scholarly journals Algebraic Solution of Tropical Polynomial Optimization Problems

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2472
Author(s):  
Nikolai Krivulin
Keyword(s):  
Optimization Problems ◽  
Polynomial Optimization ◽  
Algebraic Solution ◽  
The Novel ◽  
Backward Elimination ◽  
Variable Elimination ◽  
Novel Approach ◽  
Ordered Fields ◽  
Two Phases ◽  
Finite Number Of Iterations

We consider constrained optimization problems defined in the tropical algebra setting on a linearly ordered, algebraically complete (radicable) idempotent semifield (a semiring with idempotent addition and invertible multiplication). The problems are to minimize the objective functions given by tropical analogues of multivariate Puiseux polynomials, subject to box constraints on the variables. A technique for variable elimination is presented that converts the original optimization problem to a new one in which one variable is removed and the box constraint for this variable is modified. The novel approach may be thought of as an extension of the Fourier–Motzkin elimination method for systems of linear inequalities in ordered fields to the issue of polynomial optimization in ordered tropical semifields. We use this technique to develop a procedure to solve the problem in a finite number of iterations. The procedure includes two phases: backward elimination and forward substitution of variables. We describe the main steps of the procedure, discuss its computational complexity and present numerical examples.

scholarly journals From a Pareto Front to Pareto Regions: A Novel Standpoint for Multiobjective Optimization

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3152
Author(s):  
Carine M. Rebello ◽  
Márcio A. F. Martins ◽  
Daniel D. Santana ◽  
Alírio E. Rodrigues ◽  
José M. Loureiro ◽  
...  
Keyword(s):  
Multiobjective Optimization ◽  
Pareto Front ◽  
Optimization Problems ◽  
The Novel ◽  
Particle Swarm Optimizer ◽  
Novel Approach ◽  
Multiobjective Optimization Problems ◽  
Pressure Swing ◽  
Novel Concept

This work presents a novel approach for multiobjective optimization problems, extending the concept of a Pareto front to a new idea of the Pareto region. This new concept provides all the points beyond the Pareto front, leading to the same optimal condition with statistical assurance. This region is built using a Fisher–Snedecor test over an augmented Lagragian function, for which deductions are proposed here. This test is meant to provide an approximated depiction of the feasible operation region while using meta-heuristic optimization results to extract this information. To do so, a Constrained Sliding Particle Swarm Optimizer (CSPSO) was applied to solve a series of four benchmarks and a case study. The proposed test analyzed the CSPSO results, and the novel Pareto regions were estimated. Over this Pareto region, a clustering strategy was also developed and applied to define sub-regions that prioritize one of the objectives and an intermediary region that provides a balance between objectives. This is a valuable tool in the context of process optimization, aiming at assertive decision-making purposes. As this is a novel concept, the only way to compare it was to draw the entire regions of the benchmark functions and compare them with the methodology result. The benchmark results demonstrated that the proposed method could efficiently portray the Pareto regions. Then, the optimization of a Pressure Swing Adsorption unit was performed using the proposed approach to provide a practical application of the methodology developed here. It was possible to build the Pareto region and its respective sub-regions, where each process performance parameter is prioritized. The results demonstrated that this methodology could be helpful in processes optimization and operation. It provides more flexibility and more profound knowledge of the system under evaluation.

Exploring normative perceptions and misperceptions of private, environmentally impactful behaviours

2020 ◽  
Author(s):  
Elaine Gallagher ◽  
Bas Verplanken ◽  
Ian Walker
Keyword(s):  
Social Norms ◽  
Behaviour Change ◽  
Social Contexts ◽  
The Novel ◽  
Normative Influence ◽  
Change Mechanism ◽  
Novel Approach ◽  
Classical Studies ◽  
Referent Group

Social norms have been shown to be an effective behaviour change mechanism across diverse behaviours, demonstrated from classical studies to more recent behaviour change research. Much of this research has focused on environmentally impactful actions. Social norms are typically utilised for behaviour change in social contexts, which facilitates the important element of the behaviour being visible to the referent group. This ensures that behaviours can be learned through observation and that deviations from the acceptable behaviour can be easily sanctioned or approved by the referent group. There has been little focus on how effective social norms are in private or non-social contexts, despite a multitude of environmentally impactful behaviours occurring in the home, for example. The current study took the novel approach to explore if private behaviours are important in the context of normative influence, and if the lack of a referent groups results in inaccurate normative perceptions and misguided behaviours. Findings demonstrated variance in normative perceptions of private behaviours, and that these misperceptions may influence behaviour. These behaviours are deemed to be more environmentally harmful, and respondents are less comfortable with these behaviours being visible to others, than non-private behaviours. The research reveals the importance of focusing on private behaviours, which have been largely overlooked in the normative influence literature.

The Free Responsible Action of the Individual

2018 ◽  
Author(s):  
Michael P. DeJonge
Keyword(s):  
The Novel ◽  
Extreme Situation ◽  
The Third ◽  
Third Phase ◽  
Responsible Action ◽  
Action Type ◽  
Two Phases ◽  
The Individual ◽  
The Church

If, as Chapter 12 argues, much of Bonhoeffer’s resistance thinking remains stable even as he undertakes the novel conspiratorial resistance, what is new in his resistance thinking in the third phase? What receives new theological elaboration is the resistance activity of the individual, which in the first two phases was overshadowed by the resistance role played by the church. Indeed, as this chapter shows, Bonhoeffer’s conspiratorial activity is associated with what he calls free responsible action (type 6), and this is the action of the individual, not the church, in the exercise of vocation. As such, the conspiratorial activity is most closely related to the previously developed type 1 resistance, which includes individual vocational action in response to state injustice. But the conspiratorial activity differs from type 1 resistance as individual vocational action in the extreme situation.

scholarly journals Connectivity matrix model of quantum circuits and its application to distributed quantum circuit optimization

2021 ◽  
Vol 20 (7) ◽  
Author(s):  
Ismail Ghodsollahee ◽  
Zohreh Davarzani ◽  
Mariam Zomorodi ◽  
Paweł Pławiak ◽  
Monireh Houshmand ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Quantum Computer ◽  
Quantum Circuit ◽  
Quantum Circuits ◽  
Connectivity Matrix ◽  
Circuit Optimization ◽  
Novel Approach ◽  
The Matrix ◽  
Minimum Number ◽  
Two Phases

AbstractAs quantum computation grows, the number of qubits involved in a given quantum computer increases. But due to the physical limitations in the number of qubits of a single quantum device, the computation should be performed in a distributed system. In this paper, a new model of quantum computation based on the matrix representation of quantum circuits is proposed. Then, using this model, we propose a novel approach for reducing the number of teleportations in a distributed quantum circuit. The proposed method consists of two phases: the pre-processing phase and the optimization phase. In the pre-processing phase, it considers the bi-partitioning of quantum circuits by Non-Dominated Sorting Genetic Algorithm (NSGA-III) to minimize the number of global gates and to distribute the quantum circuit into two balanced parts with equal number of qubits and minimum number of global gates. In the optimization phase, two heuristics named Heuristic I and Heuristic II are proposed to optimize the number of teleportations according to the partitioning obtained from the pre-processing phase. Finally, the proposed approach is evaluated on many benchmark quantum circuits. The results of these evaluations show an average of 22.16% improvement in the teleportation cost of the proposed approach compared to the existing works in the literature.

scholarly journals A Novel Approach to EEG Speech Activity Detection with Visual Stimuli and Mobile BCI

2021 ◽  
Vol 11 (2) ◽  
pp. 674
Author(s):  
Marianna Koctúrová ◽  
Jozef Juhár
Keyword(s):  
Visual Stimuli ◽  
Computer Interface ◽  
Single Subject ◽  
Detection Accuracy ◽  
The Novel ◽  
Activity Detection ◽  
Speech Activity ◽  
Novel Approach ◽  
Eeg Data ◽  
Speech Activity Detection

With the ever-progressing development in the field of computational and analytical science the last decade has seen a big improvement in the accuracy of electroencephalography (EEG) technology. Studies try to examine possibilities to use high dimensional EEG data as a source for Brain to Computer Interface. Applications of EEG Brain to computer interface vary from emotion recognition, simple computer/device control, speech recognition up to Intelligent Prosthesis. Our research presented in this paper was focused on the study of the problematic speech activity detection using EEG data. The novel approach used in this research involved the use visual stimuli, such as reading and colour naming, and signals of speech activity detectable by EEG technology. Our proposed solution is based on a shallow Feed-Forward Artificial Neural Network with only 100 hidden neurons. Standard features such as signal energy, standard deviation, RMS, skewness, kurtosis were calculated from the original signal from 16 EEG electrodes. The novel approach in the field of Brain to computer interface applications was utilised to calculated additional set of features from the minimum phase signal. Our experimental results demonstrated F1 score of 86.80% and 83.69% speech detection accuracy based on the analysis of EEG signal from single subject and cross-subject models respectively. The importance of these results lies in the novel utilisation of the mobile device to record the nerve signals which can serve as the stepping stone for the transfer of Brain to computer interface technology from technology from a controlled environment to the real-life conditions.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

ChemInform Abstract: The Novel Approach to Indole Alkaloids by Using Pd(II)-Catalyzed Cyclization.

ChemInform ◽  
2015 ◽  
Vol 46 (17) ◽  
pp. no-no
Author(s):  
Hajime Yokoyama ◽  
Takayoshi Kubo ◽  
Yosuke Matsumura ◽  
Junichi Hosokawa ◽  
Masahiro Miyazawa ◽  
...  
Keyword(s):  
Indole Alkaloids ◽  
The Novel ◽  
Novel Approach

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

scholarly journals Caffeine-Induced Effects on Human Skeletal Muscle Contraction Time and Maximal Displacement Measured by Tensiomyography

Nutrients ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 815
Author(s):  
Przemysław Domaszewski ◽  
Paweł Pakosz ◽  
Mariusz Konieczny ◽  
Dawid Bączkowicz ◽  
Ewa Sadowska-Krępa
Keyword(s):  
Skeletal Muscle ◽  
Muscle Activation ◽  
Electric Pulse ◽  
Professional Athletes ◽  
Mechanical Activity ◽  
The Novel ◽  
Contraction Time ◽  
Novel Approach ◽  
Skeletal Muscle Contraction ◽  
Maximal Displacement

Studies on muscle activation time in sport after caffeine supplementation confirmed the effectiveness of caffeine. The novel approach was to determine whether a dose of 9 mg/kg/ body mass (b.m.) of caffeine affects the changes of contraction time and the displacement of electrically stimulated muscle (gastrocnemius medialis) in professional athletes who regularly consume products rich in caffeine and do not comply with the caffeine discontinuation period requirements. The study included 40 professional male handball players (age = 23.13 ± 3.51, b.m. = 93.51 ± 15.70 kg, height 191 ± 7.72, BMI = 25.89 ± 3.10). The analysis showed that in the experimental group the values of examined parameters were significantly reduced (p ≤ 0.001) (contraction time: before = 20.60 ± 2.58 ms/ after = 18.43 ± 3.05 ms; maximal displacement: before = 2.32 ± 0.80 mm/after = 1.69 ± 0.51 mm). No significant changes were found in the placebo group. The main achievement of this research was to demonstrate that caffeine at a dose of 9 mg/kg in professional athletes who regularly consume products rich in caffeine has a direct positive effect on the mechanical activity of skeletal muscle stimulated by an electric pulse.

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