Combinatorial Property of Sets of Boxes in Multidimensional Euclidean Spaces and Theorems in Olympiad Tasks

2018 ◽  
Vol 12 ◽  
pp. 111-117
Author(s):  
Pavel S. PANKOV ◽  
Azret A. KENZHALIEV
Keyword(s):  
Theorem Proving ◽  
Main Idea ◽  
Combinatorial Property ◽  
Euclidean Spaces ◽  
General Sense ◽  
Output Data ◽  
Mathematical Objects ◽  
Formal Indication ◽  
Computer Assistance

Theorems (in general sense) are constituents of inventing, analysing and solving olympiad tasks. Also, some theorems can be proved with computer assistance only. The main idea is (human) reducing of primary (unbounded) set to a finite one. Non-trivial immanent properties of mathematical objects are of interest because they can be considered as alternative definitions of these objects revealing their additional features. A non-formal indication of such property is only inital data (size of domain) and only output data (proven/not proven) in a corresponding algorithm. One new and two known examples of such properties are considered, some techniques to convert theorem-proving algorithms into olympiad tasks are proposed.

Reductibilities in intuitionistic topology

1968 ◽  
Vol 33 (3) ◽  
pp. 412-417 ◽  
Author(s):  
Dirk Van Dalen
Keyword(s):  
General Sense ◽  
Mathematical Objects ◽  
Definition Of ◽  
Intuitionistic Mathematics

In intuitionistic mathematics one distinguishes between sets with a constructive character and sets in a more general sense. The first kind consists of spreads and the latter of species. The definition of a spread utilizes so-called choice sequences (in [5] infinitely proceeding sequence or ips), i.e., sequences of well-determined mathematical objects which are chosen more or less freely. One can restrict the choices by some law, which, however, need not be predetermined (changing one's mind is allowed).

scholarly journals SELECTION OF THE OPTIMAL STRUCTURE OF HIDDEN LAYERS OF THE ARTIFICIAL NEURAL NETWORK FOR ENERGY EFFICIENCY ANALYSIS

2021 ◽  
Vol 3 (1) ◽  
pp. 30-36
Author(s):  
A. G. Kazarian ◽  
◽  
V. M. Teslyuk ◽  
I. Ya. Kazymyra ◽  
◽  
...  
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Internal Structure ◽  
Layer Structure ◽  
Operating Time ◽  
Main Idea ◽  
Optimal Structure ◽  
Output Data ◽  
Artificial Neural ◽  
Selection Of

A method for optimal structure selection of hidden layers of the artificial neural network (ANN) is proposed. Its main idea is the practical application of several internal structures of ANN and further calculation of the error of each hidden layer structure using identical data sets for ANN training. The method is based on the alternate comparison of the expected result values and the actual results of the feedforward artificial neural networks with a different number of inner layers and a different number of neurons on each layer. The method afforces searching the optimal internal structure of ANN for usage in the development of "smart" house systems and for calculation of the optimal energy consumption level in accordance with current conditions, such as room temperature, presence of people, and time of the day. The usage of the presented method allows to reduce the time spent on choosing the effective structure of the artificial neural network at the initial stages of research and to pay more attention to the relationship between the input and output data, as well as to such important parameters of the ANN learning process, as a number of training iterations, minimal training error, etc. The software has been developed that allows to carry out the processes of training, testing, and obtaining the output results of the algorithm of the artificial neural network, such as the expected value of power consumption and operating time of each individual appliance. The disadvantage of the approach used in finding the optimal internal structure of the artificial neural network is that each subsequent structure is created on the basis of the most efficient of the previously created structures without analyzing other structures that showed worse results with fewer hidden layers. It was found that to improve the solution of this problem it is necessary to create a mechanism which will be based on the analysis of input data, output data, will analyze the internal relationships between parameters and will optimize the network structure at each stage using certain logical rules according to the results obtained in the previous step. It is established that this problem is a nonlinear programming problem that can be solved in the further development of this study.

Adjustable Tensegrity Robot Based on Assur Graph Principle

2009 ◽  
Author(s):  
Offer Shai ◽  
Itay Tehori ◽  
Avner Bronfeld ◽  
Michael Slavutin ◽  
Uri Ben-Hanan
Keyword(s):  
Control System ◽  
Projective Geometry ◽  
Efficient Algorithm ◽  
Degrees Of Freedom ◽  
Theoretical Foundation ◽  
Main Idea ◽  
Output Data ◽  
Promising Application ◽  
External Loads

The paper introduces a tensegrity robot consisting of cables and actuators. Although this robot has zero degrees of freedom, it is both mobile, and capable of sustaining massive external loads. This outcome is achieved by constantly maintaining the configuration of the robot at a singular position. The underlying theoretical foundation of this work is originated from the concept of Assur Trusses (also known as Assur Groups), which are long known in the field of kinematics. During the last three years, the latter concept has been reformulated by mathematicians from rigidity theory community, and new theorems and algorithms have been developed. Since the topology of the robot is an Assur Truss, the work reported in the paper relies on Assur Trusses theorems that have been developed this year resulting in an efficient algorithm to constantly keep the robot at the singular position. In order to get an efficient characterization of the desired configurations, known techniques from projective geometry were employed. The main idea of the control system of the device, that was also mathematically proved, is that changing the length of only one element, causes the robot to be at the singular position. Therefore, the system measures the force in only one cable, and its length is modified accordingly by the control system. The topology of the device is an Assur Truss — a 3D triad, but the principles introduced in the paper are applicable to any robot whose topology is an Assur Truss, such as: tetrad, pentad, double triad and so forth. The paper includes several photos of the device and the output data of the control system indicating its promising application.

scholarly journals BliStr: The Blind Strategymaker

10.29007/8n7m ◽  
2018 ◽  
Author(s):  
Josef Urban
Keyword(s):  
Local Search ◽  
Theorem Proving ◽  
Main Idea ◽  
Large Set ◽  
Similar Improvement ◽  
New Strategies

BliStr is a system that automatically develops strong targetted theorem-proving strategies for the E prover on a large set of diverse problems. The main idea is to interleave (i) iterated low-timelimit local search for new strategies on small sets of similar easy problems with (ii) higher-timelimit evaluation of the new strategies on all problems. The accumulated results of the global higher-timelimit runs are used to define and evolve the notion of "similar easy problems'", and to control the evolution of the next strategy. The technique significantly strengthened the set of E strategies used by the MaLARea, E-MaLeS, and E systems in the CASC@Turing 2012 competition, particularly in the Mizar division. Similar improvement was obtained on the problems created from the Flyspeck corpus.

An Improved Quantitative Image Analyser

1977 ◽  
Vol 35 ◽  
pp. 226-227
Author(s):  
J.P. Fallon ◽  
P.J. Gregory ◽  
C.J. Taylor
Keyword(s):  
Feature Extraction ◽  
Quantitative Analysis ◽  
Frequency Content ◽  
General Sense ◽  
Physical Measurements ◽  
Quantitative Image ◽  
Image Analyser ◽  
Automatic Methods ◽  
Quantitative Results

Quantitative image analysis systems have been used for several years in research and quality control applications in various fields including metallurgy and medicine. The technique has been applied as an extension of subjective microscopy to problems requiring quantitative results and which are amenable to automatic methods of interpretation.Feature extraction. In the most general sense, a feature can be defined as a portion of the image which differs in some consistent way from the background. A feature may be characterized by the density difference between itself and the background, by an edge gradient, or by the spatial frequency content (texture) within its boundaries. The task of feature extraction includes recognition of features and encoding of the associated information for quantitative analysis.Quantitative Analysis. Quantitative analysis is the determination of one or more physical measurements of each feature. These measurements may be straightforward ones such as area, length, or perimeter, or more complex stereological measurements such as convex perimeter or Feret's diameter.

Digital differential hysteresis iimage processing displays what the microscope acquires but the eye can't see

1995 ◽  
Vol 53 ◽  
pp. 642-643
Author(s):  
Klaus-Ruediger Peters
Keyword(s):  
Image Processing ◽  
Visual System ◽  
High Precision ◽  
Image Data ◽  
Processing Technology ◽  
Output Data ◽  
Contrast Resolution ◽  
Pixel Intensity ◽  
Data Reading ◽  
Hysteresis Properties

Differential hysteresis processing is a new image processing technology that provides a tool for the display of image data information at any level of differential contrast resolution. This includes the maximum contrast resolution of the acquisition system which may be 1,000-times higher than that of the visual system (16 bit versus 6 bit). All microscopes acquire high precision contrasts at a level of <0.01-25% of the acquisition range in 16-bit - 8-bit data, but these contrasts are mostly invisible or only partially visible even in conventionally enhanced images. The processing principle of the differential hysteresis tool is based on hysteresis properties of intensity variations within an image.Differential hysteresis image processing moves a cursor of selected intensity range (hysteresis range) along lines through the image data reading each successive pixel intensity. The midpoint of the cursor provides the output data. If the intensity value of the following pixel falls outside of the actual cursor endpoint values, then the cursor follows the data either with its top or with its bottom, but if the pixels' intensity value falls within the cursor range, then the cursor maintains its intensity value.

Computer Assistance in the Clinical Investigation of Pulmonary Function Studies

1973 ◽  
Vol 12 (02) ◽  
pp. 102-107 ◽  
Author(s):  
D. J. Protti ◽  
Nancy Craven ◽  
A. Naimark ◽  
R. M. Cherniack
Keyword(s):  
Information System ◽  
Pulmonary Function ◽  
Additional Data ◽  
Normal Values ◽  
Clinical Investigation ◽  
Regression Equations ◽  
Beneficial Effects ◽  
Computer Assistance ◽  
Manual Methods

A previously described comprehensive respiratory information system (CRIS) has been changed to introduce new spirometric tests which are sensitive to minor abnormalities, revise on the basis of additional data the regression equations which define normal values to various parameters of pulmonary function and refine the system’s interpretation scheme. The beneficial effects of transferring the system from a large IBM 360/65 to a small CDC 1700 are presented. An analysis of the costs of processing routine pulmonary function studies reveals that a 40°/o saving is realized when a computer is used in comparison to the use of the usual manual methods.

ALGEBRA OF PREDICATES AND RELATED GEOMETRIC MODELS CREATION IN REGARDS OF UNIFIED STATE EXAM IN INFORMATICS (RUSSIAN EGE)

2019 ◽  
pp. 40-47
Author(s):  
E. A. Mironchik
Keyword(s):  
Geometric Model ◽  
Main Idea ◽  
Formal Logic ◽  
High Complexity ◽  
Geometric Models ◽  
Complexity Problem ◽  
Logical Expression ◽  
State Examination

The article discusses the method of solving the task 18 on the Unified State Examination in Informatics (Russian EGE). The main idea of the method is to write the conditions of the problem utilizing the language of formal logic, using elementary predicates. According to the laws of logic the resulting complex logical expression would be transformed into an expression, according to which a geometric model is supposed to be constructed which allows to obtain an answer. The described algorithm does allow high complexity problem to be converted into a simple one.

From Freezing to Investing: New Approaches to Monetary and Currency Policies

2008 ◽  
pp. 47-55
Author(s):  
A. Nekipelov ◽  
Yu. Goland
Keyword(s):  
Economic Policy ◽  
Property Rights ◽  
Main Idea ◽  
State Intervention ◽  
Economic Thought ◽  
Human Potential ◽  
Knowledge Based ◽  
Russian Economy ◽  
Knowledge Based Economy

The appeals to minimize state intervention in the Russian economy are counterproductive. However the excessive involvement of the state is fraught with the threat of building nomenclature capitalism. That is the main idea of the series of articles by prominent representatives of Russian economic thought who formulate their position on key elements of the long-term strategy of Russia’s development. The articles deal with such important issues as Russia’s economic policy, transition to knowledge-based economy, basic directions of monetary and structural policies, strengthening of property rights, development of human potential, foreign economic priorities of our state.

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