Theta Oscillations and Their Role in Creating Place and ... 10 Questions for György Buzsáki. Is Board of Governors Professor at the Center for Molecular and Behavioral Neuroscience at Rutgers University. His recent book, , is a clear explication of the study of network-level dynamics in the nervous system, ranging from innovations in . Rather than list his numerous awards and accomplishments, I direct you to the which have placed him at the forefront of the rapidly progressing field of systems neuroscience. and I collaborated to bring you the following ten questions.1.
Modeling necessarily requires simplification. In your view, what features of biological neural networks are so important that they must be captured in any accurate artificial neural network model? For instance, do you believe it is enough to supplement firing rate-coding units with a parameter for "phase," or do computational models need to simulate biological neural networks at a lower level?
Models can be useful in at least two different ways, inferential and inductive. 2. 3. 4. 5. 6. 7. 9. 10. NMDA receptors, place cells and hippocampal spatial memory. Buzsaki05. Spatiotemporal coupling between hippocampal acetylcholine ... A hybrid oscillatory interference/continuous attractor network model ... Intrinsic Circuit Organization and Theta–Gamma Oscillation ... Pascale Quilichini1,2, Anton Sirota1,3, and György Buzsáki1 +Show Affiliations Correspondence should be addressed to György Buzsáki, Center for Molecular and Behavioral Neuroscience, Rutgers University, 197 University Avenue, Newark, NJ 07102. buzsaki@axon.rutgers.edu.
Continuous attractor network. This article has not yet been published; it may contain inaccuracies, unapproved changes, or be unfinished. A continuous attractor network (or continuous-attractor neural network, CANN) is an attractor network possessing one or more quasicontinuous sets of attractors that in the limit of an infinite number of neuronal units merge into continuous attractor(s). Thus, a continuous attractor network is a special kind of an attractor neural network , which in turn is a special kind of a nonlinear dynamical system. The fact that the notion of a CANN only makes precise sense in the infinite limit is consistent with the fact that most rigorous results of the artificial neural network theory are known in the same limit (Amit 1989, Hertz et al. 1991, Hoppensteadt & Izhikevich 1997). A good introduction to CANN models and their biological applications is given in the book of Trappenberg (2002, pp. 207-232).
The notion of a continuous attractor Figure 1: A simple system with a continuous attractor. Hc-place-cells. Jacobian matrix and determinant. Matrix of all first-order partial derivatives of a vector-valued function Suppose f : Rn → Rm is a function such that each of its first-order partial derivatives exists on Rn. This function takes a point x ∈ Rn as input and produces the vector f(x) ∈ Rm as output. Then the Jacobian matrix of f is defined to be an m×n matrix, denoted by J, whose (i,j)th entry is , or explicitly where is the transpose (row vector) of the gradient of the -th component. The Jacobian matrix, whose entries are functions of x, is denoted in various ways; common notations include Df, Jf, , and .[5][6] Some authors define the Jacobian as the transpose of the form given above.
When m = n, the Jacobian matrix is square, so its determinant is a well-defined function of x, known as the Jacobian determinant of f. When m = 1, that is when f : Rn → R is a scalar-valued function, the Jacobian matrix reduces to the row vector ; this row vector of all first-order partial derivatives of f is the transpose of the gradient of f, i.e. Topological group. Group that is a topological space with continuous group action Topological groups have been studied extensively in the period of 1925 to 1940. Haar and Weil (respectively in 1933 and 1940) showed that the integrals and Fourier series are special cases of a very wide class of topological groups.
Formal definition[edit] A topological group, G, is a topological space that is also a group such that the group operation (in this case product): ⋅ : G × G → G, (x, y) ↦ xy and the inversion map: −1 : G → G, x ↦ x−1 are continuous. Checking continuity To show that a topology is compatible with the group operations, it suffices to check that the map G × G → G, (x, y) ↦ xy−1 is continuous. Additive notation This definition used notation for multiplicative groups; the equivalent for additive groups would be that the following two operations are continuous: + : G × G → G , (x, y) ↦ x + y − : G → G , x ↦ −x.
Hausdorffness This article will not assume that topological groups are necessarily Hausdorff. Category n×n. N. Flip-flop (electronics) Electronic circuit with two stable states An animated interactive SR latch (R1, R2 = 1 kΩ; R3, R4 = 10 kΩ). In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and will have one or two outputs. It is the basic storage element in sequential logic. Flip-flops and latches are fundamental building blocks of digital electronics systems used in computers, communications, and many other types of systems.
When a level-triggered latch is enabled it becomes transparent, but an edge-triggered flip-flop's output only changes on a single type (positive going or negative going) of clock edge. Flip-flop schematics from the Eccles and Jordan patent filed 1918, one drawn as a cascade of amplifiers with a positive feedback path, and the other as a symmetric cross-coupled pair An animated SR latch. How an SR NOR latch works. or. Field-programmable gate array. Array of logic gates that are reprogrammable A field-programmable gate array (FPGA) is a type of configurable integrated circuit that can be repeatedly programmed after manufacturing. FPGAs are a subset of logic devices referred to as programmable logic devices (PLDs). They consist of an array of programmable logic blocks with a connecting grid, that can be configured "in the field" to interconnect with other logic blocks to perform various digital functions.
FPGAs are often used in limited (low) quantity production of custom-made products, and in research and development, where the higher cost of individual FPGAs is not as important, and where creating and manufacturing a custom circuit wouldn't be feasible. Other applications for FPGAs include the telecommunications, automotive, aerospace, and industrial sectors, which benefit from their flexibility, high signal processing speed, and parallel processing abilities.
A design start is a new custom design for implementation on an FPGA. Crystal structure. The (3-D) crystal structure of H2O ice Ih (c) consists of bases of H2O ice molecules (b) located on lattice points within the (2-D) hexagonal space lattice (a). The values for the H—O—H angle and O—H distance have come from Physics of Ice[1] with uncertainties of ±1.5° and ±0.005 Å, respectively. The black box in (c) is the unit cell defined by Bernal and Fowler[2] In mineralogy and crystallography, a crystal structure is a unique arrangement of atoms, ions or molecules in a crystalline liquid or solid.[3] It describes a highly ordered structure, occurring due to the intrinsic nature of its constituents to form symmetric patterns. Patterns are located upon the points of a lattice, which is an array of points repeating periodically in three dimensions. Unit cell[edit] The atom positions within the unit cell can be calculated through application of symmetry operations to the asymmetric unit.
Miller indices[edit] Main article: Miller index Planes with different Miller indices in cubic crystals. Shearing and Coaxial/Non Coaxial Strain. Deformation- produced in response to Stress Depends upon: Type of stress applied Rock properties (minerals, discontinuities, etc) Temperature Depth Time Deformation=change in position, shape or volume or rotation as a result of applied stress. Describes the complete displacement field of a set of points in a body relative to an external reference frame. 4 deformation components are: 1. 2. 3. 4.Dilation- volume change Strain Axes: X= maximum direction of extension (or minimal compressive strain Y= intermediate strain axis Z= maximum direction of shortening (or minimum extension). Relationships between Stress and Strain: Since strain results from the actions of stresses, a geometrical relationship between the two must exist. 3 correspond with strain axes X, Y and Z. Knowledge of Undeformed States Strain analysis requires a knowledge of the original undeformed state of the material (rare in nature).
Homogeneous Strain- Situation in which strain in all points of a rock body is the same Circles become ellipses; Gradient. Multivariate derivative (mathematics) In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) whose value at a point gives the direction and the rate of fastest increase. The gradient transforms like a vector under change of basis of the space of variables of. . , the direction of the gradient is the direction in which the function increases most quickly from may be defined by: where is the total infinitesimal change in for an infinitesimal displacement , and is seen to be maximal when is in the direction of the gradient.
. , written as an upside-down triangle and pronounced "del", denotes the vector differential operator. at .[2] That is, for , its gradient is defined at the point in n-dimensional space as the vector[b] Note that the above definition for gradient is only defined for the function , if it is differentiable at . For example, the function unless at origin where The gradient is dual to the total derivative .
Monotonic function. Order-preserving mathematical function In calculus and analysis[edit] In calculus, a function defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing.[2] That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease. A function is called monotonically increasing (also increasing or non-decreasing)[3] if for all and such that one has , so preserves the order (see Figure 1) . , then , so it reverses the order (see Figure 2).
If the order in the definition of monotonicity is replaced by the strict order , one obtains a stronger requirement. Not equal to , either or and so, by monotonicity, either , thus To avoid ambiguity, the terms weakly monotone, weakly increasing and weakly decreasing are often used to refer to non-strict monotonicity. A function is said to be absolutely monotonic over an interval if the derivatives of all orders of When for. Shearing-induced asymmetry in entorhinal grid cells. Combining multiple periodic grids at different spatial scales can result in non-periodic place fields. Colocalize. English[edit] Alternative forms[edit] co-localize Etymology[edit] colocal + -ize Pronunciation[edit] IPA(key): kɔˈloʊkəlaɪz Verb[edit] colocalize (third-person singular simple present colocalizes, present participle colocalizing, simple past and past participle colocalized) (biochemistry) To occur together in the same cell.
Derived terms[edit] colocalization Related terms[edit] collocate. Grid cell. Trajectory of a rat through a square environment is shown in black. Red dots indicate locations at which a particular entorhinal grid cell fired. A grid cell is a type of neuron in the brains of many species that allows them to understand their position in space.[1][2][3][4][5][6] Grid cells derive their name from the fact that connecting the centers of their firing fields gives a triangular grid. In a typical experimental study, an electrode capable of recording the activity of an individual neuron is implanted in the cerebral cortex of a rat, in a section called the dorsomedial entorhinal cortex, and recordings are made as the rat moves around freely in an open arena.
For a grid cell, if a dot is placed at the location of the rat's head every time the neuron emits an action potential, then as illustrated in the adjoining figure, these dots build up over time to form a set of small clusters, and the clusters form the vertices of a grid of equilateral triangles. Background[edit] Discretization of continuous features. Typically data is discretized into partitions of K equal lengths/width (equal intervals) or K% of the total data (equal frequencies).[1] Mechanisms for discretizing continuous data include Fayyad & Irani's MDL method,[2] which uses mutual information to recursively define the best bins, CAIM, CACC, Ameva, and many others[3] Many machine learning algorithms are known to produce better models by discretizing continuous attributes.[4] See also[edit] References[edit] Jump up ^ Clarke, E.
Hippocampal Place Fields : Relevance to Learning and Memory: Relevance to ... Buzsaki2010Neuron. Temporal difference learning - Scholarpedia. Temporal difference (TD) learning is an approach to learning how to predict a quantity that depends on future values of a given signal. The name TD derives from its use of changes, or differences, in predictions over successive time steps to drive the learning process. The prediction at any given time step is updated to bring it closer to the prediction of the same quantity at the next time step. It is a supervised learning process in which the training signal for a prediction is a future prediction. TD algorithms are often used in reinforcement learning to predict a measure of the total amount of reward expected over the future, but they can be used to predict other quantities as well.
Continuous-time TD algorithms have also been developed. The Problem Suppose a system receives as input a time sequence of vectors (x_t, y_t)\ , t=0, 1, 2, \dots\ , where each x_t is an arbitrary signal and y_t is a real number. Where \gamma is a discount factor, with 0 \le \gamma < 1\ . Eligibility Traces. Frontiers | Inhibitory synaptic plasticity: spike timing-dependence and putative network function | Frontiers in Neural Circuits.