarkers for Bacterial Robustness: A Framework for Quantifying Correlations between Cellular Indicators and Adaptive Behavior

The ability of microorganisms to adapt to changing environments challenges the prediction of their history-dependent behavior. Cellular biomarkers that are quantitatively correlated to stress adaptive behavior will facilitate our ability to predict the impact of these adaptive traits. Here, we present a framework for identifying cellular biomarkers for mild stress induced enhanced microbial robustness towards lethal stresses. Several candidate-biomarkers were selected by comparing the genome-wide transcriptome profiles of our model-organism Bacillus cereus upon exposure to four mild stress conditions (mild heat, acid, salt and oxidative stress). These candidate-biomarkers—a transcriptional regulator (activating general stress responses), enzymes (removing reactive oxygen species), and chaperones and proteases (maintaining protein quality)—were quantitatively determined at transcript, protein and/or activity level upon exposure to mild heat, acid, salt and oxidative stress for various time intervals. Both unstressed and mild stress treated cells were also exposed to lethal stress conditions (severe heat, acid and oxidative stress) to quantify the robustness advantage provided by mild stress pretreatment. To evaluate whether the candidate-biomarkers could predict the robustness enhancement towards lethal stress elicited by mild stress pretreatment, the biomarker responses upon mild stress treatment were correlated to mild stress induced robustness towards lethal stress. Both short- and long-term biomarkers could be identified of which their induction levels were correlated to mild stress induced enhanced robustness towards lethal heat, acid and/or oxidative stress, respectively, and are therefore predictive cellular indicators for mild stress induced enhanced robustness. The identified biomarkers are among the most consistently induced cellular components in stress responses and ubiquitous in biology, supporting extrapolation to other microorganisms than B. cereus. Our quantitative, systematic approach provides a framework to search for these biomarkers and to evaluate their predictive quality in order to select promising biomarkers that can serve to early detect and predict adaptive traits