Evolution of Protein Molecules

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A Break in the Clouds: Towards a Cloud Definition

Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical systems has reached a considerable level of maturity, as reflected by several survey papers and books. However, parametric model reduction has emerged only more recently as an important and vibrant research area, with several recent advances making a survey paper timely. Thus, this paper aims to provide a resource that draws together recent contributions in different communities to survey the state of the art in parametric model reduction methods. Parametric model reduction targets the broad class of problems for wh...

/pdf/a-survey-of-projection-based-model-reduction-methods-for-3yjqbxk305.pdf

A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

Deep learning approaches to anomaly detection have recently improved the state of the art in detection performance on complex datasets such as large collections of images or text. These results have sparked a renewed interest in the anomaly detection problem and led to the introduction of a great variety of new methods. With the emergence of numerous such methods, including approaches based on generative models, one-class classification, and reconstruction, there is a growing need to bring methods of this field into a systematic and unified perspective. In this review we aim to identify the common underlying principles as well as the assumptions that are often made implicitly by various methods. In particular, we draw connections between classic 'shallow' and novel deep approaches and show how this relation might cross-fertilize or extend both directions. We further provide an empirical assessment of major existing methods that is enriched by the use of recent explainability techniques, and present specific worked-through examples together with practical advice. Finally, we outline critical open challenges and identify specific paths for future research in anomaly detection.

A Unifying Review of Deep and Shallow Anomaly Detection

This paper presents an online learning with regularized kernel based one-class extreme learning machine (ELM) classifier and is referred as online RK-OC-ELM. The baseline kernel hyperplane model considers whole data in a single chunk with regularized ELM approach for offline learning in case of one-class classification (OCC). Further, the basic hyper plane model is adapted in an online fashion from stream of training samples in this paper. Two frameworks viz., boundary and reconstruction are presented to detect the target class in online RKOC-ELM. Boundary framework based one-class classifier consists of single node output architecture and classifier endeavors to approximate all data to any real number. However, one-class classifier based on reconstruction framework is an autoencoder architecture, where output nodes are identical to input nodes and classifier endeavor to reconstruct input layer at the output layer. Both these frameworks employ regularized kernel ELM based online learning and consistency based model selection has been employed to select learning algorithm parameters. The performance of online RK-OC-ELM has been evaluated on standard benchmark datasets as well as on artificial datasets and the results are compared with existing state-of-the art one-class classifiers. The results indicate that the online learning one-class classifier is slightly better or same as batch learning based approaches. As, base classifier used for the proposed classifiers are based on the ELM, hence, proposed classifiers would also inherit the benefit of the base classifier i.e. it will perform faster computation compared to traditional autoencoder based one-class classifier.

Online Learning with Regularized Kernel for One-class Classification

In the FPGA (Field Programmable Gate Arrays) design flow, one of the most time-consuming step is the routing of nets. Therefore, there is a need to accelerate it. In a recent paper by Hoo et. al., the authors have developed a Linear Programming based framework that parallelizes this routing process to achieve significant speedups (the algorithm is termed as ParaLaR). However, this approach has certain weaknesses. Namely, the constraints violation by the solution and a local minima that could be improved. We address these two issues here. 
In our paper, we use this framework and solve it using the Primal-Dual sub-gradient method that better exploits the problem properties. We also propose a better way to update the size of the step taken by this iterative algorithm. We perform experiments on a set of standard benchmarks, where we show that our algorithm outperforms the standard existing algorithms (VPR and ParaLaR). 
We achieve up to 22% improvement in the constraints violation and the standard metric of the minimum channel width when compared with ParaLaR (which is same as in VPR). We achieve about 20% savings in another standard metric of the total wire length (when compared with VPR), which is the same as for ParaLaR. Hence, our algorithm achieves minimum value for all the three parameters. Also, the critical path delay for our algorithm is almost same as compared to VPR and ParaLaR. We achieve relative speedups of 3 times when we run a parallel version of our algorithm using 4 threads.

Parallel FPGA Router using Sub-Gradient method and Steiner tree.

In recent years, various kinds of distributed resource sharing setups have been proposed by taking social relationships into consideration. These dissimilar resource sharing setups are tagged as Social Cloud. These setups have appeared in various distributed computing forms such as community cloud, grid, volunteer computing and network services. Such setups are discrete in nature, and hence, do not conceptualize the totality of the Social Cloud concept. In fact, it is dicult to conceptualize Social Cloud without a general framework. There are three main objectives of this work. First, to present a general framework of Social Cloud. Second, to report various Social Cloud setups with corresponding architectural prototypes and current trends. Third, to discuss research challenges.

Social Cloud: Concept, Current Trends and Future Scope

Recently a new algorithm for model reduction of second order linear dynamical systems with proportional damping, the Adaptive Iterative Rational Global Arnoldi (AIRGA) algorithm (Bonin et. al., 2016), has been proposed. The main computational cost of the AIRGA algorithm is solving a sequence of linear systems. Usually, direct methods (e.g., LU) are used for solving these systems. As model sizes grow, direct methods become prohibitively expensive. Iterative methods (e.g., Krylov) scale well with size, and hence, are a good choice with an appropriate preconditioner. 
Preconditioned iterative methods introduce errors in linear solves because they are not exact. They solve linear systems up to a certain tolerance. We prove that, under mild conditions, the AIRGA algorithm is backward stable with respect to the errors introduced by these inexact linear solves. Our first assumption is use of a Ritz-Galerkin based solver that satisfies few extra orthogonality conditions. Since Conjugate Gradient (CG) is the most popular method based upon the Ritz-Galerkin theory, we use it. We show how to modify CG to achieve these extra orthogonalities. 
Modifying CG with the suggested changes is non-trivial. Hence, we demonstrate that using Recycling CG (RCG) helps us achieve these orthogonalities with no code changes. The extra cost of orthogonalizations is often offset by savings because of recycling. Our second and third assumptions involve existence, invertibility and boundedness of two matrices, which are easy to satisfy. 
While satisfying the backward stability assumptions, by numerical experiments we show that as we iteratively solve the linear systems arising in the AIRGA algorithm more accurately, we obtain a more accurate reduced system. We also show that recycling Krylov subspaces helps satisfy the backward stability assumptions (extra-orthogonalities) at almost no extra cost.

Stability Analysis of Inexact Solves in Moment Matching based Model Reduction.

Clustering genotypes based upon their phenotypic characteristics is used to obtain diverse sets of parents that are useful in their breeding programs. The Hierarchical Clustering (HC) algorithm is the current standard in clustering of phenotypic data. This algorithm suffers from low accuracy and high computational complexity issues. To address the accuracy challenge, we propose the use of Spectral Clustering (SC) algorithm. To make the algorithm computationally cheap, we propose using sampling, specifically, Pivotal Sampling that is probability based. Since application of samplings to phenotypic data has not been explored much, for effective comparison, another sampling technique called Vector Quantization (VQ) is adapted for this data as well. VQ has recently given promising results for genome data. 
The novelty of our SC with Pivotal Sampling algorithm is in constructing the crucial similarity matrix for the clustering algorithm and defining probabilities for the sampling technique. Although our algorithm can be applied to any plant genotypes, we test it on the phenotypic data obtained from about 2400 Soybean genotypes. SC with Pivotal Sampling achieves substantially more accuracy (in terms of Silhouette Values) than all the other proposed competitive clustering with sampling algorithms (i.e. SC with VQ, HC with Pivotal Sampling, and HC with VQ). The complexities of our SC with Pivotal Sampling algorithm and these three variants are almost same because of the involved sampling. In addition to this, SC with Pivotal Sampling outperforms the standard HC algorithm in both accuracy and computational complexity. We experimentally show that we are up to 45% more accurate than HC in terms of clustering accuracy. The computational complexity of our algorithm is more than a magnitude lesser than HC.

Kapil Ahuja

Papers

Online Learning with Regularized Kernel for One-class Classification

Parallel FPGA Router using Sub-Gradient method and Steiner tree.

Social Cloud: Concept, Current Trends and Future Scope

Stability Analysis of Inexact Solves in Moment Matching based Model Reduction.

Probabilistically Sampled and Spectrally Clustered Plant Genotypes using Phenotypic Characteristics