scholarly journals Mathematical models for calculating the quantitative characteristics of the optimal quantization of information

2021 ◽  
Vol 7 (1) ◽  
pp. 46-58
Author(s):  
Vladimir A. Smagin ◽  
Vladimir P. Bubnov ◽  
Shokhrukh K. Sultonov
Keyword(s):  
Probability Distribution ◽  
Mathematical Models ◽  
Normal Distribution ◽  
Amount Of Information ◽  
Fractal Distribution ◽  
Optimal Quantization ◽  
Quantitative Characteristics ◽  
Optimal Information ◽  
Made In

Various additional mathematical aspects related to solving the problem of optimal information quantization in the sense of filling are considered, such as control of quantum elements, accounting for errors of quantum elements, determining the amount of information during quantization, and determining the numerical values of fractals of distributions represented as a sequential fractal distribution. The purpose of the article is to consider additional questions based on a specific "heavy" probability distribution the normal distribution. The considered questions are made in order to facilitate the solution of applied problems for researchers dealing with the problem of information quantization.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

Research of Divergence Trajectory with a Given Risk of Ships Collisions

2021 ◽  
pp. 64-67
Author(s):  
Kostiantyn
Keyword(s):  
Mathematical Models ◽  
Normal Distribution ◽  
Control Systems ◽  
Collision Avoidance ◽  
State Vector ◽  
Measurement Errors ◽  
Local Network ◽  
Mean Square ◽  
Distribution Law ◽  
Imitation Modeling

There were considered the issues of the optimal collision avoidance in the target’s risk field. A method of optimal divergence by course maneuvering is proposed, which makes it possible to minimize the divergence trajectory for a given risk of collision and consists in organizing the movement of the vessel along the trajectory of a given risk. The risk field of the target is a normal distribution law characterized by the root-mean-square parameters of the uncertainties associated with measurement errors of the parameters of the vessel's state vector and target, errors of actuators, errors of the used mathematical models, errors of calculation, etc. The operability and efficiency of the proposed method, algorithmic and software were tested on the Imitation Modeling Stand, which is the Navi Trainer 5000 navigation simulator and a model of on-board controller included in its local network with the software of the risk divergence module. The Imitation Modeling Stand allows to work out the software of control systems, including the considered optimal divergence module, in a closed circuit with the Navi Trainer 5000 navigation simulator, using all its advantages.

scholarly journals Secret Sharing Schemes on Sparse Homogeneous Access Structures with Rank Three

10.37236/1825 ◽  
2004 ◽  
Vol 11 (1) ◽  
Author(s):  
Jaume Martí-Farré ◽  
Carles Padró
Keyword(s):  
Secret Sharing ◽  
Access Structure ◽  
Open Problems ◽  
Access Structures ◽  
The Family ◽  
Ideal Access Structures ◽  
Optimal Information ◽  
Made In ◽  
The Ideal

One of the main open problems in secret sharing is the characterization of the ideal access structures. This problem has been studied for several families of access structures with similar results. Namely, in all these families, the ideal access structures coincide with the vector space ones and, besides, the optimal information rate of a non-ideal access structure is at most $2/3$. An access structure is said to be $r$-homogeneous if there are exactly $r$ participants in every minimal qualified subset. A first approach to the characterization of the ideal $3$-homogeneous access structures is made in this paper. We show that the results in the previously studied families can not be directly generalized to this one. Nevertheless, we prove that the equivalences above apply to the family of the sparse $3$-homogeneous access structures, that is, those in which any subset of four participants contains at most two minimal qualified subsets. Besides, we give a complete description of the ideal sparse $3$-homogeneous access structures.

General Solutions to Nurses Travel in Linear and Circular Nursing Units

1974 ◽  
Vol 18 (2) ◽  
pp. 134-134
Author(s):  
Stanley Lippert
Keyword(s):  
Mathematical Models ◽  
Nursing Staff ◽  
General Solutions ◽  
Room Size ◽  
Number Of Patients ◽  
Internal Arrangement ◽  
Objective Determination ◽  
Made In

The hospital literature of the 1960's contains about a dozen reports or articles pertaining to the relative merits of circular vs. conventional (chiefly linear corridors flanked by patient rooms on both sides). The claims included items other than nurses travel, for example, patient visibility to nursing staff, subjective impressions, and building costs. This article is concerned only with general but quantitative comparisons of these two classes of nursing units with respect to nurses travel. Mathematical models have been developed which permit practically instant evaluation of nursing units where all patient rooms are for a single occupant or where all rooms are for two occupants. The model reflects changes in room size and internal arrangement. Examination of the architect's preliminary sketches permits the determination of superior ority of one layout over another in terms of travel. The fact that this is but one of hundreds of determinations to be made in hospital designs does not diminish its importance. The literature contains various claims to “efficiency” based on no objective criteria. The model provides a simple and objective determination of nurses travel, for any number of patients typically visited and for any pattern of randomness or orderliness in their assignments.

Mathematical Modeling of a Biomass Steam Gasifier—A Modified Equilibrium Approach

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Thomas Gröbl ◽  
Heimo Walter
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Models ◽  
Present Article ◽  
Equilibrium Model ◽  
Conversion Process ◽  
Thermochemical Conversion ◽  
Equilibrium Models ◽  
Gasification Process ◽  
Equilibrium Approach ◽  
Made In

A large potential is contributed to the energetic utilization of biomass, whereby thermochemical gasification seems to be especially interesting. In order to contribute to a better understanding of the thermochemical conversion process in the gasifier, mathematical models are used. An intensive effort is made in development of mathematical models describing the gasification process and a large number of models, considerably differing in their degree of simplification, and their applications are reported in literature. In the present article, a brief review of models applied, mainly focused on equilibrium models, is provided and a robust and flexible modified stoichiometric equilibrium model, for modeling a novel gasifier, is presented.

Effects of Scaling on the Correlation Coefficient: Additional Considerations

1978 ◽  
Vol 15 (2) ◽  
pp. 304-308 ◽  
Author(s):  
Warren S. Martin
Keyword(s):  
Normal Distribution ◽  
Correlation Coefficient ◽  
Correlation Coefficients ◽  
Bivariate Normal Distribution ◽  
Information Loss ◽  
Simulation Data ◽  
Pearson Product Moment Correlation ◽  
Bivariate Normal ◽  
Amount Of Information ◽  
Restricted Number

Distortion in the Pearson product moment correlation due to a restricted number of scale points is evaluated in two ways. First, a simulation of the bivariate normal distribution is used to estimate the effects of varying the number of scale points on the product moment correlation. This procedure demonstrates a substantial amount of information loss. Second, other correlation coefficients and some methods to correct for this loss are discussed and related to the simulation data.

scholarly journals A Probability Distribution for a Time-varying Quantity

1966 ◽  
Vol 19 (1) ◽  
pp. 119-122 ◽  
Author(s):  
D. A. Lloyd
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Gaussian Distribution ◽  
Time Varying ◽  
Normal Distributions

In many practical situations in the field of navigation, it has been noticed that the probability distribution of measured errors has a shape which has considerable departures from that of the normal distribution. These departures are particularly noticeable in the ‘tails’ of the distribution of practical cases, which are often higher than those of the corresponding normal distributions (see, for example, ‘Is the gaussian distribution normal’, W/Cdr. E. W. Anderson. This Journal, 18, 65).

Observations of the Earth's magnetic field made in Edinburgh from 1670 to the present day

1994 ◽  
Vol 85 (4) ◽  
pp. 239-252 ◽  
Author(s):  
D. R. Barraclough
Keyword(s):  
Magnetic Field ◽  
Mathematical Models ◽  
Secular Variation ◽  
Geomagnetic Field ◽  
Upper Atmosphere ◽  
The Difference ◽  
Time Changes ◽  
Relative Measurements ◽  
Magnetic North ◽  
Made In

AbstractMagnetic observations made at the same site give valuable information about the time changes (the secular variation) of the geomagnetic field. This paper gives details of all known measurements of the geomagnetic field in and around Edinburgh since the earliest observation of magnetic declination (the difference between true and magnetic north) by George Sinclair in 1670. Early observations of the strength of the field were only relative measurements. Approximate conversion factors are derived to enable these data to be expressed in modern absolute units (nanoteslas). Observed values of declination, inclination and the horizontal intensity of the geomagnetic field are plotted and compared with values computed from mathematical models of the field covering the interval 1690 to 1990, inclusive. The earlier observations were not corrected for the effects of the rapidly varying magnetic fields caused by electric currents in the upper atmosphere. The consequences of this are estimated.

scholarly journals A theory of meteors, and the density and temperature of the outer atmosphere to which it leads

1923 ◽  
Vol 102 (717) ◽  
pp. 411-437 ◽  
Keyword(s):  
Temperature Gradient ◽  
Consistent Theory ◽  
Amount Of Information ◽  
Outer Atmosphere ◽  
Considerable Detail ◽  
Made In

Some thirty years ago Teisserenc de Bort announced the discovery that the temperature gradient in the atmosphere, which amounts to some 6.5 . 10 -5 degree/cm. for the first 10 km., becomes negligibly small at greater heights. Since this time it has become usual to treat the temperature as constant for all heights above this limit, and various detailed numerical estimates, extending to heights of hundreds of kilometres, have been published, which are based on this assumption. So far, however, no evidence for it has been adduced beyond the “ballon sonde” observations, which scarcely extend above 25 km. The purpose of this note is to examine how much information about conditions at greater heights may be gained from a study of meteors. For this purpose it is necessary to study in considerable detail the theory of what happens when a meteor appears. It will be seen that a consistent theory can be developed, which accounts for all the observed phenomena, and that this theory enables one to derive a considerable amount of information about conditions in the upper air. It will be shown that existing observations enable us to say with considerable certainty that the density at heights above 65 kilom. is very much higher than is commonly supposed, and that the temperature must increase from its value of something like 220° abs. at heights between 12 and 50 km., to something like 300° abs. at these heights. It is evident that accurate results can only be obtained when the required quantities, viz., heights of appearance and disappearance, length of path, velocity and luminosity have been determined for a number of meteors. It is hoped that experiments, now in progress to determine these quantities photographically, will enable more accurate calculations to be made. In the meantime, the broad results obtained from the data due to W. F. Denning and his co-workers may be outlined.

Sign in / Sign up

Export Citation Format

Share Document