The problem of finding the multiple locations for new facilities with respect to the multiple existing facilities in a given environment is known as Multifacility Location Problem (MLP).Every location problem is normally bounded by some sort of area constraint. But the fact that much of the work carried out in the literature has almost neglected the area constraint which has motivated us to work on Multifacility Location Problem taking the area constraint into consideration. The mathematical model of the multifacility location problem with area constraint has been developed and the solution has been obtained using Kuhn-Tucker theory. This mathematical analysis and solution procedure is highly complex and time consuming. Hence, an attempt has been made to get the solution of a complex, constrained multifacility location problem using Scaled Conjugate Gradient Algorithm (SCGA) in Artificial Neural Networks (ANN). With the help of Numerical examples, it has been established that the solution obtained through ANN model compares well within the acceptable limits with those obtained through analytical method.

This chapter provides a qualitative and quantitative analysis which is primarily based on three characteristics of the rendering performance— the frame rate stability, transient response and adaptive tracking capability. One of the key qualitative metric considered in this research which is important in real-time 3D rendering is frame rate stability. A stable frame rate does not only bring about steady visual display that allows positive user experience, it also carries the benefit of optimised resource usage. This can lead to more effective utilisation of the computer’s processor cycles compared to a “best-effort” technique that does not guarantee a stable frame rate. The transient response of a 3D rendering application refers to the quality of its transition as the frame rate changes from one steady-state level to another typically due to changing performance objective. This quality is particularly important at low frame rate …

The determination of a protein's biochemical function from its 3D structure has proved more difficult than anticipated for structural genomics proteins, most of which are of unknown or uncertain function. Functional annotations typically have been assigned using the closest sequence or structure match, a practice that has resulted in large numbers of misannotated proteins. Recently it was reported that computed protonation properties can be used to predict the residues with catalytic and binding activity, thus providing clues about the function of the protein. We show that residues with anomalous computed protonation behavior constitute a small fraction of the protein's highly conserved residues. Results for a test set of 61 proteins reveal that the average conservation scores are high for residues with unusual protonation behavior, even for many not annotated as functionally important in the literature. Two enzymes, protein tyrosine phosphatase from Yersinia enterocolitica and glucosamine-6-phosphate deaminase from Escherichia coli, are described in detail as examples to illustrate the relationship between anomalous protonation behavior and conservation. We conclude that the residues with anomalous protonation behavior are generally highly conserved, but are fewer in number and more spatially localized than the set of all highly conserved residues in a given protein.

A new monotonicity-constrained maximum likelihood approach, called Partial Order Optimum Likelihood (POOL), is presented and applied to the problem of functional site prediction in protein 3D structures, an important current challenge in genomics. The input consists of electrostatic and geometric properties derived from the 3D structure of the query protein alone. Sequence-based conservation information, where available, may also be incorporated. Electrostatics features from THEMATICS are combined with multidimensional isotonic regression to form maximum likelihood estimates of probabilities that specific residues belong to an active site. This allows likelihood ranking of all ionizable residues in a given protein based on THEMATICS features. The corresponding ROC curves and statistical significance tests demonstrate that this method outperforms prior THEMATICS-based methods, which in turn have been shown previously to outperform other 3D-structure-based methods for identifying active site residues. Then it is shown that the addition of one simple geometric property, the size rank of the cleft in which a given residue is contained, yields improved performance. Extension of the method to include predictions of non-ionizable residues is achieved through the introduction of environment variables. This extension results in even better performance than THEMATICS alone and constitutes to date the best functional site predictor based on 3D structure only, achieving nearly the same level of performance as methods that use both 3D structure and sequence alignment data. Finally, the method also easily incorporates such sequence alignment data, and when this information is included, the resulting method is shown to outperform the best current methods using any combination of sequence alignments and 3D structures. Included is an analysis demonstrating that when THEMATICS features, cleft size rank, and alignment-based conservation scores are used individually or in combination THEMATICS features represent the single most important component of such classifiers.

Protein active site prediction is a very important problem in bioinformatics. THEMATICS is a simple and effective method based on the special electrostatic properties of ionizable residues to predict such sites from protein three-dimensional structure alone. The process involves distinguishing computed titration curves with perturbed shape from normal ones; the differences are subtle in many cases. In this dissertation, I develop and apply special machine learning techniques to automate the process and achieve higher sensitivity than results from other methods while maintaining high specificity. I first present application of support vector machines (SVM) to automate the active site prediction using THEMATICS; at the time this work was developed, it achieved better performance than any other 3D structure based methods. I then present the more recently developed Partial Order Optimal Likelihood (POOL) method, which estimates the probabilities of residues being active under certain natural monotonicity assumptions. The dissertation shows that applying the POOL method just on THEMATICS features outperforms the SVM results. Furthermore, since the overall approach is based on estimating certain probabilities from labeled training data, it provides a principled way to combine the use of THEMATICS features with other non-electrostatic features proposed by others. In particular, I consider the use of geometric features as well, and the resulting classifiers are the best structure-only predictors yet found. Finally, I show that adding in sequence-based conservation scores where applicable yields a method that outperforms all existing method while using only whatever combination of structure-based or sequence-based features is available.

Theoretical microscopic titration curves (THEMATICS) is a computational method for the identification of active sites in proteins through deviations in computed titration behavior of ionizable residues. While the sensitivity to catalytic sites is high, the previously reported sensitivity to catalytic residues was not as high, about 50%. Here THEMATICS is combined with support vector machines (SVM) to improve sensitivity for catalytic residue prediction from protein 3D structure alone. For a test set of 64 proteins taken from the Catalytic Site Atlas (CSA), the average recall rate for annotated catalytic residues is 61%; good precision is maintained selecting only 4% of all residues. The average false positive rate, using the CSA annotations is only 3.2%, far lower than other 3D-structure-based methods. THEMATICS-SVM returns higher precision, lower false positive rate, and better overall performance, compared with other 3D-structure-based methods. Comparison is also made with the latest machine learning methods that are based on both sequence alignments and 3D structures. For annotated sets of well-characterized enzymes, THEMATICS-SVM performance compares very favorably with methods that utilize sequence homology. However, since THEMATICS depends only on the 3D structure of the query protein, no decline in performance is expected when applied to novel folds, proteins with few sequence homologues, or even orphan sequences. An extension of the method to predict non-ionizable catalytic residues is also presented. THEMATICS-SVM predicts a local network of ionizable residues with strong interactions between protonation events; this appears to be a special feature of enzyme active sites.

Theoretical Microscopic Titration Curves (THEMATICS) may be used to identify chemically important residues in active sites of enzymes by characteristic deviations from the normal, sigmoidal Henderson–Hasselbalch titration behavior. Clusters of such deviant residues in physical proximity constitute reliable predictors of the location of the active site. Originally the residues with deviant predicted behavior were identified by human observation of the computed titration curves. However, it is preferable to select the unusual residues by mathematically well‐defined criteria, in order to reduce the chance of error, eliminate any possible biases, and substantially speed up the selection process. Here we present some simple statistical tests that constitute such selection criteria. The first derivatives of the predicted titration curves resemble distribution functions and are normalized. The moments of these first derivative functions are computed. It is shown that the third and fourth moments, measures of asymmetry and kurtosis, respectively, are good measures of the deviations from normal behavior. Results are presented for 44 different enzymes. Detailed results are given for 4 enzymes with 4 different types of chemistry: arginine kinase from Limulus polyphemus (horseshoe crab); β‐lactamase from Escherichia coli; glutamate racemase from Aquifex pyrophilus; and 3‐isopropylmalate dehydrogenase from Thiobacillus ferrooxidans. The relationship between the statistical measures of nonsigmoidal behavior in the predicted titration curves and the catalytic activity of the residue is discussed. Proteins 2005. © 2005 Wiley‐Liss, Inc.

Parti-game (Moore 1994a; Moore 1994b; Moore and Atkeson 1995) is a reinforcement learning (RL) algorithm that has a lot of promise in overcoming the curse of dimensionality that can plague RL algorithms when applied to high-dimensional problems. In this paper we introduce modifications to the algorithm that further improve its performance and robustness. In addition, while parti-game solutions can be improved locally by standard local path-improvement techniques, we introduce an add-on algorithm in the same spirit as parti-game that instead tries to improve solutions in a non-local manner.

Parti-game (Moore 1994a; Moore 1994b; Moore and Atkeson 1995) is a reinforcement learning (RL) algorithm that has a lot of promise in overcoming the curse of dimensionality (Bellman 1957) that can plague RL algorithms when applied to high-dimensional problems. In this paper we introduce modiications to the algorithm that further improve its performance and robustness. In addition, while parti-game solutions can be improved locally by standard local path-improvement techniques, we introduce an add-on algorithm in the same spirit as parti-game that instead tries to improve solutions in a non-local manner.

Table 2. Results of the best runs for the Geneeproblem. CENNBPROP yields both the lowest training and the lowest testing error. Training set Testing set Algorithm SSE Class. rate SSE Class. achieved the lowest SSE although RPROP normally outperforms BPROP. F or the Thyroiddproblem CENNBPROP proved to be comparable with standard RPROP. CENNRPROP always yields the best results SSE=0.0 and beats the standard RPROP which still left some residual errors. In the beginning of training, CENNBPROP has worked best for both benchmark problems. This can be explained by the fact that RPROP needs some time to adapt its step widths. The CENNoptimization improves BPROP training with respect to convergence speed and the nal quality of the trained networks. Especially, t h i s is exploited in the case of the Thyroiddproblem. Since CENNBPROP updates the weights after each pattern presentation online training, it should be well suited for applications with feedback, e.g. neural controllers. In summary, CENNoptimization has proven to outperform all the investigated BP algorithms and we guess that it is the fastest training algorithm at the time being. Of course, this claim needs to be veriied by using much more benchmarks and comparisons to other training algorithms. A direct adaptive method for faster backpropagation learning: The rprop algorithm. Table 1. Results of the best runs for the Thyroiddproblem. CENNRPROP yields both the lowest training error and the lowest testing error. training set testing set Algorithmus SSE Class. rate SSE Class. rate BPROP 246.0 For each problem 10 networks were created which are then used for the four different training algorithms. Before training, the networks were initialized by random numbers drawn from a normal distribution with zero mean and a standard deviation of 0.01. Thus, all algorithms had equal initial conditions. BPROP and CENNBPROP used a learning rate of 0.01 and a momentum of 0.9. RPROP and CENNRPROP used an initial step width of 0.001, uppdown factors of 0.551.2 and a minimallmaximal step width of 10 ,6 50.0, repectively. The results are displayed in gure 1 for the Thyroiddproblem and in gure 2 for the Geneeproblem. All the 10 runs were plotted simultaneously. Note that the standard and the CENNoptimized versions can only be compared if the SSE is plotted over the numberofepochs. In table 1 and in table 2, the results of the best runs are summarized. The generalization performance is estimated by the error with respect to …

This paper presents a novel incremental algorithm that combines Q-learning, a well-known dynamic-programming based reinforcement learning method, with the TD(λ) return estimation process, which is typically used in actor-critic learning, another well-known dynamic-programming based reinforcement learning method. The parameter λ is used to distribute credit throughout sequences of actions, leading to faster learning and also helping to alleviate the non-Markovian effect of coarse state-space quantization. The resulting algorithm, Q(λ)-learning, thus combines some of the best features of the Q-learning and actor-critic learning paradigms. The behavior of this algorithm has been demonstrated through computer simulations.

Connectionist networks having feedback connections are interesting for a number of reasons. Biological neural networks are highly recurrently connected, and many authors have studied recurrent network models of various types of perceptual and memory processes. The general property making such networks interesting and potentially useful is that they manifest highly nonlinear dynamical behavior. One such type of dY':lamical behavior that has received much attention is that of settling to a fixed stable state, but probably of greater importance both biologically and from an engineering viewpoint are time-varying behaviors. Here we consider algorithms for training recurrent networks to perform temporal supervised learning tasks, in which the specification of desired behavior is in the form of specific examples of input and desired output trajectories. One example of such a task is sequence classification, where the input is the sequence to be classified and the desired output is the correct classification, which is to be produced at the end of the sequence, as in some of the work reported by Mozer (1989; Chapter 5, this volume). Another example is sequence production, as studied by Jordan (1986), in which the input is a constant pattern and the corresponding desired output is a time-varying sequence. More generally, both the input and desired output may be time-varying, as in the prediction problems investigated by Cleeremans, Servan-Screiber, and McClelland (1989; Chapter 9, this volume) and the control problems studied by Nguyen and Widrow (Chapter 6, this volume). While limited forms of time-varying behaviors can be handled by using feedforward networks and tapped delay lines (e.g., Waibel et aI., 1987),