Atin Das

Chaotic analysis of the foreign exchange rates

In this work, we investigate chaotic property of Foreign Exchange Rates of several countries. The foreign exchange market is a 24-h financial market. The trading in the foreign exchange markets generally involves the US dollar. Some of the related earlier works found evidence of chaotic structures in foreign exchange rates, some studies found little evidence of chaos, however, many of them showed evidence of nonlinear structure. This type of conflicting claims are common in nonlinear analyses of financial data, as shown in our earlier work (2006). For the present work, daily data were collected for twelve countries, mostly over the period January 1971 to December 2005. We have thus a time series of more than 8500 points for each country. Changes in the exchange rate are related to news in the fundamentals, but previous studies showed that the nature of the relation is nonlinear. We test the nonlinearity by the foreign exchange data by surrogate method and find different degree of nonlinearity for different countries. By measuring the largest Lyapunov exponent (LLE), we found indication of deterministic chaos in all exchange rate series. We attempted to find how foreign exchange relates to fundamental news like balance of payment to US dollar. Finally, we comment on limitation of LLE to report the dynamics of the time series.

CHAOS IN A THREE-DIMENSIONAL GENERAL MODEL OF NEURAL NETWORK

The dynamics of a network of three neurons with all possible connections is studied here. The equations of control are given by three differential equations with nonlinear, positive and bounded sigmoidal response function of the neurons. The system passes from stable to periodic and then to chaotic regimes and returns to stationary regime with change in parameter values of synaptic weights and decay rates. We have developed programs and used Locbif package to study phase portraits, bifurcation diagrams which confirm the result. Lyapunov Exponents have been calculated to confirm chaos.

Chaos in a three dimensional neural network

Abstract An artificial neural network (ANN) consisting of three neurons has been considered. The equations of control are given by three differential equations (DE) with nonlinear, positive and bounded response functions of the neurons. Bifurcation diagram and three dimensional (3-D) phase portraits of the model show rich dynamics. With the change in synaptic weight and decay rate, the system passes from stable to periodic and then chaotic regimes. Interestingly, the system returns to periodic regime by further changing the synaptic weight. Computer code to calculate the Lyapunov exponent (LE) has been written to confirm chaos.

Stability and oscillations of a negative feedback delay model for the control of testosterone secretion

A modified time-lag model for the control of the secretion of the hormone testosterone is proposed. Conditions for switching of the steady state from stable to unstable are derived. Questions concerning small amplitude oscillations of solutions are addressed analytically and numerically.

Does composite index of NYSE represents chaos in the long time scale

Abstract Here we analyze the Composite Index (CI) for 32 years, from 1966 to 1997 of the New York Stock Exchange (NYSE). Individual share prices may be unpredictable—is it true for CI also—particularly in the time scale of 32 years? In the first half (consisting first 16 years) CI is confined to values in the range of 36–75 and in the second half, it rises to 600 point mark. Non-linear analysis of data confirms that CI is not unpredictable in longer time scales. Moreover, the second half of the data fits well with some growing function of time.

Neural Net Model for Featured Word Extraction

Search engines perform the task of retrieving information related to the user-supplied query words. This task has two parts; one is finding ‘featured words’ which describe an article best and the other is finding a match among these words to user-defined search terms. There are two main independent approaches to achieve this task. The first one, using the concepts of semantics, has been implemented partially. For more details see another paper of Marko et al., 2002. The second approach is reported in this paper. It is a theoretical model based on using Neural Network (NN). Instead of using keywords or reading from the first few lines from papers/articles, the present model gives emphasis on extracting ‘featured words’ from an article. Obviously we propose to exclude prepositions, articles and so on, that is, English words like “of, the, are, so, therefore,” etc. from such a list. A neural model is taken with its nodes pre-assigned energies. Whenever a match is found with featured words and user-defined search words, the node is fired and jumps to a higher energy. This firing continues until the model attains a steady energy level and total energy is now calculated. Clearly, higher match will generate higher energy; so on the basis of total energy, a ranking is done to the article indicating degree of relevance to the user’s interest. Another important feature of the proposed model is incorporating a semantic module to refine the search words; like finding association among search words, etc. In this manner, information retrieval can be improved markedly.

FRACTAL ANALYSIS OF DIFFERENT EASTERN AND WESTERN MUSICAL INSTRUMENTS

In this paper, we attempt musical analysis by measuring fractal dimension (D) of musical pieces played by several musical instruments. We collected solo performances of popular instruments of Western and Eastern origin as samples. We attempted usual spectral analysis of the selected clips to observe peaks of fundamental and harmonics in frequency regime. After appropriate processing, we converted them into time series data sets and computed their fractal dimension. Based on our results, we conclude that instrumental musical sounds may have higher Ds than those computed from vocal performances of different types of Indian songs.

Nonlinear data analysis of experimental (EEG) data and comparison with theoretical (ANN) data

In this article, nonlinear dynamical tools such as largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be used to analyze electroencephalogram (EEG) data obtained from healthy young subjects with eyes open and eyes closed condition with the view to compare brain complexity under this two condition. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding such tools will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity will be addressed by using surrogate data technique. We have extracted another data set that represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. We further attempt to compare results to find nature of chaos arising from such theoretical models.

Phase transition studies in CoSiF6.6D2O

Magnetic anisotropy and the optical property have been examined in the temperature interval 77-300K in CoSiF6.6D2O. Results show a rise of 17K in the transition temperature in CoSiF6.6D2O with respect to CoSiF6.6H2O crystal.

An anomalous electrical property of CoSiF6.6H2O near its transition temperature

The electrical resistance of the CoSiF6.6H2O crystal along its three axes and of the powdered material has been measured in the vicinity of the transition temperature. The resistance of the crystal passes through a peak at 246K, the transition temperature in the cooling cycle, during heating the resistance jumps to a much lower value at about 265K. At and above 265K in the heating cycle the DC (i- nu ) characteristics show non-linear variation. A spontaneous voltage of approximately 0.6 V, of opposite polarity to the applied voltage, is developed across the crystal after a current of a few milliamperes is passed through the crystal via Aquadag electrodes and the applied voltage withdrawn. The value of the spontaneous voltage depends on the electrode material and the temperature. The non-linearity in the (i- nu ) characteristics is absent when AC measurements are made. The powdered sample does not show any anomaly in its resistance.