This paper develops a spectral expansion approach to the valuation of contingent claims when the underlying state variable follows a one-dimensional diffusion with the infinitesimal variance a(x), drift b(x) and instantaneous discount (killing) rate r(x). The Spectral Theorem for self-adjoint operators in Hilbert space yields the spectral decomposition of the contingent claim value function. Ba...

Spectral methods are a powerful tool for inferring the parameters of certain classes of probability distributions by means of standard eigenvalueeigenvector decompositions. Spectral algorithms can be orders of magnitude faster than loglikelihood based and related iterative methods, and, thanks to the uniqueness of the spectral decomposition, they enjoy global optimality guarantees. In practice,...

We study the frequency form, popular in physics, of Maxwell equations for nonlinear spatially inhomogeneous dielectric media. Using wavepackets based on eigenmodes of the underlying linear dielectric medium we develop a mathematically consistent interpretation of the frequency form of nonlinear Maxwell operators. In particular, we construct the operator of nonlinear polarization based on freque...

Recently, there has been ample of research on indexing for structural graph queries. However, as verified by our experiments with a large number of random graphs and scale-free graphs, the performances of indexes of graph queries may vary greatly. Unfortunately, the structures of graph indexes are too often complex and ad-hoc; and deriving an accurate performance model appears a daunting task. ...

The spectral decomposition is given for the N-qubit Bell operators with two observables per qubit. It is found that the eigenstates (when non-degenerate) are N-qubit GHZ states even for those operators that do not allow the maximal violation of the corresponding inequality. We present two applications of this analysis. In particular, we discuss the existence of pure entangled states that do not...

In this paper a new approach to Temporal Decomposition (TD) of speech, called Spectral Stability Based Event Localizing Temporal Decomposition (S2BEL-TD), is presented. The original method of TD proposed by Atal (1983, Proceedings of the International Conference on Acoustics, Speech, and Signal Processing, 81–84) is known to have the drawbacks of high computational cost, and the high parameter ...

The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station­ ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...

Proteins usually consist of several structural domains which play an important role in the classification and analysis of them. As the number of known protein structures grows at an exponential rate, a computer-aided domain decomposition of proteins becomes desirable. We present three different decomposition methods in this report. They are based on a graph representation of the proteins. These...

We consider two related problems in this paper. Given an undeciphered alphabetic writing system or mono-alphabetic cipher, determine: (1) which of its letters are vowels and which are consonants; and (2) whether the writing system is a vocalic alphabet or an abjad. We are able to show that a very simple spectral decomposition based on character co-occurrences provides nearly perfect performance...

Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorit...