The Hopfield model of a neural network is extended to allow for the storage and retrieval of biased patterns, [g'";), where N 'g, g =a is arbitrary. Such patterns represent levels of activity (i.e., percentage of firing neurons) equal to 2 (1+a), —1 &a & 1. If the coupling constants (synaptic efficacies) are constructed as in the original Hopfield model, the system can retrieve at most a very s...

Time-dependent density functional theory (TDDFT) is a powerful tool allowing for accurate description of excited states in many nanoscale molecular systems; however, its application to large molecules may be plagued with difficulties that are not immediately obvious from previous experiences of applying TDDFT to small molecules. In TDDFT, the appearance of spurious charge-transfer states below ...

Cell fusion, a process that merges two or more cells into one, is required for normal development and has been explored as a tool for stem cell therapy. It has also been proposed that cell fusion causes cancer and contributes to its progression. These functions rely on a poorly understood ability of cell fusion to create new cell types. We suggest that this ability can be understood by consider...

classical explicit finite difference schemes are unsuitable for the solution of the famous black-scholes partial differential equation, since they impose severe restrictions on the time step. furthermore, they may produce spurious oscillations in the solution. we propose a new scheme that is free of spurious oscillations and guarantees the positivity of the solution for arbitrary stepsizes. the...