Calculation of Volterra kernels for solutions of nonlinear differential equations

We consider vector-valued autonomous differential equations of the form x' = f(x) + phi with analytic f and investigate the nonanticipative solution operator phi bar right arrow A(phi) in terms of its Volterra series. We show that Volterra kernels of order > 1 occurring in the series expansion of the solution operator A are continuous functions, and establish recurrence relations between the kernels allowing their explicit calculation. A practical tensor calculus is provided for the finite-dimensional case. In addition to analytically calculating the kernels, we present an algorithm to numerically obtain them from the output x(t) through sampling the input space by linear combinations of delta functions. We call this "differential sampling". It is a nonlinear analogue of the classical method of impulse response. We prove a continuity theorem stating that, in the finite-dimensional case, approximate delta functions give rise to approximate Volterra kernels and that continuity holds in the sense of weak convergence. Finally, we discuss a practical implementation of differential sampling and relate it to the Wiener method

Transplantation for renal failure secondary to enteric hyperoxaluria: a case report

Enteric hyperoxaluria can lead to renal failure. There have only been a few reports of renal transplantation as treatment of endstage renal disease secondary to enteric hyperoxaluria and results have been mixed. This report describes a patient with Crohn's disease who developed chronic renal failure from enteric hyperoxaluria. He subsequently had a successful renal transplant without any post-operative oxalate related complications and has satisfactory renal function almost three years later. Aggressive pre-transplant hemodialysis was not done. The literature associated with renal transplantation for enteric hyperoxaluria is reviewed

Genetics, recombination and clinical features of human rhinovirus species C (HRV-C) infections; interactions of HRV-C with other respiratory viruses

To estimate the frequency, molecular epidemiological and clinical associations of infection with the newly described species C variants of human rhinoviruses (HRV), 3243 diagnostic respiratory samples referred for diagnostic testing in Edinburgh were screened using a VP4-encoding region-based selective polymerase chain reaction (PCR) for HRV-C along with parallel PCR testing for 13 other respiratory viruses. HRV-C was the third most frequently detected behind respiratory syncytial virus (RSV) and adenovirus, with 141 infection episodes detected among 1885 subjects over 13 months (7.5%). Infections predominantly targeted the very young (median age 6–12 months; 80% of infections in those <2 years), occurred throughout the year but with peak incidence in early winter months. HRV-C was detected significantly more frequently among subjects with lower (LRT) and upper respiratory tract (URT) disease than controls without respiratory symptoms; HRV-C mono-infections were the second most frequently detected virus (behind RSV) in both disease presentations (6.9% and 7.8% of all cases respectively). HRV variants were classified by VP4/VP2 sequencing into 39 genotypically defined types, increasing the current total worldwide to 60. Through sequence comparisons of the 5′untranslated region (5′UTR), the majority grouped with species A (n = 96; 68%, described as HRV-Ca), the remainder forming a phylogenetically distinct 5′UTR group (HRV-Cc). Multiple and bidirectional recombination events between HRV-Ca and HRV-Cc variants and with HRV species A represents the most parsimonious explanation for their interspersed phylogeny relationships in the VP4/VP2-encoding region. No difference in age distribution, seasonality or disease associations was identified between HRV-Ca and HRV-Cc variants. HRV-C-infected subjects showed markedly reduced detection frequencies of RSV and other respiratory viruses, providing evidence for a major interfering effect of HRV-C on susceptibility to other respiratory virus infections. HRV-C's disease associations, its prevalence and evidence for interfering effects on other respiratory viruses mandates incorporation of rhinoviruses into future diagnostic virology screening

A Cognitive Architecture Based on a Learning Classifier System with Spiking Classifiers

© 2015, Springer Science+Business Media New York. Learning classifier systems (LCS) are population-based reinforcement learners that were originally designed to model various cognitive phenomena. This paper presents an explicitly cognitive LCS by using spiking neural networks as classifiers, providing each classifier with a measure of temporal dynamism. We employ a constructivist model of growth of both neurons and synaptic connections, which permits a genetic algorithm to automatically evolve sufficiently-complex neural structures. The spiking classifiers are coupled with a temporally-sensitive reinforcement learning algorithm, which allows the system to perform temporal state decomposition by appropriately rewarding “macro-actions”, created by chaining together multiple atomic actions. The combination of temporal reinforcement learning and neural information processing is shown to outperform benchmark neural classifier systems, and successfully solve a robotic navigation task

Rhinovirus Genome Variation during Chronic Upper and Lower Respiratory Tract Infections

Routine screening of lung transplant recipients and hospital patients for respiratory virus infections allowed to identify human rhinovirus (HRV) in the upper and lower respiratory tracts, including immunocompromised hosts chronically infected with the same strain over weeks or months. Phylogenetic analysis of 144 HRV-positive samples showed no apparent correlation between a given viral genotype or species and their ability to invade the lower respiratory tract or lead to protracted infection. By contrast, protracted infections were found almost exclusively in immunocompromised patients, thus suggesting that host factors rather than the virus genotype modulate disease outcome, in particular the immune response. Complete genome sequencing of five chronic cases to study rhinovirus genome adaptation showed that the calculated mutation frequency was in the range observed during acute human infections. Analysis of mutation hot spot regions between specimens collected at different times or in different body sites revealed that non-synonymous changes were mostly concentrated in the viral capsid genes VP1, VP2 and VP3, independent of the HRV type. In an immunosuppressed lung transplant recipient infected with the same HRV strain for more than two years, both classical and ultra-deep sequencing of samples collected at different time points in the upper and lower respiratory tracts showed that these virus populations were phylogenetically indistinguishable over the course of infection, except for the last month. Specific signatures were found in the last two lower respiratory tract populations, including changes in the 5′UTR polypyrimidine tract and the VP2 immunogenic site 2. These results highlight for the first time the ability of a given rhinovirus to evolve in the course of a natural infection in immunocompromised patients and complement data obtained from previous experimental inoculation studies in immunocompetent volunteers

The Role of Demography and Markets in Determining Deforestation Rates Near Ranomafana National Park, Madagascar

The highland forests of Madagascar are home to some of the world's most unique and diverse flora and fauna and to some of its poorest people. This juxtaposition of poverty and biodiversity is continually reinforced by rapid population growth, which results in increasing pressure on the remaining forest habitat in the highland region, and the biodiversity therein. Here we derive a mathematical expression for the subsistence of households to assess the role of markets and household demography on deforestation near Ranomafana National Park. In villages closest to urban rice markets, households were likely to clear less land than our model predicted, presumably because they were purchasing food at market. This effect was offset by the large number of migrant households who cleared significantly more land between 1989–2003 than did residents throughout the region. Deforestation by migrant households typically occurred after a mean time lag of 9 years. Analyses suggest that while local conservation efforts in Madagascar have been successful at reducing the footprint of individual households, large-scale conservation must rely on policies that can reduce the establishment of new households in remaining forested areas

Evidence of Recombination and Genetic Diversity in Human Rhinoviruses in Children with Acute Respiratory Infection

International audienceOur study showed a high diversity of HRV strains that cause bronchitis and pneumonia in children. A predominance of HRV-C over HRV-A and HRV-B was observed, and two subspecies of HRV-C were identified, the diversity of which seemed to be related to recombination with former HRV-A strains. None of the HRV-C strains appeared to have a higher clinical impact than HRV-A or HRV-B on respiratory compromise

A Diverse Group of Previously Unrecognized Human Rhinoviruses Are Common Causes of Respiratory Illnesses in Infants

Human rhinoviruses (HRVs) are the most prevalent human pathogens, and consist of 101 serotypes that are classified into groups A and B according to sequence variations. HRV infections cause a wide spectrum of clinical outcomes ranging from asymptomatic infection to severe lower respiratory symptoms. Defining the role of specific strains in various HRV illnesses has been difficult because traditional serology, which requires viral culture and neutralization tests using 101 serotype-specific antisera, is insensitive and laborious.To directly type HRVs in nasal secretions of infants with frequent respiratory illnesses, we developed a sensitive molecular typing assay based on phylogenetic comparisons of a 260-bp variable sequence in the 5' noncoding region with homologous sequences of the 101 known serotypes. Nasal samples from 26 infants were first tested with a multiplex PCR assay for respiratory viruses, and HRV was the most common virus found (108 of 181 samples). Typing was completed for 101 samples and 103 HRVs were identified. Surprisingly, 54 (52.4%) HRVs did not match any of the known serotypes and had 12-35% nucleotide divergence from the nearest reference HRVs. Of these novel viruses, 9 strains (17 HRVs) segregated from HRVA, HRVB and human enterovirus into a distinct genetic group ("C"). None of these new strains could be cultured in traditional cell lines.By molecular analysis, over 50% of HRV detected in sick infants were previously unrecognized strains, including 9 strains that may represent a new HRV group. These findings indicate that the number of HRV strains is considerably larger than the 101 serotypes identified with traditional diagnostic techniques, and provide evidence of a new HRV group

Computational modeling with spiking neural networks

This chapter reviews recent developments in the area of spiking neural networks (SNN) and summarizes the main contributions to this research field. We give background information about the functioning of biological neurons, discuss the most important mathematical neural models along with neural encoding techniques, learning algorithms, and applications of spiking neurons. As a specific application, the functioning of the evolving spiking neural network (eSNN) classification method is presented in detail and the principles of numerous eSNN based applications are highlighted and discussed

The generation of phase differences and frequency changes in a network model of inferior olive subthreshold oscillations

This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the Creative Commons CC0 public domain dedicationIt is commonly accepted that the Inferior Olive (IO) provides a timing signal to the cerebellum. Stable subthreshold oscillations in the IO can facilitate accurate timing by phase-locking spikes to the peaks of the oscillation. Several theoretical models accounting for the synchronized subthreshold oscillations have been proposed, however, two experimental observations remain an enigma. The first is the observation of frequent alterations in the frequency of the oscillations. The second is the observation of constant phase differences between simultaneously recorded neurons. In order to account for these two observations we constructed a canonical network model based on anatomical and physiological data from the IO. The constructed network is characterized by clustering of neurons with similar conductance densities, and by electrical coupling between neurons. Neurons inside a cluster are densely connected with weak strengths, while neurons belonging to different clusters are sparsely connected with stronger connections. We found that this type of network can robustly display stable subthreshold oscillations. The overall frequency of the network changes with the strength of the inter-cluster connections, and phase differences occur between neurons of different clusters. Moreover, the phase differences provide a mechanistic explanation for the experimentally observed propagating waves of activity in the IO. We conclude that the architecture of the network of electrically coupled neurons in combination with modulation of the inter-cluster coupling strengths can account for the experimentally observed frequency changes and the phase differences.Peer reviewedFinal Published versio