Kernel Truncated Regression Representation for Robust Subspace Clustering

Subspace clustering aims to group data points into multiple clusters of which each corresponds to one subspace. Most existing subspace clustering approaches assume that input data lie on linear subspaces. In practice, however, this assumption usually does not hold. To achieve nonlinear subspace clustering, we propose a novel method, called kernel truncated regression representation. Our method consists of the following four steps: 1) projecting the input data into a hidden space, where each data point can be linearly represented by other data points; 2) calculating the linear representation coefficients of the data representations in the hidden space; 3) truncating the trivial coefficients to achieve robustness and block-diagonality; and 4) executing the graph cutting operation on the coefficient matrix by solving a graph Laplacian problem. Our method has the advantages of a closed-form solution and the capacity of clustering data points that lie on nonlinear subspaces. The first advantage makes our method efficient in handling large-scale datasets, and the second one enables the proposed method to conquer the nonlinear subspace clustering challenge. Extensive experiments on six benchmarks demonstrate the effectiveness and the efficiency of the proposed method in comparison with current state-of-the-art approaches.Comment: 14 page

Thermodynamics of pairing transition in hot nuclei

The pairing correlations in hot nuclei $^{162}$Dy are investigated in terms of the thermodynamical properties by covariant density functional theory. The heat capacities $C_V$ are evaluated in the canonical ensemble theory and the paring correlations are treated by a shell-model-like approach, in which the particle number is conserved exactly. A S-shaped heat capacity curve, which agrees qualitatively with the experimental data, has been obtained and analyzed in details. It is found that the one-pair-broken states play crucial roles in the appearance of the S shape of the heat capacity curve. Moreover, due to the effect of the particle-number conservation, the pairing gap varies smoothly with the temperature, which indicates a gradual transition from the superfluid to the normal state.Comment: 13 pages, 4 figure

Modeling of the inverse heat -conduction problem with application to laser chemical vapor deposition and bioheat transfer

This dissertation consists of two parts. Part one deals with three-dimensional laser induced chemical vapor deposition (3D-LCVD), whereas part two deals with a Pennes model of a 3D skin structure. LCVD is an important technique in manufacturing complex micro-structures with high aspect ratio. In part one, a numerical model was developed for simulating kinetically-limited growth of an axisymmetric cylindrical rod by pre-specifying the surface temperature distribution required for growing the rod and then by obtaining optimized laser power that gives rise to the pre-specified temperature distribution. The temperature distribution at the surface of the rod was assumed to be at the unsteady state, and a least squares method was implemented to obtain the optimized laser power by minimizing the deviation between the calculated temperature distribution and the pre-specified temperature distribution. Results from this model were compared with results from Chen\u27s[29] model, which assumed that the temperature distribution at the surface of the rod was at steady state. Also, two different mesh sizes were used in these models to measure the effects of mesh size on the final results. Investigations on instantaneous skin burn are useful for an accurate assessment of burn-evaluation and for establishing thermal protections for various purposes. The Pennes\u27 bioheat model is a widely used model for predicting the degree of skin burn. In part two, a domain decomposition method was developed for solving a 3D Pennes\u27 bioheat transfer equation in a triple-layered skin structure. The Pennes\u27 bioheat transfer equation was discretized by the Crank-Nicholson scheme. A least squares method was incorporated in the model so that one could calculate the required laser power for the skin structure to reach a pre-specified temperature at a pre-specified location after a pre-specified laser exposure time. Numerical results of this model were obtained and discussed

The Evolutionary and Functional Roles of Synonymous Codon Usage in Eukaryotes

Most amino acids are encoded by multiple synonymous codons. Although alternative usage of synonymous codons does not affect the amino acid sequences of proteins, researchers have been reporting evidence for functional synonymous codon usage at the species- and gene-specific levels for over four decades. It has been shown that variations in synonymous codon usage can affect phenotypes through diverse mechanisms such as shaping translation efficiency and mRNA stability. On the other hand, the common view that cellular and organismal phenotypes are primarily determined by proteins whose functions are primarily determined by amino acid sequences, often drives the assumption that synonymous mutations are evolutionarily neutral. Consequently, this assumption has been used extensively in evolutionary biology, population genetics, and structural biology. One explanation of the apparent contradiction between the empirical findings, which indicate that synonymous mutations can affect related phenotypes, and the theoretical models, which stipulate that synonymous mutations are neutral, is that neutral synonymous mutations represent the general rule while non-neutral synonymous mutations represent the rare exceptions. In my thesis, I examined this explanation by applying computational and experimental approaches, which indicated that: 1) Non-neutral synonymous mutations significantly affect a considerable proportion of protein-coding genes; 2) Gene-specific codon usage patterns, such as the preference for a specific combination of rare codons, are possibly associated with specific gene functions, such as enhancing tissue-specific gene expression; 3) Some protein-coding genes include codon clusters whose codon usage patterns cannot be explained by selection-independent processes, and thus such codon clusters seem to serve as domains affecting protein functions. Together, these data suggest that synonymous mutations should not be a priori considered neutral. Furthermore, my studies suggest that the biochemical functions of at least some proteins are not only shaped by the constituent amino acid residues but also by codon usage biases at the gene-specific and sub-genic levels. In conclusion, my thesis work suggests that many of the commonly used approaches for analyzing the selection on protein-coding DNA sequences, which rely on the assumption that synonymous mutations are generally neutral, may generate biased results. Furthermore, my studies indicate that selection on gene-specific codon usage bias has evolved to serve diverse biological functions, which are still mostly uncharacterized

An information-theoretic on-line update principle for perception-action coupling

Inspired by findings of sensorimotor coupling in humans and animals, there has recently been a growing interest in the interaction between action and perception in robotic systems [Bogh et al., 2016]. Here we consider perception and action as two serial information channels with limited information-processing capacity. We follow [Genewein et al., 2015] and formulate a constrained optimization problem that maximizes utility under limited information-processing capacity in the two channels. As a solution we obtain an optimal perceptual channel and an optimal action channel that are coupled such that perceptual information is optimized with respect to downstream processing in the action module. The main novelty of this study is that we propose an online optimization procedure to find bounded-optimal perception and action channels in parameterized serial perception-action systems. In particular, we implement the perceptual channel as a multi-layer neural network and the action channel as a multinomial distribution. We illustrate our method in a NAO robot simulator with a simplified cup lifting task.Comment: 8 pages, 2017 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS