Pal Rujan - Academia.edu (original) (raw)

Papers by Pal Rujan

Zeitschrift f�r Physik B Condensed Matter, 1995

The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sine-Gordo... more The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sine-Gordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to xf-Es (Es: formation energy of soliton), when Es becomes negative.

A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best dec... more A ray-tracing method inspired by ergodic billiards is used to estimate the theoretically best decision rule for a set of linear separable examples. While the Bayes-optimum requires in general a majority decision over all Perceptrons separating the example set, the problem considered here corresponds to nding the single Perceptron with best average generalization probability. For randomly distributed examples the billiard estimate agrees with known analytic results, while for real-life classi cation problems it reduces consistently the generalization error compared to the maximal stability Perceptron.

The main promise of the AMASS platform is that it can be easily extended to other application dom... more The main promise of the AMASS platform is that it can be easily extended to other application domains by redefining the way we encode relevant information into the SAMs (Signature Attribute Matrices). Note that LCI’s C;A;R;E; (Content Addressable Record Extraction) library itself is built around the concept of records consisting of independent fields. In a more abstract way, it implements a set of strings, where the strings are one-dimensional sequences like person or company names, phone numbers, etc. Version 2.0 will generalize this to either a sequence of sequences (needed in natural text analysis) or to a tree of strings. These extensions in scope are needed by specific applications requiring different types of correlations between the fields.

We reformulate the problem of supervised learning in neu ral nets to include the search for a ne... more We reformulate the problem of supervised learning in neu ral nets to include the search for a network with minimal resources . The information processing in feedforward networks is described in geometrical terms as the partitioning of the space of possible input configurations by hyperplanes corresponding to hidden units. Regu lar partitionings introduced here are a special class of partitionings. Corresponding architectures can represent any Boolean function using a single layer of hidden units whose number depends on the specific symmetries of the function. Accordin gly, a new class of pla ne-cutting algorithms is proposed that const ruct in polynomial time a "custom made" architecture implementing the desired set of inputj'ouput ex amples . We report the results of our experiments on the storage and rule-extraction abilities of three-layer perceptrons synthetized by a simple greedy algorithm. As expected, simple neuronal structures with good generalization prope...

Eprint Arxiv Cond Mat 9508130, Aug 29, 1995

Neco, 1997

A ray-tracing method inspired by ergodic billiards is used to estimatethe theoretically best deci... more A ray-tracing method inspired by ergodic billiards is used to estimatethe theoretically best decision rule for a given set of linear separableexamples. For randomly distributed examples the billiard estimateof the single Perceptron with best average generalization probabilityagrees with known analytic results, while for real-life classificationproblems the generalization probability is consistently enhanced whencompared to the maximal stability Perceptron.1 IntroductionNeural...

Journal of Statistical Physics, 1987

Zeitschrift Fur Physik B Condensed Matter, 1994

Traffic on an one-lane freeway is simulated using a continuous space-discrete time probabilistic ... more Traffic on an one-lane freeway is simulated using a continuous space-discrete time probabilistic cellular automata model. The effect of different individual driving patterns is estimated by monitoring the traffic flow, the velocity and acceleration distributions, the average number of accidents, and the distribution of densitywaves (traffic jams) as a function of traffic density. The number of accidents, traffic jams, and the fuel consumption are drastically reduced by driving strategies adapting to local traffic conditions. At high traffic densities this leads, however, to a decrease in the global traffic throughout.

This work considers the behavior the Ising model of a ferromagnet subject to a strong, randomly s... more This work considers the behavior the Ising model of a ferromagnet subject to a strong, randomly switching external driving field. A formalism based on the master equation to handle such nonequilibrium systems is introduced and applied to a mean field approximation, and one-and two-dimensional variants of the model. A novel type of phase transition related to spontaneous symmetry breaking and dynamic freezing occurs which depends on the strength of the driving field. The complex analytic structure of the stationary magnetization distributions is shown to range from singular-continuous with euclidean or fractal support to all continuous. Analytic results are presented for the mean field and one-dimensional cases, whereas Monte-Carlo simulations provide insight into the two-dimensional model. Also, an interpretation of the model from a neurobiological point of view is given. 'So it's false.' 'What isn't?' 'Intellectual achievement. The exercise of skill. Human feeling.' from Iain M. Banks, "The Player of Games" Preface In the fall of 1995, I was given the chance to work for one year with the neurocomputer SYNAPSE1/N110 of Fa. Siemens-without a clue as to what one might be able to do with it apart from simulating neural networks. The only condition was to present several applications to demonstrate the power of this machine. Neglecting the strong time constraint, I was in a situation that one would consider ideal for scientific work: A great infrastructure with respect to man and machine, as well as the freedom to pursue promising subjects I deemed interesting. It was during this time that the stage was set to take the first steps towards the work presented in the following chapters. At this point, I would like to express my gratitude to my mentor, Prof. Dr. Pál Ruján, as well as to the other members of AG spÎn 1 , Dr. Harry Urbschat and Thorsten Wanschura. Their democratic ways of "doing science" provide an atmosphere of friendship that procures the excitement and enjoyment of scientific work I have come to value in the past three and a half years. Also, thanks go to those involved with the proofreading. Next, I would like to thank Linus Torvalds for providing the computer community with Linux, one of the best computer operating systems around. And finally, I would like to thank my girlfriend for putting up with me all this time.

We present below a simple ray-tracing algorithm for estimating the Bayes classifier for a given c... more We present below a simple ray-tracing algorithm for estimating the Bayes classifier for a given class of parameterized kernels.

International Journal of Modern Physics B, 1989

Spin-models in random fields (RFs) are good representations of many impure materials. Their macro... more Spin-models in random fields (RFs) are good representations of many impure materials. Their macroscopic collective behaviour is dominated by the fluctuations in the random fields which accumulate on large scales even if the local field is arbitrarily small. This feature is shared by other weakly disordered models, like flux lines or domain walls in random media. We review some of the main theoretical attempts to describe such systems. A modification of Harris’ argument demonstrates that at the critical point the RF disorder is relevant and that (hyper)scaling must be changed. A domain argument invented by Imry and Ma shows that long-range order is not destroyed by weak RFs in more than d=2 dimensions. This result is supported both by a more refined treatment of the domain argument and by considering the roughness of an isolated domain wall due to the randomness. The wall (or flux line) becomes rough due to disorder but if d>2 the wall remains a well-defined object in RF systems. ...

Lecture Notes in Physics, 1990

International Journal of Modern Physics B - IJMPB, 1989

Spin-models in random fields (RFs) are good representations of many impure materials. Their macro... more Spin-models in random fields (RFs) are good representations of many impure materials. Their macroscopic collective behaviour is dominated by the fluctuations in the random fields which accumulate on large scales even if the local field is arbitrarily small. This feature is shared by other weakly disordered models, like flux lines or domain walls in random media. We review some of the main theoretical attempts to describe such systems. A modification of Harris' argument demonstrates that at the critical point the RF disorder is relevant and that (hyper)scaling must be changed. A domain argument invented by Imry and Ma shows that long-range order is not destroyed by weak RFs in more than d=2 dimensions. This result is supported both by a more refined treatment of the domain argument and by considering the roughness of an isolated domain wall due to the randomness. The wall (or flux line) becomes rough due to disorder but if d>2 the wall remains a well-defined object in RF syst...

In conclusion we have seen that sometimes quite simple mathematics may lead to a rich body of phy... more In conclusion we have seen that sometimes quite simple mathematics may lead to a rich body of physical informations. I think that new interesting results can be obtained through different analytic continuation of these calculations. It would be also useful to use more sophisticated Ansatze as well as to consider the dynamic poperties of systems with competing interactions.

Zeitschrift f�r Physik B Condensed Matter, 1995

Eprint Arxiv Cond Mat 9508130, Aug 29, 1995

Neco, 1997

Journal of Statistical Physics, 1987

Zeitschrift Fur Physik B Condensed Matter, 1994

International Journal of Modern Physics B, 1989

Lecture Notes in Physics, 1990

International Journal of Modern Physics B - IJMPB, 1989

Spin-models in random fields (RFs) are good representations of many impure materials. Their macro... more Spin-models in random fields (RFs) are good representations of many impure materials. Their macroscopic collective behaviour is dominated by the fluctuations in the random fields which accumulate on large scales even if the local field is arbitrarily small. This feature is shared by other weakly disordered models, like flux lines or domain walls in random media. We review some of the main theoretical attempts to describe such systems. A modification of Harris' argument demonstrates that at the critical point the RF disorder is relevant and that (hyper)scaling must be changed. A domain argument invented by Imry and Ma shows that long-range order is not destroyed by weak RFs in more than d=2 dimensions. This result is supported both by a more refined treatment of the domain argument and by considering the roughness of an isolated domain wall due to the randomness. The wall (or flux line) becomes rough due to disorder but if d>2 the wall remains a well-defined object in RF syst...