Mathematical basis of an algorithm for the formation of space equipment complex for a scientific and applied RSE program

2002 ◽  
Vol 8 (2-3) ◽  
pp. 73-76
Author(s):  
O.D. Fedorovskyi ◽  
◽  
V.P. Zubko ◽  
V.G. Yakimchuk ◽  
◽  
...  
Keyword(s):  
Mathematical Basis ◽  
Equipment Complex

On the Mathematical Basis of Zelen’s Prerandomized Designs

1985 ◽  
Vol 24 (03) ◽  
pp. 120-130 ◽  
Author(s):  
E. Brunner ◽  
N. Neumann
Keyword(s):  
Clinical Trial ◽  
Normal Distribution ◽  
Random Variables ◽  
Small Samples ◽  
Selection Effects ◽  
Sample Sizes ◽  
Mathematical Basis ◽  
Additional Assumptions

SummaryThe mathematical basis of Zelen’s suggestion [4] of pre randomizing patients in a clinical trial and then asking them for their consent is investigated. The first problem is to estimate the therapy and selection effects. In the simple prerandomized design (PRD) this is possible without any problems. Similar observations have been made by Anbar [1] and McHugh [3]. However, for the double PRD additional assumptions are needed in order to render therapy and selection effects estimable. The second problem is to determine the distribution of the statistics. It has to be taken into consideration that the sample sizes are random variables in the PRDs. This is why the distribution of the statistics can only be determined asymptotically, even under the assumption of normal distribution. The behaviour of the statistics for small samples is investigated by means of simulations, where the statistics considered in the present paper are compared with the statistics suggested by Ihm [2]. It turns out that the statistics suggested in [2] may lead to anticonservative decisions, whereas the “canonical statistics” suggested by Zelen [4] and considered in the present paper keep the level quite well or may lead to slightly conservative decisions, if there are considerable selection effects.

Comparison of Rheumatological Diagnoses by a Bayesian Program and by Physicians

1991 ◽  
Vol 30 (03) ◽  
pp. 187-193 ◽  
Author(s):  
H. J. Moens ◽  
J. K. van der Korst
Keyword(s):  
Receiver Operating Characteristics ◽  
Bayesian Decision ◽  
Operating Characteristics ◽  
Likelihood Ratios ◽  
Improve Performance ◽  
Mathematical Basis ◽  
Human Expert ◽  
Test Population ◽  
Sensitivity Specificity ◽  
Diagnostic Outcome

AbstractA Bayesian decision support system was developed for the diagnosis of rheumatic disorders. Knowledge in this system is represented as evidential weights of findings. Simple weights were calculated as the logarithm of likelihood ratios on the basis of 1,000 consecutive patients from a rheumatological clinic. The effect of various methods to improve performance of the system by modification of the weights was studied. Three methods had a mathematical basis; a fourth consisted of weights adapted by a human expert, which allowed inclusion of diagnostic rules such as defined in widely accepted criteria sets. The system’s performance was measured in a test population of 570 different cases from the same clinic and compared with predictions of diagnostic outcome made by rheumatologists. The weights from a human expert gave optimal results (sensitivity 65% and specificity 96%), that were close to the physicians’ predictions (sensitivity 64% and specificity 98%). The methods to measure the performance of the various models used in this study emphasize sensitivity, specificity and the use of receiver operating characteristics.

scholarly journals A Stochastic Kinetic Type Reactions Model for COVID-19

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1221
Author(s):  
Giorgio Sonnino ◽  
Fernando Mora ◽  
Pasquale Nardone
Keyword(s):  
Real Data ◽  
Stochastic Noise ◽  
Mathematical Basis ◽  
Sis Model ◽  
Theoretical Predictions ◽  
Coronavirus Infection ◽  
Massive Distribution ◽  
Second Wave ◽  
Stochastic Sis Model

We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic SIS-model (Susceptible ⇒ Infectious ⇒ Susceptible) and the stochastic SIS-model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

MATHEMATICAL BASIS OF COMPUTATIONAL PHYSICS

1996 ◽  
Vol 07 (03) ◽  
pp. 355-359 ◽  
Author(s):  
M. SUZUKI
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Quantum Monte Carlo ◽  
Computational Physics ◽  
Numerical Calculations ◽  
Symplectic Integration ◽  
Mathematical Basis ◽  
Small Parameters ◽  
Quantum Monte Carlo Simulations

The present paper explains some general basic formulas concerning quantum Monte Carlo simulations, symplectic integration and other numerical calculations. A generalization of the BCH formula is given with an application to the decomposition of exponential operators in the presence of small parameters.

Control Reversal Effects on Swept-Back Wings

1949 ◽  
Vol 1 (1) ◽  
pp. 3-34
Author(s):  
Haydn Templeton
Keyword(s):  
Mathematical Analysis ◽  
Quantitative Estimation ◽  
Dynamic Condition ◽  
Loss Of Control ◽  
General Introduction ◽  
Mathematical Basis ◽  
Control Power ◽  
Physical Picture ◽  
The Subject ◽  
Definition Of

SummaryAileron reversal effects on swept-back wings in general and elevon reversal effects on tailless swept-back wings in particular are discussed on a non-mathematical basis, attention being confined to the orthodox flap type of control. The main purpose of the paper is to convey in the simplest terms possible a clear physical picture of the conditions producing loss of control power, emphasis being naturally laid upon the part played by structural wing distortion. Certain qualitative features relating to the two phenomena are also discussed. As a general introduction to the discussion on aileron reversal effects, the definition of “aileron power” in relation to the actual dynamic condition of rolling is described at some length. For elevon reversal effects on tailless aircraft the effect of wing flexibility on both “elevon power” and on trim in steady symmetric flight is considered. With the descriptive treatment adopted the analysis is of necessity broad and general but is designed to appeal to those not too familiar with the subject. The results of certain calculations on a hypothetical wing, which may be of interest, are included. A mathematical analysis for the quantitative estimation of both aileron and elevon reversal effects is given in the Appendix.

The Helium Stockpile: A Collaboration in Mathematical Folding Sculpture

Leonardo ◽  
2006 ◽  
Vol 39 (3) ◽  
pp. 233-235 ◽  
Author(s):  
Eric D. Demaine ◽  
Martin L. Demaine ◽  
A. Laurie Palmer
Keyword(s):  
Three Dimensional ◽  
Dimensional Chain ◽  
Mathematical Basis ◽  
One Dimensional ◽  
Dimensional Shape ◽  
Folding Structure ◽  
Three Dimensional Shape

The Helium Stockpile is a manipulable folding structure of hundreds of wooden blocks, representing the transformation between surface and solid through a foldable one-dimensional chain. The sculpture grew out of an unexpected collaboration between a sculptor and two mathematicians, giving the structure a mathematical basis through which it is guaranteed to be foldable into essentially any three-dimensional shape.

scholarly journals Analysis of security of post-quantum algorithm of Rainbow electronic signature against potential attacks

Radiotekhnika ◽  
2021 ◽  
pp. 85-93
Author(s):  
G.А. Maleeva
Keyword(s):  
Quantum Algorithm ◽  
Public Key Cryptography ◽  
Transformation Method ◽  
Accurate Estimate ◽  
Signature Scheme ◽  
Secret Key ◽  
Mathematical Basis ◽  
Electronic Signature ◽  
Post Quantum Cryptography ◽  
Band Separation

Multidimensional public key cryptography is a candidate for post-quantum cryptography, and it makes it possible  to generate particularly short signatures and quick verification. The Rainbow signature scheme proposed by J. Dean and D. Schmidt is such a multidimensional cryptosystem and it is considered to be protected against all known attacks. The need for research on Rainbow ES is justified by the fact that there is a need to develop and adopt a post-quantum national securities standard, and that in the process of the US NIST competition on the mathematical basis of cryptographic transformation method Rainbow, promising results. Therefore, it is considered important to take them into account and use them in Ukraine. The Rainbow signature scheme can be implemented simply and efficiently using linear algebra methods over a small finite field and, in particular, creates shorter signatures than those used in RSA and other post-quantum signatures [1]. In the 2nd round of NIST PQC, protected sets of Rainbow parameters are offered and several attacks on them are analyzed [1]. When comparing ES, preference is given to ES algorithms that have been selected according to unconditional criteria, as well as those that have better indicators for integral conditional criteria, because such a technique is more rational. In particular, the Rainbow-Band-Separation (RBS) attack [2] is the best known Rainbow attack with a certain set of parameters and is important. The Rainbow-Band-Separation attack restores the Rainbow secret key by solving certain systems of quadratic equations, and its complexity is measured by a well-known measure called the degree of regularity. However, as a rule, the degree of regularity is greater than the degree of solution in experiments, and it is impossible to obtain an accurate estimate. The paper proposes a new indicator of the complexity of the Rainbow-Band-Separation attack using  F4 algorithm, which gives a more accurate estimate compared to the indicator that uses the degree of regularity. The aim of the work is a comparative analysis of ES based on MQ-transformations on the criterion of stability-complexity and an attempt to understand the security of Rainbow against RBS attack using F4.

scholarly journals Approximating deformation fields for the analysis of continuous heterogeneity of biological macromolecules by 3D Zernike polynomials

IUCrJ ◽  
2021 ◽  
Vol 8 (6) ◽  
Author(s):  
David Herreros ◽  
Roy R. Lederman ◽  
James Krieger ◽  
Amaya Jiménez-Moreno ◽  
Marta Martínez ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Structural Characteristics ◽  
Normal Mode Analysis ◽  
Principal Component ◽  
Current Data ◽  
Mode Analysis ◽  
Biological Macromolecules ◽  
Mathematical Basis ◽  
Common Framework ◽  
Low Dimensional

Structural biology has evolved greatly due to the advances introduced in fields like electron microscopy. This image-capturing technique, combined with improved algorithms and current data processing software, allows the recovery of different conformational states of a macromolecule, opening new possibilities for the study of its flexibility and dynamic events. However, the ensemble analysis of these different conformations, and in particular their placement into a common variable space in which the differences and similarities can be easily recognized, is not an easy matter. To simplify the analysis of continuous heterogeneity data, this work proposes a new automatic algorithm that relies on a mathematical basis defined over the sphere to estimate the deformation fields describing conformational transitions among different structures. Thanks to the approximation of these deformation fields, it is possible to describe the forces acting on the molecules due to the presence of different motions. It is also possible to represent and compare several structures in a low-dimensional mapping, which summarizes the structural characteristics of different states. All these analyses are integrated into a common framework, providing the user with the ability to combine them seamlessly. In addition, this new approach is a significant step forward compared with principal component analysis and normal mode analysis of cryo-electron microscopy maps, avoiding the need to select components or modes and producing localized analysis.

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