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

Deep Neural Networks are one of the machine learning techniques which are increasingly used in a variety of applications. However, the significantly high memory and computation demands of deep neural networks often limit their deployment on embedded systems. Many recent works have considered this problem by proposing different types of data quantization schemes. However, most of these techniques either require post-quantization retraining of deep neural networks or bear a significant loss in output accuracy. In this paper, we propose a novel quantization technique for parameters of pre-trained deep neural networks. Our technique significantly maintains the accuracy of the parameters and does not require retraining of the networks. Compared to the single-precision floating-point numbers-based implementation, our proposed 8bit quantization technique generates only ~ 1% and ~ 0.4%, loss in the top-1 and top-5 accuracies respectively for VGG16 network using ImageNet dataset.

L2L: a highly accurate log 2 lead quantization of pre-trained neural networks

Image steganography plays a vital role in securing secret data by embedding it in the cover images. Usually, these images are communicated in a compressed format. Existing techniques achieve this but have low embedding capacity. Enhancing this capacity causes a deterioration in the visual quality of the stego-image. Hence, our goal here is to enhance the embedding capacity while preserving the visual quality of the stego-image. We also intend to ensure that our scheme is resistant to steganalysis attacks. 
This paper proposes a Compressed Sensing Image Steganography (CSIS) scheme to achieve our goal while embedding binary data in images. The novelty of our scheme is the combination of three components in attaining the above-listed goals. First, we use compressed sensing to sparsify cover image block-wise, obtain its linear measurements, and then uniquely select permissible measurements. Further, before embedding the secret data, we encrypt it using the Data Encryption Standard (DES) algorithm, and finally, we embed two bits of encrypted data into each permissible measurement. Second, we propose a novel data extraction technique, which is lossless and completely recovers our secret data. Third, for the reconstruction of the stego-image, we use the least absolute shrinkage and selection operator (LASSO) for the resultant optimization problem. 
We perform experiments on several standard grayscale images and a color image, and evaluate embedding capacity, PSNR value, mean SSIM index, NCC coefficients, and entropy. We achieve 1.53 times more embedding capacity as compared to the most recent scheme. We obtain an average of 37.92 dB PSNR value, and average values close to 1 for both the mean SSIM index and the NCC coefficients, which are considered good. Moreover, the entropy of cover images and their corresponding stego-images are nearly the same.

https://ietresearch.onlinelibrary.wiley.com/doi/pdf/10.1049/ipr2.12161

CSIS: Compressed sensing-based enhanced-embedding capacity image steganography scheme

Social Clouds have been gaining importance because of their potential for efficient and stable resource sharing without any (monetary) cost implications . There is a need, however, to look at how a social structure or relationship evolves to build a Social Cloud (by identifying factors that affect the social structure) and how social structure impacts individual resource sharing behavior. This paper presents a pairwise resource (or pairwise service) sharing social network model to explore the interdependence between social structure and resource (service) availability for an individual user or player. The paper also investigates effects of social structure on individual resource availability. Further, the paper analyzes positive and negative externalities, and aims to characterize stable social clouds.

Externalities and stability in social cloud

Science and engineering problems frequently require solving a sequence of dual linear systems. Besides having to store only few Lanczos vectors, using the BiConjugate Gradient method (BiCG) to solve dual linear systems has advantages for specific applications. For example, using BiCG to solve the dual linear systems arising in interpolatory model reduction provides a backward error formulation in the model reduction framework. Using BiCG to evaluate bilinear forms -- for example, in quantum Monte Carlo (QMC) methods for electronic structure calculations -- leads to a quadratic error bound. Since our focus is on sequences of dual linear systems, we introduce recycling BiCG, a BiCG method that recycles two Krylov subspaces from one pair of dual linear systems to the next pair. The derivation of recycling BiCG also builds the foundation for developing recycling variants of other bi-Lanczos based methods, such as CGS, BiCGSTAB, QMR, and TFQMR. 
We develop an augmented bi-Lanczos algorithm and a modified two-term recurrence to include recycling in the iteration. The recycle spaces are approximate left and right invariant subspaces corresponding to the eigenvalues closest to the origin. These recycle spaces are found by solving a small generalized eigenvalue problem alongside the dual linear systems being solved in the sequence. 
We test our algorithm in two application areas. First, we solve a discretized partial differential equation (PDE) of convection-diffusion type. Such a problem provides well-known test cases that are easy to test and analyze further. Second, we use recycling BiCG in the Iterative Rational Krylov Algorithm (IRKA) for interpolatory model reduction. IRKA requires solving sequences of slowly changing dual linear systems. We show up to 70% savings in iterations, and also demonstrate that for a model reduction problem BiCG takes (about) 50% more time than recycling BiCG.

Recycling BiCG with an Application to Model Reduction

Krylov subspace recycling is a process for accelerating the convergence of sequences of linear systems. Based on this technique, the recycling BiCG algorithm has been developed recently. Here, we now generalize and extend this recycling theory to BiCGSTAB. Recycling BiCG focuses on efficiently solving sequences of dual linear systems, while the focus here is on efficiently solving sequences of single linear systems (assuming non-symmetric matrices for both recycling BiCG and recycling BiCGSTAB). 
As compared with other methods for solving sequences of single linear systems with non-symmetric matrices (e.g., recycling variants of GMRES), BiCG based recycling algorithms, like recycling BiCGSTAB, have the advantage that they involve a short-term recurrence, and hence, do not suffer from storage issues and are also cheaper with respect to the orthogonalizations. 
We modify the BiCGSTAB algorithm to use a recycle space, which is built from left and right approximate invariant subspaces. Using our algorithm for a parametric model order reduction example gives good results. We show about 40% savings in the number of matrix-vector products and about 35% savings in runtime.

Kapil Ahuja

Papers

L2L: a highly accurate log 2 lead quantization of pre-trained neural networks

CSIS: Compressed sensing-based enhanced-embedding capacity image steganography scheme

Externalities and stability in social cloud

Recycling BiCG with an Application to Model Reduction

Recycling BiCGSTAB with an Application to Parametric Model Order Reduction