COMPUTING THE HAUSDORFF DISTANCE BETWEEN CURVED OBJECTS

2008 ◽  
Vol 18 (04) ◽  
pp. 307-320 ◽  
Author(s):  
HELMUT ALT ◽  
LUDMILA SCHARF
Keyword(s):  
Voronoi Diagram ◽  
Computer Algebra ◽  
Hausdorff Distance ◽  
Computer Algebra System ◽  
Shape Recognition ◽  
The Other ◽  
Algebraic Equations ◽  
Algebraic Computing ◽  
Intersection Points ◽  
The One

The Hausdorff distance between two sets of curves is a measure for the similarity of these objects and therefore an interesting feature in shape recognition. If the curves are algebraic computing the Hausdorff distance involves computing the intersection points of the Voronoi edges of the one set with the curves in the other. Since computing the Voronoi diagram of curves is quite difficult we characterize those points algebraically and compute them using the computer algebra system SYNAPS. This paper describes in detail which points have to be considered, by what algebraic equations they are characterized, and how they actually are computed.

scholarly journals Using Algebraic Computing To Teach General Relativity And Cosmology

2012 ◽  
Vol 56 (1) ◽  
pp. 139-144
Author(s):  
Dumitru N. Vulcanov ◽  
Remus-Ştefan Ş. Boată
Keyword(s):  
General Relativity ◽  
Exact Solutions ◽  
Undergraduate Students ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Einstein Equations ◽  
Algebraic Programming ◽  
Algebraic Computing

AbstractThe article presents some new aspects and experience on the use of computer in teaching general relativity and cosmology for undergraduate students (and not only) with some experience in computer manipulation. Some years ago certain results were reported [1] using old fashioned computer algebra platforms but the growing popularity of graphical platforms as Maple and Mathematica forced us to adapt and reconsider our methods and programs. We will describe some simple algebraic programming procedures (in Maple with GrTensorII package) for obtaining and the study of some exact solutions of the Einstein equations in order to convince a dedicated student in general relativity about the utility of a computer algebra system.

The double cusp has five minima

1978 ◽  
Vol 84 (3) ◽  
pp. 537-538 ◽  
Author(s):  
J. Callahan
Keyword(s):  
Critical Points ◽  
Standard Form ◽  
Singularity Theory ◽  
The Other ◽  
Universal Unfolding ◽  
The Real ◽  
Level Curves ◽  
Intersection Points ◽  
The One ◽  
Image Position

The double cusp is the real, compact, unimodal singularitysee (2), (4). Functions in a universal unfolding of the double cusp can have nine non-degenerate critical points near the origin, but no more. Index considerations show that precisely four of the nine are saddles, and it has long been part of the folklore of singularity theory that one of the other five must be a maximum. Indeed, a standard form of the unfolded double cusp (1), (3) is a function having a pair of intersecting ellipses as one of its level curves; see Fig. 1(a). There are saddles at the four intersection points, a maximum inside the central quadrilateral, and a minimum inside each of the other four finite regions bounded by the ellipses. The rest of Fig. 1 suggests, however, that a deformation of this function (in which one of the saddles drops below the level of the other three) might turn the maximum into a fifth minimum. The following proposition shows that a function similar to the one in Fig. 1(d) can be realized in an unfolding of the double cusp.

scholarly journals Construction Fragile Digital Watermark Used by a Team of Authors in Executable Files

2020 ◽  
Vol 18 (1) ◽  
pp. 65-73
Author(s):  
I. V. Nechta
Keyword(s):  
Unique Solution ◽  
Digital Watermark ◽  
The Other ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Statistical Research ◽  
Other Hand ◽  
Linear Algebraic Equations ◽  
Software Product ◽  
The One

According to statistical research, a violation of license agreements annually causes huge losses to software companies. On the one hand, illegal copies of the software product are created, on the other hand, some fragments of the programs are used by third parties unauthorized. Another important problem is the violation of the program integrity, for example, in terms of blocking functions of the license key checking. In this regard, the task of construction methods for protecting intellectual property in software applications is highly relevant. Previously known methods solve this problem by means of fragile digital watermarks. Below is presented a method for constructing a fragile digital watermark used in executable files. A model of a developers team creating software product protected by DWM is considered. The application of this method will allow to reveal the fact of the container integrity violation, on the one hand, and, on the other hand, will allow the author, if it is necessary, to confirm his participation in the development and embedding of the DWM. In this method we use mathematical properties of systems of linear algebraic equations, digital signature and cryptographic hash functions. The scheme is based on the Kronecker – Capelli theorem. To find the group password the co-author who is in the group finds one root of the consistent system of linear algebraic equations. The indicated system consists of n equations and contains n + 1 variables. For an outsider who is not in the group, the system of equations does not have a unique solution. The co-author of the group is able to calculate one variable in system based on their passport data. Therefore, the system of equations for such co-author has a unique solution. Various attacks on a protected by the new method are analyzed, and it is shown its efficiency. The constructed method can be applied in companies with a large team of developers.

scholarly journals Investigation of the existence domain for Dyakonov surface waves in the Sage computer algebra system

2021 ◽  
Vol 29 (2) ◽  
pp. 114-125
Author(s):  
Oleg K. Kroytor
Keyword(s):  
Surface Waves ◽  
Computer Algebra ◽  
Electromagnetic Waves ◽  
Computer Algebra System ◽  
Computer Experiments ◽  
Dielectric Tensor ◽  
Algebraic Equations ◽  
Existence Of A Solution ◽  
Theoretical Substantiation ◽  
Existence Domain

Surface electromagnetic waves (Dyakonov waves) propagating along a plane interface between an isotropic substance with a constant dielectric constant and an anisotropic crystal, whose dielectric tensor has a symmetry axis directed along the interface, are considered. It is well known that the question of the existence of such surface waves is reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities. In the present work, this system is investigated in the Sage computer algebra system. The built-in technique of exceptional ideals in Sage made it possible to describe the solution of a system of algebraic equations parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. The remaining inequalities were only partially investigated analytically. For a complete study of the solvability of the system of equations and inequalities, a symbolic-numerical algorithm is proposed and implemented in Sage, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.

Note on Selection of Coordinate Systems for Geodynamics

1975 ◽  
Vol 26 ◽  
pp. 395-407
Author(s):  
S. Henriksen
Keyword(s):  
Sea Level ◽  
The Other ◽  
Coordinate Systems ◽  
Mean Sea Level ◽  
The Earth ◽  
The One ◽  
Static Systems ◽  
Selection Of

The first question to be answered, in seeking coordinate systems for geodynamics, is: what is geodynamics? The answer is, of course, that geodynamics is that part of geophysics which is concerned with movements of the Earth, as opposed to geostatics which is the physics of the stationary Earth. But as far as we know, there is no stationary Earth – epur sic monere. So geodynamics is actually coextensive with geophysics, and coordinate systems suitable for the one should be suitable for the other. At the present time, there are not many coordinate systems, if any, that can be identified with a static Earth. Certainly the only coordinate of aeronomic (atmospheric) interest is the height, and this is usually either as geodynamic height or as pressure. In oceanology, the most important coordinate is depth, and this, like heights in the atmosphere, is expressed as metric depth from mean sea level, as geodynamic depth, or as pressure. Only for the earth do we find “static” systems in use, ana even here there is real question as to whether the systems are dynamic or static. So it would seem that our answer to the question, of what kind, of coordinate systems are we seeking, must be that we are looking for the same systems as are used in geophysics, and these systems are dynamic in nature already – that is, their definition involvestime.

Stories and the Self

2020 ◽  
Vol 32 (2) ◽  
pp. 47-58 ◽  
Author(s):  
Stefan Krause ◽  
Markus Appel
Keyword(s):  
Meta Analysis ◽  
The Self ◽  
The Other ◽  
Lower Degree ◽  
Contrast Effects ◽  
Self Perception ◽  
Self Perceptions ◽  
Other Hand ◽  
The One ◽  
Implicit And Explicit

Abstract. Two experiments examined the influence of stories on recipients’ self-perceptions. Extending prior theory and research, our focus was on assimilation effects (i.e., changes in self-perception in line with a protagonist’s traits) as well as on contrast effects (i.e., changes in self-perception in contrast to a protagonist’s traits). In Experiment 1 ( N = 113), implicit and explicit conscientiousness were assessed after participants read a story about either a diligent or a negligent student. Moderation analyses showed that highly transported participants and participants with lower counterarguing scores assimilate the depicted traits of a story protagonist, as indicated by explicit, self-reported conscientiousness ratings. Participants, who were more critical toward a story (i.e., higher counterarguing) and with a lower degree of transportation, showed contrast effects. In Experiment 2 ( N = 103), we manipulated transportation and counterarguing, but we could not identify an effect on participants’ self-ascribed level of conscientiousness. A mini meta-analysis across both experiments revealed significant positive overall associations between transportation and counterarguing on the one hand and story-consistent self-reported conscientiousness on the other hand.

Radioimmunotherapy for treatment of acute myeloid leukaemia and myelodysplastic syndrome

2005 ◽  
Vol 44 (03) ◽  
pp. 107-117
Author(s):  
R. G. Meyer ◽  
W. Herr ◽  
A. Helisch ◽  
P. Bartenstein ◽  
I. Buchmann
Keyword(s):  
Acute Myeloid Leukaemia ◽  
Myeloid Leukaemia ◽  
Primary Tumour ◽  
The Other ◽  
Haematopoietic Stem Cell ◽  
Other Hand ◽  
Primary Reduction ◽  
The One ◽  
Acute Myeloid

SummaryThe prognosis of patients with acute myeloid leukaemia (AML) has improved considerably by introduction of aggressive consolidation chemotherapy and haematopoietic stem cell transplantation (SCT). Nevertheless, only 20-30% of patients with AML achieve long-term diseasefree survival after SCT. The most common cause of treatment failure is relapse. Additionally, mortality rates are significantly increased by therapy-related causes such as toxicity of chemotherapy and complications of SCT. Including radioimmunotherapies in the treatment of AML and myelodyplastic syndrome (MDS) allows for the achievement of a pronounced antileukaemic effect for the reduction of relapse rates on the one hand. On the other hand, no increase of acute toxicity and later complications should be induced. These effects are important for the primary reduction of tumour cells as well as for the myeloablative conditioning before SCT.This paper provides a systematic and critical review of the currently used radionuclides and immunoconjugates for the treatment of AML and MDS and summarizes the literature on primary tumour cell reductive radioimmunotherapies on the one hand and conditioning radioimmunotherapies before SCT on the other hand.

Generation of Correlated Logistic-Normal Random Variates for Medical Decision Trees

1998 ◽  
Vol 37 (03) ◽  
pp. 235-238 ◽  
Author(s):  
M. El-Taha ◽  
D. E. Clark
Keyword(s):  
Monte Carlo ◽  
Decision Trees ◽  
Computer Algebra ◽  
Taylor Series ◽  
Computer Algebra System ◽  
Random Variable ◽  
Monte Carlo Analysis ◽  
Normal Random Variable ◽  
Medical Decision ◽  
Theoretical Results

AbstractA Logistic-Normal random variable (Y) is obtained from a Normal random variable (X) by the relation Y = (ex)/(1 + ex). In Monte-Carlo analysis of decision trees, Logistic-Normal random variates may be used to model the branching probabilities. In some cases, the probabilities to be modeled may not be independent, and a method for generating correlated Logistic-Normal random variates would be useful. A technique for generating correlated Normal random variates has been previously described. Using Taylor Series approximations and the algebraic definitions of variance and covariance, we describe methods for estimating the means, variances, and covariances of Normal random variates which, after translation using the above formula, will result in Logistic-Normal random variates having approximately the desired means, variances, and covariances. Multiple simulations of the method using the Mathematica computer algebra system show satisfactory agreement with the theoretical results.

Das Ende der Postdemokratie, den Pessimismus überwinden.

2017 ◽  
Vol 47 (188) ◽  
pp. 487-494
Author(s):  
Daniel Mullis
Keyword(s):  
Political Thought ◽  
Social Dynamics ◽  
Social Conditions ◽  
The Other ◽  
Economic Decline ◽  
Far Right ◽  
Windows Of Opportunity ◽  
Political Events ◽  
Political Struggles ◽  
The One

In recent years, political and social conditions have changed dramatically. Many analyses help to capture these dynamics. However, they produce political pessimism: on the one hand there is the image of regression and on the other, a direct link is made between socio-economic decline and the rise of the far-right. To counter these aspects, this article argues that current political events are to be understood less as ‘regression’ but rather as a moment of movement and the return of deep political struggles. Referring to Jacques Ranciere’s political thought, the current conditions can be captured as the ‘end of post-democracy’. This approach changes the perspective on current social dynamics in a productive way. It allows for an emphasis on movement and the recognition of the windows of opportunity for emancipatory struggles.

Tolerance is theoretical and practical principles

1996 ◽  
pp. 13-23
Author(s):  
Mykhailo Babiy
Keyword(s):  
Religious Diversity ◽  
The Other ◽  
Nodal Points ◽  
Characteristic Features ◽  
The One ◽  
Ukrainian Society

Political ideological pluralism, religious diversity are characteristic features of modern Ukrainian society. On the one hand, multiculturalism, socio-political, religious differentiation of the latter appear as important characteristics of its democracy, as a practical expression of freedom, on the other - as a factor that led to the deconsocialization of society, gave rise to "nodal points" of tension, confrontational processes, in particular, in political and religious spheres.

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