Macroscopic motion and gravitation in thermodynamics

A series of examples rarely presented to students is discussed to illustrate a property of thermodynamic equilibrium: small parts of a fully isolated system move as if points of a rigid body, so as to minimize the macroscopic (kinetic) energy EM. Most examples lie in the fields of astronomy and astrophysics, EM then including the gravitational energy. The paradoxical behaviour of gravitation, in particular in the extreme case of black holes,is discussed.

Multiple attractors, long chaotic transients, and failure in small-world networks of excitable neurons.

We study the dynamical states of a small-world network of recurrently coupled excitable neurons, through both numerical and analytical methods. The dynamics of this system depend mostly on both the number of long-range connections or ?shortcuts?, and the delay associated with neuronal interactions. We find that persistent activity emerges at low density of shortcuts, and that the system undergoes a transition to failure as their density reaches a critical value. The state of persistent activity below this transition consists of multiple stable periodic attractors, whose number increases at least as fast as the number of neurons in the network. At large shortcut density and for long enough delays the network dynamics exhibit exceedingly long chaotic transients, whose failure times follow a stretched exponential distribution. We show that this functional form arises for the ensemble-averaged activity if the failure time for each individual network realization is exponen- tially distributed

Quasi chaotic digital behaviour in an optically processing

Digital chaotic behavior in an optically processing element is reported. It is obtained as the result of processing two fixed train of bits. The process is performed with an Optically Programmable Logic Gate. Possible outputs for some specific conditions of the circuit are given. These outputs have some fractal characteristics, when input variations are considered. Digital chaotic behavior is obtained by using a feedback configuration. A random-like bit generator is presented.

Secure transmission of information by digital chaotic signals

Protecting signals is one of the main tasks in information transmission. A large number of different methods have been employed since many centuries ago. Most of them have been based on the use of certain signal added to the original one. When the composed signal is received, if the added signal is known, the initial information may be obtained. The main problem is the type of masking signal employed. One possibility is the use of chaotic signals, but they have a first strong limitation: the need to synchronize emitter and receiver. Optical communications systems, based on chaotic signals, have been proposed in a large number of papers. Moreover, because most of the communication systems are digital and conventional chaos generators are analogue, a conversion analogue-digital is needed. In this paper we will report a new system where the digital chaos is obtained from an optically programmable logic structure. This structure has been employed by the authors in optical computing and some previous results in chaotic signals have been reported. The main advantage of this new system is that an analogue-digital conversion is not needed. Previous works by the authors employed Self-Electrooptical Effect Devices but in this case more conventional structures, as semiconductor laser amplifiers, have been employed. The way to analyze the characteristics of digital chaotic signals will be reported as well as the method to synchronize the chaos generators located in the emitter and in the receiver.

Unattended motion detection system based on the mammalian retina

Sensing systems in living bodies offer a large variety of possible different configurations and philosophies able to be emulated in artificial sensing systems. Motion detection is one of the areas where different animals adopt different solutions and, in most of the cases, these solutions reflect a very sophisticated form. One of them, the mammalian visual system, presents several advantages with respect to the artificial ones. The main objective of this paper is to present a system, based on this biological structure, able to detect motion, its sense and its characteristics. The configuration adopted responds to the internal structure of the mammalian retina, where just five types of cells arranged in five layers are able to differentiate a large number of characteristics of the image impinging onto it. Its main advantage is that the detection of these properties is based purely on its hardware. A simple unit, based in a previous optical logic cell employed in optical computing, is the basis for emulating the different behaviors of the biological neurons. No software is present and, in this way, no possible interference from outside affects to the final behavior. This type of structure is able to work, once the internal configuration is implemented, without any further attention. Different possibilities are present in the architecture to be presented: detection of motion, of its direction and intensity. Moreover, some other characteristics, as symmetry may be obtained.

Analysis of digital chaotic optical signals

The main objective of this paper is to present some tools to analyze a digital chaotic signal. We have proposed some of them previously, as a new type of phase diagrams with binary signals converted to hexadecimal. Moreover, the main emphasis will be given in this paper to an analysis of the chaotic signal based on the Lempel and Ziv method. This technique has been employed partly by us to a very short stream of data. In this paper we will extend this method to long trains of data (larger than 2000 bit units). The main characteristics of the chaotic signal are obtained with this method being possible to present numerical values to indicate the properties of the chaos.

Chaotic behaviour evaluation in optical logic gates with fractal concepts

A chaotic output was obtained previously by us, from an Optical Programmable Logic Cell when a feedback is added. Some time delay is given to the feedback in order to obtain the non-linear behavior. The working conditions of such a cell is obtained from a simple diagram with fractal properties. We analyze its properties as well as the influence of time delay on the characteristics of the working diagram. A further study of the chaotic obtained signal is presented.

Time evolution of frequency components In a chaotic digital signal

The type of signals obtained has conditioned chaos analysis tools. Almost in every case, they have analogue characteristics. But in certain cases, a chaotic digital signal is obtained and theses signals need a different approach than conventional analogue ones. The main objective of this paper will be to present some possible approaches to the study of this signals and how information about their characteristics may be obtained in the more straightforward possible way. We have obtained digital chaotic signals from an Optical Logic Cell with some feedback between output and one of the possible control gates. This chaos has been reported in several papers and its characteristics have been employed as a possible method to secure communications and as a way to encryption. In both cases, the influence of some perturbation in the transmission medium gave problems both for the synchronization of chaotic generators at emitter and receiver and for the recovering of information data. A proposed way to analyze the presence of some perturbation is to study the noise contents of transmitted signal and to implement a way to eliminate it. In our present case, the digital signal will be converted to a multilevel one by grouping bits in packets of 8 bits and applying conventional methods of time-frequency analysis to them. The results give information about the change in signals characteristics and hence some information about the noise or perturbations present. Equivalent representations to the phase and to the Feigenbaum diagrams for digital signals are employed in this case.

Transmission of digital chaotic and information-bearing signals in optical communication systems

A new proposal to have secure communications in a system is reported. The basis is the use of a synchronized digital chaotic systems, sending the information signal added to an initial chaos. The received signal is analyzed by another chaos generator located at the receiver and, by a logic boolean function of the chaotic and the received signals, the original information is recovered. One of the most important facts of this system is that the bandwidth needed by the system remain the same with and without chaos.

Optically programmable logic cells as basic units for transmission and synchronization of chaotic signals

We proposed an optical communications system, based on a digital chaotic signal where the synchronization of chaos was the main objective, in some previous papers. In this paper we will extend this work. A way to add the digital data signal to be transmitted onto the chaotic signal and its correct reception, is the main objective. We report some methods to study the main characteristics of the resulting signal. The main problem with any real system is the presence of some retard between the times than the signal is generated at the emitter at the time when this signal is received. Any system using chaotic signals as a method to encrypt need to have the same characteristics in emitter and receiver. It is because that, this control of time is needed. A method to control, in real time the chaotic signals, is reported.

Some aspects of amacrine neuron simulation for motion detection

As it is known, there are five types of neurons in the mammalian retinal layer allowing the detection of several important characteristics of the visual image impinging onto the visual system, namely, photoreceptors, horizontal cells, amacrine, bipolar and ganglion cells. And it is a well known fact too, that the amacrine neuron architecture allows a first detection for objects motion, being the most important retinal cell to this function. We have already studied and simulated the Dowling retina model and we have verified that many complex processes in visual detection is performed with the basis of the amacrine cell synaptic connections. This work will show how this structure may be employed for motion detection

Depth sensors-based upper limb motion capture system for functional neurorehabilitation

Versatile and accurate motion capture systems, with the required properties to be integrated within both clinical and domiciliary environments, would represent a significant advance in following the progress of the patients as well as in allowing the incorporation of new data exploitation and analysis methods to enhance the functional neurorehabilitation therapeutic processes. Besides, these systems would permit the later development of new applications focused on the automatization of the therapeutic tasks in order to increase the therapist/patient ratio, thus decreasing the costs [1]. However, current motion capture systems are not still ready to work within uncontrolled environments.