OPTIMASS: A Package for the Minimization of Kinematic Mass Functions with Constraints

Reconstructed mass variables, such as $M_2$, $M_{2C}$, $M_T^\star$, and $M_{T2}^W$, play an essential role in searches for new physics at hadron colliders. The calculation of these variables generally involves constrained minimization in a large parameter space, which is numerically challenging. We provide a C++ code, OPTIMASS, which interfaces with the MINUIT library to perform this constrained minimization using the Augmented Lagrangian Method. The code can be applied to arbitrarily general event topologies and thus allows the user to significantly extend the existing set of kinematic variables. We describe this code and its physics motivation, and demonstrate its use in the analysis of the fully leptonic decay of pair-produced top quarks using the $M_2$ variables.Comment: 39 pages, 12 figures, (1) minor revision in section 3, (2) figure added in section 4.3, (3) reference added and (4) matched with published versio

Continuous-time Proportional-Integral Distributed Optimization for Networked Systems

In this paper we explore the relationship between dual decomposition and the consensus-based method for distributed optimization. The relationship is developed by examining the similarities between the two approaches and their relationship to gradient-based constrained optimization. By formulating each algorithm in continuous-time, it is seen that both approaches use a gradient method for optimization with one using a proportional control term and the other using an integral control term to drive the system to the constraint set. Therefore, a significant contribution of this paper is to combine these methods to develop a continuous-time proportional-integral distributed optimization method. Furthermore, we establish convergence using Lyapunov stability techniques and utilizing properties from the network structure of the multi-agent system.Comment: 23 Pages, submission to Journal of Control and Decision, under review. Takes comments from previous review process into account. Reasons for a continuous approach are given and minor technical details are remedied. Largest revision is reformatting for the Journal of Control and Decisio

Dynamical dimer method for the determination of transition states with ab initio molecular dynamics

A dynamical formulation of the dimer method for the determination of transition states is presented. The method is suited for ab-initio molecular dynamics using the fictitious Lagrangian formulation. The method has been applied to the con-rotatory ring opening of chloro-cyclo-butadiene, an example, where the application of the drag method is problematic.Comment: The final modified version will be published in JCP. After it is published, it will be found at http://jcp.aip.org

Decision-maker Trade-offs In Multiple Response Surface Optimization

The focus of this dissertation is on improving decision-maker trade-offs and the development of a new constrained methodology for multiple response surface optimization. There are three key components of the research: development of the necessary conditions and assumptions associated with constrained multiple response surface optimization methodologies; development of a new constrained multiple response surface methodology; and demonstration of the new method. The necessary conditions for and assumptions associated with constrained multiple response surface optimization methods were identified and found to be less restrictive than requirements previously described in the literature. The conditions and assumptions required for a constrained method to find the most preferred non-dominated solution are to generate non-dominated solutions and to generate solutions consistent with decision-maker preferences among the response objectives. Additionally, if a Lagrangian constrained method is used, the preservation of convexity is required in order to be able to generate all non-dominated solutions. The conditions required for constrained methods are significantly fewer than those required for combined methods. Most of the existing constrained methodologies do not incorporate any provision for a decision-maker to explicitly determine the relative importance of the multiple objectives. Research into the larger area of multi-criteria decision-making identified the interactive surrogate worth trade-off algorithm as a potential methodology that would provide that capability in multiple response surface optimization problems. The ISWT algorithm uses an ε-constraint formulation to guarantee a non-dominated solution, and then interacts with the decision-maker after each iteration to determine the preference of the decision-maker in trading-off the value of the primary response for an increase in value of a secondary response. The current research modified the ISWT algorithm to develop a new constrained multiple response surface methodology that explicitly accounts for decision-maker preferences. The new Modified ISWT (MISWT) method maintains the essence of the original method while taking advantage of the specific properties of multiple response surface problems to simplify the application of the method. The MISWT is an accessible computer-based implementation of the ISWT. Five test problems from the multiple response surface optimization literature were used to demonstrate the new methodology. It was shown that this methodology can handle a variety of types and numbers of responses and independent variables. Furthermore, it was demonstrated that the methodology can be successful using a priori information from the decision-maker about bounds or targets or can use the extreme values obtained from the region of operability. In all cases, the methodology explicitly considered decision-maker preferences and provided non-dominated solutions. The contribution of this method is the removal of implicit assumptions and includes the decision-maker in explicit trade-offs among multiple objectives or responses

KCRC-LCD: Discriminative Kernel Collaborative Representation with Locality Constrained Dictionary for Visual Categorization

We consider the image classification problem via kernel collaborative representation classification with locality constrained dictionary (KCRC-LCD). Specifically, we propose a kernel collaborative representation classification (KCRC) approach in which kernel method is used to improve the discrimination ability of collaborative representation classification (CRC). We then measure the similarities between the query and atoms in the global dictionary in order to construct a locality constrained dictionary (LCD) for KCRC. In addition, we discuss several similarity measure approaches in LCD and further present a simple yet effective unified similarity measure whose superiority is validated in experiments. There are several appealing aspects associated with LCD. First, LCD can be nicely incorporated under the framework of KCRC. The LCD similarity measure can be kernelized under KCRC, which theoretically links CRC and LCD under the kernel method. Second, KCRC-LCD becomes more scalable to both the training set size and the feature dimension. Example shows that KCRC is able to perfectly classify data with certain distribution, while conventional CRC fails completely. Comprehensive experiments on many public datasets also show that KCRC-LCD is a robust discriminative classifier with both excellent performance and good scalability, being comparable or outperforming many other state-of-the-art approaches

A Survey on Potential of the Support Vector Machines in Solving Classification and Regression Problems

Kernel methods and support vector machines have become the most popular learning from examples paradigms. Several areas of application research make use of SVM approaches as for instance hand written character recognition, text categorization, face detection, pharmaceutical data analysis and drug design. Also, adapted SVM’s have been proposed for time series forecasting and in computational neuroscience as a tool for detection of symmetry when eye movement is connected with attention and visual perception. The aim of the paper is to investigate the potential of SVM’s in solving classification and regression tasks as well as to analyze the computational complexity corresponding to different methodologies aiming to solve a series of afferent arising sub-problems.Support Vector Machines, Kernel-Based Methods, Supervised Learning, Regression, Classification