scholarly journals Speed up linear scan in high-dimensions by sorting one-dimensional projections

2011 ◽  
Vol 3 (4) ◽  
pp. 41-48
Author(s):  
Jiangtao Cui ◽  
Bin Xiao ◽  
Gengdai Liu ◽  
Lian Jiang
Keyword(s):  
High Dimensions ◽  
One Dimensional ◽  
Speed Up

scholarly journals Estimating Differential Entropy using Recursive Copula Splitting

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 236 ◽  
Author(s):  
Gil Ariel ◽  
Yoram Louzoun
Keyword(s):  
Compact Support ◽  
Mixed Type ◽  
Random Variables ◽  
Differential Entropy ◽  
High Dimensions ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Different Dimensions

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.

scholarly journals A ‘metric’ semi-Lagrangian Vlasov–Poisson solver

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Stéphane Colombi ◽  
Christophe Alard
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Second Order ◽  
Space Distribution ◽  
Third Order ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Poisson Solver ◽  
Dimensional Phase Space ◽  
Speed Up

We propose a new semi-Lagrangian Vlasov–Poisson solver. It employs metric elements to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $\boldsymbol{Q}(\boldsymbol{P})$ of any test particle $\boldsymbol{P}$, by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $\boldsymbol{P}$ by proper interpolation of initial conditions, following Liouville theorem. When distortion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third-order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four- or six-dimensional phase space. It can also be trivially generalised to plasmas.

scholarly journals Improved Approximation for Fréchet Distance on c-Packed Curves Matching Conditional Lower Bounds

2017 ◽  
Vol 27 (01n02) ◽  
pp. 85-119 ◽  
Author(s):  
Karl Bringmann ◽  
Marvin Künnemann
Keyword(s):  
Lower Bounds ◽  
Time Complexity ◽  
Linear Time ◽  
High Dimensions ◽  
Fréchet Distance ◽  
Worst Case ◽  
One Dimensional ◽  
Dimension Formula ◽  
Frechet Distance ◽  
Special Case

The Fréchet distance is a well studied and very popular measure of similarity of two curves. The best known algorithms have quadratic time complexity, which has recently been shown to be optimal assuming the Strong Exponential Time Hypothesis (SETH) [Bringmann, FOCS'14]. To overcome the worst-case quadratic time barrier, restricted classes of curves have been studied that attempt to capture realistic input curves. The most popular such class are [Formula: see text]-packed curves, for which the Fréchet distance has a [Formula: see text]-approximation in time [Formula: see text] [Driemel et al., DCG'12]. In dimension [Formula: see text] this cannot be improved to [Formula: see text] for any [Formula: see text] unless SETH fails [Bringmann, FOCS'14]. In this paper, exploiting properties that prevent stronger lower bounds, we present an improved algorithm with time complexity [Formula: see text]. This improves upon the algorithm by Driemel et al. for any [Formula: see text]. Moreover, our algorithm's dependence on [Formula: see text], [Formula: see text] and [Formula: see text] is optimal in high dimensions apart from lower order factors, unless SETH fails. Our main new ingredients are as follows: For filling the classical free-space diagram we project short subcurves onto a line, which yields one-dimensional separated curves with roughly the same pairwise distances between vertices. Then we tackle this special case in near-linear time by carefully extending a greedy algorithm for the Fréchet distance of one-dimensional separated curves.

scholarly journals Wake and wave resistance on viscous thin films

2016 ◽  
Vol 792 ◽  
pp. 829-849 ◽  
Author(s):  
René Ledesma-Alonso ◽  
Michael Benzaquen ◽  
Thomas Salez ◽  
Elie Raphaël
Keyword(s):  
Pressure Field ◽  
Finite Size ◽  
External Source ◽  
External Pressure ◽  
Wave Resistance ◽  
Two Dimensional ◽  
Pressure Source ◽  
One Dimensional ◽  
Speed Up

The effect of an external pressure disturbance, being displaced with a constant speed along the free surface of a viscous thin film, is studied theoretically in the lubrication approximation in one- and two-dimensional geometries. In the comoving frame, the imposed pressure field creates a stationary deformation of the interface – a wake – that spatially vanishes in the far region. The shape of the wake and the way it vanishes depend on both the speed and size of the external source and the properties of the film. The wave resistance, namely the force that has to be externally furnished in order to maintain the wake, is analysed in detail. For finite-size pressure disturbances, it increases with the speed, up to a certain transition value, above which a monotonic decrease occurs. The role of the horizontal extent of the pressure field is studied as well, revealing that for a smaller disturbance the latter transition occurs at a higher speed. Eventually, for a Dirac pressure source, the wave resistance either saturates for a one-dimensional geometry, or diverges for a two-dimensional geometry.

scholarly journals PERENCANAAN PREFABRICATED VERTICAL DRAIN MENGGUNAKAN METODE ELEMEN UNTUK MEMPEROLEH POLA DAN JARAK YANG EFEKTIF

2020 ◽  
Vol 3 (3) ◽  
pp. 937
Author(s):  
Joshua Michael ◽  
Aksan Kawanda
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
One Dimensional ◽  
Vertical Drain ◽  
Soil Loading ◽  
Prefabricated Vertical Drain ◽  
Long Time ◽  
Speed Up ◽  
Push Out ◽  
Element Method

As a city develops, less areas will be available for constructions. Out of these available lands, a large quantity of areas has low soil bearing capacity and great amount of settlement. For this type of soil, loading is required in order to stabilize it. This will push out porewater contained inside the soil. However, reaching the expected settlement requires a long time, which can be solved by using prefabricated vertical drain to speed up the process. This is possible because prefabricated vertical drain decreases the travel distance of porewater to half of the vertical drain. Calculations for this thesis are done using one dimensional consolidation method, finite element method, and asaoka method for actual data calculation from the field. Using one dimensional consolidation method, with prefabricated vertical drain distance of 1.2 m in triangular pattern, resulted in settlement level of 2.048 m for 110 days. Using finite element method resulted in settlement level of 2.604 m for 120 days. On the other hand, using asaoka method resulted in settlement level of 1.422 m for 102 days. This difference is caused by lack of depth data from the laboratory.Semakin berkembangnya jaman maka pembangunan semakin banyak sehingga lahan untuk dilakukannya pembangunan semakin sedikit. Sekarang banyak tanah yang memiliki daya dukung kecil dan penurunan yang besar contohnya seperti tanah lunak. Agar tanah model ini dapat memiliki kondisi yang stabil , maka solusinya diberi beban sehingga air pori dari dalam tanah dapat tertekan keluar. Namun untuk mencapai penurunan yang diinginkan membutuhkan waktu yang cukup lama, disini digunakan metode prefabricated vertical drain untuk mempercepat penurunan. Prefabricated vertical drain disini membuat jarak tempuh air pori tanah yang sebelumnya setebal tanah lunak, menjadi setengah jarak antar prefabricated vertical drain. Perhitungan analisa pada skripsi ini menggunakan metode one dimensional consolidation, metode elemen hingga, dan metode asaoka sebagai perhitungan hasil aktual dari data lapangan. Penurunan total menggunakan metode one dimensional consolidation dengan jarak antar prefabricated vertical drain 1.2m dengan pola segitiga sebesar 2.048 m selama 110 hari, sedangkan dari metode elemen hingga didapatkan penurunan sebesar 2.604 m selama 120 hari. Dari data settlement recording yang dihitung menggunakan metode asaoka terjadi penurunan sebesar 1.422 m selama 102 hari. Perbedaan disini disebabkan oleh kurang banyaknya sample kedalaman dari data laboratorium.

scholarly journals Litters of self-replicating origami cross-tiles

2019 ◽  
Vol 116 (6) ◽  
pp. 1952-1957 ◽  
Author(s):  
Rebecca Zhuo ◽  
Feng Zhou ◽  
Xiaojin He ◽  
Ruojie Sha ◽  
Nadrian C. Seeman ◽  
...  
Keyword(s):  
Growth Rate ◽  
Population Growth ◽  
Directed Evolution ◽  
Exponential Growth ◽  
Growth Conditions ◽  
One Dimensional ◽  
Replication System ◽  
Speed Up ◽  
Self Replication ◽  
Dimensional Crystal

Self-replication and exponential growth are ubiquitous in nature but until recently there were few examples of artificial self-replication. Often replication is a templated process where a parent produces a single offspring, doubling the population in each generation. Many species however produce more than one offspring at a time, enabling faster population growth and higher probability of species perpetuation. We have made a system of cross-shaped origami tiles that yields a number of offspring, four to eight or more, depending on the concentration of monomer units to be assembled. The parent dimer template serves as a seed to crystallize a one-dimensional crystal, a ladder. The ladder rungs are then UV–cross-linked and the offspring are then released by heating, to yield a litter of autonomous daughters. In the complement study, we also optimize the growth conditions to speed up the process and yield a 103increase in the growth rate for the single-offspring replication system. Self-replication and exponential growth of autonomous motifs is useful for fundamental studies of selection and evolution as well as for materials design, fabrication, and directed evolution. Methods that increase the growth rate, the primary evolutionary drive, not only speed up experiments but provide additional mechanisms for evolving materials toward desired functionalities.

The Face Detection Research Based on Multi-Scale and Rectangle Feature

2012 ◽  
Vol 198-199 ◽  
pp. 1383-1388
Author(s):  
Hong Hai Liu ◽  
Xiang Hua Hou
Keyword(s):  
Feature Extraction ◽  
Image Features ◽  
Face Image ◽  
High Dimensions ◽  
Feature Extraction Method ◽  
Face Features ◽  
Haar Feature ◽  
The Face ◽  
Speed Up ◽  
Feature Expression

When extracting the face image features based on pixel distribution in face image, there always exist large amount of calculation and high dimensions of feature sector generated after feature extraction. This paper puts forward a feature extraction method based on prior knowledge of face and Haar feature. Firstly, the Haar feature expressions of face images are classified and the face features are decomposed into edge feature, line feature and center-surround feature, which are further concluded into the expressions of two rectangles, three rectangles and four rectangles. In addition, each rectangle varies in size. However, for face image combination, there exist too much redundancy and large calculation amount in this kind of expression. In order to solve the problem of large amount of calculation, the integral image is adopted to speed up the rectangle feature calculation. In addition, the thought based on classified trainer is adopted to reduce the redundancy expression. The results show that using face image of Haar feature expression can improve the speed and efficiency of recognition.

COMMUNICATION COMPLEXITY AND SPEED-UP IN THE EXPLICIT DIFFERENCE METHOD

2006 ◽  
Vol 16 (03) ◽  
pp. 313-321 ◽  
Author(s):  
PAVOL PURCZ
Keyword(s):  
Parabolic Equation ◽  
Parallel Algorithm ◽  
Difference Method ◽  
Communication Complexity ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Time Level ◽  
One Dimensional ◽  
Speed Up ◽  
Initial Boundary Value

An earlier suggested parallel "ring" algorithm for solving the spatially one-dimensional initial-boundary-value problem (IBVP) for a parabolic equation using an explicit difference method is shortly described. Theoretical estimates for both of the speed-up function and the communication complexity of this parallel algorithm are studied. The speed-up function is determined as the ratio between times for realization of the algorithm in sequentional and parallel cases. Theoretical estimates of the speed-up function show the significant speed-up of the parallel algorithm in comparison with the serial one for a large number of values computed by one processor during one time level and it is shown that the the speed-up tends to the number of used processors. Communication complexity is determined as a ratio between the number of interchanges and the number of arithmetical operations. It has been proven that the coefficient of the communication complexity for spatially m-dimensional IBVP tends in general to ¾.

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