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Neural simulation of a system that learns representations of sensory experience
The pyriform cortex forms stable representations of smells to allow their subsequent recognition. Clustering systems are shown to perform a similar function, so they provide a guide to understanding the operation of the pyriform. A neural model of a sample of pyriform cortex was built that adheres to most known biological constraints, including learning by long-term potentiation. Results of early simulations suggest some interesting properties. The effort has implications for the knowledge representations used in artificial intelligence work
The Mathematics of Information Science
This paper describes a course, The Mathematics of Information Science, which was taught at Towson University in Spring 1998, 1999, and 2000. This course is the junior level interdisciplinary course of the Maryland Collaborative for Teacher Preparation program. The effectiveness of the course in teaching problem solving techniques and abstract mathematical ideas is documented. The students constructed their own knowledge from laboratory experiences involving digital logic circuits. They were subsequently challenged to abstract this knowledge and to find ways to solve progressively more difficult problems using these digital logic circuits. The mathematics of encoding and decoding information constituted the major mathematical content of the course. This course is shown to be effective in introducing prospective elementary and middle school teachers to abstract mathematical ideas and problem solving techniques
Metric Features of a Dipolar Model
The lattice spin model, with nearest neighbor ferromagnetic exchange and long
range dipolar interaction, is studied by the method of time series for
observables based on cluster configurations and associated partitions, such as
Shannon entropy, Hamming and Rohlin distances. Previous results based on the
two peaks shape of the specific heat, suggested the existence of two possible
transitions. By the analysis of the Shannon entropy we are able to prove that
the first one is a true phase transition corresponding to a particular melting
process of oriented domains, where colored noise is present almost
independently of true fractality. The second one is not a real transition and
it may be ascribed to a smooth balancing between two geometrical effects: a
progressive fragmentation of the big clusters (possibly creating fractals), and
the slow onset of a small clusters chaotic phase. Comparison with the nearest
neighbor Ising ferromagnetic system points out a substantial difference in the
cluster geometrical properties of the two models and in their critical
behavior.Comment: 20 pages, 15 figures, submitted to JPhys
The Short Path Algorithm Applied to a Toy Model
We numerically investigate the performance of the short path optimization
algorithm on a toy problem, with the potential chosen to depend only on the
total Hamming weight to allow simulation of larger systems. We consider classes
of potentials with multiple minima which cause the adiabatic algorithm to
experience difficulties with small gaps. The numerical investigation allows us
to consider a broader range of parameters than was studied in previous rigorous
work on the short path algorithm, and to show that the algorithm can continue
to lead to speedups for more general objective functions than those considered
before. We find in many cases a polynomial speedup over Grover search. We
present a heuristic analytic treatment of choices of these parameters and of
scaling of phase transitions in this model.Comment: 11 pages, 9 figures; v2 final version published in Quantu
Learning an Interactive Segmentation System
Many successful applications of computer vision to image or video
manipulation are interactive by nature. However, parameters of such systems are
often trained neglecting the user. Traditionally, interactive systems have been
treated in the same manner as their fully automatic counterparts. Their
performance is evaluated by computing the accuracy of their solutions under
some fixed set of user interactions. This paper proposes a new evaluation and
learning method which brings the user in the loop. It is based on the use of an
active robot user - a simulated model of a human user. We show how this
approach can be used to evaluate and learn parameters of state-of-the-art
interactive segmentation systems. We also show how simulated user models can be
integrated into the popular max-margin method for parameter learning and
propose an algorithm to solve the resulting optimisation problem.Comment: 11 pages, 7 figures, 4 table
Competition of Languages and their Hamming Distance
We consider the spreading and competition of languages that are spoken by a
population of individuals. The individuals can change their mother tongue
during their lifespan, pass on their language to their offspring and finally
die. The languages are described by bitstrings, their mutual difference is
expressed in terms of their Hamming distance. Language evolution is determined
by mutation and adaptation rates. In particular we consider the case where the
replacement of a language by another one is determined by their mutual Hamming
distance. As a function of the mutation rate we find a sharp transition between
a scenario with one dominant language and fragmentation into many language
clusters. The transition is also reflected in the Hamming distance between the
two languages with the largest and second to largest number of speakers. We
also consider the case where the population is localized on a square lattice
and the interaction of individuals is restricted to a certain geometrical
domain. Here it is again the Hamming distance that plays an essential role in
the final fate of a language of either surviving or being extinct.Comment: 18 pages, 19 figure
Predicting evolution and visualizing high-dimensional fitness landscapes
The tempo and mode of an adaptive process is strongly determined by the
structure of the fitness landscape that underlies it. In order to be able to
predict evolutionary outcomes (even on the short term), we must know more about
the nature of realistic fitness landscapes than we do today. For example, in
order to know whether evolution is predominantly taking paths that move upwards
in fitness and along neutral ridges, or else entails a significant number of
valley crossings, we need to be able to visualize these landscapes: we must
determine whether there are peaks in the landscape, where these peaks are
located with respect to one another, and whether evolutionary paths can connect
them. This is a difficult task because genetic fitness landscapes (as opposed
to those based on traits) are high-dimensional, and tools for visualizing such
landscapes are lacking. In this contribution, we focus on the predictability of
evolution on rugged genetic fitness landscapes, and determine that peaks in
such landscapes are highly clustered: high peaks are predominantly close to
other high peaks. As a consequence, the valleys separating such peaks are
shallow and narrow, such that evolutionary trajectories towards the highest
peak in the landscape can be achieved via a series of valley crossingsComment: 12 pages, 7 figures. To appear in "Recent Advances in the Theory and
Application of Fitness Landscapes" (A. Engelbrecht and H. Richter, eds.).
Springer Series in Emergence, Complexity, and Computation, 201
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