Manifold splines
Constructing splines whose parametric domain is an arbitrary manifold and effectively computing such splines in real-world applications are of fundamental importance in solid and shape modeling, geometric design, graphics, etc. This paper presents a general theoretical and computational framework, in which spline surfaces defined over planar domains can be systematically extended to manifold domains with arbitrary topology with or without boundaries. We study the affine structure of domain manifolds in depth and prove that the existence of manifold splines is equivalent to the existence of a manifold's affine atlas. Based on our theoretical breakthrough, we also develop a set of practical algorithms to generalize triangular B-spline surfaces from planar domains to manifold domains. We choose triangular B-splines mainly because of its generality and many of its attractive properties. As a result, our new spline surface defined over any manifold is a piecewise polynomial surface with high parametric continuity without the need for any patching and/or trimming operations. Through our experiments, we hope to demonstrate that our novel manifold splines are both powerful and efficient in modeling arbitrarily complicated geometry and representing continuously-varying physical quantities defined over shapes of arbitrary topology.

title: Computing surface hyperbolic structure and real projective structure
abstract: Geometric structures are natural structures of surfaces, which enable different geometries to be defined on the surfaces. Algorithms designed for planar domains based on a specific geometry can be systematically generalized to surface domains via the corresponding geometric structure. For example, polar form splines with planar domains are based on affine invariants. Polar form splines can be generalized to manifold splines on the surfaces which admit affine structures and are equipped with affine geometries.Surfaces with negative Euler characteristic numbers admit hyperbolic structures and allow hyperbolic geometry. All surfaces admit real projective structures and are equipped with real projective geometry. Because of their general existence, both hyperbolic structures and real projective structures have the potential to replace the role of affine structures in defining manifold splines.This paper introduces theoretically rigorous and practically simple algorithms to compute hyperbolic structures and real projective structures for general surfaces. The method is based on a novel geometric tool - discrete variational Ricci flow. Any metric surface admits a special uniformization metric, which is conformal to its original metric and induces constant curvature. Ricci flow is an efficient method to calculate the uniformization metric, which determines the hyperbolic structure and real projective structure.The algorithms have been verified on real surfaces scanned from sculptures. The method is efficient and robust in practice. To the best of our knowledge, this is the first work of introducing algorithms based on Ricci flow to compute hyperbolic structure and real projective structure.More importantly, this work introduces the framework of general geometric structures, which enable different geometries to be defined on manifolds and lay down the theoretical foundation for many important applications in geometric modeling.

title: Multiple Genome Rearrangement by Reversals
abstract: In this paper, we discuss a multiple genome rearrangement problem: Given a collection of genomes represented by permutations, we generate the collection from some fixed genome, e.g., the identity permutation, in a minimum number of signed reversals. It is NP-hard, so efficient heuristics is important for finding its optimal solution. We at first discuss how to generate two and three genomes from a fixed genome by polynomial algorithms for some special cases. Then based on the polynomial algorithms, we obtain some approximation algorithms for generating two and three genomes in general, respectively. Finally, we apply these approximation algorithms to design a new approximation algorithm for generating more genomes. We also show by some experimental examples that the algorithms are efficient.

title: A programming framework for quality-aware ubiquitous multimedia applications
abstract: Ubiquitous computing promises a computing environment that seamlessly and pervasively delivers applications to the user, despite changes of resources, devices, and locations. However, few ubiquitous multimedia applications (UMAs) exist up-to-date. One of the main reasons lies in the fact that it is difficult and error-prone to build a UMA which is mobile and deployable in different ubiquitous environments, and still provides acceptable application-specific Quality-of-Service (QoS) guarantees. In this paper, we present the design and implementation of a novel programming framework, called 'QCompiler" to address the challenges. The framework includes (1) a high-level application specification for the application developer to easily write a UMA with specific quality, mobility, and ubiquity supports, (2) a meta-data compilation, which provides automated consistency checks, translations, and substitutions, to relieve the application developer from dealing with complex programming related to quality, mobility, and ubiquity, (3) a binding, which prepares a quality-aware specification to be executable, in a specific deployment environment, and (4)a run-time meta-data execution, utilizing the meta-data compilation's results, to manage and control a quality-aware multimedia application. As a case study, we apply the programming framework to build a mobile Video-on-Demand (VoD) application. The experimental results show tradeoffs between easiness and flexibility to develop and deploy UMA, and overheads during UMA instantiation and adaptation.

title: Adaptive offloading inference for delivering applications in pervasive computing environments
abstract: Pervasive computing allows a user to access an application on heterogeneous devices continuously and consistently. However it is challenging to deliver complex applications on resource-constrained mobile devices, such as cellular telephones and PDA. Different approaches, such as application-based or system-based adaptations, have been proposed to address the problem. However existing solutions often require degrading application fidelity. We believe that this problem can be overcome by dynamically partitioning the application and offloading part of the application execution to a powerful nearby surrogate. This will enable pervasive application delivery to be realized without significant fidelity degradation or expensive application rewriting. Because pervasive computing environments are highly dynamic, the runtime offloading system needs to adapt to both application execution patterns and resource fluctuations. Using the fuzzy control model, we have developed an offloading inference engine to adaptively solve two key decision-making problems during runtime offloading: (1) timely triggering of adaptive offloading, and (2) intelligent selection of an application partitioning policy. Extensive trace-driven evaluations show the effectiveness of the offloading inference engine.

title: Mathematical Modeling for Functional Divergence after Gene Duplication
abstract: In this paper, I present a statistical framework for modeling the functional divergence after gene duplication. A rate-component model to describe the rate covariation among homologous genes of a gene family is implemented when a phylogenetic tree is known. The Markov chain model is rigorous but may require a huge amount of computational time when the number of sequences is large. On the other hand, the Poisson-based model is mathematically analytical so that computation is very fast even for a large dataset. Moreover, under the posterior framework, we have developed a site-specific profile for predicting important amino acid residues responsible for these functional differences between member genes of a gene family. Our study may have great potential for functional genomics because it is cost-effective, and these predictions can be further tested by biological experimentation.

title: Computational methodologies for modelling, analysis and simulation of signalling networks
abstract: This article is a critical review of computational techniques used to model, analyse and simulate signalling networks. We propose a conceptual framework, and discuss the role of signalling networks in three major areas: signal transduction, cellular rhythms and cell-to-cell communication. In order to avoid an overly abstract and general discussion, we focus on three case studies in the areas of receptor signalling and kinase cascades, cell-cycle regulation and wound healing. We report on a variety of modelling techniques and associated tools, in addition to the traditional approach based on ordinary differential equations (ODEs), which provide a range of descriptive and analytical powers. As the field matures, we expect a wider uptake of these alternative approaches for several reasons, including the need to take into account low protein copy numbers and noise and the great complexity of cellular organisation. An advantage offered by many of these alternative techniques, which have their origins in computing science, is the ability to perform sophisticated model analysis which can better relate predicted behaviour and observations.