Search results for: uniformly convex and uniformly smooth Banach space

Authors: S. Som-Am, B. Grechuk

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Moser’s worm problem is the unsolved problem in geometry which asks for the minimal area of a convex region on the plane which can cover all curves of unit length, assuming that curves may be rotated and translated to fit inside the region. We study a version of this problem asking for a minimal convex cover for closed unit curves. By combining geometric methods with numerical box’s search algorithm, we show that any such cover should have an area at least 0.0975. This improves the best previous lower bound of 0.096694. In fact, we show that the minimal area of convex hull of circle, equilateral triangle, and rectangle of perimeter 1 is between 0.0975 and 0.09763.

Keywords: Moser’s worm problem, closed arcs, convex cover, minimal-area cover

Procedia PDF Downloads 182

Authors: Elham Kiyani, S. Mansour Vaezpour, Javad Tavakoli

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In this paper, we first introduce a new distance function in a linear space not necessarily endowed with a topology. The algebraic concepts of interior and closure are useful to study optimization problems without topology. So, we define Q-weak efficient solutions generated by the algebraic interior of a set Q, where Q is not necessarily convex. Studying nonconvex vector optimization is valuable since, for a convex cone K in topological spaces, we have int(K)=cor(K), which means that topological interior of a convex cone K is equal to the algebraic interior of K. Moreover, we used the scalarization technique including the distance function generated by the vectorial closure of a set to characterize these Q-weak efficient solutions. Scalarization is a useful approach for solving vector optimization problems. This technique reduces the optimization problem to a scalar problem which tends to be an optimization problem with a real-valued objective function. For instance, Q-weak efficient solutions of vector optimization problems can be characterized and computed as solutions of appropriate scalar optimization problems. In the convex case, linear functionals can be used as objective functionals of the scalar problems. But in the nonconvex case, we should present a suitable objective function. It is the aim of this paper to present a new distance function that be useful to obtain sufficient and necessary conditions for Q-weak efficient solutions of general optimization problems via scalarization.

Keywords: weak efficient, algebraic interior, vector closure, linear space

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Authors: Sima Hassankhali, Ildar Sadeqi

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In the theory of Pareto efficient points, the existence of a bounded base for a cone K of a normed space X is so important. In this article, we study the geometric structure of a nonzero closed convex cone K with a bounded base. For this aim, we study the structure of the polar cone K# of K. Furthermore, we obtain a necessary and sufficient condition for a nonempty closed convex set C so that its recession cone C∞ has a bounded base.

Keywords: solid cones, recession cones, polar cones, bounded base

Procedia PDF Downloads 234

Authors: M. Khouil, N. Saber, M. Mestari

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In this paper, a different architecture of a collision detection neural network (DCNN) is developed. This network, which has been particularly reviewed, has enabled us to solve with a new approach the problem of collision detection between two convex polyhedra in a fixed time (O (1) time). We used two types of neurons, linear and threshold logic, which simplified the actual implementation of all the networks proposed. The study of the collision detection is divided into two sections, the collision between a point and a polyhedron and then the collision between two convex polyhedra. The aim of this research is to determine through the AMAXNET network a mini maximum point in a fixed time, which allows us to detect the presence of a potential collision.

Keywords: collision identification, fixed time, convex polyhedra, neural network, AMAXNET

Procedia PDF Downloads 389

Authors: Elham Kiyani

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In this paper, we first introduce the concept of Q-efficient solutions in a real linear space not necessarily endowed with a topology, where Q is some nonempty (not necessarily convex) set. We also used the scalarization technique including the Gerstewitz function generated by a nonconvex set to characterize these Q-efficient solutions. The algebraic concepts of interior and closure are useful to study optimization problems without topology. Studying nonconvex vector optimization is valuable since topological interior is equal to algebraic interior for a convex cone. So, we use the algebraic concepts of interior and closure to define Q-weak efficient solutions and Q-Henig proper efficient solutions of set-valued optimization problems, where Q is not a convex cone. Optimization problems with set-valued maps have a wide range of applications, so it is expected that there will be a useful analytical tool in optimization theory for set-valued maps. These kind of optimization problems are closely related to stochastic programming, control theory, and economic theory. The paper focus on nonconvex problems, the results are obtained by assuming generalized non-convexity assumptions on the data of the problem. In convex problems, main mathematical tools are convex separation theorems, alternative theorems, and algebraic counterparts of some usual topological concepts, while in nonconvex problems, we need a nonconvex separation function. Thus, we consider the Gerstewitz function generated by a general set in a real linear space and re-examine its properties in the more general setting. A useful approach for solving a vector problem is to reduce it to a scalar problem. In general, scalarization means the replacement of a vector optimization problem by a suitable scalar problem which tends to be an optimization problem with a real valued objective function. The Gerstewitz function is well known and widely used in optimization as the basis of the scalarization. The essential properties of the Gerstewitz function, which are well known in the topological framework, are studied by using algebraic counterparts rather than the topological concepts of interior and closure. Therefore, properties of the Gerstewitz function, when it takes values just in a real linear space are studied, and we use it to characterize Q-efficient solutions of vector problems whose image space is not endowed with any particular topology. Therefore, we deal with a constrained vector optimization problem in a real linear space without assuming any topology, and also Q-weak efficient and Q-proper efficient solutions in the senses of Henig are defined. Moreover, by means of the Gerstewitz function, we provide some necessary and sufficient optimality conditions for set-valued vector optimization problems.

Keywords: algebraic interior, Gerstewitz function, vector closure, vector optimization

Procedia PDF Downloads 192

Authors: Irina Maria Artinescu, Costin Radu Boldea, Eduard-Ionut Matei

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The paper is a comparative study of two classical variants of parallel projection methods for solving the convex feasibility problem with their equivalents that involve variable weights in the construction of the solutions. We used a graphical representation of these methods for inpainting a convex area of an image in order to investigate their effectiveness in image reconstruction applications. We also presented a numerical analysis of the convergence of these four algorithms in terms of the average number of steps and execution time in classical CPU and, alternatively, in parallel GPU implementation.

Keywords: convex feasibility problem, convergence analysis, inpainting, parallel projection methods

Procedia PDF Downloads 138

Authors: Lawrence A. Farinola

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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

Procedia PDF Downloads 100

Authors: Jagroop Singh Sidhu, Buta Singh

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A low computational deblocking filter including three frequency related modes (smooth mode, intermediate mode, and non-smooth mode for low-frequency, mid-frequency, and high frequency regions, respectively) is proposed. The suggested approach requires zero additions, zero subtractions, zero multiplications (for intermediate region), no divisions (for non-smooth region) and no comparison. The suggested method thus keeps the computation lower and thus suitable for image coding systems based on blocks. Comparison of average number of operations for smooth, non-smooth, intermediate (per pixel vector for each block) using filter suggested by Chen and the proposed method filter suggests that the proposed filter keeps the computation lower and is thus suitable for fast processing algorithms.

Keywords: blocking artifacts, computational complexity, non-smooth, intermediate, smooth

Procedia PDF Downloads 436

Authors: I. A. Farhat

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The dynamic economic dispatch (DED) problem is one of the complex, constrained optimization problems that have nonlinear, con-convex and non-smooth objective functions. The purpose of the DED is to determine the optimal economic operation of the committed units while meeting the load demand. Associated to this constrained problem there exist highly nonlinear and non-convex practical constraints to be satisfied. Therefore, classical and derivative-based methods are likely not to converge to an optimal or near optimal solution to such a dynamic and large-scale problem. In this paper, an Artificial Immune System technique (AIS) is implemented and applied to solve the DED problem considering the transmission power losses and the valve-point effects in addition to the other operational constraints. To demonstrate the effectiveness of the proposed technique, two case studies are considered. The results obtained using the AIS are compared to those obtained by other methods reported in the literature and found better.

Keywords: artificial immune system, dynamic economic dispatch, optimal economic operation, large-scale problem

Procedia PDF Downloads 210

Authors: Kun Xue, Lvlan Miu, Jiarui Li

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Jetting structures are widely found in particle rings or shells dispersed by the central explosion. In contrast, some explosive dispersal of particles only results in a dispersed cloud without distinctive structures. Employing the coupling method of the compressible computational fluid mechanics and discrete element method (CCFD-DEM), we reveal the underlying physics governing the formation of the jetting structure, which is related to the competition between the shock compaction and gas infiltration, two major processes during the shock interaction with the granular media. If the shock compaction exceeds the gas infiltration, the discernable jetting structures are expected, precipitated by the agglomerates of fast-moving particles induced by the heterogenous network of force chains. Otherwise, particles are uniformly accelerated by the interstitial flows, and no distinguishable jetting structures are formed. We proceed to devise the phase map of the jetting formation in the space defined by two dimensionless parameters which characterize the timescales of the shock compaction and the gas infiltration, respectively.

Keywords: compressible multiphase flows, DEM, granular jetting, pattern formation

Procedia PDF Downloads 45

Authors: Yixun Shi

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Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

Procedia PDF Downloads 371

Authors: Thanida Sujarittham, Narumon Emarat, Jintawat Tanamatayarat, Kwan Arayathanitkul, Suchai Nopparatjamjomras

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Electric field is an important fundamental concept in electrostatics. In high-school, generally Thai students have already learned about definition of electric field, electric field due to a point charge, and superposition of electric fields due to multiple-point charges. Those are the prerequisite basic knowledge students holding before entrancing universities. In the first-year university level, students will be quickly revised those basic knowledge and will be then introduced to a more complicated topic—electric field due to continuous charged distributions. We initially found that our freshman students, who were from the Faculty of Science and enrolled in the introductory physic course (SCPY 158), often seriously struggled with the basic physics concepts—superposition of electric fields and inverse square law and mathematics being relevant to this topic. These also then resulted on students’ understanding of advanced topics within the course such as Gauss's law, electric potential difference, and capacitance. Therefore, it is very important to determine students' understanding of electric field due to continuous charged distributions. The open-ended question about sketching net electric field vectors from a uniformly charged insulating rod was administered to 260 freshman science students as pre- and post-tests. All of their responses were analyzed and classified into five levels of understandings. To get deep understanding of each level, 30 students were interviewed toward their individual responses. The pre-test result found was that about 90% of students had incorrect understanding. Even after completing the lectures, there were only 26.5% of them could provide correct responses. Up to 50% had confusions and irrelevant ideas. The result implies that teaching methods in Thai high schools may be problematic. In addition for our benefit, these students’ alternative conceptions identified could be used as a guideline for developing the instructional method currently used in the course especially for teaching electrostatics.

Keywords: alternative conceptions, electric field of continuous charged distributions, inverse square law, levels of student understandings, superposition principle

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Authors: Anteneh Getachew Gebrie, Rabian Wangkeeree

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The purpose of this paper is to introduce iterative algorithm solving split system of minimization problem given as a task of finding a common minimizer point of finite family of proper, lower semicontinuous convex functions and whose image under a bounded linear operator is also common minimizer point of another finite family of proper, lower semicontinuous convex functions. We obtain strong convergence of the sequence generated by our algorithm under some suitable conditions on the parameters. The iterative schemes are developed with a way of selecting the step sizes such that the information of operator norm is not necessary. Some applications and numerical experiment is given to analyse the efficiency of our algorithm.

Keywords: Hilbert Space, minimization problems, Moreau-Yosida approximate, split feasibility problem

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Authors: H. Zormati, J. Chebil, J. Bel Hadj Tahar

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Next generation wireless transmission technology (5G) is expected to support the development of channel models for higher frequency bands, so clarification of high frequency bands is the most important issue in radio propagation research for 5G, multiple urban microcellular measurements have been carried out at 60 GHz. In this paper, the collected data is uniformly analyzed with focus on the path loss (PL), the objective is to compare simulation results of some studied channel models with the purpose of testing the performance of each one.

Keywords: 5G, channel model, 60GHz channel, millimeter-wave, urban microcell

Procedia PDF Downloads 278

Authors: Sergei Zhevnenko

Abstract:

Сontinuous layer of tantalum boride is formed on the surface as a result of reactive wetting of oxidized tantalum by copper melt with boron at a temperatures above 1150 °C. An increase in the wetting temperature above 1400 °C leads to a change in the formation mechanism of tantalum borides, they are formed in the nanosized flakes. In the presented work, we studied the process of copper-based in-situ composite formation, strengthened by the particles of tantalum borides. We investigated the structure of the formed particles, the conditions, and the kinetics of their formation. Dissolving boride particles do not have time to mix uniformly in the melt upon sufficiently rapid cooling and form a macrostructure, partly repeating the shape of the metallic tantalum. This allows to set different gradient structures in the copper alloy. Such macrostructures have been obtained. Boride particles and microstructures were studied by scanning and transmission electron microscopy, and regions with particles were investigated by nanoindentation. In this work, we also measured the kinetics of impregnation of porous tantalum with copper-boron melt and studied the structures of the composite, in which the melt filling the interpore space is saturated with boride particles.

Keywords: copper, tantalum borides, in-situ composites, wetting, imbibition

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Authors: Gulsharat A. Baigonakova, Ekaterina S. Marchenko, Venera R. Luchsheva

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The preferred materials for bone grafting are titanium-nickel alloys. They have a porous, permeable structure similar to that of bone tissue, can withstand long-term physiological stress in the body, and retain the scaffolding function for bone tissue ingrowth. Despite the excellent functional properties of these alloys, there is a possibility of post-operative infectious complications that prevent the newly formed bone tissue from filling the spaces created in a timely manner and prolong the rehabilitation period of patients. In order to minimise such consequences, it is necessary to use biocompatible materials capable of simultaneously fulfilling the function of a long-term functioning implant and an osteoreplacement carrier saturated with drugs. Methods to modify the surface by saturation with bioactive substances, in particular macrocyclic compounds, for the controlled release of drugs, biologically active substances, and cells are becoming increasingly important. This work is dedicated to the functionalisation of the surface of porous titanium nickelide by the deposition of macrocyclic compounds in order to provide titanium nickelide with antibacterial activity and accelerated osteogenesis. The paper evaluates the effect of macrocyclic compound deposition methods on the continuity, structure, and cytocompatibility of the surface properties of porous titanium nickelide. Macrocyclic compounds were deposited on the porous surface of titanium nickelide under the influence of various physical effects. Structural research methods have allowed the evaluation of the surface morphology of titanium nickelide and the nature of the distribution of these compounds. The method of surface functionalisation of titanium nickelide influences the size of the deposited bioactive molecules and the nature of their distribution. The surface functionalisation method developed has enabled titanium nickelide to be deposited uniformly on the inner and outer surfaces of the pores, which will subsequently enable the material to be uniformly saturated with various drugs, including antibiotics and inhibitors. The surface-modified porous titanium nickelide showed high biocompatibility and low cytotoxicity in in vitro studies. The research was carried out with financial support from the Russian Science Foundation under Grant No. 22-72-10037.

Keywords: biocompatibility, NiTi, surface, porous structure

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Authors: Oleg Vlasovets, Fabian Schaipp, Christian L. Mueller

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we conduct a network analysis and predict the sex of 1000 participants based on ”connectome” - pairwise Pearson’s correlation across 436 brain parcels. We solve the non-smooth convex optimization problem, known under the name of Graphical Lasso, where the solution includes a low-rank component. With this solution and machine learning model for a sex prediction, we explain the brain parcels-sex connectivity patterns.

Keywords: network analysis, neuroscience, machine learning, optimization

Procedia PDF Downloads 113

Authors: Dhiflaoui Hafedh, Khlifi Kaouther, Ben Cheikh Larbi Ahmed

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Monolayer and multilayer coatings of CrN and AlCrN deposited on 100Cr6 (AISI 52100) substrate by PVD magnetron sputtering system. The micro structures of the coatings were characterized using atomic force microscopy (AFM). The AFM analysis revealed the presence of domes and craters which are uniformly distributed over all surfaces of the various layers. Nano indentation measurement of CrN coating showed maximum hardness (H) and modulus (E) of 14 GPa and 240 GPa, respectively. The measured H and E values of AlCrN coatings were found to be 30 GPa and 382 GPa, respectively. The improved hardness in both the coatings was attributed mainly to a reduction in crystallite size and decrease in surface roughness. The incorporation of Al into the CrN coatings has improved both hardness and Young’s modulus.

Keywords: CrN, AlCrN coatings, hardness, nanoindentation

Procedia PDF Downloads 538

Authors: Mohamed Gouda

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Antibacterial wound dressings based on cellulose nanofibers containing different metal nanoparticles (CMC-MNPs) were synthesized using an electrospinning technique. First, the composite of carboxymethyl cellulose containing different metal nanoparticles (CMC/MNPs), such as copper nanoparticles (CuNPs), iron nanoparticles (FeNPs), zinc nanoparticles (ZnNPs), cadmium nanoparticles (CdNPs) and cobalt nanoparticles (CoNPs) were synthesized, and finally, these composites were transferred to the electrospinning process. Synthesized CMC-MNPs were characterized using scanning electron microscopy (SEM) coupled with high-energy dispersive X-ray (EDX) and UV-visible spectroscopy used to confirm nanoparticle formation. The SEM images clearly showed regular flat shapes with semi-porous surfaces. All MNPs were well distributed inside the backbone of the cellulose without aggregation. The average particle diameters were 29-39 nm for ZnNPs, 29-33 nm for CdNPs, 25-33 nm for CoNPs, 23-27 nm for CuNPs and 22-26 nm for FeNPs. Surface morphology, water uptake and release of MNPs from the nanofibers in water and antimicrobial efficacy were studied. SEM images revealed that electrospun CMC-MNPs nanofibers are smooth and uniformly distributed without bead formation with average fiber diameters in the range of 300 to 450 nm. Fiber diameters were not affected by the presence of MNPs. TEM images showed that MNPs are present in/on the electrospun CMC-MNPs nanofibers. The diameter of the electrospun nanofibers containing MNPs was in the range of 300–450 nm. The MNPs were observed to be spherical in shape. The CMC-MNPs nanofibers showed good hydrophilic properties and had excellent antibacterial activity against the Gram-negative bacteria Escherichia coli and the Gram-positive bacteria Staphylococcus aureus.

Keywords: electrospinning technique, metal nanoparticles, cellulosic nanofibers, wound dressing

Procedia PDF Downloads 299

Authors: Ekrem Canli, Thomas Glade

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The precise prediction of rainfall in space and time is a key element to most landslide early warning systems. Unfortunately, the spatial variability of rainfall in many early warning applications is often disregarded. A common simplification is to use uniformly distributed rainfall to characterize aerial rainfall intensity. With spatially differentiated rainfall information, real-time comparison with rainfall thresholds or the implementation in process-based approaches might form the basis for improved landslide warnings. This study suggests an automated workflow from the hourly, web-based collection of rain gauge data to the generation of spatially differentiated rainfall predictions based on kriging. Because the application of kriging is usually a labor intensive task, a simplified and consequently automated variogram modeling procedure was applied to up-to-date rainfall data. The entire workflow was carried out purely with open source technology. Validation results, albeit promising, pointed out the challenges that are involved in pure distance based, automated geostatistical interpolation techniques for ever-changing environmental phenomena over short temporal and spatial extent.

Keywords: kriging, landslide early warning system, spatial rainfall prediction, variogram modelling, web scraping

Procedia PDF Downloads 258

Authors: S. Henine, A. Youkana

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This work is devoted to study the global existence and asymptotic behavior of solutions for Gierer-Meinhardt systems arising in biological phenomena. We prove that the solutions are global and uniformly bounded by a positive constant independent of the time. Our technique is based on Lyapunov functional argument. Under suitable conditions, we established a result on the asymptotic behavior of solutions. These results are valid for any positive continuous initial data, and improve some recently results established.

Keywords: asymptotic behavior, Gierer-Meinhardt systems, global existence, Lyapunov functional

Procedia PDF Downloads 358

Authors: Obaid Algahtani

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An interval may be defined as a convex combination as follows: I=[a,b]={x_α=(1-α)a+αb: α∈[0,1]}. Consequently, we may adopt interval operations by applying the scalar operation point-wise to the corresponding interval points: I ∙J={x_α∙y_α ∶ αϵ[0,1],x_α ϵI ,y_α ϵJ}, With the usual restriction 0∉J if ∙ = ÷. These operations are associative: I+( J+K)=(I+J)+ K, I*( J*K)=( I*J )* K. These two properties, which are missing in the usual interval operations, will enable the extension of the usual linear system concepts to the interval setting in a seamless manner. The arithmetic introduced here avoids such vague terms as ”interval extension”, ”inclusion function”, determinants which we encounter in the engineering literature that deal with interval linear systems. On the other hand, these definitions were motivated by our attempt to arrive at a definition of interval random variables and investigate the corresponding statistical properties. We feel that they are the natural ones to handle interval systems. We will enable the extension of many results from usual state space models to interval state space models. The interval state space model we will consider here is one of the form X_((t+1) )=AX_t+ W_t, Y_t=HX_t+ V_t, t≥0, where A∈ 〖IR〗^(k×k), H ∈ 〖IR〗^(p×k) are interval matrices and 〖W 〗_t ∈ 〖IR〗^k,V_t ∈〖IR〗^p are zero – mean Gaussian white-noise interval processes. This feeling is reassured by the numerical results we obtained in a simulation examples.

Keywords: interval analysis, interval matrices, state space model, Kalman Filter

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Authors: Jun Liu

Abstract:

This paper introduces a new bipartite key agreement (2PKA) protocol which provides unconditionally security and lightweight. The unconditional security is stemmed from the known impossibility of distinguishing a particular solution from all possible solutions of an underdetermined system of equations. The indistinguishability prevents an adversary from inferring to the common secret-key even with the access to an unlimited amount of computing capability. This new 2PKA protocol is also lightweight because that the calculation of a common secret-key only makes use of simple modular arithmetic. This information-theoretic 2PKA scheme provides the desired features of Key Confirmation (KC), Session Key (SK) security, Know-Key (KK) security, protection of individual privacy, and uniformly distributed value of a common key under prime modulus.

Keywords: bipartite key agreement, information-theoretic cryptography, perfect security, lightweight

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Authors: Abdullah Özköse, Ahmet Tamkoç

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The present study was conducted to determine the yield and yield components of smooth bromegrass lines under the environmental conditions of the Konya region during the growing seasons between 2011 and 2013. The experiment was performed in the randomized complete block design (RCBD) with four replications. It was found that the selected lines had a statistically significant effect on all the investigated traits, except for the main stem length and the number of nodes in the main stem. According to the two-year average calculated for various parameters checked in the smooth bromegrass lines, the main stem length ranged from 71.6 cm to 79.1 cm, the main stem diameter from 2.12 mm from 2.70 mm, the number of nodes in the main stem from 3.2 to 3.7, the internode length from 11.6 cm to 18.9 cm, flag leaf length from 9.7 cm to 12.7 cm, flag leaf width from 3.58 cm to 6.04 mm, herbage yield from 221.3 kg da^–1 to 354.7 kg da^–1 and hay yield from 100.4 kg da^–1 to 190.1 kg da^–1. The study concluded that the smooth bromegrass lines differ in terms of yield and yield components. Therefore, it is very crucial to select suitable varieties of smooth bromegrass to obtain optimum yield.

Keywords: semiarid region, smooth bromegrass, yield, yield components

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Authors: B. Sellami, Y. Laskri, M. Belloufi

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Conjugate gradient methods are an important class of methods for unconstrained optimization, especially for large-scale problems. Recently, they have been much studied. In this paper, a new family of conjugate gradient method is proposed for unconstrained optimization. This method includes the already existing two practical nonlinear conjugate gradient methods, which produces a descent search direction at every iteration and converges globally provided that the line search satisfies the Wolfe conditions. The numerical experiments are done to test the efficiency of the new method, which implies the new method is promising. In addition the methods related to this family are uniformly discussed.

Keywords: conjugate gradient method, global convergence, line search, unconstrained optimization

Procedia PDF Downloads 380

Authors: S. Jamshidi, E. Feizi Ashtiani, M. Ardestani, A. Feizi Ashtiani

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Waste load allocation (WLA) strategies usually intend to find economical policies for water resource management. Water quality trading (WQT) is an approach that uses discharge permit market to reduce total environmental protection costs. This primarily requires assigning discharge limits known as total maximum daily loads (TMDLs). These are determined by monitoring organizations with respect to the receiving water quality and remediation capabilities. The purpose of this study is to compare two approaches of TMDL assignment for WQT policy in small catchment area of Haraz River, in north of Iran. At first, TMDLs are assigned uniformly for the whole point sources to keep the concentrations of BOD and dissolved oxygen (DO) at the standard level at checkpoint (terminus point). This was simply simulated and controlled by Qual2kw software. In the second scenario, TMDLs are assigned using multi objective particle swarm optimization (MOPSO) method in which the environmental violation at river basin and total treatment costs are minimized simultaneously. In both scenarios, the equity index and the WLA based on trading discharge permits (TDP) are calculated. The comparative results showed that using economically optimized TMDLs (2nd scenario) has slightly more cost savings rather than uniform TMDL approach (1st scenario). The former annually costs about 1 M$ while the latter is 1.15 M$. WQT can decrease these annual costs to 0.9 and 1.1 M$, respectively. In other word, these approaches may save 35 and 45% economically in comparison with command and control policy. It means that using multi objective decision support systems (DSS) may find more economical WLA, however its outcome is not necessarily significant in comparison with uniform TMDLs. This may be due to the similar impact factors of dischargers in small catchments. Conversely, using uniform TMDLs for WQT brings more equity that makes stakeholders not feel that much envious of difference between TMDL and WQT allocation. In addition, for this case, determination of TMDLs uniformly would be much easier for monitoring. Consequently, uniform TMDL for TDP market is recommended as a sustainable approach. However, economical TMDLs can be used for larger watersheds.

Keywords: waste load allocation (WLA), water quality trading (WQT), total maximum daily loads (TMDLs), Haraz River, multi objective particle swarm optimization (MOPSO), equity

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Authors: Bastien Batardière, Joon Kwon

Abstract:

For finite-sum optimization, variance-reduced gradient methods (VR) compute at each iteration the gradient of a single function (or of a mini-batch), and yet achieve faster convergence than SGD thanks to a carefully crafted lower-variance stochastic gradient estimator that reuses past gradients. Another important line of research of the past decade in continuous optimization is the adaptive algorithms such as AdaGrad, that dynamically adjust the (possibly coordinate-wise) learning rate to past gradients and thereby adapt to the geometry of the objective function. Variants such as RMSprop and Adam demonstrate outstanding practical performance that have contributed to the success of deep learning. In this work, we present AdaLVR, which combines the AdaGrad algorithm with loopless variance-reduced gradient estimators such as SAGA or L-SVRG that benefits from a straightforward construction and a streamlined analysis. We assess that AdaLVR inherits both good convergence properties from VR methods and the adaptive nature of AdaGrad: in the case of L-smooth convex functions we establish a gradient complexity of O(n + (L + √ nL)/ε) without prior knowledge of L. Numerical experiments demonstrate the superiority of AdaLVR over state-of-the-art methods. Moreover, we empirically show that the RMSprop and Adam algorithm combined with variance-reduced gradients estimators achieve even faster convergence.

Keywords: convex optimization, variance reduction, adaptive algorithms, loopless

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Authors: Kejal Khatri, Vishnu Narayan Mishra

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We compute the degree of approximation of functions\tilde{f}\in H_w, a new Banach space using (T.E^1) summability means of conjugate Fourier series. In this paper, we extend the results of Singh and Mahajan which in turn generalizes the result of Lal and Yadav. Some corollaries have also been deduced from our main theorem and particular cases.

Keywords: conjugate Fourier series, degree of approximation, Hölder metric, matrix summability, product summability

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Authors: Jeong Min Baik

Abstract:

We present that the electroluminescence (EL) properties and electrical output power of flexible N-face p-type GaN thin films can be tuned by strain-induced piezo-potential generated across the metal-semiconductor-metal structures. Under different staining conditions (convex and concave bending modes), the transport properties of the GaN films can be changed due to the spontaneous polarization of the films. The I-V characteristics with the bending modes show that the convex bending can increase the current across the films by the decrease in the barrier height at the metal-semiconductor contact, increasing the EL intensity of the P-N junction. At convex bending, it is also shown that the flexible p-type GaN films can generate an output voltage of up to 1.0 V, while at concave bending, 0.4 V. The change of the band bending with the crystal polarity of GaN films was investigated using high-resolution photoemission spectroscopy. This study has great significance on the practical applications of GaN in optoelectronic devices and nanogenerators under a working environment.

Keywords: GaN, flexible, laser lift-off, nanogenerator

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Authors: Yuhan Lin, Rohan Kekatpure, Cassidy Yeung

Abstract:

In Digital Marketing, robust quantification of View-through attribution (VTA) is necessary for evaluating channel effectiveness. VTA occurs when a product purchase is aided by an Ad but without an explicit click (e.g. a TV ad). A lack of a tracking mechanism makes VTA estimation challenging. Most prevalent VTA estimation techniques rely on post-purchase in-product user surveys. User surveys enable the calculation of channel multipliers, which are the ratio of the view-attributed to the click-attributed purchases of each marketing channel. Channel multipliers thus provide a way to estimate the unknown VTA for a channel from its known click attribution. In this work, we use Convex Optimization to compute channel multipliers in a way that enables a mathematical encoding of the expected channel behavior. Large fluctuations in channel attributions often result from overfitting the calculations to user surveys. Casting channel attribution as a Convex Optimization problem allows an introduction of constraints that limit such fluctuations. The result of our study is a distribution of channel multipliers across the entire marketing funnel, with important implications for marketing spend optimization. Our technique can be broadly applied to estimate Ad effectiveness in a privacy-centric world that increasingly limits user tracking.

Keywords: digital marketing, survey analysis, operational research, convex optimization, channel attribution

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