Augmented planar reflective symmetry transform

Symmetry has been playing an increasing role in 3D shape processing. Recently introduced planar reflective symmetry transform (PRST) has been found useful for canonical coordinate frame determination, shape matching, retrieval, and segmentation. Guided by the intuition that every imperfect symmetry is imperfect in its own way, we investigate the possibility of incorporating more information into symmetry transforms like PRST. As a step in this direction, the concept of augmented symmetry transform is introduced; we obtain a family of symmetry transforms indexed by a parameter. While the original PRST measures how much the symmetry is broken, the augmented PRST also gives some information about how it is broken. Several approaches to calculating the augmented transform are described. We demonstrate that the augmented transform is beneficial for shape retrieval.     

基于对称性的颌骨复位方法研究及应用

针对严重错位骨折的颌骨复位口腔外科手术,提出一种帮助医生进行术前规划和准备的破损颌骨复位方法。首先使用移动立方体(MC)算法从患者CT 图像中提取颌骨的面片模型;然后结合图割算法、形状直径函数(SDF)描述子和混合高斯模型的交互式分割方法,允许医生通过简单的勾画快速分割出破损骨块;最后基于颌骨的对称性特性自动完成破损骨块复位。通过破损骨块复位完成颌骨模型重构,能完整保留对医生非常重要的骨折线信息。该方法已应用于自主开发的计算机辅助破损颌骨复位系统,并使用安徽医科大学附属医院的患者数据进行了测试,结果表明了该方法的有效性。     

Two-dimensional quantum walk with position-dependent phase defects

We demonstrate localization effect in a two-dimensional quantum walk architecture. With position-dependent phase defects, the symmetry of standard quantum walk is broken; the walker is trapped in a fixed position dynamically. We show how the factors such as the phase defect, initial state and coin flipping affect on the localization effect in the quantum walk architecture.     

Quantum computation in the decoherence-free subspaces with cavity QED

We present a scheme to implement quantum computation in decoherence-free subspaces (DFSs) with four atoms in a single-mode cavity. A four-dimensional DFS is constituted to protect quantum information when the full symmetry of interaction between system and environment is broken in a specific way, and entangling two-qubit logic gates and noncommuting single-qubit gates are implemented in such DFS. The gate fidelity is numerically calculated, and the feasibility of the approximations taken in this work is verified based on the numerical calculations.     

DE-DM Unification Based on Space-Time Symmetry

The algebraic classification of stress-energy tensors includes tensors whose symmetry is partly broken as compared with Einstein’s maximally symmetric cosmological term. This allows us to introduce, in a general setting, a vacuum dark fluid with variable density and pressures approaching the cosmological constant in certain space-time regions. The relevant class of Einstein equations describes cosmological models with time-evolving and spatially inhomogeneous vacuum dark energy and compact objects with de Sitter interiors generically related to vacuum dark energy, which can be responsible for observational effects typical of dark matter. The mass of objects is generically related to breaking of space-time symmetry from the de Sitter group. We outline the basic generic properties of regular cosmological models with vacuum dark energy, and of dark matter candidates with de Sitter interiors, including their observational signatures.     

Symmetry breaking and the twisted elastic ring

Symmetry breaking is considered in the context of a parameter-dependent two-point boundary value problem describing a twisted elastic ring that arises as a model of DNA minicircles. We explicitly determine, via a perturbation expansion, those representatives of a manifold of solutions to a symmetric BVP that persist when the symmetry is broken. Conditions generating a generic splitting are identified, and some degenerate cases are studied. In both the generic and degenerate cases, the results of the perturbation expansion are used to improve the efficiency of existing algorithms for computing symmetry-broken bifurcation diagrams.     

A low complexity scheme for entanglement distributor buses

For technological purposes and theoretical curiosity, it is very interesting to have a building block that produces a considerable amount of entanglement between on-demand sites through a simple control of a few sites. Here, we consider permanently-coupled spin networks and study entanglement generation between qubit pairs to find low-complexity structures capable of generating considerable entanglement between various qubit pairs. We find that in axially symmetric networks the generated entanglement between some qubit pairs is rather larger than generic networks. We show that in uniformly-coupled spin rings each pair can be considerably entangled through controlling suitable vertices. To set the location of controlling-vertices, we observe that the symmetry has to be broken for a definite time. To achieve this, a magnetic flux can be applied to break symmetry via Aharonov-Bohm effect. Such a set up can serve as an efficient entanglement distributor bus in which each vertex-pair can be efficiently entangled through exciting only one fixed vertex and controlling the evolution time. The low-complexity of this scheme makes it attractive for use in nanoscale quantum information processors.     

A Unified Scheme for Generalized Sectors Based on Selection Criteria: Order Parameters of Symmetries and of Thermality and Physical Meanings of Adjunctions

A unified scheme for treating generalized superselection sectors is proposed on the basis of the notion of selection criteria to characterize states of relevance to each specific domain in quantum physics, ranging from the relativistic quantum fields in the vacuum situations with unbroken and spontaneously broken internal symmetries, through equilibrium and non-equilibrium states to some basic aspects in measurement processes. This is achieved by the help of c q and q c channels: the former determines the states to be selected and to be parameterized by the order parameters, and the latter provides the physical interpretations of selected states in terms of order parameters. This formulation extends the traditional range of applicability of the Doplicher-Roberts construction method for recovering the field algebra and the gauge group (of the first kind) from the data of group invariant observables to the situations with spontaneous symmetry breakdown: in use of the machinery proposed, the physical and mathematical meaning of basic structural ingredients associated with the spontaneously broken symmetry are re-examined, such as the degenerate vacua parameterized by the variables belonging to the relevant homogeneous space, the Goldstone modes and condensates, etc. The geometrical meaning of the space of order parameters is naturally understood in relation with the adjunction as the classifying space of a sector structure. As further examples of applications, some basic notions arising in the mathematical framework of quantum theory are reformulated and examined in connection with control theory.     

Involution Narrowing Algebra

The narrowing algebra formalism underlying CLP(intervals) consists of lattice-ordered monoids of monotone contractions on the lattice of states; these are generated by the canonical idempotent operators of the primitive relations of the constraint system used for the problem. This mathematical structure has some similarities with that of some classical operator rings, even though the underlying states form a non-Boolean lattice instead of a linear space. In this paper we show that in the restricted case of certain binary interval convex primitives, there is a broken symmetry which can be restored by generalizing the state lattice to produce an involution on the important fragment of the narrowing algebra. This involution allows some basic theorems of classical *-rings to be ported into this domain.