5,859 research outputs found
Resultants and subresultants of p-adic polynomials
We address the problem of the stability of the computations of resultants and
subresultants of polynomials defined over complete discrete valuation rings
(e.g. Zp or k[[t]] where k is a field). We prove that Euclide-like algorithms
are highly unstable on average and we explain, in many cases, how one can
stabilize them without sacrifying the complexity. On the way, we completely
determine the distribution of the valuation of the principal subresultants of
two random monic p-adic polynomials having the same degree
Optimal rates for plug-in estimators of density level sets
In the context of density level set estimation, we study the convergence of
general plug-in methods under two main assumptions on the density for a given
level . More precisely, it is assumed that the density (i) is smooth
in a neighborhood of and (ii) has -exponent at level
. Condition (i) ensures that the density can be estimated at a
standard nonparametric rate and condition (ii) is similar to Tsybakov's margin
assumption which is stated for the classification framework. Under these
assumptions, we derive optimal rates of convergence for plug-in estimators.
Explicit convergence rates are given for plug-in estimators based on kernel
density estimators when the underlying measure is the Lebesgue measure. Lower
bounds proving optimality of the rates in a minimax sense when the density is
H\"older smooth are also provided.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ184 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Zernike velocity moments for sequence-based description of moving features
The increasing interest in processing sequences of images motivates development of techniques for sequence-based object analysis and description. Accordingly, new velocity moments have been developed to allow a statistical description of both shape and associated motion through an image sequence. Through a generic framework motion information is determined using the established centralised moments, enabling statistical moments to be applied to motion based time series analysis. The translation invariant Cartesian velocity moments suffer from highly correlated descriptions due to their non-orthogonality. The new Zernike velocity moments overcome this by using orthogonal spatial descriptions through the proven orthogonal Zernike basis. Further, they are translation and scale invariant. To illustrate their benefits and application the Zernike velocity moments have been applied to gait recognition—an emergent biometric. Good recognition results have been achieved on multiple datasets using relatively few spatial and/or motion features and basic feature selection and classification techniques. The prime aim of this new technique is to allow the generation of statistical features which encode shape and motion information, with generic application capability. Applied performance analyses illustrate the properties of the Zernike velocity moments which exploit temporal correlation to improve a shape's description. It is demonstrated how the temporal correlation improves the performance of the descriptor under more generalised application scenarios, including reduced resolution imagery and occlusion
Wavelet Factorization and Related Polynomials
Our goal is exploring and better understanding factorizations of polyphase matrices for finite impulse response (FIR) filters. In particular, we focus on nearest neighbor factorizations discussed by Wickerhauser and Zhu that allow for efficient implementation of the discrete wavelet transform (DWT) for the algorithms of Daubechies and Sweldens and Mallat. Nearest neighbor lifting is a specific form of the general lifting scheme that improves the lifting algorithm by optimizing the number of efficient memory accesses. Nearest neighbor lifting factorizations are typically generated by implementing the Euclidean algorithm for Laurent polynomials, which introduces multiple choices of factorizations of a polyphase matrix associated with a filter, and are the main focus of this work
Recognizing and forecasting the sign of financial local trends using hidden Markov models
The problem of forecasting financial time series has received great attention in the past, from both
Econometrics and Pattern Recognition researchers. In this context, most of the efforts were spent to
represent and model the volatility of the financial indicators in long time series. In this paper a different
problem is faced, the prediction of increases and decreases in short (local) financial trends. This problem,
poorly considered by the researchers, needs specific models, able to capture the movement in the short
time and the asymmetries between increase and decrease periods. The methodology presented in this
paper explicitly considers both aspects, encoding the financial returns in binary values (representing the
signs of the returns), which are subsequently modelled using two separate Hidden Markov models, one for
increases and one for decreases, respectively. The approach has been tested with different experiments
with the Dow Jones index and other shares of the same market of different risk, with encouraging results
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