Search results for "Transform"
showing 10 items of 3975 documents
The Herzog-Vasconcelos conjecture for affine semigroup rings
1999
Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.
Error-Free Affine, Unitary, and Probabilistic OBDDs
2018
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata versions of these models.
Any AND-OR Formula of Size N Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
2007
Consider the problem of evaluating an AND-OR formula on an $N$-bit black-box input. We present a bounded-error quantum algorithm that solves this problem in time $N^{1/2+o(1)}$. In particular, approximately balanced formulas can be evaluated in $O(\sqrt{N})$ queries, which is optimal. The idea of the algorithm is to apply phase estimation to a discrete-time quantum walk on a weighted tree whose spectrum encodes the value of the formula.
Burrows-Wheeler transform and Run-Length Enconding
2017
In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-…
On n–Fold Blocking Sets
1986
An n-fold blocking set is a set of n-disjoint blocking sets. We shall prove upper and lower bounds for the number of components in an n-fold blocking set in projective and affine spaces.
Error-Free Affine, Unitary, and Probabilistic OBDDs
2021
We introduce the affine OBDD model and show that zero-error affine OBDDs can be exponentially narrower than bounded-error unitary and probabilistic OBDDs on certain problems. Moreover, we show that Las-Vegas unitary and probabilistic OBDDs can be quadratically narrower than deterministic OBDDs. We also obtain the same results for the automata counterparts of these models.
Developing and Integrating Advanced Movement Features Improves Automated Classification of Ciliate Species
2015
Recent advances in tracking technologies such as GPS or video tracking systems describe the movement paths of individuals in unprecedented details and are increasingly used in different fields, including ecology. However, extracting information from raw movement data requires advanced analysis techniques, for instance to infer behaviors expressed during a certain period of the recorded trajectory, or gender or species identity in case data is obtained from remote tracking. In this paper, we address how different movement features affect the ability to automatically classify the species identity, using a dataset of unicellular microbes (i.e., ciliates). Previously, morphological attributes a…
Regression Wavelet Analysis for Lossless Coding of Remote-Sensing Data
2016
A novel wavelet-based scheme to increase coefficient independence in hyperspectral images is introduced for lossless coding. The proposed regression wavelet analysis (RWA) uses multivariate regression to exploit the relationships among wavelet-transformed components. It builds on our previous nonlinear schemes that estimate each coefficient from neighbor coefficients. Specifically, RWA performs a pyramidal estimation in the wavelet domain, thus reducing the statistical relations in the residuals and the energy of the representation compared to existing wavelet-based schemes. We propose three regression models to address the issues concerning estimation accuracy, component scalability, and c…
Data Compression Using Wavelet and Local Cosine Transforms
2015
The chapter describes an algorithm that compresses two-dimensional data arrays, which are piece-wise smooth in one direction and have oscillating events in the other direction. Seismic, hyper-spectral and fingerprints data, for example, have such a mixed structure. The transform part of the compression process is an algorithm that combines wavelet and local cosine transform (LCT). The quantization and the entropy coding parts of the compression are taken from the SPIHT codec. To efficiently apply the SPIHT codec to a mixed coefficients array, reordering of the LCT coefficients takes place. On the data arrays, which have the mixed structure, this algorithm outperforms other algorithms that a…
Automated detection and localization system of myocardial infarction in single-beat ECG using Dual-Q TQWT and wavelet packet tensor decomposition.
2019
Abstract Background and objective It is challenging to conduct real-time identification of myocardial infarction (MI) due to artifact corruption and high dimensionality of multi-lead electrocardiogram (ECG). In the present study, we proposed an automated single-beat MI detection and localization system using dual-Q tunable Q-factor wavelet transformation (Dual-Q TQWT) denoising algorithm. Methods After denoising and segmentation of ECG, a fourth-order wavelet tensor (leads × subbands × samples × beats) was constructed based on the discrete wavelet packet transform (DWPT), to represent the features considering the information of inter-beat, intra-beat, inter-frequency, and inter-lead. To red…