Swaminathan Sethuraman

Noise-based logic hyperspace with the superposition of 2N states in a single wire

Abstract In the introductory paper [L.B. Kish, Phys. Lett. A 373 (2009) 911], about noise-based logic, we showed how simple superpositions of single logic basis vectors can be achieved in a single wire. The superposition components were the N orthogonal logic basis vectors. Supposing that the different logic values have “on/off” states only, the resultant discrete superposition state represents a single number with N bit accuracy in a single wire, where N is the number of orthogonal logic vectors in the base. In the present Letter, we show that the logic hyperspace (product) vectors defined in the introductory paper can be generalized to provide the discrete superposition of 2 N orthogonal system states. This is equivalent to a multi-valued logic system with 2 2 N logic values per wire. This is a similar situation to quantum informatics with N qubits, and hence we introduce the notion of noise-bit. This system has major differences compared to quantum informatics. The noise-based logic system is deterministic and each superposition element is instantly accessible with the high digital accuracy, via a real hardware parallelism, without decoherence and error correction, and without the requirement of repeating the logic operation many times to extract the probabilistic information. Moreover, the states in noise-based logic do not have to be normalized, and non-unitary operations can also be used. As an example, we introduce a string search algorithm which is O ( M ) times faster than Grovers quantum algorithm (where M is the number of string entries), while it has the same hardware complexity class as the quantum algorithm.

NON-BREAKABLE DATA ENCRYPTION WITH CLASSICAL INFORMATION

Secure encryption of data is one of the most important parts of information technology and major concern of data security, military, defense and homeland security applications. The main aim of the paper is to propose a new way of approach to encryption. We propose a new possible approach [1] to encryption, which could be a fast, simple, inexpensive, robust, flexible, and mobile way of data encryption for absolutely secure data transmission by using classical digital information. The Eavesdropper is allowed to know the received signal thus the method has a higher level of protection than that of quantum encryption. Factorization algorithms do not help to break the code. Proper scrambling operators, which are necessary for the method, are study of current research.

Noise-Based Logic and Computing: From Boolean Logic Gates to Brain Circuitry and Its Possible Hardware Realization

When noise dominates an information system, like in nano-electronic systems of the foreseeable future, a natural question occurs: Can we perhaps utilize the noise as information carrier? Another question is: Can a deterministic logic scheme be constructed that may explain how the brain efficiently processes information, with random neural spike trains of less than 100 Hz frequency, and with a similar number of human brain neurons as the number of transistors in a 16 GB Flash dive? The answers to these questions are yes. Related developments indicate reduced power consumption with noise-based deterministic Boolean logic gates and the more powerful multivalued logic versions with an arbitrary number of logic values. Similar schemes as the Hilbert space of quantum informatics can also be constructed with noise-based logic by utilizing the noise-bits and their multidimensional hyperspace without the limitations of quantum-collapse of wavefunctions. A noise-based string search algorithm faster than Grover’s quantum search algorithm can be obtained, with the same hardware complexity class as the quantum engine. This logic hyperspace scheme has also been utilized to construct the noise-based neuro-bits and a deterministic multivalued logic scheme for the brain. Some of the corresponding circuitry of neurons is shown. Some questions and answers about a chip realization of such a random spike based deterministic multivalued logic scheme are presented.

Non Breakable Data Encryption With Classical Information

With the Kish‐Sethuraman (KS) cipher an attempt was made, by using special operators and communication, to reach absolutely secure classical communication. First the message is bounced back with additional encryption by the Receiver and then the original encryption is removed and the message is resent by the Sender. The mechanical analogy of this operation is using two padlocks; one by the Sender and one by the Receiver. Klappenecker has pointed out that finding an efficient software realization of the operators is equivalent of proving the P ≠ NP problem. Various open problems are discussed.

Cross-spectral measurement of neural signal transfer

The phenomenon of noise enhanced signal transfer, or stochastic resonance, has been observed in many nonlinear systems such as neurons and ion channels. Initial studies of stochastic resonance focused on systems driven by a periodic signal, and hence used a signal to noise ratio based measure for comparison between the input and output of the system. It has been pointed out that for the more general case of aperiodic signals other measures are required, such as cross-correlation or information theoretical tools. In this paper we present simulation results obtained in a model neural system driven by a broadband aperiodic signal, and producing a signal imitating neural spikes. The system is analyzed by using cross-spectral measures.

Cross spectra measure of neural signals and noise

Shannons information rate formula does not work for wideband (aperiodic) signals with nonlinear transfer. The classical signal and noise measures used to characterize stochastic resonance do not work either because their way of distinguishing signal from noise fails. In a study published earlier, a new way of measuring and identifying noise and aperiodic (wideband) signals during strongly nonlinear transfer was introduced. The method was based on using cross-spectra between the input and the output. According to the study, in the case of linear transfer and sinusoidal signals, the method gives the same results as the classical method and in the case of aperiodic signals it gives a sensible measure. In this paper we refine the theory and present detailed simulations which validate and refine the conclusions reached in that study. The simulation results clearly confirm that the cross-spctral identifications of output signal and noise are sensible measures and we put the theory on a firm footing. As neural and ion channel signal transfer is nolinear and aperiodic, the new method has direct applicability in biophysics and neural science.

Blue shot noise

Finite pulse width effects in level crossing detectors and similar systems, such as neurons, cause an output noise which is a monotonically increasing function of frequency in the low frequency limit. The effect is also relevant for shot noise phenomena with reduced strength.

Motion Planning of a Group of Agents Using the Homotopy Approach

In this paper motion planning of a group of agents is done to move the group from an initial configuration to a final configuration through obstacles in 2-D. Also we introduce a new homotopy approach which uses potential fields to find paths in polynomial space. We use the homotopy approach for changing the group shape of the mobile agents and at the same time treat the group as a single agent by finding a bounding disc for it to plan the motion of the group through obstacles. A time varying polynomial is constructed, the roots of which represent the current positions of the mobile agents in a frame attached to the bounding disc. The real and imaginary parts of the roots of this polynomial represent the x and y coordinates of the mobile agents in this frame. This polynomial is constructed such that it avoids the discriminant variety or the set of polynomials having multiple roots. This is equivalent to saying that the mobile agents do not collide with each other at all times. The bounding disc is then used to plan the motion of the agents through obstacles such that the group avoids the obstacles at all times.Copyright

A New Method of Motion Coordination of a Group of Mobile Agents

This paper presents a new method for coordinated motion planning of multiple mobile agents. The position in 2-D of each mobile agent is mapped to a complex number and a time varying polynomial contains information regarding the current positions of all mobile agents, the degree of the polynomial being the number of mobile agents and the roots of the polynomial representing the position in 2-D of the mobile agents at a given time. This polynomial is constructed by finding a path parameterized in time from the initial to the goal polynomial which represent the initial and goal positions of the mobile agents so that the discriminant variety or the set of polynomials with multiple roots is avoided in polynomial space. This is equivalent to saying that there is no collision between any two agents in going from initial position to goal position.Copyright

BLUE NOISE EFFECTS IN A NON-DYNAMICAL NEURAL MODEL SYSTEM

Finite pulse width effects in level crossing detectors and similar systems, such as neurons, can yield an output noise that is, in the low frequency limit, a monotonically increasing function of the frequency. The phenomenon can well be observed at excitations with strong noise when the firing frequency is high. Blue noise effects have been observed in stochastically driven dynamical systems like harmonic oscillators. However it is surprising that it exists in a non-dynamical system like the level crossing detector.