Biological neurons are connected to each other in a complex, recurrent fashion. These connections are, unlike most artificial neural networks, sparse and most likely, specific. It is not known how information is transmitted through such sparsely connected networks. It is also unknown what the computational functions, if any, of these specific connectivity patterns are.The interactions of neurons in a small network can be often reduced to simple models such as the Ising model. The statistical mechanics of such simple systems are wellcharacterized theoretically. There have been some recent evidence that suggests that dynamics of arbitrary neuronal networks can be reduced to pairwise interactions Schneidman et al, 2006; Shlens et al, 2006. It's unknown, however, whether such descriptive dynamics impart any important computational function. With the emergence of twophoton microscopy and calcium imaging, we now have powerful experimental methods with which to test the new theories regarding neuronal networks.While many neurotheorists prefer models with reduced complexity, others argue that uncovering structure function relations depends on including as much neuronal and network structure as possible.
Models of this type are typically built in large simulations platforms like GENESIS software or Neuron software. There have been some attempts to provide unified methods that bridge, and integrate, these levels of complexity Eliasmith & Anderson, 2003.Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force.It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.This ability to make macroscopic predictions based on microscopic properties is the main asset of statistical mechanics over thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.
Computational modeling of higher cognitive functions has only begun recently. Experimental data comes primarily from single unit recording in primates. The frontal lobe and parietal lobe function as integrators of information from multiple sensory modalities. There are some tentative ideas regarding how simple mutually inhibitory functional circuits in these areas may carry out biologically relevant computation Machens et al, 2005.The brain seems to be able to discriminate and adapt particularly well in certain contexts. For instance, human beings seem to have an enormous capacity for memorizing and recognizing faces. One of the key goals of computational neuroscience is to dissect how biological systems carry out these complex computations efficiently and potentially replicate these processes in building intelligent machines.The ultimate goal of neuroscience is to be able to explain the every day experience of conscious life. Francis Crick and Christof Koch made some attempts in formulating a consistent framework for future work in neural correlates of consciousness NCC, though much of the work in this field remains speculative. for a review, see Koch and Crick, 2003.The parietal lobe is a lobe in the brain. It is positioned above superior to the occipital lobe and behind posterior to the frontal lobe.
The parietal lobe integrates sensory information from different modalities, particularly determining spatial sense and navigation. For example, it comprises somatosensory cortex and the dorsal stream of the visual system. This enables regions of the parietal cortex to map objects perceived visually into body coordinate positions.The parietal lobe is defined by four anatomical boundaries the central sulcus separates the parietal lobe from the frontal lobe; the parietooccipital sulcus separates the parietal and occipital lobe; the lateral sulcus sylvian fissure is the most lateral boundary separating it from the temporal lobe; and the medial longitudinal fissure divides the two hemispheres.Immediately posterior to the central sulcus, and the most anterior part of the parietal lobe, is the postcentral gyrus Brodmann area 3, the primary somatosensory cortical area. Dividing this and the posterior parietal cortex is the postcentral sulcus.The posterior parietal cortex can be subdivided into the superior parietal lobule Brodmann areas 5 + 7 and the inferior parietal lobule 39 + 40, separated by the intraparietal sulcus IP. The intraparietal sulcus and adjacent gyri are essential in guidance of limb and eye movement, and based on cytoarchitectural and functional differences is further divided into medial MIP, lateral LIP, ventral VIP, and anterior AIP areas.
In order to have a description of what constitutes intelligent behavior, one must study behavior itself. This type of research is closely tied to that in cognitive psychology and psychophysics. By measuring behavioral responses to different stimuli, one can understand something about how those stimuli are processed.Reaction time. The time between the presentation of a stimulus and an appropriate response can indicate differences between two cognitive processes, and can indicate some things about their nature. For example, if in a search task the reaction times vary proportionally with the number of elements, then it is evident that this cognitive process of searching involves serial instead of parallel processing.Psychophysical responses. Psychophysical experiments are an old psychological technique, which has been adopted by cognitive psychology. They typically involve making judgments of some physical property, e.g. the loudness of a sound. Correlation of subjective scales between individuals can show cognitive or sensory biases as compared to actual physical measurements. Some examples include.This methodology is used to study a variety of cognitive processes, most notably visual perception and language processing. The fixation point of the eyes is linked to an individual's focus of attention. Thus, by monitoring eye movements, we can study what information is being processed at a given time. Eye tracking allows us to study cognitive processes on extremely short time scales. Eye movements reflect online decision making during a task, and they provide us with some insight into the ways in which those decisions may be processed.
Image of the human head with the brain. The arrow indicates the position of the hypothalamus.Brain imaging involves analyzing activity within the brain while performing various cognitive tasks. This allows us to link behavior and brain function to help understand how information is processed. Different types of imaging techniques vary in their temporal timebased and spatial locationbased resolution. Brain imaging is often used in cognitive neuroscience.Single photon emission computed tomography and Positron emission tomography. SPECT and PET use radioactive isotopes, which are injected into the subject's bloodstream and taken up by the brain. By observing which areas of the brain take up the radioactive isotope, we can see which areas of the brain are more active than other areas. PET has similar spatial resolution to fMRI, but it has extremely poor temporal resolution.Electroencephalography.
EEG measures the electrical fields generated by large populations of neurons in the cortex by placing a series of electrodes on the scalp of the subject. This technique has an extremely high temporal resolution, but a relatively poor spatial resolution.Functional magnetic resonance imaging. fMRI measures the relative amount of oxygenated blood flowing to different parts of the brain. More oxygenated blood in a particular region is assumed to correlate with an increase in neural activity in that part of the brain. This allows us to localize particular functions within different brain regions. fMRI has moderate spatial and temporal resolution.Optical imaging. This technique uses infrared transmitters and receivers to measure the amount of light reflectance by blood near different areas of the brain. Since oxygenated and deoxygenated blood reflects light by different amounts, we can study which areas are more active i.e., those that have more oxygenated blood. Optical imaging has moderate temporal resolution, but poor spatial resolution. It also has the advantage that it is extremely safe and can be used to study infants' brains.Magnetoencephalography. MEG measures magnetic fields resulting from cortical activity. It is similar to EEG, except that it has improved spatial resolution since the magnetic fields it measures are not as blurred or attenuated by the scalp, meninges and so forth as the electrical activity measured in EEG is. MEG uses SQUID sensors to detect tiny magnetic fields.
Research in computational neuroscience can be roughly categorized into several lines of inquiries. Most computational neuroscientists collaborate closely with experimentalists in analyzing novel data and synthesizing new models of biological phenomena.Even single neurons have complex biophysical characteristics. Hodgkin and Huxley's original model only employed two voltagesensitive currents, the fastacting sodium and the inwardrectifying potassium. Though successful in predicting the timing and qualitative features of the action potential, it nevertheless failed to predict a number of important features such as adaptation and shunting. Scientists now believe that there are a wide variety of voltagesensitive currents, and the implications of the differing dynamics, modulations and sensitivity of these currents is an important topic of computational neuroscience for reference, see Johnston and Wu, 1994.
The computational functions of complex dendrites are also under intense investigation. There is a large body of literature regarding how different currents interact with geometric properties of neurons for reference, see Koch, 1998.Some models are also tracking biochemical pathways at very small scales such as spines or synaptic clefts.How do axons and dendrites form during development How do axons know where to target and how to reach these targets How do neurons migrate to the proper position in the central and peripheral systems How do synapses form We know from molecular biology that distinct parts of the nervous system release distinct chemical cues, from growth factors to hormones that modulate and influence the growth and development of functional connections between neurons.Theoretical investigations into the formation and patterning of synaptic connection and morphology is still nascent. One hypothesis that has recently garnered some attention is the minimal wiring hypothesis, which postulates that the formation of axons and dendrites effectively minimizes resource allocation while maintaining maximal information storage. for a review, see Chklovskii, 2004.
Computational neuroscience is an interdisciplinary science that links the diverse fields of neuroscience, cognitive science, electrical engineering, computer science, physics and mathematics. Historically, the term was introduced by Eric L. Schwartz, who organized a conference, held in 1985 in Carmel, California at the request of the Systems Development Foundation, to provide a summary of the current status of a field which until that point was referred to by a variety of names, such as neural modeling, brain theory and neural networks. The proceedings of this definitional meeting were later published as the book Computational Neuroscience, MIT Press1990. The early historical roots of the field can be traced to the work of people such as Hodgkin & Huxley, Hubel & Wiesel, and David Marr, to name but a few. Hodgkin & Huxley developed the voltage clamp and created the first mathematical model of the action potential.
Hubel & Wiesel discovered that neurons in primary visual cortex, the first cortical area to process information coming from the retina, have oriented receptive fields and are organized in columns Hubel & Wiesel, 1962. David Marr's work focused on the interactions between neurons, suggesting computational approaches to the study of how functional groups of neurons within the hippocampus and neocortex interact, store, process, and transmit information. Computational modeling of biophysically realistic neurons and dendrites began with the work of Wilfrid Rall, with the first multicompartmental model using cable theory.Computational neuroscience is distinct from psychological connectionism and theories of learning from disciplines such as machine learning, neural networks and statistical learning theory in that it emphasizes descriptions of functional and biologically realistic neurons and neural systems and their physiology and dynamics. These models capture the essential features of the biological system at multiple spatialtemporal scales, from membrane currents, protein and chemical coupling to network oscillations, columnar and topographic architecture and learning and memory. These computational models are used to test hypotheses that can be directly verified by current or future biological experiments.Currently, the field is undergoing a rapid expansion. There are many software packages, such as GENESIS and NEURON, that allow rapid and systematic in silico modeling of realistic neurons. Blue Brain, a collaboration between IBM and École Polytechnique Fédérale de Lausanne, aims to construct a biophysically detailed simulation of a cortical column on the Blue Gene supercomputer.
Computational models require a mathematically and logically formal representation of a problem. Computer models are used in the simulation and experimental verification of different specific and general properties of intelligence. Computational modelling can help us to understand the functional organization of a particular cognitive phenomenon. There are two basic approaches to the cognition modeling. The first is focused on abstract mental functions of an intelligent mind and operates using symbols, and the second, which follows the neural and associative properties of the human brain, and is called subsymbolic.Symbolic modeling evolved from the computer science paradigms using the technologies of KnowledgeBased Systems, as well as a philosophical perspective, see for example Good OldFashioned Artificial Intelligence GOFAI.
They are developed by the first cognitive researchers and later used in information engineering for expert systems . Since the early 1990s it was generalized in systemics for the investigation of functional humanlike intelligence models, such as personoids, and, in parallel, developed as the SOAR environment. Recently, especially in the context of cognitive decision making, symbolic cognitive modeling is extended to sociocognitive approach including social and organization cognition interrelated with a subsymbolic not conscious layer.Subsymbolic modeling includes Connectionist/neural network models. Connectionism relies on the idea that the mind/brain is composed of simple nodes and that the power of the system comes primarily from the existence and manner of connections between the simple nodes. Neural nets are textbook implementations of this approach. Some critics of this approach feel that while these models approach biological reality as a repetition of how the system works, they lack explanative powers as complicated systems of connections with even simple rules are extremely complex and often less interpretable than the system they model.
All the above approaches tend to be generalized to the form of integrated computational models of a synthetic/abstract intelligence, in order to be applied to the explanation and improvement of individual and social/organizational decisionmaking.Research methods borrowed directly from neuroscience and neuropsychology can also help us to understand aspects of intelligence. These methods allow us to understand how intelligent behavior is implemented in a physical system.Cognitive science has much to its credit. Among other accomplishments, it has given rise to models of human cognitive bias and risk perception, and has been influential in the development of behavioral finance, part of economics.
It has also given rise to a new theory of the philosophy of mathematics, and many theories of artificial intelligence, persuasion and coercion. It has made its presence firmly known in the philosophy of language and epistemology a modern revival of rationalism as well as constituting a substantial wing of modern linguistics.The philosophical underpinnings of research in cognitive science have been continually criticized by philosophers and scientists alike. See Functionalism psychology for an extended entry on this.Some of the more recognized names in cognitive science are usually either the most controversial or the most cited. Within philosophy familiar names include Daniel Dennett who writes from a computational systems perspective, John Searle known for his controversial Chinese Room, Jerry Fodor who advocates functionalism, and Douglas Hofstadter. Hofstadter, famous for writing Gödel, Escher, Bach, which questions the nature of words and thought, is Director of the Fluid Analogies Research Group of the Center for Research on Concepts and Cognition at Indiana University. In the realm of linguistics, Noam Chomsky and George Lakoff have been influential. Popular names in the discipline of psychology include James McClelland and Steven Pinker.
Early models of sensory processing understood within a theoretical framework is credited to Horace Barlow. Somewhat similar to the minimal wiring hypothesis described in the preceding section, Barlow understood the processing of the early sensory systems to be a form of efficient coding, where the neurons encoded information which minimized the number of spikes. Experimental and computational work have since supported this hypothesis in one form or another.Current research in sensory processing is divided among biophysical modelling of different subsystems and more theoretical modelling function of perception. Current models of perception have suggested that the brain performs some form of Bayesian inference and integration of different sensory information in generating our perception of the physical world.Earlier models of memory are primarily based on the postulates of Hebbian learning.
Biologically relevant models such as Hopfield net have been developed to address the properties of associative, rather than contentaddressable style of memory that occur in biological systems. These attempts are primarily focusing on the formation of mediumterm and longterm memory, localizing in the hippocampus. Models of working memory, relying on theories of network oscillations and persistent activity, have been built to capture some features of the prefrontal cortex in contextrelated memory. For review, see Durstewitz et al, 2000.One of the major problems in biological memory is how it is maintained and changed through multiple time scales. Unstable synapses are easy to train but also prone to stochastic disruption. Stable synapses forget less easily, but they are also harder to consolidate. One recent computational hypothesis involves cascades of plasticity Fusi et al, 2005 that allow synapses to function at multiple time scales. Stereochemically detailed models of the acetylcholine receptorbased synapse with Monte Carlo method, working at the time scale of microseconds, have been built Coggan et al, 2005. It is likely that computational tools will contribute greatly to our understanding of how synapses function and change in relation to external stimulus in the coming decades.