3,968 research outputs found
A computer simulation of oscillatory behavior in primary visual cortex
Periodic variations in correlated cellular activity have been observed in many regions of the cerebral cortex. The recent discovery of stimulus-dependent, spatially-coherent oscillations in primary visual cortex of the cat has led to suggestions of neural information encoding schemes based on phase and/or frequency variation. To explore the mechanisms underlying this behavior and their possible functional consequences, we have developed a realistic neural model, based on structural features of visual cortex, which replicates observed oscillatory phenomena. In the model, this oscillatory behavior emerges directly from the structure of the cortical network and the properties of its intrinsic neurons; however, phase coherence is shown to be an average phenomenon seen only when measurements are made over multiple trials. Because average coherence does not ensure synchrony of firing over the course of single stimuli, oscillatory phase may not be a robust strategy for directly encoding stimulus-specific information. Instead, the phase and frequency of cortical oscillations may reflect the coordination of general computational processes within and between cortical areas. Under this interpretation, coherence emerges as a result of horizontal interactions that could be involved in the formation of receptive field properties
The Effects of a Goal Setting Intervention and Dispositional Optimism/Pessimism on Selected Golf Skills: A Qualitative Design
The purpose of this study was to examine the effects of a goal setting intervention on selected golf skills over the course of a competitive golf season. A secondary purpose of this study was to investigate a comparison of optimism and pessimism in relationship to goal attainment. Subjects (n=7) were elite golfers from a university men\u27s golf team. A two-month goal setting intervention was implemented consisting of the individual golfers selecting three golf skills from five separate categories (fairways in regulation, greens in regulation, total putts per round, up and downs conversion rate, and putts per green in regulation) to set and implement performance goals. Baseline data were gathered through statistical charting of the five categories during practice and competition rounds. Goal setting data were collected from the practice and competitive rounds during the golf team\u27s spring season. Optimism and pessimism was measured by the Optimism and Pessimism Scale (Dember et al., 1989). The following research questions were posed: 1) Would there be improvement in the targeted golf skills selected due to the goal setting intervention? 2) Would there be an appreciable change in the non-targeted golf skills 3) Would there be a positive relationship between optimism and goal attainability? 4) Would there be a negative relationship between pessimism and goal attainability? Results indicated that six of the seven golfers improved in at least one of their three targeted golf skills. While four of the golfers improved in at least two of their three targeted golf skills. Changes did occur in the non-targeted golf skills, however these changes were in direct relation to changes in the targeted golf skills. A statistical relationship was found to exist between those individuals scoring higher in optimism and goal attainability. The five golfers with the highest optimism scores, also attained the highest percentage of their goals. Lastly, the two golfers with the lowest optimism scores and two of the three highest pessimism scores, were found to have had the lowest percentage of goal attainability. Results from this study supported the previous research that goal setting may be an effective psychological tool for improved performance and that optimism/pessimism may play an important role towards goal attainability
Program Verification in the presence of complex numbers, functions with branch cuts etc
In considering the reliability of numerical programs, it is normal to "limit
our study to the semantics dealing with numerical precision" (Martel, 2005). On
the other hand, there is a great deal of work on the reliability of programs
that essentially ignores the numerics. The thesis of this paper is that there
is a class of problems that fall between these two, which could be described as
"does the low-level arithmetic implement the high-level mathematics". Many of
these problems arise because mathematics, particularly the mathematics of the
complex numbers, is more difficult than expected: for example the complex
function log is not continuous, writing down a program to compute an inverse
function is more complicated than just solving an equation, and many algebraic
simplification rules are not universally valid.
The good news is that these problems are theoretically capable of being
solved, and are practically close to being solved, but not yet solved, in
several real-world examples. However, there is still a long way to go before
implementations match the theoretical possibilities
Using the distribution of cells by dimension in a cylindrical algebraic decomposition
We investigate the distribution of cells by dimension in cylindrical
algebraic decompositions (CADs). We find that they follow a standard
distribution which seems largely independent of the underlying problem or CAD
algorithm used. Rather, the distribution is inherent to the cylindrical
structure and determined mostly by the number of variables.
This insight is then combined with an algorithm that produces only
full-dimensional cells to give an accurate method of predicting the number of
cells in a complete CAD. Since constructing only full-dimensional cells is
relatively inexpensive (involving no costly algebraic number calculations) this
leads to heuristics for helping with various questions of problem formulation
for CAD, such as choosing an optimal variable ordering. Our experiments
demonstrate that this approach can be highly effective.Comment: 8 page
A "Piano Movers" Problem Reformulated
It has long been known that cylindrical algebraic decompositions (CADs) can
in theory be used for robot motion planning. However, in practice even the
simplest examples can be too complicated to tackle. We consider in detail a
"Piano Mover's Problem" which considers moving an infinitesimally thin piano
(or ladder) through a right-angled corridor.
Producing a CAD for the original formulation of this problem is still
infeasible after 25 years of improvements in both CAD theory and computer
hardware. We review some alternative formulations in the literature which use
differing levels of geometric analysis before input to a CAD algorithm. Simpler
formulations allow CAD to easily address the question of the existence of a
path. We provide a new formulation for which both a CAD can be constructed and
from which an actual path could be determined if one exists, and analyse the
CADs produced using this approach for variations of the problem.
This emphasises the importance of the precise formulation of such problems
for CAD. We analyse the formulations and their CADs considering a variety of
heuristics and general criteria, leading to conclusions about tackling other
problems of this form.Comment: 8 pages. Copyright IEEE 201
Choosing a variable ordering for truth-table invariant cylindrical algebraic decomposition by incremental triangular decomposition
Cylindrical algebraic decomposition (CAD) is a key tool for solving problems
in real algebraic geometry and beyond. In recent years a new approach has been
developed, where regular chains technology is used to first build a
decomposition in complex space. We consider the latest variant of this which
builds the complex decomposition incrementally by polynomial and produces CADs
on whose cells a sequence of formulae are truth-invariant. Like all CAD
algorithms the user must provide a variable ordering which can have a profound
impact on the tractability of a problem. We evaluate existing heuristics to
help with the choice for this algorithm, suggest improvements and then derive a
new heuristic more closely aligned with the mechanics of the new algorithm
Stochastic Weighted Graphs: Flexible Model Specification and Simulation
In most domains of network analysis researchers consider networks that arise
in nature with weighted edges. Such networks are routinely dichotomized in the
interest of using available methods for statistical inference with networks.
The generalized exponential random graph model (GERGM) is a recently proposed
method used to simulate and model the edges of a weighted graph. The GERGM
specifies a joint distribution for an exponential family of graphs with
continuous-valued edge weights. However, current estimation algorithms for the
GERGM only allow inference on a restricted family of model specifications. To
address this issue, we develop a Metropolis--Hastings method that can be used
to estimate any GERGM specification, thereby significantly extending the family
of weighted graphs that can be modeled with the GERGM. We show that new
flexible model specifications are capable of avoiding likelihood degeneracy and
efficiently capturing network structure in applications where such models were
not previously available. We demonstrate the utility of this new class of
GERGMs through application to two real network data sets, and we further assess
the effectiveness of our proposed methodology by simulating non-degenerate
model specifications from the well-studied two-stars model. A working R version
of the GERGM code is available in the supplement and will be incorporated in
the gergm CRAN package.Comment: 33 pages, 6 figures. To appear in Social Network
A comparison of three heuristics to choose the variable ordering for CAD
Cylindrical algebraic decomposition (CAD) is a key tool for problems in real
algebraic geometry and beyond. When using CAD there is often a choice over the
variable ordering to use, with some problems infeasible in one ordering but
simple in another. Here we discuss a recent experiment comparing three
heuristics for making this choice on thousands of examples
Computer Simulation of Oscillatory Behavior in Cerebral Cortical Networks
It has been known for many years that specific regions of the working
cerebral cortex display periodic variations in correlated cellular
activity. While the olfactory system has been the focus of much of
this work, similar behavior has recently been observed in primary
visual cortex. We have developed models of both the olfactory
and visual cortex which replicate the observed oscillatory properties
of these networks. Using these models we have examined the
dependence of oscillatory behavior on single cell properties and network
architectures. We discuss the idea that the oscillatory events
recorded from cerebral cortex may be intrinsic to the architecture
of cerebral cortex as a whole, and that these rhythmic patterns
may be important in coordinating neuronal activity during sensory
processing
A Computer Simulation of Olfactory Cortex with Functional Implications for Storage and Retrieval of Olfactory Information
Based on anatomical and physiological data, we have developed a computer simulation of piriform
(olfactory) cortex which is capable of reproducing spatial and temporal patterns of actual
cortical activity under a variety of conditions. Using a simple Hebb-type learning rule in conjunction
with the cortical dynamics which emerge from the anatomical and physiological organization
of the model, the simulations are capable of establishing cortical representations for different
input patterns. The basis of these representations lies in the interaction of sparsely distributed,
highly divergent/convergent interconnections between modeled neurons. We have shown that
different representations can be stored with minimal interference. and that following learning
these representations are resistant to input degradation, allowing reconstruction of a representation
following only a partial presentation of an original training stimulus. Further, we have
demonstrated that the degree of overlap of cortical representations for different stimuli can
also be modulated. For instance similar input patterns can be induced to generate distinct cortical
representations (discrimination). while dissimilar inputs can be induced to generate overlapping
representations (accommodation). Both features are presumably important in classifying olfactory
stimuli
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