Affine Scaling Research Articles

Hybrid chaos optimization and affine scaling search algorithm for solving linear programming problems

In this study, we addressed Single Objective Linear Programming (SOLP). This article proposed a new combination of Chaos Optimization Algorithm (COA) with Affine Scaling Search (AFS) to be used as a Hybrid COA and AFS algorithm (Chaos AFS) for solving SOLP. The potential of COA as an emerging optimization algorithm to improve efficiency and effectiveness of AFS is investigated. Chaos AFS method is so-called numerical search algorithm that searches through the domain of decision variables of SOLP to obtain final feasible solution. An initial solution point, obtained from COA, will be used as starting solution point in AFS algorithm to improve the performance of AFS algorithm. The result shows that Hybrid COA and AFS for solving SOLP problems significantly improves the results of objective value compared to pure AFS and reduces the number of iteration steps compared to simplex and pure AFS.

The Colloidal State of Tannins Impacts the Nature of Their Interaction with Proteins: The Case of Salivary Proline-Rich Protein/Procyanidins Binding

While the definition of tannins has been historically associated with its propensity to bind proteins in a nonspecific way, it is now admitted that specific interaction also occurs. The case of the astringency perception is a good example to illustrate this phenomenon: astringency is commonly described as a tactile sensation induced by the precipitation of a complex composed of proline-rich proteins present in the human saliva and tannins present in beverages such as tea or red wines. In the present work, the interactions between a human saliva protein segment and three different procyanidins (B1, B3, and C2) were investigated at the atomic level by NMR and molecular dynamics. The data provided evidence for (i) an increase in affinity compared to shortest human saliva peptides, which is accounted for by protein "wraping around" the tannin, (ii) a specificity in the interaction below tannin critical micelle concentration (CMC) of ca. 10 mM, with an affinity scale such that C2 > B1 > B3, and (iii) a nonspecific binding above tannin CMC that conducts irremediably to the precipitation of the tannins/protein complex. Such physicochemical findings describe in accurate terms saliva protein-tannin interactions and provide support for a more subtle description by oenologists of wine astringency perception in the mouth.

Model updating based on an affine scaling interior optimization algorithm

Finite element model updating is usually considered as an optimization process. Affine scaling interior algorithms are powerful optimization algorithms that have been developed over the past few years. A new finite element model updating method based on an affine scaling interior algorithm and a minimization of modal residuals is proposed in this article, and a general finite element model updating program is developed based on the proposed method. The performance of the proposed method is studied through numerical simulation and experimental investigation using the developed program. The results of the numerical simulation verified the validity of the method. Subsequently, the natural frequencies obtained experimentally from a three-dimensional truss model were used to update a finite element model using the developed program. After updating, the natural frequencies of the truss and finite element model matched well.

An Automatic Algorithm for Object Recognition and Detection Based on Asift Keypoints

Object recognition is an important task in image processing and computer vision. This paper presents a perfect method for object recognition with full boundary detection by combining affine scale invariant feature transform (ASIFT) and a region merging algorithm. ASIFT is a fully affine invariant algorithm that means features are invariant to six affine parameters namely translation (2 parameters), zoom, rotation and two camera axis orientations. The features are very reliable and give us strong keypoints that can be used for matching between different images of an object. We trained an object in several images with different aspects for finding best keypoints of it. Then, a robust region merging algorithm is used to recognize and detect the object with full boundary in the other images based on ASIFT keypoints and a similarity measure for merging regions in the image. Experimental results show that the presented method is very efficient and powerful to recognize the object and detect it with high accuracy.

A trust region affine scaling method for bound constrained optimization

We study a new trust region affine scaling method for general bound constrained optimization problems. At each iteration, we compute two trial steps. We compute one along some direction obtained by solving an appropriate quadratic model in an ellipsoidal region. This region is defined by an affine scaling technique. It depends on both the distances of current iterate to boundaries and the trust region radius. For convergence and avoiding iterations trapped around nonstationary points, an auxiliary step is defined along some newly defined approximate projected gradient. By choosing the one which achieves more reduction of the quadratic model from the two above steps as the trial step to generate next iterate, we prove that the iterates generated by the new algorithm are not bounded away from stationary points. And also assuming that the second-order sufficient condition holds at some nondegenerate stationary point, we prove the Q-linear convergence of the objective function values. Preliminary numerical experience for problems with bound constraints from the CUTEr collection is also reported.

A Quantitative Approach of the Interaction between Metal Triflates and Organic Ligands Using Electrospray Mass Spectrometry

The interaction between two Lewis "superacid" catalysts Zn(OTf)(2) and In(OTf)(3) and series of amide and phosphate ligands is quantitatively characterized by electrospray ionization mass spectrometry (ESI-MS). A specific feature of the ESI-MS spectra of the mixture of metal triflates and Lewis bases is the formation of ionic adducts resulting from the displacement of one triflate anion by two neutral ligands. A ligand competition model is developed, which describes the relative intensities of the ionic adducts as a function of relative ligand concentrations. The relative affinities deduced from the ligand competition method are combined in an affinity scale for the metal triflate.

Infeasible constraint-reduced interior-point methods for linear optimization

Constraint-reduction schemes have been proposed for the solution by means of interior-point methods of linear programs with many more inequality constraints than variables in the standard dual form. Such schemes have been shown to be provably convergent and highly efficient in practice. A critical requirement of these schemes is the availability of an initial dual-feasible point. In this paper, building on a general framework (which encompasses several previously proposed approaches) for dual-feasible constraint-reduced interior-point optimization, for which we prove convergence to a single point of the sequence of dual iterates, we propose a framework for ‘infeasible’ constraint-reduced interior-point optimization. Central to this framework is an exact (ℓ1 or ) penalty function scheme endowed with a mechanism for iterative adjustment of the penalty parameter, which aims at yielding, after a finite number of iterations, a value that guarantees feasibility (for the original problem) of the minimizers. Finiteness of the sequence of penalty parameter adjustments is proved under mild assumptions for all algorithms that fit within the framework, including ‘infeasible’ extensions of a ‘dual’ algorithm proposed in the early 1990s (Dantzig and Ye, A build-up interior-point method for linear programming: Affine scaling form, Working paper, Department of Management Science, University of Iowa, 1991) and of two recently proposed ‘primal–dual’ algorithms (Tits, Absil, and Woessner, Constraint reduction for linear programs with many inequality constraints, SIAM J. Optim. 17 (2006), pp. 119–146; Winternitz, Nicholls, Tits, and O’Leary, A constraint-reduced variant of Mehrotra’s predictor–corrector algorithm, Comput. Optim. Appl. (published on-line as of January 2011), DOI: 10.1007/s10589-010-9389-4). The last one, a constraint-reduced variant of Mehrotra’s Predictor–Corrector algorithm, is then more specifically considered: further convergence results are proved, and numerical results are reported that demonstrate that the approach is of practical interest.

Developing and Validating AFFINITY: A New Scale to Measure Consumer Affinity toward Foreign Countries

ABSTRACT Consumers do not look at attitudinal objects (products, nations) in terms of black and white. Because conflicting attitudes exist, it is important to understand how these translate into consumer buying behavior. Our objective is to build a parsimonious affinity scale (AFFINITY) by collecting data from Thai consumers concerning their affinity and animosity toward the U.S. and Singapore. We find that affinity and animosity form different constructs and relate to different stages in the purchase decision process.

Polynomial Convergence of Second-Order Mehrotra-Type Predictor-Corrector Algorithms over Symmetric Cones

This paper presents an extension of the variant of Mehrotra’s predictor–corrector algorithm which was proposed by Salahi and Mahdavi-Amiri (Appl. Math. Comput. 183:646–658, 2006) for linear programming to symmetric cones. This algorithm incorporates a safeguard in Mehrotra’s original predictor–corrector algorithm, which keeps the iterates in the prescribed neighborhood and allows us to get a reasonably large step size. In our algorithm, the safeguard strategy is not necessarily used when the affine scaling step behaves poorly, which is different from the algorithm of Salahi and Mahdavi-Amiri. We slightly modify the maximum step size in the affine scaling step and extend the algorithm to symmetric cones using the machinery of Euclidean Jordan algebras. Based on the Nesterov–Todd direction, we show that the iteration-complexity bound of the proposed algorithm is \(\mathcal{O}(r\log\varepsilon^{-1})\), where r is the rank of the associated Euclidean Jordan algebras and e>0 is the required precision.

An affine scaling method for solving network flow problems

Interior Point Methods, for the solution of large scale Network Flow Problems are of great practical significance. Many works have been done in the implementation of IPM to Minimum Cost Network Flow Problems (MCNFP). Out of several computational methods, affine scaling algorithm is one of the notable Interior Point Method (IPM). The focus is on the implementation of affine scaling algorithm on large scale MCNFP. The affine scaling algorithm draws attention of many researchers because of several reasons out of which finding the initial interior solution is one of the important area. The present work suggests an alternative of finding initial interior feasible solution. The suggested method of finding initial interior solution is verified as better than the existing Big-M method.

An admissible dual internal point method for a linear semidefinite programming problem

We consider a linear semidefinite programming problem. To solve this problem, we propose a dual numerical method from the class of affine scaling methods. We use Ostrovskii's theorem to establish its local convergence. We also show results for test problems.

Extrapolation of Wideband Electromagnetic Response Using Sparse Representation

Wideband electromagnetic response can be extrapolated using combined low frequency and early time information, which can substantially reduce the computational load. Most existing extrapolation methods are based on orthogonal polynomials, but selecting optimal parameters of orthogonal polynomials is not straightforward. This work proposes to extrapolate wideband electromagnetic response using sparse representation. The electromagnetic response is expressed as linear combination of atoms from an overcomplete dictionary. Optimal linear combination of atoms is then sought through the affine scaling transformation and the support vector regression. By increasing the data length step by step, convergence of the sparse solution is used as a criterion to determine the sufficient data length. Performance analysis shows that our proposed extrapolation method retains lower computational complexity and renders more flexibility in reconstructing a signal. Numerical examples are presented to show the efficacy and advantages of the proposed extrapolation method.

Capillary electrophoresis–inductively coupled plasma-mass spectrometry hyphenation for the determination at the nanogram scale of metal affinities and binding constants of phosphorylated ligands

A screening strategy based on hyphenated capillary electrophoresis and inductively coupled plasma mass spectrometry (CE–ICP-MS) was developed to classify phosphorylated ligands according to their europium(III) binding affinity in a hydro-organic medium (sodium formate, pH 3.7, H2O/MeOH 90:10, v/v). Taking advantage of the high sensibility of ICP-MS for detecting phosphorus, this method enabled to assess the affinity of a variety of phosphorylated compounds, including phosphine oxides, thiophosphines, phosphonates, and phosphinates, in less than 1h and using less than 5ng of substance. By varying the total europium concentration, complexation constants could be determined according to a sequential multiple run strategy, which proved to be in excellent agreement with the values obtained by UV–Vis absorption spectrophotometric titrations.

Hopfield neural networks in large-scale linear optimization problems

Hopfield neural networks and affine scaling interior point methods are combined in a hybrid approach for solving linear optimization problems. The Hopfield networks perform the early stages of the optimization procedures, providing enhanced feasible starting points for both primal and dual affine scaling interior point methods, thus facilitating the steps towards optimality. The hybrid approach is applied to a set of real world linear programming problems. The results show the potential of the integrated approach, indicating that the combination of neural networks and affine scaling interior point methods can be a good alternative to obtain solutions for large-scale optimization problems.

How Lewis acidic is your cation? Putting phosphenium ions on the fluoride ion affinity scale

The fluoride ion affinities (FIAs) of 33 phosphenium ions with a range of substituents were calculated using ab inito and DFT methods. The use of these FIA data as a measure of the Lewis acidities of phosphenium ions is described and the FIAs of the species studied here are compared to FIA data for more commonly encountered Lewis acids. Phosphenium ions are often stronger Lewis acids than neutral species, but in many cases are less Lewis acidic than highly electrophilic cations such as [Me(3)C](+) or [Me(3)Si](+). The impact of mesomeric, inductive and steric substituent effects on FIAs are discussed and related to the underlying electronic structures of different cation types. A comparison between the FIAs of known "free" phosphenium ions with those that are currently unknown and other highly electrophilic cations suggests that some diaryl- and dialkylphosphenium ions may yet be accessible under the right conditions.

改訂版テレビ親近感尺度の信頼性と妥当性

The purpose of this study was to improve the Japanese version of the Television Affinity Scale (TAS), and to examine the relationship between affinity for television and viewing behavior. Data was based on a random sample of 552 people in Hachioji City (Tokyo, Japan); the response rate was 55.2%. The results revealed the following: (a) the TAS 6-item version had sufficient reliability and validity, (b) the TAS provided information which could not be explained directly by demographic factors, and (c) affinity for television was positively correlated with unplanned and non-concentrated television viewing. These results are consistent with the findings of Erikawa, Yamada, Kawabata, and Numazaki (2007). In addition, the TAS scores correlated positively with entertainment program viewing. This is consistent with the findings of Rubin (1984) that television affinity correlated with ritualized television viewing. The implications of these results for contemporary television viewing are discussed.

Can Quantum-Mechanical Calculations Yield Reasonable Estimates of Hydrogen-Bonding Acceptor Strength? The Case of Hydrogen-Bonded Complexes of Methanol

The thermodynamics and some vibrational properties of hydrogen-bonded complexes of methanol with 23 hydrogen-bond acceptors (HBAs) have been determined in CCl(4) by FTIR spectrometry. The experimental sample contains carbon, nitrogen, oxygen, sulfur, fluorine, and chlorine organic bases and covers an energetic range of 13 kJ mol(-1) in the basicity scale (-ΔG), 22 kJ mol(-1) in the affinity scale (-ΔH), and 400 cm(-1) in the spectroscopic scale (Δν((OH))) (from benzene to trimethylphosphane oxide and amines). The experimental results in CCl(4) are compared to those computed in the gas phase at various levels of theory. Ninety five percent of the variance of the red shift and 89% of the variance of the intensification of the OH stretching upon hydrogen bonding are explained by gas-phase B3LYP/6-31+G(d,p) calculations. However, this level does not satisfactorily explain the thermodynamic properties. Only 68% of the variance of the methanol affinity (-ΔH) is taken into account. MP2/aug-cc-pVTZ//B3LYP/6-31+G(d,p) affinity calculations raise the explanation to 77% for all HBAs and to 93% when three outliers (Me(2)SO, Me(3)PO, and tetrahydrothiophene) are excluded. Discrepancies are analyzed in terms of experimental errors, calculation approximations, and solvation.

A class of primal affine scaling algorithms

We obtain a class of primal affine scaling algorithms which generalize some known algorithms. This class, depending on a r-parameter, is constructed through a family of metrics generated by − r power, r ⩾ 1, of the diagonal iterate vector matrix. We prove the so-called weak convergence of the primal class for nondegenerate linearly constrained convex programming. We observe the computational performance of the class of primal affine scaling algorithms, accomplishing tests with linear programs from the NETLIB library and with some quadratic programming problems described in the Maros and Mészáros repository.

An Overview of Lewis Basicity and Affinity Scales

The impossibility of establishing a universal scale of Lewis basicity does not prevent the determination of the quantitative behavior of Lewis bases, thanks to scales constructed against particular Lewis acids: BF3, 4-FC6H4OH, I2, Li+, Na+, K+, Al+, Mn+, CpNi+, and CH3NH3+. These scales encompass important types of bonds formed in a Lewis acid–base adduct: the dative bond, the conventional and ionic hydrogen bonds, the halogen bond and cation–molecule bonds for metal cations of groups 1, 7, 10, 11, and 13. Moreover, although these scales are generally not interrelated, there exist family-dependent relationships that permit ranking, in a rather general order, of bases belonging to a given chemical family, for example, the family of oxygen bases. Therefore, the skepticism about the quantitative usefulness of the Lewis concept of acids and bases is no longer founded.

The perception of 3D shape from planar cut contours

A new computational analysis is described for estimating 3D shapes from orthographic images of surfaces that are textured with planar cut contours. For any given contour pattern, this model provides a family of possible interpretations that are all related by affine scaling and shearing transformations in depth, depending on the specific values of its free parameters that are used to compute the shape estimate. Two psychophysical experiments were performed in an effort to compare the model predictions with observers' judgments of 3D shape for developable and non-developable surfaces. The results reveal that observers' perceptions can be systematically distorted by affine scaling and shearing transformations in depth and that the magnitude and direction of these distortions vary systematically with the 3D orientations of the contour planes.