http://precedings.nature.com/tags/Mathematical%20model Recently posted documents tagged with 'Mathematical model' Nature Publishing Group en Nature Precedings http://precedings.nature.com/images/header_logo.gif http://precedings.nature.com http://precedings.nature.com/documents/3348/version/1 The problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is introduced that simulates the internal information processing of brain compartments. Synaptic potentials are integrated over small number of realistically coupled neurons to obtain macroscopic quantities. The striatal complex, an important part of the basal ganglia circuit in the brain for regulating motor activity, has been investigated as an example for the validation of the model. http://precedings.nature.com/documents/3348/version/1 Fri, 19 Jun 2009 14:06:35 UTC Averaging Transformations of Synaptic Potentials on Networks hdl:10101/npre.2009.3348.1 2009-06-19 Hamid Reza Noori Nature Precedings 2009-06-19T14:06:35Z Manuscript Neuroscience http://creativecommons.org/licenses/by/3.0/ http://precedings.nature.com/documents/1703/version/1 The neuron, when considered as a signal processing device, itsinputs are the frequency of pulses received at the synapses, and its output is the frequency of action potentials generated- in essence, a neuron is a pulse frequency signal processing device. In comparison, electrical devices use either digital or analog signals for communication or processing, and the mathematics behind these subjects is well understood. However, in regards to pulse frequency processing devices, there has not yet been a clear and persuasive mathematical model to describe the functions of neurons. It goes without saying that such a model is very important, not only for understanding neuron and neural system behavior, but also for undeveloped potential applications in industry. This paper proposes a method for obtaining the mathematical relationship between the input and output signals of a neuron based on physiological facts. The proposed method focuses on the currents across the postsynaptic membrane of each synapse, and the key is to recognize that the net charge across the whole membrane of a neuron over each action potential cycle must equal to zero. By analyzing the relationship between the input of a synapse and the currents across the postsynaptic membranes, a dynamic pulse frequency model of the neuron can be obtained. Here, we show that the transfer function of a neuron depends on the function of thepostsynaptic current of each synapse in resting state, which can be found by detecting the postsynaptic current when a pulse is received at the synapse. The transfer function of a typical neuron generally includes addition and subtraction of feedthrough terms and/or first order lag functions. To focus on the most basic characteristics of a neuron, accommodation, adaptation, learning, etc. are not discussed in this paper. http://precedings.nature.com/documents/1703/version/1 Wed, 26 Mar 2008 15:35:23 UTC A Mathematical Model of a Neuron with Synapses based on Physiology hdl:10101/npre.2008.1703.1 2008-05-07 Xiaolin Zhang Nature Precedings 2008-03-26T15:35:23Z Manuscript Neuroscience http://creativecommons.org/licenses/by/3.0/ http://precedings.nature.com/documents/1539/version/1 Most malaria-endemic countries are implementing a change in antimalarial drug policy to artemisinin combination therapy (ACT). The impact of different drug choices and implementation strategies is uncertain. A comprehensive model was constructed incorporating important epidemiological and biological factors and used to illustrate the spread of resistance in low and high transmission settings. The model predicts robustly that in low transmission settings drug resistance spreads faster than in high transmission settings, and that in low transmission areas ACTs slows the spread of drug resistance to a partner drug, especially at high coverage rates. This effect decreases exponentially with increasing delay in deploying the ACT and decreasing rates of coverage. A major obstacle to achieving the benefits of high coverage is the current cost of the drugs. This argues strongly for a global subsidy to make ACTs generally available and affordable in endemic areas. http://precedings.nature.com/documents/1539/version/1 Thu, 24 Jan 2008 14:53:00 UTC The spread of antimalarial drug resistance: A mathematical model with practical implications for ACT drug policies hdl:10101/npre.2008.1539.1 2008-08-18 Wirichada Pongtavornpinyo Nature Precedings 2008-01-24T14:53:00Z Manuscript Microbiology Pharmacology Bioinformatics http://creativecommons.org/licenses/by/3.0/ http://dx.doi.org/10.1038/npre.2007.1373.1 The Centers for Disease Control (CDC) is currently attempting to eliminate syphilis in the United States (US); to ensure that their control strategies will be effective it is important to understand the transmission dynamics of syphilis. Epidemics of certain infectious diseases (e.g., influenza) can rise and fall with a well-defined periodicity; this cycling behavior is important because it can have significant implications for the design and effectiveness of control strategies. Here we discuss the methodology that has been used to identify epidemic cycles in longitudinal data sets, and the endogenous and exogenous mechanisms that generate cycling. We then examine the recently proposed hypothesis that syphilis epidemics cycle. This hypothesis was proposed based upon the results of a spectral analysis of a longitudinal data set that had been collected by the (CDC), and the analysis of a syphilis transmission model. We use spectral analysis to reanalyze the CDC’s data set, as well as to analyze a longitudinal mortality data set provided by the CDC. We also use published transmission models to predict the expected dynamics of syphilis epidemics. In contrast to the previous findings we find that: (i) that neither of the CDC’s data sets provide compelling evidence that syphilis epidemics cycle and (ii) published transmission models predict that syphilis epidemics should monotonically decrease (as a function of the treatment rate) rather than cycle. We explain the reasons why previous authors had proposed that syphilis epidemics cycle. Finally, we discuss the implications of our findings regarding the transmission dynamics of syphilis for the CDC’s elimination plan. http://dx.doi.org/10.1038/npre.2007.1373.1 Fri, 30 Nov 2007 18:29:36 UTC The transmission dynamics of syphilis and the CDC’s elimination plan doi:10.1038/npre.2007.1373.1 2007-11-30 Virginie Supervie Nature Precedings 2007-11-30T18:29:36Z Manuscript Ecology http://creativecommons.org/licenses/by/3.0/