Necessary and sufficient conditions of solution uniqueness in ℓ1\ell_1 minimization

This paper shows that the solutions to various convex $\ell_1$ minimization problems are \emph{unique} if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other $\ell_1$ models that either minimize $f(Ax-b)$ or impose the constraint $f(Ax-b)\leq\sigma$, where $f$ is a strictly convex function. For these models, this paper proves that, given a solution $x^*$ and defining I=\supp(x^*) and s=\sign(x^*_I), $x^*$ is the unique solution if and only if $A_I$ has full column rank and there exists $y$ such that $A_I^Ty=s$ and $|a_i^Ty|_\infty<1$ for $i\not\in I$. This condition is previously known to be sufficient for the basis pursuit model to have a unique solution supported on $I$. Indeed, it is also necessary, and applies to a variety of other $\ell_1$ models. The paper also discusses ways to recognize unique solutions and verify the uniqueness conditions numerically.Comment: 6 pages; revised version; submitte

Discontinuous Galerkin finite element scheme for a conserved higher-order traffic flow model by exploring Riemann solvers

postprin

Computer games: A double-edged sword?

Excessive computer game playing (ECGP) has already become a serious social problem. However, limited data from experimental lab studies are available about the negative consequences of ECGP on players' cognitive characteristics. In the present study, we compared three groups of participants (current ECGP participants, previous ECGP participants, and control participants) on a Multiple Object Tracking (MOT) task. The previous ECGP participants performed significantly better than the control participants, which suggested a facilitation effect of computer games on visuospatial abilities. Moreover, the current ECGP participants performed significantly worse than the previous ECGP participants. This more important finding indicates that ECGP may be related to cognitive deficits. Implications of this study are discussed. © 2008 Mary Ann Liebert, Inc.published_or_final_versio

Variable DNA methylation of transposable elements: The case study of mouse Early Transposons

Phenotypic variation stems from both genetic and epigenetic differences between individuals. In order to elucidate how phenotypes are determined, it is necessary to understand the forces that generate variation in genome sequence as well as its epigenetic state. In both contexts, transposable elements (TEs) may play an important role. It is well established that TE activity is a major generator of genetic variation, but recent research also suggests that TEs contribute to epigenetic variation. Stochastic epigenetic silencing of some TE insertions in mice has been shown to cause phenotypic variability between individuals. However, the prevalence of this phenomenon has never been evaluated. Here, we use 18 insertions of a mouse Endogenous Retrovirus (ERV) family, the Early Transposons (ETns), to detect insertion-dependent determinants of DNA methylation levels and variability between both cells and individuals. We show that the structure and age of insertions influence methylation levels and variability, resulting in a subgroup of loci that displays unexpectedly high variability in methylation and suggesting stochastic events during methylation establishment. Despite variation in methylation according to the age and structure of each locus, homologous CpG sites show similar tendencies in methylation levels across loci, emphasizing the role of the insertion's sequence in methylation determination. Our results show that differences in methylation of ETns between individuals is not a sporadic phenomenon and support the hypothesis that ERVs contribute to phenotypic variability through their stochastic silencing

Solitary wave solution to Aw-Rascle viscous model of traffic flow

A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.postprin

High-yield cellulase production in solid-state fermentation by Trichoderma reesei SEMCC-3.217 using water hyacinth (Eichhornia crassipes)

In this study, the strain Trichoderma reesei SEMCC-3.217 was used for producing cellulase in solid-state fermentation with water hyacinth (Eichhornia crassipes). The results of fractional factorial design showed that, the addition amount of wheat bran, (NH4)2SO4, CaCl2 and Tween 80 had significant effect on the cellulase production. Then, these four factors were selected for further optimization by central composite design for the yield of cellulase. The statistical analysis of the results showed that, the optimum composition were: 5 g of substrate containing 3.9 g water hyacinth, 1% corn steep liquor, 1% soybean meal, 0.2% NH4NO3, 0.2% KH2PO4, 0.08% MgSO4·7H2O, 2.8% (NH4)2SO4, 1.5% urea, 13.9% wheat bran, 0.08% ZnSO4·7H2O, 0.08% FeCl2 0.05% CaCl2, 0.08% NaNO3, 0.08% KCl and 0.27% (v/v) Tween-80. Under these conditions, the cellulase production was 4-fold increased (13.4 FPIU/g dry solid) compared with the initial level (3.4 FPIU/g dry solid) after 7 days of fermentation in a 250 ml Erlenmeyer flask.Key words: Cellulase, solid-state fermentation, optimization, water hyacinth, Trichoderma reesei

Positive selection for elevated gene expression noise in yeast

It is well known that the expression noise is lessened by natural selection for genes that are important for cell growth or are sensitive to dosage. In theory, expression noise can also be elevated by natural selection when noisy gene expression is advantageous. Here we analyze yeast genome-wide gene expression noise data and show that plasma-membrane transporters show significantly elevated expression noise after controlling all confounding factors. We propose a model that explains why and under what conditions elevated expression noise may be beneficial and subject to positive selection. Our model predicts and the simulation confirms that, under certain conditions, expression noise also increases the evolvability of gene expression by promoting the fixation of favorable expression level-altering mutations. Indeed, yeast genes with higher noise show greater between-strain and between-species divergences in expression, even when all confounding factors are excluded. Together, our theoretical model and empirical results suggest that, for yeast genes such as plasma-membrane transporters, elevated expression noise is advantageous, is subject to positive selection, and is a facilitator of adaptive gene expression evolution

Distributed Formation Control for Multi-Vehicle Systems With Splitting and Merging Capability

This letter develops a novel strategy for splitting and merging of agents travelling in formation. The method converts the formation control problem into an optimization problem, which is solved among the agents in a distributed fashion. The proposed control strategy is one type of Distributed Model Predictive Control (DMPC) which allows the system to cope with disturbances and dynamic environments. A modified Alternating Direction Method of Multipliers (ADMM) is designed to solve the trajectory optimization problem and achieve formation scaling. Furthermore, a mechanism is designed to implement path homotopy in splitting and merging of the formation, which examines the H-signature of the generated trajectories. Simulation shows that, by using the proposed method, the formation is able to automatically resize and dynamically split to better avoid obstacles, even in the case of losing communication among agents. Upon splitting the newly formed groups proceed and merge again when it becomes possible