Periodicities in the Hodgkin-Huxley model and versions of this model with stochastic input

A field of computational neuroscience develops mathematical models to describe neuronal systems. The aim is to better understand the nervous system. Historically, the integrate-and-fire model, developed by Lapique in 1907, was the first model describing a neuron. In 1952 Hodgkin and Huxley [8] described the so called Hodgkin-Huxley model in the article “A Quantitative Description of Membrane Current and Its Application to Conduction and Excitation in Nerve”. The Hodgkin-Huxley model is one of the most successful and widely-used biological neuron models. Based on experimental data from the squid giant axon, Hodgkin and Huxley developed their mathematical model as a four-dimensional system of first-order ordinary differential equations. One of these equations characterizes the membrane potential as a process in time, whereas the other three equations depict the opening and closing state of sodium and potassium ion channels. The membrane potential is proportional to the sum of ionic current flowing across the membrane and an externally applied current. For various types of external input the membrane potential behaves differently. This thesis considers the following three types of input: (i) Rinzel and Miller [15] calculated an interval of amplitudes for a constant applied current, where the membrane potential is repetitively spiking; (ii) Aihara, Matsumoto and Ikegaya [1] said that dependent on the amplitude and the frequency of a periodic applied current the membrane potential responds periodically; (iii) Izhikevich [12] stated that brief pulses of positive and negative current with different amplitudes and frequencies can lead to a periodic response of the membrane potential. In chapter 1 the Hodgkin-Huxley model is introduced according to Izhikevich [12]. Besides the definition of the model, several biological and physiological notes are made, and further concepts are described by examples. Moreover, the numerical methods to solve the equations of the Hodgkin-Huxley model are presented which were used for the computer simulations in chapter 2 and chapter 3. In chapter 2 the statements for the three different inputs (i), (ii) and (iii) will be verified, and periodic behavior for the inputs (ii) and (iii) will be investigated. In chapter 3 the inputs are embedded in an Ornstein-Uhlenbeck process to see the influence of noise on the results of chapter 2.

Simulating event related potentials in tasks involving conflict resolution: a neural network

In this thesis, the main Executive Control theories are exposed. Methods typical of Cognitive and Computational Neuroscience are introduced and the role of behavioural tasks involving conflict resolution in the response elaboration, after the presentation of a stimulus to the subject, are highlighted. In particular, the Eriksen Flanker Task and its variants are discussed. Behavioural data, from scientific literature, are illustrated in terms of response times and error rates. During experimental behavioural tasks, EEG is registered simultaneously. Thanks to this, event related potential, related with the current task, can be studied. Different theories regarding relevant event related potential in this field - such as N2, fERN (feedback Error Related Negativity) and ERN (Error Related Negativity) – are introduced. The aim of this thesis is to understand and simulate processes regarding Executive Control, including performance improvement, error detection mechanisms, post error adjustments and the role of selective attention, with the help of an original neural network model. The network described here has been built with the purpose to simulate behavioural results of a four choice Eriksen Flanker Task. Model results show that the neural network can simulate response times, error rates and event related potentials quite well. Finally, results are compared with behavioural data and discussed in light of the mentioned Executive Control theories. Future perspective for this new model are outlined.

Deep learning for computer vision: a comparison between convolutional neural networks and hierarchical temporal memories on object recognition tasks

In recent years, Deep Learning techniques have shown to perform well on a large variety of problems both in Computer Vision and Natural Language Processing, reaching and often surpassing the state of the art on many tasks. The rise of deep learning is also revolutionizing the entire field of Machine Learning and Pattern Recognition pushing forward the concepts of automatic feature extraction and unsupervised learning in general. However, despite the strong success both in science and business, deep learning has its own limitations. It is often questioned if such techniques are only some kind of brute-force statistical approaches and if they can only work in the context of High Performance Computing with tons of data. Another important question is whether they are really biologically inspired, as claimed in certain cases, and if they can scale well in terms of "intelligence". The dissertation is focused on trying to answer these key questions in the context of Computer Vision and, in particular, Object Recognition, a task that has been heavily revolutionized by recent advances in the field. Practically speaking, these answers are based on an exhaustive comparison between two, very different, deep learning techniques on the aforementioned task: Convolutional Neural Network (CNN) and Hierarchical Temporal memory (HTM). They stand for two different approaches and points of view within the big hat of deep learning and are the best choices to understand and point out strengths and weaknesses of each of them. CNN is considered one of the most classic and powerful supervised methods used today in machine learning and pattern recognition, especially in object recognition. CNNs are well received and accepted by the scientific community and are already deployed in large corporation like Google and Facebook for solving face recognition and image auto-tagging problems. HTM, on the other hand, is known as a new emerging paradigm and a new meanly-unsupervised method, that is more biologically inspired. It tries to gain more insights from the computational neuroscience community in order to incorporate concepts like time, context and attention during the learning process which are typical of the human brain. In the end, the thesis is supposed to prove that in certain cases, with a lower quantity of data, HTM can outperform CNN.

Synaptic regulation of spike firing in interneurons of the striatum in vivo

The striatum, the major input nucleus of the basal ganglia, is numerically dominated by a single class of principal neurons, the GABAergic spiny projection neuron (SPN) that has been extensively studied both in vitro and in vivo. Much less is known about the sparsely distributed interneurons, principally the cholinergic interneuron (CIN) and the GABAergic fast-spiking interneuron (FSI). Here, we summarize results from two recent studies on these interneurons where we used in vivo intracellular recording techniques in urethane-anaesthetized rats (Schulz et al., J Neurosci 31[31], 2011; J Physiol, in press). Interneurons were identified by their characteristic responses to intracellular current steps and spike waveforms. Spontaneous spiking contained a high proportion (~45%) of short inter-spike intervals (ISI) of <30 ms in FSIs, but virtually none in CINs. Spiking patterns in CINs covered a broad spectrum ranging from regular tonic spiking to phasic activity despite very similar unimodal membrane potential distributions across neurons. In general, phasic spiking activity occurred in phase with the slow ECoG waves, whereas CINs exhibiting tonic regular spiking were little affected by afferent network activity. In contrast, FSIs exhibited transitions between Down and Up states very similar to SPNs. Compared to SPNs, the FSI Up state membrane potential was noisier and power spectra exhibited significantly larger power at frequencies in the gamma range (55-95 Hz). Cortical-evoked inputs had faster dynamics in FSIs than SPNs and the membrane potential preceding spontaneous spike discharge exhibited short and steep trajectories, suggesting that fast input components controlled spike output in FSIs. Intrinsic resonance mechanisms may have further enhanced the sensitivity of FSIs to fast oscillatory inputs. Induction of an activated ECoG state by local ejection of bicuculline into the superior colliculus, resulted in increased spike frequency in both interneuron classes without changing the overall distribution of ISIs. This manipulation also made CINs responsive to a light flashed into the contralateral eye. Typically, the response consisted of an excitation at short latency followed by a pause in spike firing, via an underlying depolarization-hyperpolarization membrane sequence. These results highlight the differential sensitivity of striatal interneurons to afferent synaptic signals and support a model where CINs modulate the striatal network in response to salient sensory bottom-up signals, while FSIs serve gating of top-down signals from the cortex during action selection and reward-related learning.

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current--is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of +/-2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

Modulating the granularity of category formation by global cortical states

The unsupervised categorization of sensory stimuli is typically attributed to feedforward processing in a hierarchy of cortical areas. This purely sensory-driven view of cortical processing, however, ignores any internal modulation, e.g., by top-down attentional signals or neuromodulator release. To isolate the role of internal signaling on category formation, we consider an unbroken continuum of stimuli without intrinsic category boundaries. We show that a competitive network, shaped by recurrent inhibition and endowed with Hebbian and homeostatic synaptic plasticity, can enforce stimulus categorization. The degree of competition is internally controlled by the neuronal gain and the strength of inhibition. Strong competition leads to the formation of many attracting network states, each being evoked by a distinct subset of stimuli and representing a category. Weak competition allows more neurons to be co-active, resulting in fewer but larger categories. We conclude that the granularity of cortical category formation, i.e., the number and size of emerging categories, is not simply determined by the richness of the stimulus environment, but rather by some global internal signal modulating the network dynamics. The model also explains the salient non-additivity of visual object representation observed in the monkey inferotemporal (IT) cortex. Furthermore, it offers an explanation of a previously observed, demand-dependent modulation of IT activity on a stimulus categorization task and of categorization-related cognitive deficits in schizophrenic patients.

Introduction to Realistic Neural Modeling

This document corresponds to the tutorial on realistic neural modeling given by David Beeman at WAM-BAMM*05, the first annual meeting of the World Association of Modelers (WAM) Biologically Accurate Modeling Meeting (BAMM) on March 31, 2005 in San Antonio, TX. Part I - Introduction to Realistic Neural Modeling for the Beginner: This is a general overview and introduction to compartmental cell modeling and realistic network simulation for the beginner. Although examples are drawn from GENESIS simulations, the tutorial emphasizes the general modeling approach, rather than the details of using any particular simulator. Part II - Getting Started with Modeling Using GENESIS: This builds upon the background of Part I to describe some details of how this approach is used to construct cell and network simulations in GENESIS. It serves as an introduction and roadmap to the extended hands-on GENESIS Modeling Tutorial.

GENESIS Modeling Tutorial

This tutorial is intended to be a "quick start" to creating simulations with GENESIS. It should give you the tools and enough information to let you quickly begin creating cells and networks with GENESIS, making use of the provided example simulations. Advanced topics are covered by appropriate links to the Advanced Tutorials on Realistic Neural Modeling.

Realistic Single Cell Modeling – from Experiment to Simulation

This tutorial gives a step by step explanation of how one uses experimental data to construct a biologically realistic multicompartmental model. Special emphasis is given on the many ways that this process can be imprecise. The tutorial is intended for both experimentalists who want to get into computer modeling and for computer scientists who use abstract neural network models but are curious about biological realistic modeling. The tutorial is not dependent on the use of a specific simulation engine, but rather covers the kind of data needed for constructing a model, how they are used, and potential pitfalls in the process.

Teaching Cognitive Modeling Using PDP++

PDP++ is a freely available, open source software package designed to support the development, simulation, and analysis of research-grade connectionist models of cognitive processes. It supports most popular parallel distributed processing paradigms and artificial neural network architectures, and it also provides an implementation of the LEABRA computational cognitive neuroscience framework. Models are typically constructed and examined using the PDP++ graphical user interface, but the system may also be extended through the incorporation of user-written C++ code. This article briefly reviews the features of PDP++, focusing on its utility for teaching cognitive modeling concepts and skills to university undergraduate and graduate students. An informal evaluation of the software as a pedagogical tool is provided, based on the author’s classroom experiences at three research universities and several conference-hosted tutorials.

Interactive Curriculum Based on Models of Mind & Brain

What does it mean for curriculum to be interactive? It encourages student engagement and active participation in both individual and group work. It offers teachers a coherent set of materials to choose from that can enhance their classes. It is the product of on-going development and continuous improvement based on research and feedback from the field. This paper will introduce work in progress from the Center for Excellence in Education, Science, and Technology (CELEST), an NSF Science of Learning Center. Among its many goals, CELEST is developing a unique educational curriculum, an interactive curriculum based upon models of mind and brain. Teachers, administrators, and governments are naturally concerned with how students learn. Students are greatly concerned about how minds work, including how to learn. CELEST aims to introduce curricula that not only meet current U.S. standards in mathematics, science, and psychology but also influence plans to improve those standards. Software and support materials are in development and available at http://cns.bu.edu/celest/private/. Interested parties are invited to contact the author for access.

Modulation of orientation-selective neurons by motion: when additive, when multiplicative?

The recurrent interaction among orientation-selective neurons in the primary visual cortex (V1) is suited to enhance contours in a noisy visual scene. Motion is known to have a strong pop-up effect in perceiving contours, but how motion-sensitive neurons in V1 support contour detection remains vastly elusive. Here we suggest how the various types of motion-sensitive neurons observed in V1 should be wired together in a micro-circuitry to optimally extract contours in the visual scene. Motion-sensitive neurons can be selective about the direction of motion occurring at some spot or respond equally to all directions (pandirectional). We show that, in the light of figure-ground segregation, direction-selective motion neurons should additively modulate the corresponding orientation-selective neurons with preferred orientation orthogonal to the motion direction. In turn, to maximally enhance contours, pandirectional motion neurons should multiplicatively modulate all orientation-selective neurons with co-localized receptive fields. This multiplicative modulation amplifies the local V1-circuitry among co-aligned orientation-selective neurons for detecting elongated contours. We suggest that the additive modulation by direction-specific motion neurons is achieved through synaptic projections to the somatic region, and the multiplicative modulation by pandirectional motion neurons through projections to the apical region of orientation-specific pyramidal neurons. For the purpose of contour detection, the V1-intrinsic integration of motion information is advantageous over a downstream integration as it exploits the recurrent V1-circuitry designed for that task.