Wavelets are a powerful new mathematical tool which offers the possibility to treat in a natural way quantities characterized by several length scales. In this article we will show how wavelets can be used to solve partial differential equations which are characterized by widely varying length scales and which are therefore hardly accessible by other numerical methods. The standard way to solve...

The ReachOut clinical psychology shared task challenge addresses the problem of providing an automatic triage for posts to a support forum for people with a history of mental health issues. Posts are classified into green, amber, red and crisis. The non-green categories correspond to increasing levels of urgency for some form of intervention. The Thomson Reuters submissions arose from an idea a...

A novel cross term deleted Wigner representation can be obtained by expanding the Wigner Distribution (WD) in terms of two complementary Gabor coe cients of the signal and a translated set of Wigner basis functions. Two such complementary Gabor coe cients of a signal can be obtained by reversing the role of Gabor synthesis window h(t) and its biorthogonal function b(t). Such a representation is...

In this research, Quantum-mechanical calculations were performed at the HF method with the 6-31+G*basis set and at the B3LYP method with the 6-31+G* basis set in the gas phase and five solvents such as water, DMSO, methanol, ethanol and dichloromethane at six temperatures. According to these theoretical results of IR, we extracted thermo chemical parameters such as enthalpy (∆H Kcal/mol), Gibbs...

Density fitting (DF), also known as the resolution of identity (RI), is a widely used technique in quantum chemical calculations with various types atomic basis sets─Gaussian-type orbitals, Slater-type well numerical orbitals─to speed up density functional, Hartree–Fock (HF), and post-HF calculations. Traditionally, custom auxiliary sets are hand-optimized for each orbital set; however, some au...

The contribution is focused on change point detection in a one-dimensional stochastic process by sparse parameter estimation from an overparametrized model. A stochastic process with change in the mean is estimated using dictionary consisting of Heaviside functions. The basis pursuit algorithm is used to get sparse parameter estimates. The mentioned method of change point detection in a stochas...

We consider the set M = { ( a . 11): n bh mod.rL') of all solutions of the key equation for alternant codes, where h is the syndrome polynomial. In decoding these codes a particular solution (d. (T) E M is sought, subject to d and being relatively prime and satisfying certain degree conditions. We prove that these requirements specify (d. (T ) uniquely as the minimal element of M (analogous to ...

A novel classi®er for the analysis of remote-sensing images is proposed. Such a classi®er is based on Radial Basis Function (RBF) neural networks and relies on an incremental-learning technique. This technique allows the periodical acquisition of new information whenever a new training set becomes available, while preserving the knowledge learnt by the network on previous training sets. In addi...

It has been widely known that complete decoding for binary linear codes can be regarded as an linear integer programming problem with binary arithmetic conditions. Conti and Traverso [8] have proposed an efficient algorithm which uses Gröbner bases to solve integer programming with ordinary integer arithmetic conditions. Ikegami and Kaji [11] extended the Conti-Traverso algorithm to solve integ...

The objective of this note is the presentation of a procedure for converting a given Gröbner basis (Buchberger, 1965) of a polynomial ideal I to a Gröbner basis of I with respect to another term order. This procedure, which we call the Gröbner walk, is completely elementary and does not require any assumptions about the dimension or the number of variables of the ideal. The Gröbner walk breaks ...