Modifications of the Limited Memory BFGS Algorithm for Large-scale Nonlinear Optimization

In this paper we present two new numerical methods for unconstrained large-scale optimization. These methods apply update formulae, which are derived by considering different techniques of approximating the objective function. Theoretical analysis is given to show the advantages of using these update formulae. It is observed that these update formulae can be employed within the framework of limited memory strategy with only a modest increase in the linear algebra cost. Comparative results with limited memory BFGS (L-BFGS) method are presented.</p

Technology Assisted Review of Legal Documents

A legal prediction-based approach will help judges and solicitors to take judicial decisions on current cases, which are going on in courts, and make predictions on new cases on the basis of existing references and judgments. This model also helps law students learn about legal references. This application was developed specifically for the “Supreme Court of Pakistan (SCP)” and the “Pakistan Bar Council (PBC)” to expedite their judgments and provide legal guidance to lawyers based on historical data and constitutions

Do malaria preventive interventions reach the poor? Socioeconomic inequities in expenditure on and use of mosquito control tools in Sudan.

OBJECTIVES: To determine levels of socioeconomic inequities in the prevention of malaria, and to examine the implications of the findings for improving the equitable control of malaria in the Sudan. METHODS: A cross-sectional survey using a pre-tested interviewer-administered questionnaire was administered to 720 randomly selected householders from six localities in Gezira and Khartoum States. A socioeconomic status (SES) index, which was developed using principal components analysis, was used to examine socioeconomic inequity in the prevention of malaria. FINDINGS: Socioeconomic status was positively related to expenditures and use of vector control tools. The poorest households spent the least amounts of money to prevent malaria and were the least likely to own mosquito nets. CONCLUSION: The inequity in the prevention of malaria in the study areas has to be redressed before malaria can be effectively controlled in Sudan. Malaria control managers should continually determine the extent to which malaria preventive tools reach the poorest socioeconomic groups, and fashion strategies that will ensure that equity is always maintained

Stability analysis of predator - prey population model with time delay and constant rate of harvesting

This paper studies the effect of time delay and harvesting on the dynamics of the predator - prey model with a time delay in the growth rate of the prey equation. The predator and prey are then harvested with constant rates. The constant rates may drive the model to one, two, or none positive equilibrium points. When there exist two positive equilibrium points, one of them is possibly stable. In the case of the constant rates are quite small and the equilibrium point is not stable, an asymptotically stable limit cycle occurs. The result showed that the time delay can induce instability of the stable equilibrium point, Hopf bifurcation and stability switches

Predicting minimum energy structure of a peptide via a modified potential smoothing kernel

A global optimization approach is proposed for finding the global minimum energy configuration of a peptide. First, the original nonsmooth total potential energy function of a peptide, composed using the AMBER model, is transformed to a smoother function (shifted-impulsive transformation) via a procedure performed for each pair potential that constitute the total potential energy function. Then, the Potential Smoothing and Search (PSS) procedure is used to provide the global minimum. Based on this procedure global optimum solution is generated for a synthesis peptide named Compstatin

Positive-definite memoryless symmetric rank one method for large-scale unconstrained optimization

Memoryless quasi-Newton method is exactly the quasi-Newton method for which the approximation to the inverse of Hessian, at each step, is updated from a positive multiple of identity matrix. Hence, its search direction can be computed without the storage of matrices, namely O(n2) storages. in this paper, a memoryless symmetric rank one (SR1) method for solving large-scale unconstrained optimization problems is presented. The basic idea is to incorporate the SR1 update within the framework of the memoryless quasi-method. However, it is well-known that the SR1 update may not preserve positive definiteness even when updated from the positive definite matrix. Therefore, we propose that the memoryless SR1 method is updated from the positive scaled of the identity, in which the scaling factor is derived in such a way to preserve the positive definiteness and improves the condition the scale memoryless SR1 update. Under some standard conditions it is shown that the method is globally and R-linearly convergent. Numerical results show that the memoryless SR1 method is very encouraging

Optimizing Frequency Queries for Data Mining Applications

Data mining algorithms use various Trie and bitmap-based representations to optimize the support (i.e., frequency) counting performance. In this paper, we compare the memory requirements and support counting performance of FP Tree, and Compressed Patricia Trie against several novel variants of vertical bit vectors. First, borrowing ideas from the VLDB domain, we compress vertical bit vectors using WAH encoding. Second, we evaluate the Gray code rank-based transaction reordering scheme, and show that in practice, simple lexicographic ordering, obtained by applying LSB Radix sort, outperforms this scheme. Led by these results, we propose HDO, a novel Hamming-distance-based greedy transaction reordering scheme, and aHDO, a linear-time approximation to HDO. We present results of experiments performed on 15 common datasets with varying degrees of sparseness, and show that HDO- reordered, WAH encoded bit vectors can take as little as 5% of the uncompressed space, while aHDO achieves similar compression on sparse datasets. Finally, with results from over a billion database and data mining style frequency query executions, we show that bitmap-based approaches result in up to hundreds of times faster support counting, and HDO-WAH encoded bitmaps offer the best space-time tradeoff