Singular Value Decomposition of Operators on Reproducing Kernel Hilbert Spaces

Reproducing kernel Hilbert spaces (RKHSs) play an important role in many statistics and machine learning applications ranging from support vector machines to Gaussian processes and kernel embeddings of distributions. Operators acting on such spaces are, for instance, required to embed conditional probability distributions in order to implement the kernel Bayes rule and build sequential data models. It was recently shown that transfer operators such as the Perron-Frobenius or Koopman operator can also be approximated in a similar fashion using covariance and cross-covariance operators and that eigenfunctions of these operators can be obtained by solving associated matrix eigenvalue problems. The goal of this paper is to provide a solid functional analytic foundation for the eigenvalue decomposition of RKHS operators and to extend the approach to the singular value decomposition. The results are illustrated with simple guiding examples

Autoencoder extreme learning machine for fingerprint-based positioning: A good weight initialization is decisive

Indoor positioning based on machine-learning (ML) models has attracted widespread interest in the last few years, given its high performance and usability. Supervised, semisupervised, and unsupervised models have thus been widely used in this field, not only to estimate the user position, but also to compress, clean, and denoise fingerprinting datasets. Some scholars have focused on developing, improving, and optimizing ML models to provide accurate solutions to the end user. This article introduces a novel method to initialize the input weights in autoencoder extreme learning machine (AE-ELM), namely factorized input data (FID), which is based on the normalized form of the orthogonal component of the input data. AE-ELM with FID weight initialization is used to efficiently reduce the radio map. Once the dimensionality of the dataset is reduced, we use k -nearest neighbors to perform the position estimation. This research work includes a comparative analysis with several traditional ways to initialize the input weights in AE-ELM, showing that FID provide a significantly better reconstruction error. Finally, we perform an assessment with 13 indoor positioning datasets collected from different buildings and in different countries. We show that the dimensionality of the datasets can be reduced more than 11 times on average, while the positioning error suffers only a small increment of 15% (on average) in comparison to the baseline

Diffusion maps tailored to arbitrary non-degenerate Ito processes

We present two generalizations of the popular diffusion maps algorithm. The first generalization replaces the drift term in diffusion maps, which is the gradient of the sampling density, with the gradient of an arbitrary density of interest which is known up to a normalization constant. The second generalization allows for a diffusion map type approximation of the forward and backward generators of general Ito diffusions with given drift and diffusion coefficients. We use the local kernels introduced by Berry and Sauer, but allow for arbitrary sampling densities. We provide numerical illustrations to demonstrate that this opens up many new applications for diffusion maps as a tool to organize point cloud data, including biased or corrupted samples, dimension reduction for dynamical systems, detection of almost invariant regions in flow fields, and importance sampling

Discovery of sultam-containing small-molecule disruptors of the huntingtin–calmodulin protein–protein interaction

The aberrant protein–protein interaction between calmodulin and mutant huntingtin protein in Huntington’s disease patients has been found to contribute to Huntington’s disease progression. A high-throughput screen for small molecules capable of disrupting this interaction revealed a sultam series as potent small-molecule disruptors. Diversification of the sultam scaffold afforded a set of 24 analogs or further evaluation. Several structure–activity trends within the analog set were found, most notably a negligible effect of absolute stereochemistry and a strong beneficial correlation with electron-withdrawing aromatic substituents. The most promising analogs were profiled for off-target effects at relevant kinases and, ultimately, one candidate molecule was evaluated for neuroprotection in a neuronal cell model of Huntington’s disease

Resonances in a chaotic attractor crisis of the Lorenz Flow

Local bifurcations of stationary points and limit cycles have successfully been characterized in terms of the critical exponents of these solutions. Lyapunov exponents and their associated covariant Lyapunov vectors have been proposed as tools for supporting the understanding of critical transitions in chaotic dynamical systems. However, it is in general not clear how the statistical properties of dynamical systems change across a boundary crisis during which a chaotic attractor collides with a saddle. This behavior is investigated here for a boundary crisis in the Lorenz flow, for which neither the Lyapunov exponents nor the covariant Lyapunov vectors provide a criterion for the crisis. Instead, the convergence of the time evolution of probability densities to the invariant measure, governed by the semigroup of transfer operators, is expected to slow down at the approach of the crisis. Such convergence is described by the eigenvalues of the generator of this semigroup, which can be divided into two families, referred to as the stable and unstable Ruelle--Pollicott resonances, respectively. The former describes the convergence of densities to the attractor (or escape from a repeller) and is estimated from many short time series sampling the state space. The latter is responsible for the decay of correlations, or mixing, and can be estimated from a long times series, invoking ergodicity. It is found numerically for the Lorenz flow that the stable resonances do approach the imaginary axis during the crisis, as is indicative of the loss of global stability of the attractor. On the other hand, the unstable resonances, and a fortiori the decay of correlations, do not flag the proximity of the crisis, thus questioning the usual design of early warning indicators of boundary crises of chaotic attractors and the applicability of response theory close to such crises

Epigenetic silencing of DSC3 is a common event in human breast cancer

INTRODUCTION: Desmocollin 3 (DSC3) is a member of the cadherin superfamily of calcium-dependent cell adhesion molecules and a principle component of desmosomes. Desmosomal proteins such as DSC3 are integral to the maintenance of tissue architecture and the loss of these components leads to a lack of adhesion and a gain of cellular mobility. DSC3 expression is down-regulated in breast cancer cell lines and primary breast tumors; however, the loss of DSC3 is not due to gene deletion or gross rearrangement of the gene. In this study, we examined the prevalence of epigenetic silencing of DSC3 gene expression in primary breast tumor specimens. METHODS: We used bisulfite genomic sequencing to analyze the methylation state of the DSC3 promoter region from 32 primary breast tumor specimens. We also used a quantitative real-time RT-PCR approach, and analyzed all breast tumor specimens for DSC3 expression. Finally, in addition to bisulfite sequencing and RT-PCR, we used an in vivo nuclease accessibility assay to determine the chromatin architecture of the CpG island region from DSC3-negative breast cancer cells lines. RESULTS: DSC3 expression was downregulated in 23 of 32 (72%) breast cancer specimens comprising: 22 invasive ductal carcinomas, 7 invasive lobular breast carcinomas, 2 invasive ductal carcinomas that metastasized to the lymph node, and a mucoid ductal carcinoma. Of the 23 specimens showing a loss of DSC3 expression, 13 (56%) were associated with cytosine hypermethylation of the promoter region. Furthermore, DSC3 expression is limited to cells of epithelial origin and its expression of mRNA and protein is lost in a high proportion of breast tumor cell lines (79%). Lastly, DNA hypermethylation of the DSC3 promoter is highly correlated with a closed chromatin structure. CONCLUSION: These results indicate that the loss of DSC3 expression is a common event in primary breast tumor specimens, and that DSC3 gene silencing in breast tumors is frequently linked to aberrant cytosine methylation and concomitant changes in chromatin structure

Custom Hardware Versus Cloud Computing in Big Data

The computational and data handling challenges in big data are immense yet a market is steadily growing traditionally supported by technologies such as Hadoop for management and processing of huge and unstructured datasets. With this ever increasing deluge of data we now need the algorithms, tools and computing infrastructure to handle the extremely computationally intense data analytics, looking for patterns and information pertinent to creating a market edge for a range of applications. Cloud computing has provided opportunities for scalable high-performance solutions without the initial outlay of developing and creating the core infrastructure. One vendor in particular, Amazon Web Services, has been leading this field. However, other solutions exist to take on the computational load of big data analytics. This chapter provides an overview of the extent of applications in which big data analytics is used. Then an overview is given of some of the high-performance computing options that are available, ranging from multiple Central Processing Unit (CPU) setups, Graphical Processing Units (GPUs), Field Programmable Gate Arrays (FPGAs) and cloud solutions. The chapter concludes by looking at some of the state of the art solutions for deep learning platforms in which custom hardware such as FPGAs and Application Specific Integrated Circuits (ASICs) are used within a cloud platform for key computational bottlenecks

Continuing education around the world

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On the numerical approximation of the Perron-Frobenius and Koopman operator

Information about the behavior of dynamical systems can often be obtained by analyzing the eigenvalues and corresponding eigenfunctions of linear operators associated with a dynamical system. Examples of such operators are the Perron-Frobenius and the Koopman operator. In this paper, we will review different methods that have been developed over the last decades to compute finite-dimensional approximations of these infinite-dimensional operators - e.g. Ulam's method and Extended Dynamic Mode Decomposition (EDMD) - and highlight the similarities and differences between these approaches. The results will be illustrated using simple stochastic differential equations and molecular dynamics examples