THE RESONATE-AND-FIRE NEURON: TIME DEPENDENT AND FREQUENCY SELECTIVE NEURONS IN NEURAL NETWORKS

The means through which the nervous system perceives its environment is one of the most fascinating questions in contemporary science. Our endeavors to comprehend the principles of neural science provide an instance of how biological processes may inspire novel methods in mathematical modeling and engineering. The application ofmathematical models towards understanding neural signals and systems represents a vibrant field of research that has spanned over half a century. During this period, multiple approaches to neuronal modeling have been adopted, and each approach is adept at elucidating a specific aspect of nervous system function. Thus while bio-physical models have strived to comprehend the dynamics of actual physical processes occurring within a nerve cell, the phenomenological approach has conceived models that relate the ionic properties of nerve cells to transitions in neural activity. Further-more, the field of neural networks has endeavored to explore how distributed parallel processing systems may become capable of storing memory. Through this project, we strive to explore how some of the insights gained from biophysical neuronal modeling may be incorporated within the field of neural net-works. We specifically study the capabilities of a simple neural model, the Resonate-and-Fire (RAF) neuron, whose derivation is inspired by biophysical neural modeling. While reflecting further biological plausibility, the RAF neuron is also analytically tractable, and thus may be implemented within neural networks. In the following thesis, we provide a brief overview of the different approaches that have been adopted towards comprehending the properties of nerve cells, along with the framework under which our specific neuron model relates to the field of neuronal modeling. Subsequently, we explore some of the time-dependent neurocomputational capabilities of the RAF neuron, and we utilize the model to classify logic gates, and solve the classic XOR problem. Finally we explore how the resonate-and-fire neuron may be implemented within neural networks, and how such a network could be adapted through the temporal backpropagation algorithm.

On Time Series Analysis of Public Health and Biomedical Data

A time series is a sequence of observations made over time. Examples in public health include daily ozone concentrations, weekly admissions to an emergency department or annual expenditures on health care in the United States. Time series models are used to describe the dependence of the response at each time on predictor variables including covariates and possibly previous values in the series. Time series methods are necessary to account for the correlation among repeated responses over time. This paper gives an overview of time series ideas and methods used in public health research.

Concentration- and time-dependent effects of the synthetic estrogen, 17alpha-ethinylestradiol, on reproductive capabilities of the zebrafish, Danio rerio

Partial or full life-cycle tests are needed to assess the potential of endocrine-disrupting compounds (EDCs) to adversely affect development and reproduction of fish. Small fish species such as zebrafish, Danio rerio, are under consideration as model organisms for appropriate test protocols. The present study examines how reproductive effects resulting from exposure of zebrafish to the synthetic estrogen 17alpha-ethinylestradiol (EE2) vary with concentration (0.05 to 10 ng EE2 L(-1), nominal), and with timing/duration of exposure (partial life-cycle, full life-cycle, and two-generation exposure). Partial life-cycle exposure of the parental (F1) generation until completion of gonad differentiation (0-75 d postfertilization, dpf) impaired juvenile growth, time to sexual maturity, adult fecundity (egg production/female/day), and adult fertilization success at 1.1 ng EE2 L(-1) and higher. Lifelong exposure of the F1 generation until 177 dpf resulted in lowest observed effect concentrations (LOECs) for time to sexual maturity, fecundity, and fertilization success identical to those of the developmental test (0-75 dpf), but the slope of the concentration-response curve was steeper. Reproduction of zebrafish was completely inhibited at 9.3 ng EE2 L(-1), and this was essentially irreversible as a 3-mo depuration restored fertilization success to only a very low rate. Accordingly, elevated endogenous vitellogenin (VTG) synthesis and degenerative changes in gonad morphology persisted in depurated zebrafish. Full life-cycle exposure of the filial (F2) generation until 162 dpf impaired growth, delayed onset of spawning and reduced fecundity and fertilization success at 2.0 ng EE2 L(-1). In conclusion, results show that the impact of estrogenic agents on zebrafish sexual development and reproductive functions as well as the reversibility of effects, varies with exposure concentration (reversibility at < or = 1.1 ng EE2 L(-1) and irreversibility at 9.3 ng EE2 L(-1)), and between partial and full life-cycle exposure (exposure to 10 ng EE2 L(-1) during critical period exerted no permanent effect on sexual differentiation, but life-cycle exposure did).

Statistical evaluation of time-dependent metabolite concentrations: estimation of post-mortem intervals based on in situ 1H-MRS of the brain

Knowledge of the time interval from death (post-mortem interval, PMI) has an enormous legal, criminological and psychological impact. Aiming to find an objective method for the determination of PMIs in forensic medicine, 1H-MR spectroscopy (1H-MRS) was used in a sheep head model to follow changes in brain metabolite concentrations after death. Following the characterization of newly observed metabolites (Ith et al., Magn. Reson. Med. 2002; 5: 915-920), the full set of acquired spectra was analyzed statistically to provide a quantitative estimation of PMIs with their respective confidence limits. In a first step, analytical mathematical functions are proposed to describe the time courses of 10 metabolites in the decomposing brain up to 3 weeks post-mortem. Subsequently, the inverted functions are used to predict PMIs based on the measured metabolite concentrations. Individual PMIs calculated from five different metabolites are then pooled, being weighted by their inverse variances. The predicted PMIs from all individual examinations in the sheep model are compared with known true times. In addition, four human cases with forensically estimated PMIs are compared with predictions based on single in situ MRS measurements. Interpretation of the individual sheep examinations gave a good correlation up to 250 h post-mortem, demonstrating that the predicted PMIs are consistent with the data used to generate the model. Comparison of the estimated PMIs with the forensically determined PMIs in the four human cases shows an adequate correlation. Current PMI estimations based on forensic methods typically suffer from uncertainties in the order of days to weeks without mathematically defined confidence information. In turn, a single 1H-MRS measurement of brain tissue in situ results in PMIs with defined and favorable confidence intervals in the range of hours, thus offering a quantitative and objective method for the determination of PMIs.

Development of record-breaking statistics for climatological time-series analysis

The number of record-breaking events expected to occur in a strictly stationary time-series depends only on the number of values in the time-series, regardless of distribution. This holds whether the events are record-breaking highs or lows and whether we count from past to present or present to past. However, these symmetries are broken in distinct ways by trends in the mean and variance. We define indices that capture this information and use them to detect weak trends from multiple time-series. Here, we use these methods to answer the following questions: (1) Is there a variability trend among globally distributed surface temperature time-series? We find a significant decreasing variability over the past century for the Global Historical Climatology Network (GHCN). This corresponds to about a 10% change in the standard deviation of inter-annual monthly mean temperature distributions. (2) How are record-breaking high and low surface temperatures in the United States affected by time period? We investigate the United States Historical Climatology Network (USHCN) and find that the ratio of record-breaking highs to lows in 2006 increases as the time-series extend further into the past. When we consider the ratio as it evolves with respect to a fixed start year, we find it is strongly correlated with the ensemble mean. We also compare the ratios for USHCN and GHCN (minus USHCN stations). We find the ratios grow monotonically in the GHCN data set, but not in the USHCN data set. (3) Do we detect either mean or variance trends in annual precipitation within the United States? We find that the total annual and monthly precipitation in the United States (USHCN) has increased over the past century. Evidence for a trend in variance is inconclusive.

Time-dependent hierarchical organization of spatial working memory: a transcranial magnetic stimulation study

The performance of memory-guided saccades with two different delays (3 and 30 s of memorization) was studied in seven healthy subjects. Double-pulse transcranial magnetic stimulation (dTMS) with an interstimulus interval of 100 ms was applied over the right dorsolateral prefrontal cortex (DLPFC) early (1 s after target presentation) and late (28 s after target presentation). Early stimulation significantly increased in both delays the percentage of error in amplitude (PEA) of contralateral memory-guided saccades compared to the control experiment without stimulation. dTMS applied late in the delay had no significant effect on PEA. Furthermore, we found a significantly smaller effect of early stimulation in the long-delay paradigm. These results suggest a time-dependent hierarchical organization of the spatial working memory with a functional dominance of DLPFC during the early memorization, independent from the memorization delay. For a long memorization delay, however, working memory seems to have an additional, DLPFC-independent component.

Radiation metabolomics. 2. Dose- and time-dependent urinary excretion of deaminated purines and pyrimidines after sublethal gamma-radiation exposure in mice

Gamma-radiation exposure of humans is a major public health concern as the threat of terrorism and potential hostile use of radiological devices increases worldwide. We report here the effects of sublethal gamma-radiation exposure on the mouse urinary metabolome determined using ultra-performance liquid chromatography-coupled time-of-flight mass spectrometry-based metabolomics. Five urinary biomarkers of sublethal radiation exposure that were statistically significantly elevated during the first 24 h after exposure to doses ranging from 1 to 3 Gy were unequivocally identified by tandem mass spectrometry. These are deaminated purine and pyrimidine derivatives, namely, thymidine, 2'-deoxyuridine, 2'-deoxyxanthosine, xanthine and xanthosine. Furthermore, the aminopyrimidine 2'-deoxycytidine appeared to display reduced urinary excretion at 2 and 3 Gy. The elevated biomarkers displayed a time-dependent excretion, peaking in urine at 8-12 h but returning to baseline by 36 h after exposure. It is proposed that 2'-deoxyuridine and 2'-deoxyxanthosine arise as a result of gamma irradiation by nitrosative deamination of 2'-deoxycytidine and 2'-deoxyguanosine, respectively, and that this further leads to increased synthesis of thymidine, xanthine and xanthosine. The urinary excretion of deaminated purines and pyrimidines, at the expense of aminopurines and aminopyrimidines, appears to form the core of the urinary radiation metabolomic signature of mice exposed to sublethal doses of ionizing radiation.

Campylobacter monitoring in German broiler flocks: an explorative time series analysis

Campylobacter, a major zoonotic pathogen, displays seasonality in poultry and in humans. In order to identify temporal patterns in the prevalence of thermophilic Campylobacter spp. in a voluntary monitoring programme in broiler flocks in Germany and in the reported human incidence, time series methods were used. The data originated between May 2004 and June 2007. By the use of seasonal decomposition, autocorrelation and cross-correlation functions, it could be shown that an annual seasonality is present. However, the peak month differs between sample submission, prevalence in broilers and human incidence. Strikingly, the peak in human campylobacterioses preceded the peak in broiler prevalence in Lower Saxony rather than occurring after it. Significant cross-correlations between monthly temperature and prevalence in broilers as well as between human incidence, monthly temperature, rainfall and wind-force were identified. The results highlight the necessity to quantify the transmission of Campylobacter from broiler to humans and to include climatic factors in order to gain further insight into the epidemiology of this zoonotic disease.