Numerical Solutions of ODEs using Volterra Series

We propose a numerical approach for solving systems of nonautonomous ordinary di®erential equations under suitable assumptions. This approach is based on expansion of the solutions by Volterra series and allows to estimate the accuracy of the approximation. Also we can solve some ordinary di®erential equations for which the classical numerical methods fail

Immobilization of Bacteriocins from Lactic Acid Bacteria and Possibilities for Application in Food Biopreservation

Bacteriocins are biologically active compounds produced by a large number of bacteria, including lactic acid bacteria (LAB), which exhibit antimicrobial activity against various saprophytic and pathogenic microorganisms. In recent decades, bacteriocins are increasingly becoming more important in different branches of the industry due to their broad antibacterial and antifungal spectrum - in the food industry for natural food preservation and expiry date extension; in the health sector for preparation of probiotic foods and beverages; in the clinical practice as alternatives of conventional antibiotics; in the agriculture as biocontrol agents of plant pathogens and alternatives of chemical pesticides for plant protection. The broad antimicrobial spectrum of bacteriocins has stimulated the research attention on their application mainly in the food industry as natural preservatives. Most scientific achievements concerning the application food biopreservation are related to bacteriocins produced by LAB. The lactic acid bacteria bacteriocins can be produced in the food substrate during its natural fermentation or can be added in the food products after obtaining by in vitro fermentations under optimal physical and chemical conditions. Moreover, the immobilization of LAB bacteriocins on different matrices of organic and inorganic origin has been proposed as an advanced approach in the natural food preservation for their specific antimicrobial activity, anti-biofilm properties and potential use as tools for pathogen detection

On the Strong Invariance Property for Non-Lipschitz Dynamics

We provide a new sufficient condition for strong invariance for differential inclusions, under very general conditions on the dynamics, in terms of a Hamiltonian inequality. In lieu of the usual Lipschitzness assumption on the multifunction, we assume a feedback realization condition that can in particular be satisfied for measurable dynamics that are neither upper nor lower semicontinuous.Comment: 15 pages, 0 figures. For this revision, the authors added a remark about an alternative nonconstructive proof of the main resul

High-Order Control Variations and Small-Time Local Controllability

The importance of “control variations” for obtaining local approximations of the reachable set of nonlinear control systems is well known. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable (STLC). Two concepts of control variations of higher order are introduced for the case of smooth control systems. The relation between these variations and the small-time local controllability is studied and a new sufficient STLC condition is proved.* This work is partly supported by the Bulgarian Ministry of Science and Higher Education – National Fund for Science Research under contract DO 02–359/2008

Optimized Entanglement Purification

We investigate novel protocols for entanglement purification of qubit Bell pairs. Employing genetic algorithms for the design of the purification circuit, we obtain shorter circuits achieving higher success rates and better final fidelities than what is currently available in the literature. We provide a software tool for analytical and numerical study of the generated purification circuits, under customizable error models. These new purification protocols pave the way to practical implementations of modular quantum computers and quantum repeaters. Our approach is particularly attentive to the effects of finite resources and imperfect local operations - phenomena neglected in the usual asymptotic approach to the problem. The choice of the building blocks permitted in the construction of the circuits is based on a thorough enumeration of the local Clifford operations that act as permutations on the basis of Bell states

Controllability of Discontinuous Systems

This report presents an approach to the local controllability problem for a discontinuous system. The approach is based on a concept of tangent vector field to a generalized dynamic system, which makes possible the differential geometry tools to be applied in the discontinuous case. Sufficient controllability conditions are derived

Polyphenols as Suitable control for Obesity and Diabetes

Modern life is characterized by physical inactivity and poor food choices, which is often a prerequisite for unhealthy weight gain and overweight/obesity. These factors unlock the emergence of a number of diseases including diabetes, cardiovascular problems, different types of cancer, etc. The pursuit of scientists to seek strategies to prevent, relieve and cure the patient leads to the usage of natural compounds of potential beneficial effect. Polyphenols are a large group of naturally occurring secondary metabolites mainly found in plants and beverages. The presence of these secondary metabolites seems to decrease the manifestation of miscellaneous disease-causing symptoms. The purpose of this review is to synthesize information about polyphenols and their potential in controlling obesity and diabetes. Polyphenols are considered as health-beneficial sources and thus could be involved in novel strategies for preventing diabetes and obesity complications

Exchange rates volatility modelling

We investigate the empirical relevance of structural breaks in the unconditional variance of exchange rate returns for seven currency pairs vis-à-vis the US Dollar over the 2002 - 2018 period. We find evidence of structural breaks in the unconditional variance for five of the seven currencies under our scope with a high degree of persistence and variability in the parameter estimates of the GARCH (1,1) model across the various subsamples defined by the structural breaks. When analysing the time of occurrence of these breaks, we are able to associate a vast majority of them to relevant social, political and economic events occurring on both a regional and a global scale. Our research indicates that structural breaks are an empirically relevant feature of exchange rate volatility modelling and should be accounted for when performing volatility forecastsNeste estudo investigamos a relevância empírica de quebras estruturais na variância dos retornos de sete taxas de câmbio vis-à-vis o US Dólar no período compreendido entre 2012 e 2018. Encontramos evidência empírica da existência de quebras estruturais na variância de cinco dos sete pares em estudo, com um elevado grau de persistência e variabilidade nos parâmetros do modelo GARCH (1,1) ao longo das diferentes subamostras definidas pelas quebras estruturais. Ao analisar o momento do tempo em que estas quebras ocorrem, somos capazes de associar a maioria delas a ocorrências significativas do ponto de vista social, político e económico, quer numa escala regional quer nacional. Os nossos resultados indicam que as quebras estruturais são relevantes do ponto de visa empírico no que à modelização de retornos de taxas de câmbio diz respeito e devem ser tidos em conta aquando da realização de exercícios de previsão de volatilidade