From quantum circuits to adiabatic algorithms

This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically, we look for a smooth time-dependent Hamiltonian whose unique ground state slowly changes from the initial state of the circuit to its final state. Since this construction requires in general an n-local Hamiltonian, we will study whether approximation is possible using previous results on ground state entanglement and perturbation theory. Finally we will point out how the adiabatic model can be relaxed in various ways to allow for 2-local partially adiabatic algorithms as well as 2-local holonomic quantum algorithms.Comment: Version accepted by and to appear in Phys. Rev.

Effective algebraic degeneracy

We prove that any nonconstant entire holomorphic curve from the complex line C into a projective algebraic hypersurface X = X^n in P^{n+1}(C) of arbitrary dimension n (at least 2) must be algebraically degenerate provided X is generic if its degree d = deg(X) satisfies the effective lower bound: d larger than or equal to n^{{(n+1)}^{n+5}}

Finite Generation of Canonical Ring by Analytic Method

In the 80th birthday conference for Professor LU Qikeng in June 2006 I gave a talk on the analytic approach to the finite generation of the canonical ring for a compact complex algebraic manifold of general type. This article is my contribution to the proceedings of that conference from my talk. In this article I give an overview of the analytic proof and focus on explaining how the analytic method handles the problem of infinite number of interminable blow-ups in the intuitive approach to prove the finite generation of the canonical ring. The proceedings of the LU Qikeng conference will appear as Issue No. 4 of Volume 51 of Science in China Series A: Mathematics (www.springer.com/math/applications/journal/11425)

On the cohomology of pseudoeffective line bundles

The goal of this survey is to present various results concerning the cohomology of pseudoeffective line bundles on compact K{\"a}hler manifolds, and related properties of their multiplier ideal sheaves. In case the curvature is strictly positive, the prototype is the well known Nadel vanishing theorem, which is itself a generalized analytic version of the fundamental Kawamata-Viehweg vanishing theorem of algebraic geometry. We are interested here in the case where the curvature is merely semipositive in the sense of currents, and the base manifold is not necessarily projective. In this situation, one can still obtain interesting information on cohomology, e.g. a Hard Lefschetz theorem with pseudoeffective coefficients, in the form of a surjectivity statement for the Lefschetz map. More recently, Junyan Cao, in his PhD thesis defended in Grenoble, obtained a general K{\"a}hler vanishing theorem that depends on the concept of numerical dimension of a given pseudoeffective line bundle. The proof of these results depends in a crucial way on a general approximation result for closed (1,1)-currents, based on the use of Bergman kernels, and the related intersection theory of currents. Another important ingredient is the recent proof by Guan and Zhou of the strong openness conjecture. As an application, we discuss a structure theorem for compact K{\"a}hler threefolds without nontrivial subvarieties, following a joint work with F.Campana and M.Verbitsky. We hope that these notes will serve as a useful guide to the more detailed and more technical papers in the literature; in some cases, we provide here substantially simplified proofs and unifying viewpoints.Comment: 39 pages. This survey is a written account of a lecture given at the Abel Symposium, Trondheim, July 201

Section Extension from Hyperbolic Geometry of Punctured Disk and Holomorphic Family of Flat Bundles

The construction of sections of bundles with prescribed jet values plays a fundamental role in problems of algebraic and complex geometry. When the jet values are prescribed on a positive dimensional subvariety, it is handled by theorems of Ohsawa-Takegoshi type which give extension of line bundle valued square-integrable top-degree holomorphic forms from the fiber at the origin of a family of complex manifolds over the open unit 1-disk when the curvature of the metric of line bundle is semipositive. We prove here an extension result when the curvature of the line bundle is only semipositive on each fiber with negativity on the total space assumed bounded from below and the connection of the metric locally bounded, if a square-integrable extension is known to be possible over a double point at the origin. It is a Hensel-lemma-type result analogous to Artin's application of the generalized implicit function theorem to the theory of obstruction in deformation theory. The motivation is the need in the abundance conjecture to construct pluricanonical sections from flatly twisted pluricanonical sections. We also give here a new approach to the original theorem of Ohsawa-Takegoshi by using the hyperbolic geometry of the punctured open unit 1-disk to reduce the original theorem of Ohsawa-Takegoshi to a simple application of the standard method of constructing holomorphic functions by solving the d-bar equation with cut-off functions and additional blowup weight functions

Proteasome inhibition alleviates prolonged moderate compression-induced muscle pathology

Background: The molecular mechanism initiating deep pressure ulcer remains to be elucidated. The present study tested the hypothesis that the ubiquitin proteasome system is involved in the signalling mechanism in pressure-induced deep tissue injury. Methods. Adult Sprague Dawley rats were subjected to an experimental compression model to induce deep tissue injury. The tibialis region of the right hind limb was subjected to 100 mmHg of static pressure for six hours on each of two consecutive days. The compression pressure was continuously monitored by a three-axial force transducer within the compression indentor. The left hind limb served as the intra-animal control. Muscle tissues underneath the compressed region were collected and used for analyses. Results: Our results demonstrated that the activity of 20S proteasome and the protein abundance of ubiquitin and MAFbx/atrogin-1 were elevated in conjunction with pathohistological changes in the compressed muscle, as compared to control muscle. The administration of the proteasome inhibitor MG132 was found to be effective in ameliorating the development of pathological histology in compressed muscle. Furthermore, 20S proteasome activity and protein content of ubiquitin and MAFbx/atrogin-1 showed no apparent increase in the MG132-treated muscle following compression. Conclusion: Our data suggest that the ubiquitin proteasome system may play a role in the pathogenesis of pressure-induced deep tissue injury. © 2011 Siu et al; licensee BioMed Central Ltd.Link_to_subscribed_fulltex

Interpersonal Competence and Service Leadership

According to the Hong Kong Institute of Service Leadership and Management, interpersonal competence is an important component of an effective service leader. The present paper introduces a lecture embedded in a service leadership subject that focuses on promoting students’ interpersonal competence. Several topics are covered in this lecture. First, concepts and theories about interpersonal competence are introduced. Second, the relevance of interpersonal competence to service leadership is outlined. Third, methods of developing interpersonal competence are presented, particularly different conflict management strategies and assertiveness skills. Finally, conclusions and reflections on students’ own interpersonal competence and its relevance to the service leadership in one’s professional field are discussed. Different activities have been designed and incorporated in the lecture to facilitate students’ active learning and self-reflection. Students are also encouraged to explore their own ways to promote the development of interpersonal competence

Prosocial Norms as a Positive Youth Development Construct: A Conceptual Review

Prosocial norms like reciprocity, social responsibility, altruism, and volunteerism are ethical standards and beliefs that youth development programs often want to promote. This paper reviews evolutionary, social-cognitive, and developmental theories of prosocial development and analyzes how young people learn and adopt prosocial norms. The paper showed that very few current theories explicitly address the issue of how prosocial norms, in form of feelings of moral obligations, may be challenged by a norm of self-interest and social circumstances when prosocial acts are needed. It is necessary to develop theories which put prosocial norms as a central construct, and a new social cognitive theory of norm activation has the potential to help us understand how prosocial norms may be applied. This paper also highlights how little we know about young people perceiving and receiving prosocial norms and how influential of school policies and peer influence on the prosocial development. Lastly, while training of interpersonal competence (e.g., empathy, moral reasoning, etc.) was commonly used in the youth development, their effectiveness was not systematically evaluated. It will also be interesting to examine how computer and information technology or video games may be used in e-learning of prosocial norms

Recognition for Positive Behavior as a Critical Youth Development Construct: Conceptual Bases and Implications on Youth Service Development

Recognition for positive behavior is an appropriate response of the social environment to elicit desirable external behavior among the youth. Such positive responses, rendered from various social systems, include tangible and intangible reinforcements. The following theories are used to explain the importance of recognizing positive behavior: operational conditioning, observational learning, self-determination, and humanistic perspective. In the current work, culturally and socially desirable behaviors are discussed in detail with reference to Chinese adolescents. Positive behavior recognition is especially important to adolescent development because it promotes identity formation as well as cultivates moral reasoning and social perspective thinking from various social systems. The significance of recognizing positive behavior is illustrated through the support, tutorage, invitation, and subsidy provided by Hong Kong's social systems in recognition of adolescent volunteerism. The practical implications of positive behavior recognition on youth development programs are also discussed in this work