Analysis of nonlinear noisy integrate & fire neuron models: blow-up and steady states

Nonlinear Noisy Leaky Integrate and Fire (NNLIF) models for neurons networks can be written as Fokker-Planck-Kolmogorov equations on the probability density of neurons, the main parameters in the model being the connectivity of the network and the noise. We analyse several aspects of the NNLIF model: the number of steady states, a priori estimates, blow-up issues and convergence toward equilibrium in the linear case. In particular, for excitatory networks, blow-up always occurs for initial data concentrated close to the firing potential. These results show how critical is the balance between noise and excitatory/inhibitory interactions to the connectivity parameter.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

Technology, business models and network structure in the airline industry

Network airlines have been increasingly focusing their operations on hub airports through the exploitation of connecting traffic, allowing them to take advantage of economies of traffic density, which are unequivocal in the airline industry. Less attention has been devoted to airlines' decisions on point-to-point thin routes, which could be served using different aircraft technologies and different business models. This paper examines, both theoretically and empirically, the impact on airlines' networks of the two major innovations in the airline industry in the last two decades: the regional jet technology and the low-cost business model. We show that, under certain circumstances, direct services on point-to-point thin routes can be viable and thus airlines may be interested in deviating passengers out of the hub. Keywords: regional jet technology; low-cost business model; point-to-point network; hub-and-spoke network JEL Classi…fication Numbers: L13; L2; L93

Estimation of parametric and nonparametric models for univariate claim severity distributions - an approach using R

This paper presents an analysis of motor vehicle insurance claims relating to vehicle damage and to associated medical expenses. We use univariate severity distributions estimated with parametric and non-parametric methods. The methods are implemented using the statistical package R. Parametric analysis is limited to estimation of normal and lognormal distributions for each of the two claim types. The nonparametric analysis presented involves kernel density estimation. We illustrate the benefits of applying transformations to data prior to employing kernel based methods. We use a log-transformation and an optimal transformation amongst a class of transformations that produces symmetry in the data. The central aim of this paper is to provide educators with material that can be used in the classroom to teach statistical estimation methods, goodness of fit analysis and importantly statistical computing in the context of insurance and risk management. To this end, we have included in the Appendix of this paper all the R code that has been used in the analysis so that readers, both students and educators, can fully explore the techniques described

What do we gain from simplicity versus complexity in species distribution models?

Species distribution models (SDMs) are widely used to explain and predict species ranges and environmental niches. They are most commonly constructed by inferring species' occurrence-environment relationships using statistical and machine-learning methods. The variety of methods that can be used to construct SDMs (e.g. generalized linear/additive models, tree-based models, maximum entropy, etc.), and the variety of ways that such models can be implemented, permits substantial flexibility in SDM complexity. Building models with an appropriate amount of complexity for the study objectives is critical for robust inference. We characterize complexity as the shape of the inferred occurrence-environment relationships and the number of parameters used to describe them, and search for insights into whether additional complexity is informative or superfluous. By building 'under fit' models, having insufficient flexibility to describe observed occurrence-environment relationships, we risk misunderstanding the factors shaping species distributions. By building 'over fit' models, with excessive flexibility, we risk inadvertently ascribing pattern to noise or building opaque models. However, model selection can be challenging, especially when comparing models constructed under different modeling approaches. Here we argue for a more pragmatic approach: researchers should constrain the complexity of their models based on study objective, attributes of the data, and an understanding of how these interact with the underlying biological processes. We discuss guidelines for balancing under fitting with over fitting and consequently how complexity affects decisions made during model building. Although some generalities are possible, our discussion reflects differences in opinions that favor simpler versus more complex models. We conclude that combining insights from both simple and complex SDM building approaches best advances our knowledge of current and future species ranges.

Participation of interleukin-5, interleukin-8 and leukotriene B4 in eosinophil accumulation in two different experimental models

There are several experimental models describing in vivo eosinophil (EO) migration, including ip injection of a large volume of saline (SAL) or Sephadex beads (SEP). The aim of this study was to investigate the mechanisms involved in the EO migration in these two models. Two consecutive injections of SAL given 48 hr apart, induced a selective recruitment of EO into peritoneal cavity of rats, which peaked 48 hr after the last injection. SEP, when injected ip, promoted EO accumulation in rats. The phenomenom was dose-related and peaked 48 hr after SEP injection. To investigate the mediators involved in this process we showed that BW A4C, MK 886 and dexamethasone (DXA) inhibited the EO migration induced by SAL and SEP. To investigate the source of the EO chemotactic factor we showed that mast cells, macrophages (MO), but not lymphocytes, incubated in vitro in presence of SAL released a factor which induced EO migration. With SEP, only mast cells release a factor that induced EO migration, which was inhibited by BW A4C, MK 886 and DXA. Furthermore, the chemotactic activity of SAL-stimulated mast cells was inhibited by antisera against IL-5 and IL-8 (interleukin). SAL-stimulated MO were only inhibited by anti-IL-8 antibodies as well SEP-stimulated mast cells. These results suggest that the EO migration induced by SAL may be dependent on resident mast cells and MO and mediated by LTB4, IL-5 and IL-8. SEP-induced EO migration was dependent on mast cells and may be mediated by LTB4 and IL-8. Furthermore, IL-5 and IL-8 induced EO migration, which was also dependent on resident cells and mediated by LTB4 . In conclusion, EO migration induced by SAL is dependent on mast cells and MO, whereas that induced by SEP is dependent on mast cells alone. Stimulated mast cells release LTB4, IL-5 and IL-8 while MO release LTB4 and IL-8. The IL-5 and IL-8 release by the SAL or SEP-stimulated resident cells may act in an autocrine fashion, thus potentiating LTB4 release.

Role of eosinophilic airway inflammation in models of asthma

Eosinophils play a central role in the establishment and outcome of bronchial inflammation in asthma. Animal models of allergy are useful to answer questions related to mechanisms of allergic inflammation. We have used models of sensitized and boosted guinea pigs to investigate the nature of bronchial inflammation in allergic conditions. These animals develop marked bronchial infiltration composed mainly of CD4+ T-lymphocytes and eosinophils. Further provocation with antigen leads to degranulation of eosinophils and ulceration of the bronchial mucosa. Eosinophils are the first cells to increase in numbers in the mucosa after antigen challenge and depend on the expression of alpha 4 integrin to adhere to the vascular endothelium and transmigrate to the mucosa. Blockage of alpha4 integrin expression with specific antibody prevents not only the transmigration of eosinophils but also the development of bronchial hyperresponsiveness (BHR) to agonists in sensitized and challenged animals, clearly suggesting a role for this cell type in this altered functional state. Moreover, introduction of antibody against Major Basic Protein into the airways also prevents the development of BHR in similar model. BHR can also be suppressed by the use of FK506, an immunosuppressor that reduces in almost 100% the infiltration of eosinophils into the bronchi of allergic animals. These data support the concept that eosinophil is the most important pro-inflammatory factor in bronchial inflammation associated with allergy.

Mechanisms of cell accumulation induced by Mycobacterium bovis BCG

Mycobacteria, specially Mycobacterium tuberculosis are among the micro-organisms that are increasing dramatically the number of infections with death, all over the world. A great number of animal experimental models have been proposed to investigate the mechanisms involved in the host response against these intracellular parasites. Studies of airway infection in guinea-pigs and rabbits, as well as, in mice intravenously infected with BCG have made an important contribution to our understanding of the virulence, pathogenesis and the immunology of mycobacterial infections. Although, there are few models to study the mechanisms of the initial inflammatory process induced by the first contact with the Mycobacteria, and the relevance of the acute generation of inflammatory mediators, cytokines and leukocyte infiltration to the development of the mycobacterial infection. In this work we reviewed our results obtained with a model of M. bovis BCG-induced pleurisy in mice, describing the mechanisms involved in the leukocyte influx induced by BCG at 24 hr. Different mechanisms appear to be related with the influx of neutrophils, eosinophils and mononuclear cells and distinct inflammatory mediators, cytokines and adhesion molecules are involved in the BCG-induced cell accumulation.

Influence of CRTC1 Polymorphisms on Body Mass Index and Fat Mass in Psychiatric Patients and the General Adult Population.

IMPORTANCE There is a high prevalence of obesity in psychiatric patients, possibly leading to metabolic complications and reducing life expectancy. The CREB-regulated transcription coactivator 1 (CRTC1) gene is involved in energy balance and obesity in animal models, but its role in human obesity is unknown. OBJECTIVE To determine whether polymorphisms within the CRTC1 gene are associated with adiposity markers in psychiatric patients and the general population. DESIGN, SETTING, AND PARTICIPANTS Retrospective and prospective data analysis and population-based samples at Lausanne and Geneva university hospitals in Switzerland and a private clinic in Lausanne, Switzerland. The effect of 3 CRTC1 polymorphisms on body mass index (BMI) and/or fat mass was investigated in a discovery cohort of psychiatric outpatients taking weight gain-inducing psychotropic drugs (sample 1, n = 152). The CRTC1 variant that was significantly associated with BMI and survived Bonferroni corrections for multiple comparison was then replicated in 2 independent psychiatric samples (sample 2, n = 174 and sample 3, n = 118) and 2 white population-based samples (sample 4, n = 5338 and sample 5, n = 123 865). INTERVENTION Noninterventional studies. MAIN OUTCOME AND MEASURE Difference in BMI and/or fat mass between CRTC1 genotype groups. RESULTS Among the CRTC1 variants tested in the first psychiatric sample, only rs3746266A>G was associated with BMI (Padjusted = .003). In the 3 psychiatric samples, carriers of the rs3746266 G allele had a lower BMI than noncarriers (AA genotype) (sample 1, P = .001; sample 2, P = .05; and sample 3, P = .0003). In the combined analysis, excluding patients taking other weight gain-inducing drugs, G allele carriers (n = 98) had a 1.81-kg/m2 lower BMI than noncarriers (n = 226; P < .0001). The strongest association was observed in women younger than 45 years, with a 3.87-kg/m2 lower BMI in G allele carriers (n = 25) compared with noncarriers (n = 48; P < .0001), explaining 9% of BMI variance. In the population-based samples, the T allele of rs6510997C>T (a proxy of the rs3746266 G allele; r2 = 0.7) was associated with lower BMI (sample 5, n = 123 865; P = .01) and fat mass (sample 4, n = 5338; P = .03). The strongest association with fat mass was observed in premenopausal women (n = 1192; P = .02). CONCLUSIONS AND RELEVANCE These findings suggest that CRTC1 contributes to the genetics of human obesity in psychiatric patients and the general population. Identification of high-risk subjects could contribute to a better individualization of the pharmacological treatment in psychiatry.

EGFR signalling as a negative regulator of Notch1 gene transcription and function in proliferating keratinocytes and cancer.

The Notch1 gene has an important role in mammalian cell-fate decision and tumorigenesis. Upstream control mechanisms for transcription of this gene are still poorly understood. In a chemical genetics screen for small molecule activators of Notch signalling, we identified epidermal growth factor receptor (EGFR) as a key negative regulator of Notch1 gene expression in primary human keratinocytes, intact epidermis and skin squamous cell carcinomas (SCCs). The underlying mechanism for negative control of the Notch1 gene in human cells, as well as in a mouse model of EGFR-dependent skin carcinogenesis, involves transcriptional suppression of p53 by the EGFR effector c-Jun. Suppression of Notch signalling in cancer cells counteracts the differentiation-inducing effects of EGFR inhibitors while, at the same time, synergizing with these compounds in induction of apoptosis. Thus, our data reveal a key role of EGFR signalling in the negative regulation of Notch1 gene transcription, of potential relevance for combinatory approaches for cancer therapy.

Mixture of bivariate Poisson regression models with an application to insurance

In a recent paper Bermúdez [2009] used bivariate Poisson regression models for ratemaking in car insurance, and included zero-inflated models to account for the excess of zeros and the overdispersion in the data set. In the present paper, we revisit this model in order to consider alternatives. We propose a 2-finite mixture of bivariate Poisson regression models to demonstrate that the overdispersion in the data requires more structure if it is to be taken into account, and that a simple zero-inflated bivariate Poisson model does not suffice. At the same time, we show that a finite mixture of bivariate Poisson regression models embraces zero-inflated bivariate Poisson regression models as a special case. Additionally, we describe a model in which the mixing proportions are dependent on covariates when modelling the way in which each individual belongs to a separate cluster. Finally, an EM algorithm is provided in order to ensure the models’ ease-of-fit. These models are applied to the same automobile insurance claims data set as used in Bermúdez [2009] and it is shown that the modelling of the data set can be improved considerably.

Climate-based empirical models show biased predictions of butterfly communities along environmental gradients

A better understanding of the factors that mould ecological community structure is required to accurately predict community composition and to anticipate threats to ecosystems due to global changes. We tested how well stacked climate-based species distribution models (S-SDMs) could predict butterfly communities in a mountain region. It has been suggested that climate is the main force driving butterfly distribution and community structure in mountain environments, and that, as a consequence, climate-based S-SDMs should yield unbiased predictions. In contrast to this expectation, at lower altitudes, climate-based S-SDMs overpredicted butterfly species richness at sites with low plant species richness and underpredicted species richness at sites with high plant species richness. According to two indices of composition accuracy, the Sorensen index and a matching coefficient considering both absences and presences, S-SDMs were more accurate in plant-rich grasslands. Butterflies display strong and often specialised trophic interactions with plants. At lower altitudes, where land use is more intense, considering climate alone without accounting for land use influences on grassland plant richness leads to erroneous predictions of butterfly presences and absences. In contrast, at higher altitudes, where climate is the main force filtering communities, there were fewer differences between observed and predicted butterfly richness. At high altitudes, even if stochastic processes decrease the accuracy of predictions of presence, climate-based S-SDMs are able to better filter out butterfly species that are unable to cope with severe climatic conditions, providing more accurate predictions of absences. Our results suggest that predictions should account for plants in disturbed habitats at lower altitudes but that stochastic processes and heterogeneity at high altitudes may limit prediction success of climate-based S-SDMs.