Search results for "approximation"
showing 10 items of 818 documents
How Low Can Approximate Degree and Quantum Query Complexity Be for Total Boolean Functions?
2012
It has long been known that any Boolean function that depends on n input variables has both degree and exact quantum query complexity of Omega(log n), and that this bound is achieved for some functions. In this paper we study the case of approximate degree and bounded-error quantum query complexity. We show that for these measures the correct lower bound is Omega(log n / loglog n), and we exhibit quantum algorithms for two functions where this bound is achieved.
Population Monte Carlo Schemes with Reduced Path Degeneracy
2017
Population Monte Carlo (PMC) algorithms are versatile adaptive tools for approximating moments of complicated distributions. A common problem of PMC algorithms is the so-called path degeneracy; the diversity in the adaptation is endangered due to the resampling step. In this paper we focus on novel population Monte Carlo schemes that present enhanced diversity, compared to the standard approach, while keeping the same implementation structure (sample generation, weighting and resampling). The new schemes combine different weighting and resampling strategies to reduce the path degeneracy and achieve a higher performance at the cost of additional low computational complexity cost. Computer si…
Low-Rate Reduced Complexity Image Compression using Directionlets
2006
The standard separable two-dimensional (2-D) wavelet transform (WT) has recently achieved a great success in image processing because it provides a sparse representation of smooth images. However, it fails to capture efficiently one-dimensional (1-D) discontinuities, like edges and contours, that are anisotropic and characterized by geometrical regularity along different directions. In our previous work, we proposed a construction of critically sampled perfect reconstruction anisotropic transform with directional vanishing moments (DVM) imposed in the corresponding basis functions, called directionlets. Here, we show that the computational complexity of our transform is comparable to the co…
Market reaction to a bid-ask spread change: a power-law relaxation dynamics.
2009
We study the relaxation dynamics of the bid-ask spread and of the midprice after a sudden variation of the spread in a double auction financial market. We find that the spread decays as a power law to its normal value. We measure the price reversion dynamics and the permanent impact, i.e., the long-time effect on price, of a generic event altering the spread and we find an approximately linear relation between immediate and permanent impact. We hypothesize that the power-law decay of the spread is a consequence of the strategic limit order placement of liquidity providers. We support this hypothesis by investigating several quantities, such as order placement rates and distribution of price…
Using Applications and Tools to Visualize ab initio Calculations Performed in VASP
2018
Visualization of the results of the ab initio calculations is important for the analysis of these results. It improves the quality of the analysis by supplementing the plain numbers received as the output of the calculations with various graphical images and facilitates the analysis of the results. In addition to that visualization helps avoiding some mistakes or inconsistencies. Various tools have been used in this work to construct the unit cell models of the calculated lattices, to check and analyze the calculated lattice structure before and after the relaxation, to plot total and difference electron charge density maps.
The integral‐direct coupled cluster singles and doubles model
1996
An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening. © 1996 American Institute of Physics.
Group Nonnegative Matrix Factorization with Sparse Regularization in Multi-set Data
2021
Constrained joint analysis of data from multiple sources has received widespread attention for that it allows us to explore potential connections and extract meaningful hidden components. In this paper, we formulate a flexible joint source separation model termed as group nonnegative matrix factorization with sparse regularization (GNMF-SR), which aims to jointly analyze the partially coupled multi-set data. In the GNMF-SR model, common and individual patterns of particular underlying factors can be extracted simultaneously with imposing nonnegative constraint and sparse penalty. Alternating optimization and alternating direction method of multipliers (ADMM) are combined to solve the GNMF-S…
Automatic left ventricle volume calculation with explainability through a deep learning weak-supervision methodology
2021
[EN] Background and objective: Magnetic resonance imaging is the most reliable imaging technique to assess the heart. More specifically there is great importance in the analysis of the left ventricle, as the main pathologies directly affect this region. In order to characterize the left ventricle, it is necessary to extract its volume. In this work we present a neural network architecture that is capable of directly estimating the left ventricle volume in short axis cine Magnetic Resonance Imaging in the end-diastolic frame and provide a segmentation of the region which is the basis of the volume calculation, thus offering explain-ability to the estimated value. Methods: The network was des…
The Use of Easily Computed Checks as a Trigger for Error Elimination
1970
Several checks have been inserted in the three main programs in order to learn about their correlation to the average relative error.
Classification of Melanoma Lesions Using Sparse Coded Features and Random Forests
2016
International audience; Malignant melanoma is the most dangerous type of skin cancer, yet it is the most treatable kind of cancer, conditioned by its early diagnosis which is a challenging task for clinicians and dermatologists. In this regard, CAD systems based on machine learning and image processing techniques are developed to differentiate melanoma lesions from benign and dysplastic nevi using dermoscopic images. Generally, these frameworks are composed of sequential processes: pre-processing, segmentation, and classification. This architecture faces mainly two challenges: (i) each process is complex with the need to tune a set of parameters, and is specific to a given dataset; (ii) the…