Thermodynamic vs kinetic control of particle assembly and pattern replication

This research aims to investigate how particles assemble together through thermodynamic and kinetic control. Particle assembly with thermodynamic control is achieved in part due to electrostatic attraction between particles. Electrostatic attraction between particles can be achieved by functionalizing polystyrene or SiO2 particles with different charges. Particles with different charges will come together in solution slowly and self-assemble to form ordered crystals with different patterns based on size and charge ratios of two oppositely charged particles. Kinetic control of particle assembly is achieved by pattern aided exponential amplification of nanoscale structures. Some of these nanoscale structures are difficult to build with other conventional synthetic methods. On the other hand, as for kinetically controlled particle replication, the patterns can be synthesized by one of two ways i) crystal products which are produced by thermodynamically controlled particle assembly or ii) single particle deposition. Specifically, kinetically controlled particle assembly focuses on constructing SiO2 particles. Exponential replication of SiO2 particles is achieved by growing a bridge layer , between templates of SiO2 particles and next generation SiO2 replicas. By dissolving the bridge layer, two times the amount of the SiO2 particles with the shape of the original templates can be formed. In the next generation, all the particles serve as template particles. Thus, after n cycles of replication, 2n amount of products can be formed. If successful, particle assembly can be thermodynamic controlled and particle exponential replication can be kinetical controlled, which will enable new ways to build particles with well-defined shapes from readily available building blocks

Well-rounded equivariant deformation retracts of Teichm\"uller spaces

In this paper, we construct spines, i.e., \Mod_g-equivariant deformation retracts, of the Teichm\"uller space \T_g of compact Riemann surfaces of genus $g$. Specifically, we define a \Mod_g-stable subspace $S$ of positive codimension and construct an intrinsic \Mod_g-equivariant deformation retraction from \T_g to $S$. As an essential part of the proof, we construct a canonical \Mod_g-deformation retraction of the Teichm\"uller space \T_g to its thick part \T_g(\varepsilon) when $\varepsilon$ is sufficiently small. These equivariant deformation retracts of \T_g give cocompact models of the universal space \underline{E}\Mod_g for proper actions of the mapping class group \Mod_g. These deformation retractions of \T_g are motivated by the well-rounded deformation retraction of the space of lattices in $\R^n$. We also include a summary of results and difficulties of an unpublished paper of Thurston on a potential spine of the Teichm\"uller space.Comment: A revised version. L'Enseignement Mathematique, 201

Estimating Maximally Probable Constrained Relations by Mathematical Programming

Estimating a constrained relation is a fundamental problem in machine learning. Special cases are classification (the problem of estimating a map from a set of to-be-classified elements to a set of labels), clustering (the problem of estimating an equivalence relation on a set) and ranking (the problem of estimating a linear order on a set). We contribute a family of probability measures on the set of all relations between two finite, non-empty sets, which offers a joint abstraction of multi-label classification, correlation clustering and ranking by linear ordering. Estimating (learning) a maximally probable measure, given (a training set of) related and unrelated pairs, is a convex optimization problem. Estimating (inferring) a maximally probable relation, given a measure, is a 01-linear program. It is solved in linear time for maps. It is NP-hard for equivalence relations and linear orders. Practical solutions for all three cases are shown in experiments with real data. Finally, estimating a maximally probable measure and relation jointly is posed as a mixed-integer nonlinear program. This formulation suggests a mathematical programming approach to semi-supervised learning.Comment: 16 page

Computational Strategies for Scalable Genomics Analysis.

The revolution in next-generation DNA sequencing technologies is leading to explosive data growth in genomics, posing a significant challenge to the computing infrastructure and software algorithms for genomics analysis. Various big data technologies have been explored to scale up/out current bioinformatics solutions to mine the big genomics data. In this review, we survey some of these exciting developments in the applications of parallel distributed computing and special hardware to genomics. We comment on the pros and cons of each strategy in the context of ease of development, robustness, scalability, and efficiency. Although this review is written for an audience from the genomics and bioinformatics fields, it may also be informative for the audience of computer science with interests in genomics applications