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Perception, decisions, and sensations are all encoded into trains of action potentials in the brain. The relation between stimulus strength and all-or-nothing spiking of neurons is widely believed to be the basis of this coding. This initiated the development of spiking neuron models; one of today's most powerful conceptual tool for the analysis and emulation of neural dynamics. The success of electronic circuit models and their physical realization within silicon field-effect transistor circuits lead to elegant technical approaches. Recently, the spectrum of electronic devices for neural computing has been extended by memristive devices, mainly used to emulate static synaptic functionality. Their capabilities for emulations of neural activity were recently demonstrated using a memristive neuristor circuit, while a memristive neuron circuit has so far been elusive. Here, a spiking neuron model is experimentally realized in a compact circuit comprising memristive and memcapacitive devices based on the strongly correlated electron material vanadium dioxide (VO2) and on the chemical electromigration cell Ag/TiO2-x /Al. The circuit can emulate dynamical spiking patterns in response to an external stimulus including adaptation, which is at the heart of firing rate coding as first observed by E.D. Adrian in 1926.

In this study, the authors propose a novel extended continuous time birth–death model for reliability analysis of a nanocell device. A nanocell consists of conducting nanoparticles connected via randomly placed self‐assembled monolayer of molecules. These molecules behave as a negative differential resistor. The mathematical expression for expected nanocell lifetime and its availability, in presence of transient errors is computed. On the basis of the model, an algorithm is developed and implemented in MATLAB, PERL and HSPICE, to automatically generate the proposed model representation for a given nanocell. It is used to estimate the success_ratio as well as the nanocell reliability, while considering the uncertainties induced by transient errors. The theoretical results for reliability are validated by simulating HSPICE model of nanocell in presence of varying defect rates. It is observed that the device reliability increases with increase in the number of nanoparticles and molecules. A lower and upper bounds for nanocell reliability are calculated in theory which is validated in simulations.

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called \"imaginary numbers\"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive \"numbers\" in all of mathematics.Some images inside the book are unavailable due to digital copyright restrictions.