The principal component analysis (PCA) is a staple statistical and unsupervised machine learning technique in finance. application of PCA financial setting associated with several difficulties, such as numerical instability nonstationarity. We attempt to resolve them by proposing two new variants PCA: an iterated (IPCA) exponentially weighted moving (EWMPCA). Both rely on the Ogita-Aishima iter...

We review recent results on necessary and sufficient conditions for measures on R and ∂D to yield exponential decay of the recursion coefficients of the corresponding orthogonal polynomials. We include results on the relation of detailed asymptotics of the recursion coefficients to detailed analyticity of the measures. We present an analog of Carmona’s formula for OPRL. A major role is played b...

We show that the hitting time of the discrete time quantum random walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum random walks. We provide the framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We t...

This paper studies the steady-state availability of systems with times to outages and recoveries that are generally distributed. Availability bounds are derived for systems with limited information about the distributions. Also investigated are the applicability of convenient exponential models in evaluating availability for systems that have two-sided bounded distributions of times to planned ...

It is well-known that every planar or projective planar graph can be 3-colored so that each color class induces a forest. This bound is sharp. In this paper, we show that there are in fact exponentially many 3-colorings of this kind for any (projective) planar graph. The same result holds in the setting of 3-list-colorings.

The assessment of the stability and the vulnerability of complex networks is the important concept while studying of them. In the literature, a sort of measures have been given in order to assessment the stability of systems. And also, some graph-theoretic parameters have been formed to provide formulas which calculate the reliability of a network. In this paper, we study the vulnerability of s...

We consider an M/G/∞ model with exponentially distributed setup times. Arrivals result in an off server starting a setup. Upon completing a setup, a server begins serving a waiting customer. Upon completing service, with probability p the server becomes eligible to serve another waiting customer. Among other things, we show, in steady state, that the number of busy servers is Poisson distribute...

The Mel’nikov equation is a (2+1) dimensional nonlinear evolution equation admitting boomeron type solutions. In this paper, after showing that it satisfies the Painlevé property, we obtain exponentially localized dromion type solutions from the bilinearized version which have not been reported so far. We also obtain more general dromion type solutions with spatially varying amplitude as well a...

We explore a mean-field model for the evolution of exponentially growing populations of mutating replicators. Motivated by recent in vitro experiments devised to analyze phenotypic properties of bacterial and viral populations subjected to serial population transfers, we allow our in silico individuals to undergo unrestricted growth before applying bottleneck events. Different dynamical regimes...