Biologically-inspired stochastic vector matching for noise-robust information processing

“End of Moore’s Law” has recently become a topic. Keeping the signal-to-noise ratio (SNR) at the same level in the future will surely increase the energy density of smaller-sized transistors. Lowering the operating voltage will prevent this, but the SNR would inevitably degrade. Meanwhile, biological systems such as cells and brains possess robustness against noise in their information processing in spite of the strong influence of stochastic thermal noise. Inspired by the information processing of organisms, we propose a stochastic computing model to acquire information from noisy signals. Our model is based on vector matching, in which the similarities between the input vector carrying external noisy signals and the reference vectors prepared in advance as memorized templates are evaluated in a stochastic manner. This model exhibited robustness against the noise strength and its performance was improved by addition of noise with an appropriate strength, which is similar to a phenomenon observed in stochastic resonance. Because the stochastic vector matching we propose here has robustness against noise, it is a candidate for noisy information processing that is driven by stochastically-operating devices with low energy consumption in future. Moreover, the stochastic vector matching may be applied to memory-based information processing like that of the brain.     

A note on a symmetry analysis and exact solutions of a nonlinear fin equation

A similarity analysis of a nonlinear fin equation has been carried out by M. Pakdemirli and A.Z. Sahin [Similarity analysis of a nonlinear fin equation, Appl. Math. Lett. (2005) (in press)]. Here, we consider a further group theoretic analysis that leads to an alternative set of exact solutions or reduced equations with an emphasis on travelling wave solutions, steady state type solutions and solutions not appearing elsewhere.     

The solution of Navier equations of classical elasticity using Lie symmetry groups

The analytical solutions of axially-symmetric Navier equations in classical elasticity are found by applying Lie group theory. We investigate two different systems of partial differential equations corresponding elastostatics and elastodynamics problems, and find similarity solutions of both cases by solving the reduced system of ordinary differential equations which have fewer independent variables. As an example of the elastostatics case, the displacements and stress components are obtained for porous, polymeric foam material by using similarity solutions.     

Similarity analysis in magnetohydrodynamics: Hall effects on free convection flow and mass transfer past a semi-infinite vertical flat plate

Heat and mass transfer along a semi-infinite vertical flat plate under the combined buoyancy force effects of thermal and species diffusion is investigated in the presence of a strong non-uniform magnetic field and the Hall currents are taken into account. The induced magnetic field due to the motion of the electrically conducting fluid is negligible. This assumption is valid for a small magnetic Reynolds number. The similarity solutions are obtained using the scale group of transformations. These are the only symmetry transformations admitted by the field equations. The non-linear boundary layer equations with the boundary conditions are transferred to a system of non-linear ordinary differential equations with the appropriate boundary conditions. Furthermore, the similarity equations are solved numerically by using a fourth order Runge-Kutta scheme with the shooting method. Numerical results for the velocity profiles, the temperature profiles and the concentration profiles are presented graphically for various values of the magnetic parameter M in the range of 0-1 with the Hall parameter m taking the values 0.5, 1, 2, and 3.     

Similarity of L-fuzzy Relations Based on L-topologies Induced by L-fuzzy Rough Approximation Operators

This paper proposes similarity of L-fuzzy relations based on L-topologies induced by L-fuzzy rough approximation operators. First, the notion L-fuzzy rough set is generalized and the relationship between generalized L-fuzzy rough sets and L-topologies on an arbitrary universe is investigated. It shows that Alexandrov L-topologies can be induced by L-fuzzy relations without any preconditions. Second, the concept of similarity of L-fuzzy relations is introduced and variations of an L-fuzzy relation are investigated. Third, algebraic structures on similarity of L-fuzzy relations are obtained. Finally, we prove that the subset of the transitive L-fuzzy relations similar to a fixed L-fuzzy relation is a complete distributive lattice.     

Exact solutions of some general nonlinear wave equations in elasticity

A similarity analysis of a nonlinear wave equation in elasticity is studied; in particular, one with anharmonic corrections. The symmetry transformation give rise to exact solutions via the method of invariants. In some cases, graphical figure of the solutions are presented. Furthermore, we consider some cases wherein the velocities of the longitudinal and transversal plane waves are variable. Finally, a brief discussion on how a symmetry analysis on a perturbation of the elasticity equation can be pursued.     

Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption

We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745].     

Numerical similarity reductions of the (1+3)-dimensional Burgers equation

We consider the (1+3)-dimensional Burgers equation u_t = u_xx + u_yy + u_zz + uu_x which has considerable interest in mathematical physics. Lie symmetries are used to reduce it to certain ordinary differential equations. We employ numerical methods to solve a number of these ordinary differential equations.     

Flow and heat transfer over a generalized stretching/shrinking wall problem—Exact solutions of the Navier-Stokes equations

In this paper, we investigate the steady momentum and heat transfer of a viscous fluid flow over a stretching/shrinking sheet. Exact solutions are presented for the Navier-Stokes equations. The new solutions provide a more general formulation including the linearly stretching and shrinking wall problems as well as the asymptotic suction velocity profiles over a moving plate. Interesting non-linear phenomena are observed in the current results including both exponentially decaying solution and algebraically decaying solution, multiple solutions with infinite number of solutions for the flow field, and velocity overshoot. The energy equation ignoring viscous dissipation is solved exactly and the effects of the mass transfer parameter, the Prandtl number, and the wall stretching/shrinking strength on the temperature profiles and wall heat flux are also presented and discussed. The exact solution of this general flow configuration is a rare case for the Navier-Stokes equation.     

Fingerprint developing of coffee flavor by gas chromatography-mass spectrometry and combined chemometrics methods

In this paper, chromatographic fingerprint was firstly used for quality control of tobacco flavors. Based on gas chromatography-mass spectrometry (GC-MS) and combined chemometrics methods, a simple, reliable and reproducible method for developing chromatographic fingerprint of coffee flavor, one of tobacco flavors, was described. Six coffee flavor samples obtained from different locations were used to establish the fingerprint. The qualitative and quantitative analysis of coffee flavor sample from Shenzhen was completed with the help of subwindow factor analysis (SFA). Fifty-two components of 68 separated constituents in coffee flavor sample from Shenzhen, accounting for 88.42% of the total content, were identified and quantified. Then, spectral correlative chromatography (SCC) was used to extract the common peaks from other five studied coffee flavor samples. Thirty-eight components were found to exist in all six samples. Finally, the method validation of fingerprint analysis was performed based on the relative retention time and the relative peak area of common peaks, sample stability and similarity analysis. The similarities of six coffee flavor samples were more than 0.9104 and showed that samples from different locations were consistent to some extent. The developed chromatographic fingerprint was successfully used to differentiate coffee flavor from coco flavor and some little difference sample prepared with coffee flavor and coco flavor by both similarity comparison and principal component projection analysis. The developed method can be used for quality control of coffee flavor.