scholarly journals A New Binomial Recurrence Arising in a Graphical Compression Algorithm

2012 ◽  
Vol DMTCS Proceedings vol. AQ,... (Proceedings) ◽  
Author(s):  
Yongwook Choi ◽  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Nonnegative Integer ◽  
Path Length ◽  
Compression Algorithm ◽  
Simple Rule ◽  
Two Dimensional ◽  
Mellin Transforms ◽  
International Audience ◽  
The Right

International audience In a recently proposed graphical compression algorithm by Choi and Szpankowski (2009), the following tree arose in the course of the analysis. The root contains n balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability $p$) or the right subtree (with probability 1-$p$). A new node is created as long as there is at least one ball in that node. Furthermore, a nonnegative integer $d$ is given, and at level $d$ or greater one ball is removed from the leftmost node before the balls move down to the next level. These steps are repeated until all balls are removed (i.e., after $n+d$ steps). Observe that when $d=∞$ the above tree can be modeled as a $\textit{trie}$ that stores $n$ independent sequences generated by a memoryless source with parameter $p$. Therefore, we coin the name $(n,d)$-tries for the tree just described, and to which we often refer simply as $d$-tries. Parameters of such a tree (e.g., path length, depth, size) are described by an interesting two-dimensional recurrence (in terms of $n$ and $d$) that – to the best of our knowledge – was not analyzed before. We study it, and show how much parameters of such a $(n,d)$-trie differ from the corresponding parameters of regular tries. We use methods of analytic algorithmics, from Mellin transforms to analytic poissonization.

scholarly journals On a Recurrence Arising in Graph Compression

10.37236/2540 ◽  
2012 ◽  
Vol 19 (3) ◽  
Author(s):  
Yongwook Choi ◽  
Charles Knessl ◽  
Wojciech Szpankowski
Keyword(s):  
Nonnegative Integer ◽  
Path Length ◽  
Compression Algorithm ◽  
Simple Rule ◽  
Mellin Transforms ◽  
Graph Compression ◽  
The Right

In a recently proposed graphical compression algorithm by Choi and Szpankowski (2012), the following tree arose in the course of the analysis. The root contains $n$ balls that are consequently distributed between two subtrees according to a simple rule: In each step, all balls independently move down to the left subtree (say with probability $p$) or the right subtree (with probability $1-p$). A new node is created as long as there is at least one ball in that node. Furthermore, a nonnegative integer $d$ is given, and at level $d$ or greater one ball is removed from the leftmost node before the balls move down to the next level. These steps are repeated until all balls are removed (i.e., after $n+d$ steps). Observe that when $d=\infty$ the above tree can be modeled as a trie that stores $n$ independent sequences generated by a binary memoryless source with parameter $p$. Therefore, we coin the name $(n,d)$-tries for the tree just described, and to which we often refer simply as $d$-tries. We study here in detail the path length, and show how much the path length of such a $d$-trie differs from that of regular tries. We use methods of analytic algorithmics, from Mellin transforms to analytic poissonization.

scholarly journals Top Coefficients of the Denumerant

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Velleda Baldoni ◽  
Nicole Berline ◽  
Brandon Dutra ◽  
Matthias Köppe ◽  
Michele Vergne ◽  
...  
Keyword(s):  
Nonnegative Integer ◽  
Fixed Number ◽  
Lattice Points ◽  
Combinatorial Number Theory ◽  
International Audience ◽  
Integer Solutions ◽  
Combinatorial Function ◽  
Rational Generating Function ◽  
Rational Generating Functions ◽  
The Right

International audience For a given sequence $\alpha = [\alpha_1,\alpha_2,\ldots , \alpha_N, \alpha_{N+1}]$ of $N+1$ positive integers, we consider the combinatorial function $E(\alpha)(t)$ that counts the nonnegative integer solutions of the equation $\alpha_1x_1+\alpha_2 x_2+ \ldots+ \alpha_Nx_N+ \alpha_{N+1}x_{N+1}=t$, where the right-hand side $t$ is a varying nonnegative integer. It is well-known that $E(\alpha)(t)$ is a quasipolynomial function of $t$ of degree $N$. In combinatorial number theory this function is known as the $\textit{denumerant}$. Our main result is a new algorithm that, for every fixed number $k$, computes in polynomial time the highest $k+1$ coefficients of the quasi-polynomial $E(\alpha)(t)$ as step polynomials of $t$. Our algorithm is a consequence of a nice poset structure on the poles of the associated rational generating function for $E(\alpha)(t)$ and the geometric reinterpretation of some rational generating functions in terms of lattice points in polyhedral cones. Experiments using a $\texttt{MAPLE}$ implementation will be posted separately. Considérons une liste $\alpha = [\alpha_1,\alpha_2,\ldots , \alpha_N, \alpha_{N+1}]$ de $N+1$ entiers positifs. Le dénumérant $E(\alpha)(t)$ est lafonction qui compte le nombre de solutions en entiers positifs ou nuls de l’équation $\sum^{N+1}_{i=1}x_i\alpha_i=t$, où $t$ varie dans les entiers positifs ou nuls. Il est bien connu que cette fonction est une fonction quasi-polynomiale de $t$, de degré $N$. Nous donnons un nouvel algorithme qui calcule, pour chaque entier fixé $k$ (mais $N$ n’est pas fixé, les $k+1$ plus hauts coefficients du quasi-polynôme $E(\alpha)(t)$ en termes de fonctions en dents de scie. Notre algorithme utilise la structure d’ensemble partiellement ordonné des pôles de la fonction génératrice de $E(\alpha)(t)$. Les $k+1$ plus hauts coefficients se calculent à l’aide de fonctions génératrices de points entiers dans des cônes polyèdraux de dimension inférieure ou égale à $k$.

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

scholarly journals Ocular Echobiometry and Resistivity Index of External Ophthalmic Artery in Agoutis (Dasyprocta prymnolopha)

2021 ◽  
Vol 49 ◽  
Author(s):  
Sabrina Barros Araújo ◽  
Flávio Ribeiro Alves ◽  
Gerson Tavares Pessoa ◽  
Renan Paraguassu De Sá Rodrigues ◽  
Laecio Da Silva Moura ◽  
...  
Keyword(s):  
Anterior Chamber ◽  
Ophthalmic Artery ◽  
Color Doppler ◽  
Two Dimensional ◽  
Wild Rodents ◽  
Resistivity Index ◽  
Lens Thickness ◽  
Ocular Ultrasound ◽  
The Mean ◽  
The Right

Background: Veterinary Ophthalmology provides complementary information for the diagnosis of ocular pathologies. Studies in wild species are essential. Among the diagnostic techniques in ophthalmology, two-dimensional ultrasonography stands out. The agouti is a rodent belonging to the Dasyproctidae family that has been widely used as an experimental model. For these animals, sight is one of the crucial senses for their survival. The aim of this study was to evaluate the effectiveness of the two-dimensional ocular ultrasound technique to obtain anatomical measurements and the external ophthalmic artery resistivity index, presumably normal in the species Dasyprocta prymnolopha.Materials, Methods & Results: Forty eye bulbs of 20 adult rodents of the species were evaluated by ultrasonography. In these animals, B-mode echobiometry was performed using the transpalpebral approach and the hemodynamic study of the external ophthalmic artery using the color Doppler technique. All examinations were initiated by the left eye bulb and all measurements were performed by only one examiner. The collected data related to echobiometry were analyzed using Bioest 5.0 for Windows. Initially, normality was tested using the Shapiro-Wilk test for each parameter, then the paired t-test was performed, comparing right and left eyes, and a significance level of 5% (P < 0.05) was adopted. Based on the methodology used, the following values were obtained for the right and left eyeballs, respectively: anterior chamber thickness - mean of 1.28 ± 0.3 mm and 1.22 ± 0.1 mm; lens thickness - 8.27 ± 0.9 mm and 8.11 ± 0.9 mm; vitreous chamber thickness - 5.35 ± 0.48 mm and 5.30 ± 0.47 mm and axial length - 12.7 ± 0.9 mm and 13 ± 0.68 mm. The mean external ophthalmic artery resistivity values were 0.4305 ± 0.0390 and 0.4258 ± 0.0387 (right and left eye, respectively), characterizing a low resistance. There was no statistical difference between the right and left eyeballs in any of the studied parameters.Discussion: The use of the convex transducer was feasible, promoting adequate contact with the ocular surface and images of satisfactory quality for obtaining measurements, similar to what was observed in studies evaluating the ocular biometry of primates and dogs. The anterior chamber thickness values in this experiment did not differ statistically between the antimers, as well as observed for dogs. The data obtained for lens thickness did not differ statistically for antimers, like those obtained for other rodent species evaluated with the same methodology. The mean values of vitreous chamber thickness were like those observed in chinchillas but correspond to about half of that obtained for capybaras. In this study, the external ophthalmic artery was characterized in all animals, but obtaining the spectral tracing was difficult due to its fine caliber. In wild animals, and especially in wild rodents, there are few data reporting the resistivity of the ophthalmic artery, and there is a lack of studies, which can be explained by the behavioral characteristics of defense and by the high susceptibility to stress in capture, since the performing the technique requires, as in other procedures, the use of chemical containment.Keywords: Doppler flow, ultrasound, eye, agouti.

scholarly journals Solutions de similitude d'un jeu différentiel stochastique

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Differential Equation ◽  
Stochastic Process ◽  
Partial Differential Equation ◽  
Differential Equations ◽  
Similarity Solutions ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Controlled Processes ◽  
International Audience ◽  
First Time

International audience A two-dimensional controlled stochastic process defined by a set of stochastic differential equations is considered. Contrary to the most frequent formulation, the control variables appear only in the infinitesimal variances of the process, rather than in the infinitesimal means. The differential game ends the first time the two controlled processes are equal or their difference is equal to a given constant. Explicit solutions to particular problems are obtained by making use of the method of similarity solutions to solve the appropriate partial differential equation. On considère un processus stochastique commandé bidimensionnel défini par un ensemble d'équations différentielles stochastiques. Contrairement à la formulation la plus fréquente, les variables de commande apparaissent dans les variances infinitésimales du processus, plutôt que dans les moyennes infinitésimales. Le jeu différentiel prend fin lorsque les deux processus sont égaux ou que leur différence est égale à une constante donnée. Des solutions explicites à des problèmes particuliers sont obtenues en utilisant la méthode des similitudes pour résoudre l'équation aux dérivées partielles appropriée.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals The Hyper-spectral Image Compression Based on K-Means Clustering and Parallel Prediction Algorithm*

2018 ◽  
Vol 173 ◽  
pp. 03071
Author(s):  
Wu Wenbin ◽  
Yue Wu ◽  
Jintao Li
Keyword(s):  
Image Compression ◽  
Clustering Algorithm ◽  
Compression Algorithm ◽  
Prediction Algorithm ◽  
Two Dimensional ◽  
Spectral Image ◽  
Compression Algorithms ◽  
Serial Processing ◽  
Compression Time ◽  
Hyper Spectral

In this paper, we propose a lossless compression algorithm for hyper-spectral images with the help of the K-Means clustering and parallel prediction. We use K-Means clustering algorithm to classify hyper-spectral images, and we obtain a number of two dimensional sub images. We use the adaptive prediction compression algorithm based on the absolute ratio to compress the two dimensional sub images. The traditional prediction algorithm is adopted in the serial processing mode, and the processing time is long. So we improve the efficiency of the parallel prediction compression algorithm, to meet the needs of the rapid compression. In this paper, a variety of hyper-spectral image compression algorithms are compared with the proposed method. The experimental results show that the proposed algorithm can effectively improve the compression ratio of hyper-spectral images and reduce the compression time effectively.

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