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In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in $n$ compatible ways. For this we extend the previous spectral system construction of the author, and we…
This paper examines the problem of testing whether a discrete time-series vector contains a periodic signal or is merely noise. To do this we examine the stochastic behaviour of the maximum intensity of the observed time-series vector and…
The optimum interval method for finding an upper limit of a one-dimensionally distributed signal in the presence of an unknown background is extended to the case of high statistics. There is also some discussion of how the method can be…
In this paper we formulate a solution of the robust linear regression problem in a general framework of correntropy maximization. Our formulation yields a unified class of estimators which includes the Gaussian and Laplacian kernel-based…
In this article, we propose a new algorithm for supervised learning methods, by which one can both capture the non-linearity in data and also find the best subset model. To produce an enhanced subset of the original variables, an ideal…
Maximum-length sequences (m-sequences for short) over finite fields are generated by linear feedback shift registers with primitive characteristic polynomials. These sequences have nice mathematical structures and good randomness properties…
This paper proposes a constrained maximum likelihood estimator for sequential search models, using the MPEC (Mathematical Programming with Equilibrium Constraints) approach. This method enhances numerical accuracy while avoiding ad hoc…
After giving an overview of the existing theory regarding the periods of sequences defined by linear recurrences over finite fields, we give explicit descriptions of the sets of periods that arise if one considers all sequences over…
We present necessary and sufficient conditions for the termination of linear homogeneous programs. We also develop a complete method to check termination for this class of programs. Our complete characterization of termination for such…
This paper analyzes the performance of sequential importance sampling algorithms for estimating the number of perfect matchings in bipartite graphs. Precise bounds on the number of samples required to yield an accurate estimate are derived.…
This paper shows a mathematical formalization, algorithms and computation software of volume optimal cycles, which are useful to understand geometric features shown in a persistence diagram. Volume optimal cycles give us concrete and…
With the increasing size of today's data sets, finding the right parameter configuration in model selection via cross-validation can be an extremely time-consuming task. In this paper we propose an improved cross-validation procedure which…
We are interested to detect periodic signals in Hilbert space valued time series when the length of the period is unknown. A natural test statistic is the maximum Hilbert-Schmidt norm of the periodogram operator over all fundamental…
Pathwise predictability of continuous time processes is studied in deterministic setting. We discuss uniform prediction in some weak sense with respect to certain classes of inputs. More precisely, we study possibility of approximation of…
Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction…
Ongoing and future surveys with repeat imaging in multiple bands are producing (or will produce) time-spaced measurements of brightness, resulting in the identification of large numbers of variable sources in the sky. A large fraction of…
Free-space quantum key distribution requires to synchronize the transmitted and received signals. A timing and synchronization system for this purpose based on a de Bruijn sequence has been proposed and studied recently for a channel…
Monte Carlo simulations are one of the major tools in statistical physics, complex system science, and other fields, and an increasing number of these simulations is run on distributed systems like clusters or grids. This raises the issue…
A simple method called symbolic representation for piecewise linear functions on the real line is introduced and used to compute the numbers of periodic points of all periods for some such functions. Since, for every positive integer m, the…
Sequential sampling occurs when the entire population is not known in advance and data are obtained one at a time or in groups of units. This manuscript proposes a new algorithm to sequentially select a balanced sample. The algorithm…