On bifurcation and symmetry of solutions of symmetric nonlinear equations with odd-harmonic forcings

In this work we study existence, bifurcation, and symmetries of small solutions of the nonlinear equation Lx = N(x, p, epsilon) + mu f, which is supposed to be equivariant under the action of a group OHm, and where f is supposed to be OHm-invariant. We assume that L is a linear operator and N(., p, epsilon) is a nonlinear operator, both defined in a Banach space X, with values in a Banach space Z, and p, mu, and epsilon are small real parameters. Under certain conditions we show the existence of symmetric solutions and under additional conditions we prove that these are the only feasible solutions. Some examples of nonlinear ordinary and partial differential equations are analyzed. (C) 1995 Academic Press, Inc.

Lamé differential equations and electrostatics

The problem of existence and uniqueness of polynomial solutions of the Lamé differential equation A(x)y″ + 2B(x)y′ + C(x)y = 0, where A(x),B(x) and C(x) are polynomials of degree p + 1,p and p - 1, is under discussion. We concentrate on the case when A(x) has only real zeros aj and, in contrast to a classical result of Heine and Stieltjes which concerns the case of positive coefficients rj in the partial fraction decomposition B(x)/A(x) = ∑j p=0 rj/(x - aj), we allow the presence of both positive and negative coefficients rj. The corresponding electrostatic interpretation of the zeros of the solution y(x) as points of equilibrium in an electrostatic field generated by charges rj at aj is given. As an application we prove that the zeros of the Gegenbauer-Laurent polynomials are the points of unique equilibrium in a field generated by two positive and two negative charges. © 2000 American Mathematical Society.

Stochastic exponential stability of singular linear systems with Markov jump parameters

This paper deals with exponential stability of discrete-time singular systems with Markov jump parameters. We propose a set of coupled generalized Lyapunov equations (CGLE) that provides sufficient conditions to check this property for this class of systems. A method for solving the obtained CGLE is also presented, based on iterations of standard singular Lyapunov equations. We present also a numerical example to illustrate the effectiveness of the approach we are proposing.

Improved Upper Limits on the Stochastic Gravitational-Wave Background from 2009-2010 LIGO and Virgo Data

Gravitational waves from a variety of sources are predicted to superpose to create a stochastic background. This background is expected to contain unique information from throughout the history of the Universe that is unavailable through standard electromagnetic observations, making its study of fundamental importance to understanding the evolution of the Universe. We carry out a search for the stochastic background with the latest data from the LIGO and Virgo detectors. Consistent with predictions from most stochastic gravitational-wave background models, the data display no evidence of a stochastic gravitational-wave signal. Assuming a gravitational-wave spectrum of Omega(GW)(f) = Omega(alpha)(f/f(ref))(alpha), we place 95% confidence level upper limits on the energy density of the background in each of four frequency bands spanning 41.5-1726 Hz. In the frequency band of 41.5-169.25 Hz for a spectral index of alpha = 0, we constrain the energy density of the stochastic background to be Omega(GW)(f) < 5.6 x 10(-6). For the 600-1000 Hz band, Omega(GW)(f) < 0.14(f/900 Hz)(3), a factor of 2.5 lower than the best previously reported upper limits. We find Omega(GW)(f) < 1.8 x 10(-4) using a spectral index of zero for 170-600 Hz and Omega(GW)(f) < 1.0(f/1300 Hz)(3) for 1000-1726 Hz, bands in which no previous direct limits have been placed. The limits in these four bands are the lowest direct measurements to date on the stochastic background. We discuss the implications of these results in light of the recent claim by the BICEP2 experiment of the possible evidence for inflationary gravitational waves.

On a class of abstract neutral functional differential equations

By using the theory of semigroups of growth α, we discuss the existence of mild solutions for a class of abstract neutral functional differential equations. A concrete application to partial neutral functional differential equations is considered.

Equações estocásticas aplicadas a sistemas biofísicos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Observational constraints on a phenomenological f (R, partial derivative R)-model

This paper analyses the cosmological consequences of amodified theory of gravity whose action integral is built from a linear combination of the Ricci scalar R and a quadratic term in the covariant derivative of R. The resulting Friedmann equations are of the fifth-order in the Hubble function. These equations are solved numerically for a flat space section geometry and pressureless matter. The cosmological parameters of the higher-order model are fit using SN Ia data and X-ray gas mass fraction in galaxy clusters. The best-fit present-day t(0) values for the deceleration parameter, jerk and snap are given. The coupling constant beta of the model is not univocally determined by the data fit, but partially constrained by it. Density parameter Omega(m0) is also determined and shows weak correlation with the other parameters. The model allows for two possible future scenarios: there may be either an eternal expansion or a Rebouncing event depending on the set of values in the space of parameters. The analysis towards the past performed with the best-fit parameters shows that the model is not able to accommodate a matter-dominated stage required to the formation of structure.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence space comprises two representative spatial structures for both human and mosquito populations. The human population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR) dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic and the non-epidemic states are also obtained by performing Monte Carlo simulations. References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006 (2011).

Multimodality and flexibility of stochastic gene expression

We consider a general class of mathematical models for stochastic gene expression where the transcription rate is allowed to depend on a promoter state variable that can take an arbitrary (finite) number of values. We provide the solution of the master equations in the stationary limit, based on a factorization of the stochastic transition matrix that separates timescales and relative interaction strengths, and we express its entries in terms of parameters that have a natural physical and/or biological interpretation. The solution illustrates the capacity of multiple states promoters to generate multimodal distributions of gene products, without the need for feedback. Furthermore, using the example of a three states promoter operating at low, high, and intermediate expression levels, we show that using multiple states operons will typically lead to a significant reduction of noise in the system. The underlying mechanism is that a three-states promoter can change its level of expression from low to high by passing through an intermediate state with a much smaller increase of fluctuations than by means of a direct transition.

Impatto di rifaximina sul microbiota intestinale: selezione di bifidobatteri antibiotico resistenti

The ideal approach for the long term treatment of intestinal disorders, such as inflammatory bowel disease (IBD), is represented by a safe and well tolerated therapy able to reduce mucosal inflammation and maintain homeostasis of the intestinal microbiota. A combined therapy with antimicrobial agents, to reduce antigenic load, and immunomodulators, to ameliorate the dysregulated responses, followed by probiotic supplementation has been proposed. Because of the complementary mechanisms of action of antibiotics and probiotics, a combined therapeutic approach would give advantages in terms of enlargement of the antimicrobial spectrum, due to the barrier effect of probiotic bacteria, and limitation of some side effects of traditional chemiotherapy (i.e. indiscriminate decrease of aggressive and protective intestinal bacteria, altered absorption of nutrient elements, allergic and inflammatory reactions). Rifaximin (4-deoxy-4’-methylpyrido[1’,2’-1,2]imidazo[5,4-c]rifamycin SV) is a product of synthesis experiments designed to modify the parent compound, rifamycin, in order to achieve low gastrointestinal absorption while retaining good antibacterial activity. Both experimental and clinical pharmacology clearly show that this compound is a non systemic antibiotic with a broad spectrum of antibacterial action, covering Gram-positive and Gram-negative organisms, both aerobes and anaerobes. Being virtually non absorbed, its bioavailability within the gastrointestinal tract is rather high with intraluminal and faecal drug concentrations that largely exceed the MIC values observed in vitro against a wide range of pathogenic microorganisms. The gastrointestinal tract represents therefore the primary therapeutic target and gastrointestinal infections the main indication. The little value of rifaximin outside the enteric area minimizes both antimicrobial resistance and systemic adverse events. Fermented dairy products enriched with probiotic bacteria have developed into one of the most successful categories of functional foods. Probiotics are defined as “live microorganisms which, when administered in adequate amounts, confer a health benefit on the host” (FAO/WHO, 2002), and mainly include Lactobacillus and Bifidobacterium species. Probiotic bacteria exert a direct effect on the intestinal microbiota of the host and contribute to organoleptic, rheological and nutritional properties of food. Administration of pharmaceutical probiotic formula has been associated with therapeutic effects in treatment of diarrhoea, constipation, flatulence, enteropathogens colonization, gastroenteritis, hypercholesterolemia, IBD, such as ulcerative colitis (UC), Crohn’s disease, pouchitis and irritable bowel syndrome. Prerequisites for probiotics are to be effective and safe. The characteristics of an effective probiotic for gastrointestinal tract disorders are tolerance to upper gastrointestinal environment (resistance to digestion by enteric or pancreatic enzymes, gastric acid and bile), adhesion on intestinal surface to lengthen the retention time, ability to prevent the adherence, establishment and/or replication of pathogens, production of antimicrobial substances, degradation of toxic catabolites by bacterial detoxifying enzymatic activities, and modulation of the host immune responses. This study was carried out using a validated three-stage fermentative continuous system and it is aimed to investigate the effect of rifaximin on the colonic microbial flora of a healthy individual, in terms of bacterial composition and production of fermentative metabolic end products. Moreover, this is the first study that investigates in vitro the impact of the simultaneous administration of the antibiotic rifaximin and the probiotic B. lactis BI07 on the intestinal microbiota. Bacterial groups of interest were evaluated using culture-based methods and molecular culture-independent techniques (FISH, PCR-DGGE). Metabolic outputs in terms of SCFA profiles were determined by HPLC analysis. Collected data demonstrated that rifaximin as well as antibiotic and probiotic treatment did not change drastically the intestinal microflora, whereas bacteria belonging to Bifidobacterium and Lactobacillus significantly increase over the course of the treatment, suggesting a spontaneous upsurge of rifaximin resistance. These results are in agreement with a previous study, in which it has been demonstrated that rifaximin administration in patients with UC, affects the host with minor variations of the intestinal microflora, and that the microbiota is restored over a wash-out period. In particular, several Bifidobacterium rifaximin resistant mutants could be isolated during the antibiotic treatment, but they disappeared after the antibiotic suspension. Furthermore, bacteria belonging to Atopobium spp. and E. rectale/Clostridium cluster XIVa increased significantly after rifaximin and probiotic treatment. Atopobium genus and E. rectale/Clostridium cluster XIVa are saccharolytic, butyrate-producing bacteria, and for these characteristics they are widely considered health-promoting microorganisms. The absence of major variations in the intestinal microflora of a healthy individual and the significant increase in probiotic and health-promoting bacteria concentrations support the rationale of the administration of rifaximin as efficacious and non-dysbiosis promoting therapy and suggest the efficacy of an antibiotic/probiotic combined treatment in several gut pathologies, such as IBD. To assess the use of an antibiotic/probiotic combination for clinical management of intestinal disorders, genetic, proteomic and physiologic approaches were employed to elucidate molecular mechanisms determining rifaximin resistance in Bifidobacterium, and the expected interactions occurring in the gut between these bacteria and the drug. The ability of an antimicrobial agent to select resistance is a relevant factor that affects its usefulness and may diminish its useful life. Rifaximin resistance phenotype was easily acquired by all bifidobacteria analyzed [type strains of the most representative intestinal bifidobacterial species (B. infantis, B. breve, B. longum, B. adolescentis and B. bifidum) and three bifidobacteria included in a pharmaceutical probiotic preparation (B. lactis BI07, B. breve BBSF and B. longum BL04)] and persisted for more than 400 bacterial generations in the absence of selective pressure. Exclusion of any reversion phenomenon suggested two hypotheses: (i) stable and immobile genetic elements encode resistance; (ii) the drug moiety does not act as an inducer of the resistance phenotype, but enables selection of resistant mutants. Since point mutations in rpoB have been indicated as representing the principal factor determining rifampicin resistance in E. coli and M. tuberculosis, whether a similar mechanism also occurs in Bifidobacterium was verified. The analysis of a 129 bp rpoB core region of several wild-type and resistant bifidobacteria revealed five different types of miss-sense mutations in codons 513, 516, 522 and 529. Position 529 was a novel mutation site, not previously described, and position 522 appeared interesting for both the double point substitutions and the heterogeneous profile of nucleotide changes. The sequence heterogeneity of codon 522 in Bifidobacterium leads to hypothesize an indirect role of its encoded amino acid in the binding with the rifaximin moiety. These results demonstrated the chromosomal nature of rifaximin resistance in Bifidobacterium, minimizing risk factors for horizontal transmission of resistance elements between intestinal microbial species. Further proteomic and physiologic investigations were carried out using B. lactis BI07, component of a pharmaceutical probiotic preparation, as a model strain. The choice of this strain was determined based on the following elements: (i) B. lactis BI07 is able to survive and persist in the gut; (ii) a proteomic overview of this strain has been recently reported. The involvement of metabolic changes associated with rifaximin resistance was investigated by proteomic analysis performed with two-dimensional electrophoresis and mass spectrometry. Comparative proteomic mapping of BI07-wt and BI07-res revealed that most differences in protein expression patterns were genetically encoded rather than induced by antibiotic exposure. In particular, rifaximin resistance phenotype was characterized by increased expression levels of stress proteins. Overexpression of stress proteins was expected, as they represent a common non specific response by bacteria when stimulated by different shock conditions, including exposure to toxic agents like heavy metals, oxidants, acids, bile salts and antibiotics. Also, positive transcription regulators were found to be overexpressed in BI07-res, suggesting that bacteria could activate compensatory mechanisms to assist the transcription process in the presence of RNA polymerase inhibitors. Other differences in expression profiles were related to proteins involved in central metabolism; these modifications suggest metabolic disadvantages of resistant mutants in comparison with sensitive bifidobacteria in the gut environment, without selective pressure, explaining their disappearance from faeces of patients with UC after interruption of antibiotic treatment. The differences observed between BI07-wt e BI07-res proteomic patterns, as well as the high frequency of silent mutations reported for resistant mutants of Bifidobacterium could be the consequences of an increased mutation rate, mechanism which may lead to persistence of resistant bacteria in the population. However, the in vivo disappearance of resistant mutants in absence of selective pressure, allows excluding the upsurge of compensatory mutations without loss of resistance. Furthermore, the proteomic characterization of the resistant phenotype suggests that rifaximin resistance is associated with a reduced bacterial fitness in B. lactis BI07-res, supporting the hypothesis of a biological cost of antibiotic resistance in Bifidobacterium. The hypothesis of rifaximin inactivation by bacterial enzymatic activities was verified by using liquid chromatography coupled with tandem mass spectrometry. Neither chemical modifications nor degradation derivatives of the rifaximin moiety were detected. The exclusion of a biodegradation pattern for the drug was further supported by the quantitative recovery in BI07-res culture fractions of the total rifaximin amount (100 μg/ml) added to the culture medium. To confirm the main role of the mutation on the β chain of RNA polymerase in rifaximin resistance acquisition, transcription activity of crude enzymatic extracts of BI07-res cells was evaluated. Although the inhibition effects of rifaximin on in vitro transcription were definitely higher for BI07-wt than for BI07-res, a partial resistance of the mutated RNA polymerase at rifaximin concentrations > 10 μg/ml was supposed, on the basis of the calculated differences in inhibition percentages between BI07-wt and BI07-res. By considering the resistance of entire BI07-res cells to rifaximin concentrations > 100 μg/ml, supplementary resistance mechanisms may take place in vivo. A barrier for the rifaximin uptake in BI07-res cells was suggested in this study, on the basis of the major portion of the antibiotic found to be bound to the cellular pellet respect to the portion recovered in the cellular lysate. Related to this finding, a resistance mechanism involving changes of membrane permeability was supposed. A previous study supports this hypothesis, demonstrating the involvement of surface properties and permeability in natural resistance to rifampicin in mycobacteria, isolated from cases of human infection, which possessed a rifampicin-susceptible RNA polymerase. To understand the mechanism of membrane barrier, variations in percentage of saturated and unsaturated FAs and their methylation products in BI07-wt and BI07-res membranes were investigated. While saturated FAs confer rigidity to membrane and resistance to stress agents, such as antibiotics, a high level of lipid unsaturation is associated with high fluidity and susceptibility to stresses. Thus, the higher percentage of saturated FAs during the stationary phase of BI07-res could represent a defence mechanism of mutant cells to prevent the antibiotic uptake. Furthermore, the increase of CFAs such as dihydrosterculic acid during the stationary phase of BI07-res suggests that this CFA could be more suitable than its isomer lactobacillic acid to interact with and prevent the penetration of exogenous molecules including rifaximin. Finally, the impact of rifaximin on immune regulatory functions of the gut was evaluated. It has been suggested a potential anti-inflammatory effect of rifaximin, with reduced secretion of IFN-γ in a rodent model of colitis. Analogously, it has been reported a significant decrease in IL-8, MCP-1, MCP-3 e IL-10 levels in patients affected by pouchitis, treated with a combined therapy of rifaximin and ciprofloxacin. Since rifaximin enables in vivo and in vitro selection of Bifidobacterium resistant mutants with high frequency, the immunomodulation activities of rifaximin associated with a B. lactis resistant mutant were also taken into account. Data obtained from PBMC stimulation experiments suggest the following conclusions: (i) rifaximin does not exert any effect on production of IL-1β, IL-6 and IL-10, whereas it weakly stimulates production of TNF-α; (ii) B. lactis appears as a good inducer of IL-1β, IL-6 and TNF-α; (iii) combination of BI07-res and rifaximin exhibits a lower stimulation effect than BI07-res alone, especially for IL-6. These results confirm the potential anti-inflammatory effect of rifaximin, and are in agreement with several studies that report a transient pro-inflammatory response associated with probiotic administration. The understanding of the molecular factors determining rifaximin resistance in the genus Bifidobacterium assumes an applicative significance at pharmaceutical and medical level, as it represents the scientific basis to justify the simultaneous use of the antibiotic rifaximin and probiotic bifidobacteria in the clinical treatment of intestinal disorders.

Probabilistic Envelope Curves for Extreme Rainfall Events - Curve Inviluppo Probabilistiche per Precipitazioni Estreme

A regional envelope curve (REC) of flood flows summarises the current bound on our experience of extreme floods in a region. RECs are available for most regions of the world. Recent scientific papers introduced a probabilistic interpretation of these curves and formulated an empirical estimator of the recurrence interval T associated with a REC, which, in principle, enables us to use RECs for design purposes in ungauged basins. The main aim of this work is twofold. First, it extends the REC concept to extreme rainstorm events by introducing the Depth-Duration Envelope Curves (DDEC), which are defined as the regional upper bound on all the record rainfall depths at present for various rainfall duration. Second, it adapts the probabilistic interpretation proposed for RECs to DDECs and it assesses the suitability of these curves for estimating the T-year rainfall event associated with a given duration and large T values. Probabilistic DDECs are complementary to regional frequency analysis of rainstorms and their utilization in combination with a suitable rainfall-runoff model can provide useful indications on the magnitude of extreme floods for gauged and ungauged basins. The study focuses on two different national datasets, the peak over threshold (POT) series of rainfall depths with duration 30 min., 1, 3, 9 and 24 hrs. obtained for 700 Austrian raingauges and the Annual Maximum Series (AMS) of rainfall depths with duration spanning from 5 min. to 24 hrs. collected at 220 raingauges located in northern-central Italy. The estimation of the recurrence interval of DDEC requires the quantification of the equivalent number of independent data which, in turn, is a function of the cross-correlation among sequences. While the quantification and modelling of intersite dependence is a straightforward task for AMS series, it may be cumbersome for POT series. This paper proposes a possible approach to address this problem.

Purging e alte dosi di chemioterapia con reinfusione di cellule staminali autologhe in linfomi non Hodgkin follicolari resistenti/refrattari

In the era of monoclonal antibodies the role of autologous stem cell transplantation (ASCT) in the management of follicular lymphoma (FL) is still debated. To evaluate the safety and efficacy of myeloablative therapy with rescue of purged or unpurged harvests in FL pts. At our institution form 1997 to 2007 28 pts with refractory/resistant FL were eligible for ASCT. Before high dose therapy they received 2-3 cycles of CHOP-like regimen (ACOD), followed by Cyclophosphamide 4g/mq to mobilize the stem cells (SC). After SC collection the pts underwent 3 cycles of subcutaneous Cladribine at a daily dose of 0,14-0,10 mg/Kg for Day 1-5 every 3-4 weeks. The conditioning regimen was based on Mitoxantrone 60mg/mq + Melphalan 180 mg/mq, followed by SC re-infusion 24-hours later and G-CSF starting 24 hours after re-infusion. In 19 pts the SC underwent purging: in 10 harvests the CD34+ were selected by immunomagnetic beads, while in the other 9 pts, only Rituximab was used as “purging in vivo” agent. The remaining 9 pts received unpurged SC. Before ASCT 11 pts were in complete response (CR), 9 in partial response (PR) and 2 in stable disease. Two pts were not eligible for ASCT because of progressive disease (PD). The remaining 25 pts were eligible for ASCT. The engraftment was at a median of 11 days for leucocytes and 14 days for platelets (>20.000/mmc), with a delay of one day in the pts, who received purged SC. Grade 3-4 mucositis was described in 8 pts. During aplasia a 48% infection rate was reported, without differences between pts with purged or unpurged SC. One patient in CR presented myelodysplastic syndrome at 18 months from ASCT. After ASCT 22 pts were in CR, 2 in PR and one patient were not valuable, because died before response assessment. Nine pts in CR showed PD at a median time of 14 months from ASCT. With a median follow up of 5 years (range 2 months -10 years), 22 pts are alive and 11 (44%) in CR. Ten pts died, 5 for progressive disease and 5 for treatment-related causes; in particular 7 of them received in-vitro purged SC. Conclusions: Our chemotherapy regimen, which included the purine analogue Cladribine in the induction phase, seems safe and feasible. The high rate of CR reported and the sustained freedom from progression up to now, makes such modality of treatment a valid option principally in relapsing FL patients. In our experience, the addition of a monoclonal antibody as part of treatment confirms its role “in vivo purging” without observing an increased incidence of infection.

Studio e sviluppo di un motore a 2 tempi diesel veloce di nuova concezione per applicazioni automobilistiche

The Department of Mechanical and Civil Engineering (DIMeC) of the University of Modena and Reggio Emilia is developing a new type of small capacity HSDI 2-Stroke Diesel engine (called HSD2), featuring a specifically designed combustion system, aimed to reduce weight, size and manufacturing costs, and improving pollutant emissions at partial load. The present work is focused on the analysis of the combustion and the scavenging process, investigated by means of a version of the KIVA-3V code customized by the University of Chalmers and modified by DIMeC. The customization of the KIVA-3V code includes a detailed combustion chemistry approach, coupled with a comprehensive oxidation mechanism for diesel oil surrogate and the modeling of turbulence/chemistry interaction through the PaSR (Partially Stirred Reactor) model. A four stroke automobile Diesel engine featuring a very close bore size is taken as a reference, for both the numerical models calibration and for a comparison with the 2-Stroke engine. Analysis is carried out trough a comparison between HSD2 and FIAT 1300 MultiJet in several operating conditions, at full and partial load. Such a comparison clearly demonstrates the effectiveness of the two stroke concept in terms of emissions reduction and high power density. However, HSD2 is still a virtual engine, and experimental results are needed to assume the reliability of numerical results.