**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3134

# Search results for: quadratic loss function.

##### 3134 Estimation of Bayesian Sample Size for Binomial Proportions Using Areas P-tolerance with Lowest Posterior Loss

**Authors:**
H. Bevrani,
N. Najafi

**Abstract:**

**Keywords:**
Bayesian inference,
Beta-binomial Distribution,
LPLcriteria,
quadratic loss function.

##### 3133 Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II

**Authors:**
Ahmet Tekcan,
Arzu Özkoç

**Abstract:**

Let D = 1 be a positive non-square integer and let δ = √D or 1+√D 2 be a real quadratic irrational with trace t =δ + δ and norm n = δδ. Let γ = P+δ Q be a quadratic irrational for positive integers P and Q. Given a quadratic irrational γ, there exist a quadratic ideal Iγ = [Q, δ + P] and an indeﬁnite quadratic form Fγ(x, y) = Q(x−γy)(x−γy) of discriminant Δ = t 2−4n. In the ﬁrst section, we give some preliminaries form binary quadratic forms, quadratic irrationals and quadratic ideals. In the second section, we obtain some results on γ, Iγ and Fγ for some speciﬁc values of Q and P.

**Keywords:**
Quadratic irrationals,
quadratic ideals,
indefinite quadratic forms,
extended modular group.

##### 3132 Performance Evaluation of Complex Valued Neural Networks Using Various Error Functions

**Authors:**
Anita S. Gangal,
P. K. Kalra,
D. S. Chauhan

**Abstract:**

**Keywords:**
Complex backpropagation algorithm,
complex errorfunctions,
complex valued neural network,
split activation function.

##### 3131 A Deterministic Dynamic Programming Approach for Optimization Problem with Quadratic Objective Function and Linear Constraints

**Authors:**
S. Kavitha,
Nirmala P. Ratchagar

**Abstract:**

This paper presents the novel deterministic dynamic programming approach for solving optimization problem with quadratic objective function with linear equality and inequality constraints. The proposed method employs backward recursion in which computations proceeds from last stage to first stage in a multi-stage decision problem. A generalized recursive equation which gives the exact solution of an optimization problem is derived in this paper. The method is purely analytical and avoids the usage of initial solution. The feasibility of the proposed method is demonstrated with a practical example. The numerical results show that the proposed method provides global optimum solution with negligible computation time.

**Keywords:**
Backward recursion,
Dynamic programming,
Multi-stage decision problem,
Quadratic objective function.

##### 3130 Transmission Loss Allocation via Loss Function Decomposition and Current Projection Concept

**Authors:**
M.R. Ebrahimi,
Z. Ghofrani,
M. Ehsan

**Abstract:**

**Keywords:**
Transmission loss,
loss allocation,
current projectionconcept,
loss function decomposition.

##### 3129 Preliminary Study on Fixture Layout Optimization Using Element Strain Energy

**Authors:**
Zeshan Ahmad,
Matteo Zoppi,
Rezia Molfino

**Abstract:**

**Keywords:**
Fixture layout,
optimization,
strain energy,
quadratic
programming.

##### 3128 Lagrange and Multilevel Wavelet-Galerkin with Polynomial Time Basis for Heat Equation

**Authors:**
Watcharakorn Thongchuay,
Puntip Toghaw,
Montri Maleewong

**Abstract:**

**Keywords:**
Galerkin finite element method,
Heat equation ,
Lagrange basis function,
Wavelet basis function.

##### 3127 Positive Definite Quadratic Forms, Elliptic Curves and Cubic Congruences

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Binary quadratic form,
elliptic curves,
cubic congruence.

##### 3126 Robust Quadratic Stabilization of Uncertain Impulsive Switched Systems

**Authors:**
Xiu Liu,
Shouming Zhong,
Xiuyong Ding

**Abstract:**

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law realizing the robust stabilization of the closed-loop system is constructed.

**Keywords:**
Impulsive systems,
switched systems,
quadratic stabilization,
robust stabilization.

##### 3125 Enhanced Particle Swarm Optimization Approach for Solving the Non-Convex Optimal Power Flow

**Authors:**
M. R. AlRashidi,
M. F. AlHajri,
M. E. El-Hawary

**Abstract:**

**Keywords:**
Particle Swarm Optimization,
Optimal Power Flow,
Economic Dispatch.

##### 3124 Performance Analysis of MATLAB Solvers in the Case of a Quadratic Programming Generation Scheduling Optimization Problem

**Authors:**
Dávid Csercsik,
Péter Kádár

**Abstract:**

**Keywords:**
Economic dispatch,
optimization,
quadratic
programming,
MATLAB.

##### 3123 Solving the Quadratic Assignment Problems by a Genetic Algorithm with a New Replacement Strategy

**Authors:**
Yongzhong Wu,
Ping Ji

**Abstract:**

**Keywords:**
Quadratic assignment problem,
Genetic algorithm,
Replacement strategy,
QAPLIB.

##### 3122 Loss Function Optimization for CNN-Based Fingerprint Anti-Spoofing

**Authors:**
Yehjune Heo

**Abstract:**

As biometric systems become widely deployed, the security of identification systems can be easily attacked by various spoof materials. This paper contributes to finding a reliable and practical anti-spoofing method using Convolutional Neural Networks (CNNs) based on the types of loss functions and optimizers. The types of CNNs used in this paper include AlexNet, VGGNet, and ResNet. By using various loss functions including Cross-Entropy, Center Loss, Cosine Proximity, and Hinge Loss, and various loss optimizers which include Adam, SGD, RMSProp, Adadelta, Adagrad, and Nadam, we obtained significant performance changes. We realize that choosing the correct loss function for each model is crucial since different loss functions lead to different errors on the same evaluation. By using a subset of the Livdet 2017 database, we validate our approach to compare the generalization power. It is important to note that we use a subset of LiveDet and the database is the same across all training and testing for each model. This way, we can compare the performance, in terms of generalization, for the unseen data across all different models. The best CNN (AlexNet) with the appropriate loss function and optimizers result in more than 3% of performance gain over the other CNN models with the default loss function and optimizer. In addition to the highest generalization performance, this paper also contains the models with high accuracy associated with parameters and mean average error rates to find the model that consumes the least memory and computation time for training and testing. Although AlexNet has less complexity over other CNN models, it is proven to be very efficient. For practical anti-spoofing systems, the deployed version should use a small amount of memory and should run very fast with high anti-spoofing performance. For our deployed version on smartphones, additional processing steps, such as quantization and pruning algorithms, have been applied in our final model.

**Keywords:**
Anti-spoofing,
CNN,
fingerprint recognition,
loss function,
optimizer.

##### 3121 Neighbors of Indefinite Binary Quadratic Forms

**Authors:**
Ahmet Tekcan

**Abstract:**

**Keywords:**
Quadratic form,
indefinite form,
cycle,
proper cycle,
right neighbor,
left neighbor.

##### 3120 Orthogonal Functions Approach to LQG Control

**Authors:**
B. M. Mohan,
Sanjeeb Kumar Kar

**Abstract:**

In this paper a unified approach via block-pulse functions (BPFs) or shifted Legendre polynomials (SLPs) is presented to solve the linear-quadratic-Gaussian (LQG) control problem. Also a recursive algorithm is proposed to solve the above problem via BPFs. By using the elegant operational properties of orthogonal functions (BPFs or SLPs) these computationally attractive algorithms are developed. To demonstrate the validity of the proposed approaches a numerical example is included.

**Keywords:**
Linear quadratic Gaussian control,
linear quadratic estimator,
linear quadratic regulator,
time-invariant systems,
orthogonal functions,
block-pulse functions,
shifted legendre polynomials.

##### 3119 A Dual Method for Solving General Convex Quadratic Programs

**Authors:**
Belkacem Brahmi,
Mohand Ouamer Bibi

**Abstract:**

In this paper, we present a new method for solving quadratic programming problems, not strictly convex. Constraints of the problem are linear equalities and inequalities, with bounded variables. The suggested method combines the active-set strategies and support methods. The algorithm of the method and numerical experiments are presented, while comparing our approach with the active set method on randomly generated problems.

**Keywords:**
Convex quadratic programming,
dual support methods,
active set methods.

##### 3118 Ranking - Convex Risk Minimization

**Authors:**
Wojciech Rejchel

**Abstract:**

The problem of ranking (rank regression) has become popular in the machine learning community. This theory relates to problems, in which one has to predict (guess) the order between objects on the basis of vectors describing their observed features. In many ranking algorithms a convex loss function is used instead of the 0-1 loss. It makes these procedures computationally efficient. Hence, convex risk minimizers and their statistical properties are investigated in this paper. Fast rates of convergence are obtained under conditions, that look similarly to the ones from the classification theory. Methods used in this paper come from the theory of U-processes as well as empirical processes.

**Keywords:**
Convex loss function,
empirical risk minimization,
empirical process,
U-process,
boosting,
euclidean family.

##### 3117 Fast Intra Prediction Algorithm for H.264/AVC Based on Quadratic and Gradient Model

**Authors:**
A. Elyousfi,
A. Tamtaoui,
E. Bouyakhf

**Abstract:**

**Keywords:**
Intra prediction,
H.264/AVC,
video coding,
encodercomplexity.

##### 3116 Quadratic Pulse Inversion Ultrasonic Imaging(QPI): A Two-Step Procedure for Optimization of Contrast Sensitivity and Specificity

**Authors:**
Mamoun F. Al-Mistarihi

**Abstract:**

**Keywords:**
Volterra Filter,
Pulse Inversion,
Ultrasonic Imaging,
Contrast Agent.

##### 3115 Beyond Taguchi’s Concept of the Quality Loss Function

**Authors:**
Atul Dev,
Pankaj Jha

**Abstract:**

Dr. Genichi Taguchi looked at quality in a broader term and gave an excellent definition of quality in terms of loss to society. However the scope of this definition is limited to the losses imparted by a poor quality product to the customer only and are considered during the useful life of the product and further in a certain situation this loss can even be zero. In this paper, it has been proposed that the scope of quality of a product shall be further enhanced by considering the losses imparted by a poor quality product to society at large, due to associated environmental and safety related factors, over the complete life cycle of the product. Moreover, though these losses can be further minimized with the use of techno-safety interventions, the net losses to society however can never be made zero. This paper proposes an entirely new approach towards defining product quality and is based on Taguchi’s definition of quality.

**Keywords:**
Existing concept,
goal post philosophy,
life cycle,
proposed concept,
quality loss function.

##### 3114 The Number of Rational Points on Elliptic Curves y2 = x3 + a3 on Finite Fields

**Authors:**
Musa Demirci,
Nazlı Yıldız İkikardeş,
Gökhan Soydan,
İsmail Naci Cangül

**Abstract:**

**Keywords:**
Elliptic curves over finite fields,
rational points,
quadratic residue.

##### 3113 The Number of Rational Points on Conics Cp,k : x2 − ky2 = 1 over Finite Fields Fp

**Authors:**
Ahmet Tekcan

**Abstract:**

Let p be a prime number, Fp be a finite field, and let k ∈ F*p. In this paper, we consider the number of rational points onconics Cp,k: x2 − ky2 = 1 over Fp. We proved that the order of Cp,k over Fp is p-1 if k is a quadratic residue mod p and is p + 1 if k is not a quadratic residue mod p. Later we derive some resultsconcerning the sums ΣC[x]p,k(Fp) and ΣC[y]p,k(Fp), the sum of x- and y-coordinates of all points (x, y) on Cp,k, respectively.

**Keywords:**
Elliptic curve,
conic,
rational points.

##### 3112 A Modification on Newton's Method for Solving Systems of Nonlinear Equations

**Authors:**
Jafar Biazar,
Behzad Ghanbari

**Abstract:**

In this paper, we are concerned with the further study for system of nonlinear equations. Since systems with inaccurate function values or problems with high computational cost arise frequently in science and engineering, recently such systems have attracted researcher-s interest. In this work we present a new method which is independent of function evolutions and has a quadratic convergence. This method can be viewed as a extension of some recent methods for solving mentioned systems of nonlinear equations. Numerical results of applying this method to some test problems show the efficiently and reliability of method.

**Keywords:**
System of nonlinear equations.

##### 3111 A Quadratic Approach for Generating Pythagorean Triples

**Authors:**
P. K. Rahul Krishna,
S. Sandeep Kumar,
Jayanthi Sunder Raj

**Abstract:**

The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

**Keywords:**
Arithmetic progression,
hypotenuse leg difference method,
natural numbers,
Pythagorean triplets,
quadratic equation.

##### 3110 Restarted Generalized Second-Order Krylov Subspace Methods for Solving Quadratic Eigenvalue Problems

**Authors:**
Liping Zhou,
Liang Bao,
Yiqin Lin,
Yimin Wei,
Qinghua Wu

**Abstract:**

**Keywords:**
Quadratic eigenvalue problem,
Generalized secondorder Krylov subspace,
Generalized second-order Arnoldi process,
Projection technique,
Refined technique,
Restarting.

##### 3109 Ride Control of Passenger Cars with Semi-active Suspension System Using a Linear Quadratic Regulator and Hybrid Optimization Algorithm

**Authors:**
Ali Fellah Jahromi,
Wen Fang Xie,
Rama B. Bhat

**Abstract:**

**Keywords:**
Full car model,
Linear Quadratic Regulator,
Sequential Quadratic Programming,
Genetic Algorithm

##### 3108 A Novel Multiresolution based Optimization Scheme for Robust Affine Parameter Estimation

**Authors:**
J.Dinesh Peter

**Abstract:**

**Keywords:**
Image Processing,
Affine parameter estimation,
Outliers,
Robust Statistics,
Robust M-estimators

##### 3107 Applications of Conic Optimization and Quadratic Programming in the Investigation of Index Arbitrage in the Thai Derivatives and Equity Markets

**Authors:**
Satjaporn Tungsong,
Gun Srijuntongsiri

**Abstract:**

**Keywords:**
Conic optimization,
Equity index arbitrage,
Executionlags,
Quadratic programming,
SET50 index futures,
ThaiDEX SET50ETF,
Transaction costs

##### 3106 A Parametric Study of an Inverse Electrostatics Problem (IESP) Using Simulated Annealing, Hooke & Jeeves and Sequential Quadratic Programming in Conjunction with Finite Element and Boundary Element Methods

**Authors:**
Ioannis N. Koukoulis,
Clio G. Vossou,
Christopher G. Provatidis

**Abstract:**

The aim of the current work is to present a comparison among three popular optimization methods in the inverse elastostatics problem (IESP) of flaw detection within a solid. In more details, the performance of a simulated annealing, a Hooke & Jeeves and a sequential quadratic programming algorithm was studied in the test case of one circular flaw in a plate solved by both the boundary element (BEM) and the finite element method (FEM). The proposed optimization methods use a cost function that utilizes the displacements of the static response. The methods were ranked according to the required number of iterations to converge and to their ability to locate the global optimum. Hence, a clear impression regarding the performance of the aforementioned algorithms in flaw identification problems was obtained. Furthermore, the coupling of BEM or FEM with these optimization methods was investigated in order to track differences in their performance.

**Keywords:**
Elastostatic,
inverse problem,
optimization.

##### 3105 Perturbation Based Search Method for Solving Unconstrained Binary Quadratic Programming Problem

**Authors:**
Muthu Solayappan,
Kien Ming Ng,
Kim Leng Poh

**Abstract:**

**Keywords:**
unconstrained binary quadratic programming,
perturbation,
interior point methods