Formalising Overlap Algebras in Matita

2011 ◽  
Vol 21 (4) ◽  
pp. 763-793 ◽  
Author(s):  
CLAUDIO SACERDOTI COEN ◽  
ENRICO TASSI
Keyword(s):  
Intuitionistic Logic ◽  
Scientific Collaboration ◽  
Optimal Solution ◽  
The Other ◽  
Theorem Prover ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Size Information ◽  
Predicative Logic

We describe some formal topological results, formalised in Matita 1/2, presented in predicative intuitionistic logic and in terms of Overlap Algebras.Overlap Algebras are new algebraic structures designed to ease reasoning about subsets in an algebraic way within intuitionistic logic. We find that they also ease the formalisation of formal topological results in an interactive theorem prover.Our main result is the existence of a functor between two categories of ‘generalised topological spaces’, one with points (Basic Pairs) and the other point-free (Basic Topologies). This formalisation is part of a wider scientific collaboration with the inventor of the theory, Giovanni Sambin. His goal is to verify in what sense his theory is ‘implementable’, and to discover what problems may arise in the process. We check that all intermediate constructions respect the stringent size requirements imposed by predicative logic. The formalisation is quite unusual, since it has to make explicit size information that is often hidden.We found that the version of Matita used for the formalisation was largely inappropriate. The formalisation drove several major improvements of Matita that will be integrated in the next major release (Matita 1.0). We show some motivating examples, taken directly from the formalisation, for these improvements. We also describe a possibly sub-optimal solution in Matita 1/2, which is exploitable in other similar systems. We briefly discuss a better solution available in Matita 1.0.

p-semisimple modules and type submodules

2019 ◽  
Vol 19 (04) ◽  
pp. 2050078
Author(s):  
A. Mozaffarikhah ◽  
E. Momtahan ◽  
A. R. Olfati ◽  
S. Safaeeyan
Keyword(s):  
Abelian Groups ◽  
Large Family ◽  
The Other ◽  
Topological Spaces ◽  
Algebraic Structures ◽  
Semisimple Modules ◽  
Other Hand ◽  
One To One ◽  
Regular Closed

In this paper, we introduce the concept of [Formula: see text]-semisimple modules. We prove that a multiplication reduced module is [Formula: see text]-semisimple if and only if it is a Baer module. We show that a large family of abelian groups are [Formula: see text]-semisimple. Furthermore, we give a topological characterizations of type submodules (ideals) of multiplication reduced modules ([Formula: see text]-semisimple rings). Moreover, we observe that there is a one-to-one correspondence between type ideals of some algebraic structures on one hand and regular closed subsets of some related topological spaces on the other hand. This also characterizes the form of closed ideals in [Formula: see text].

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals An evolutionary-based optimization algorithm for truss sizing design

2016 ◽  
Vol 38 (4) ◽  
pp. 307-317
Author(s):  
Pham Hoang Anh
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
The Other ◽  
Truss Structures ◽  
Benchmark Problems ◽  
Discrete Variables ◽  
Objective Functions

In this paper, the optimal sizing of truss structures is solved using a novel evolutionary-based optimization algorithm. The efficiency of the proposed method lies in the combination of global search and local search, in which the global move is applied for a set of random solutions whereas the local move is performed on the other solutions in the search population. Three truss sizing benchmark problems with discrete variables are used to examine the performance of the proposed algorithm. Objective functions of the optimization problems are minimum weights of the whole truss structures and constraints are stress in members and displacement at nodes. Here, the constraints and objective function are treated separately so that both function and constraint evaluations can be saved. The results show that the new algorithm can find optimal solution effectively and it is competitive with some recent metaheuristic algorithms in terms of number of structural analyses required.

scholarly journals CONTINUOUS ORDER REPRESENTABILITY PROPERTIES OF TOPOLOGICAL SPACES AND ALGEBRAIC STRUCTURES

2012 ◽  
Vol 49 (3) ◽  
pp. 449-473 ◽  
Author(s):  
Maria Jesus Campion ◽  
Juan Carlos Candeal ◽  
Esteban Indurain ◽  
Ghanshyam Bhagvandas Mehta
Keyword(s):  
Topological Spaces ◽  
Algebraic Structures

scholarly journals Multiple infill criterion-assisted hybrid evolutionary optimization for medium-dimensional computationally expensive problems

2021 ◽  
Author(s):  
Shufen Qin ◽  
Chan Li ◽  
Chaoli Sun ◽  
Guochen Zhang ◽  
Xiaobo Li
Keyword(s):  
Evolutionary Algorithms ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Global Search ◽  
Model Management ◽  
The Other ◽  
Local Searches ◽  
Fitness Value ◽  
Expensive Problems ◽  
Computationally Expensive

AbstractSurrogate-assisted evolutionary algorithms have been paid more and more attention to solve computationally expensive problems. However, model management still plays a significant importance in searching for the optimal solution. In this paper, a new method is proposed to measure the approximation uncertainty, in which the differences between the solution and its neighbour samples in the decision space, and the ruggedness of the objective space in its neighborhood are both considered. The proposed approximation uncertainty will be utilized in the surrogate-assisted global search to find a solution for exact objective evaluation to improve the exploration capability of the global search. On the other hand, the approximated fitness value is adopted as the infill criterion for the surrogate-assisted local search, which is utilized to improve the exploitation capability to find a solution close to the real optimal solution as much as possible. The surrogate-assisted global and local searches are conducted in sequence at each generation to balance the exploration and exploitation capabilities of the method. The performance of the proposed method is evaluated on seven benchmark problems with 10, 20, 30 and 50 dimensions, and one real-world application with 30 and 50 dimensions. The experimental results show that the proposed method is efficient for solving the low- and medium-dimensional expensive optimization problems by compared to the other six state-of-the-art surrogate-assisted evolutionary algorithms.

scholarly journals Optimalisasi Alokasi Sumberdaya Rumahtangga Petani Di Ekosistem Lahan Pasang Surut di Kalimantan Selatan = Optimizing The Allocation Of Farm-household Resources In Tidal Swamp Area In South Kalimantan

Agro Ekonomi ◽  
2016 ◽  
Vol 10 (2) ◽  
pp. 29
Author(s):  
Emy Rahmawaty ◽  
Dibyo Prabowo ◽  
Slamet Hartono ◽  
Ismet Ahmad
Keyword(s):  
Programming Model ◽  
Optimal Solution ◽  
The Other ◽  
Survey Method ◽  
Cropping Pattern ◽  
Acid Sulphate ◽  
Household Resources ◽  
Tidal Swamp ◽  
Drastic Increase ◽  
Potential Land

The objective of this research is to analyses the allocation of farmer household resources in tidal swamp area. The survey method was used to collect farmer data located in tidal swamps land villages with acid sulphate land, peatyland,. and potential land typologies in South Kalimantan. Quantitative analysis of data was carried out using linear programming model and sensitivity analysis, utilizing the BLPX 88 program.The findings of the analysis showed that villages allocated resources differently with the implication that incomes earned by the villages differed from one village to the other. However, it was found out too that optimal solution showed the need for the continuation of rice growing in the areas. Farmers who were located in potential areas where tangerine were grown produce higher incomes than the other two villages. To replicate the cropping pattern farmers in potential land in acid sulphate land and peatyland, resulted into a drastic increase in income earned by farmers

scholarly journals Variable and sub-optimal responses to a choice problem are a persistent default mode

2019 ◽  
Author(s):  
Amelia R. Hunt ◽  
Warren James ◽  
Josephine Reuther ◽  
Melissa Spilioti ◽  
Eleanor Mackay ◽  
...  
Keyword(s):  
Optimal Strategy ◽  
Decision Rules ◽  
Optimal Solution ◽  
The Other ◽  
Rational Decision ◽  
Choice Problem ◽  
Default Mode ◽  
Potential Benefits ◽  
Simple Logic ◽  
Simple Decision Rule

Here we report persistent choice variability in the presence of a simple decision rule. Two analogous choice problems are presented, both of which involve making decisions about how to prioritize goals. In one version, participants choose a place to stand to throw a beanbag into one of two hoops. In the other, they must choose a place to fixate to detect a target that could appear in one of two boxes. In both cases, participants do not know which of the locations will be the target when they make their choice. The optimal solution to both problems follows the same, simple logic: when targets are close together, standing at/fixating the midpoint is the best choice. When the targets are far apart, accuracy from the midpoint falls, and standing/fixating close to one potential target achieves better accuracy. People do not follow, or even approach, this optimal strategy, despite substantial potential benefits for performance. Two interventions were introduced to try and shift participants from sub-optimal, variable responses to following a fixed, rational rule. First, we put participants into circumstances in which the solution was obvious. After participants correctly solved the problem there, we immediately presented the slightly-less-obvious context. Second, we guided participants to make choices that followed an optimal strategy, and then removed the guidance and let them freely choose. Following both of these interventions, participants immediately returned to a variable, sub-optimal pattern of responding. The results show that while constructing and implementing rational decision rules is possible, making variable responses to choice problems is a strong and persistent default mode. Borrowing concepts from classic animal learning studies, we suggest this default may persist because choice variability can provide opportunities for reinforcement learning.

scholarly journals LAYOUT OPTIMIZATION FOR A FACTORY OF A MEXICAN RECYCLING COMPANY

2020 ◽  
Vol 6 (6) ◽  
pp. 146-165
Author(s):  
Oscar Bravo ◽  
Mara Belmonte ◽  
Beatriz Oechler ◽  
Uriel Rovero ◽  
Rodrigo de Icaza ◽  
...  
Keyword(s):  
Negative Impact ◽  
Optimal Solution ◽  
Layout Optimization ◽  
The Other

The present format is an investigation of the principal problems found at the present time at a Mexican Recycling factory. Said problems were analyzed and the ones with greater urgency to be solved or with greater negative impact were selected. These selected problems were analyzed, measured and calculated to find the optimal solution or the best recommendation possible. A change in the current layout was done with the objective of optimizing the resources of the plant as decreasing costs and errors that create an inefficient productivity inside the plant. This recommendations in the accommodation will be replicable in the other plants the company has around the Mexican Republic

Postnikov “Invariants” in 2004

2005 ◽  
Vol 12 (1) ◽  
pp. 139-155
Author(s):  
Julio Rubio ◽  
Francis Sergeraert
Keyword(s):  
Decision Problem ◽  
The Other ◽  
Topological Spaces ◽  
Exact Nature ◽  
Other Hand

Abstract The very nature of the so-called Postnikov invariants is carefully studied. Two functors, precisely defined, explain the exact nature of the connection between the category of topological spaces and the category of Postnikov towers. On one hand, these functors are in particular effective and lead to concrete machine computations through the general machine program Kenzo. On the other hand, the Postnikov “invariants” will be actual invariants only when an arithmetical decision problem – currently open – will be solved; it is even possible this problem is undecidable.

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