Remark on the Limit Case of Positive Mass Theorem for Manifolds with Inner Boundary

In [5] Herzlich proved a new positive mass theorem for Riemannian 3-manifolds $(N, g)$ whose mean curvature of the boundary allows some positivity. In this paper we study what happens to the limit case of the theorem when, at a point of the boundary, the smallest positive eigenvalue of the Dirac operator of the boundary is strictly larger than one-half of the mean curvature (in this case the mass $m(g)$ must be strictly positive). We prove that the mass is bounded from below by a positive constant $c(g), m(g) \geq c(g)$, and the equality $m(g) = c(g)$ holds only if, outside a compact set, $(N, g)$ is conformally flat and the scalar curvature vanishes. The constant $c(g)$ is uniquely determined by the metric $g$ via a Dirac-harmonic spinor.Comment: 12 pages, latex2

Some extensions of the Einstein-Dirac equation

We considered an extension of the standard functional for the Einstein-Dirac equation where the Dirac operator is replaced by the square of the Dirac operator and a real parameter controlling the length of spinors is introduced. For one distinguished value of the parameter, the resulting Euler-Lagrange equations provide a new type of Einstein-Dirac coupling. We establish a special method for constructing global smooth solutions of a newly derived Einstein-Dirac system called the {\it CL-Einstein-Dirac equation of type II} (see Definition 3.1).Comment: 21page

Relaxing Synchronization in Distributed Simulated Annealing

Simulated annealing is an attractive, but expensive, heuristic for approximating the solution to combinatorial optimization problems. Since simulated annealing is a general purpose method, it can be applied to the broad range of NP-complete problems such as the traveling salesman problem, graph theory, and cell placement with a careful control of the cooling schedule. Attempts to parallelize simulated annealing, particularly on distributed memory multicomputers, are hampered by the algorithm’s requirement of a globally consistent system state. In a multicomputer, maintaining the global state S involves explicit message traffic and is a critical performance bottleneck. One way to mitigate this bottleneck is to amortize the overhead of these state updates over as many parallel state changes as possible. By using this technique, errors in the actual cost C(S) of a particular state S will be introduced into the annealing process. This dissertation places analytically derived bounds on the cost error in order to assure convergence to the correct result. The resulting parallel Simulated Annealing algorithm dynamically changes the frequency of global updates as a function of the annealing control parameter, i.e. temperature. Implementation results on an Intel iPSC/2 are reported

Parallel Error Tolerance Scheme Based on the Hill Climbing Nature of Simulated Annealing

In parallelizing simulated annealing in a multicomputer, maintaining the global state S involves explicit message traffic and is a critical performance bottleneck. One way to mitigate this bottleneck is to amortize the overhead of these state updates over as many parallel state changes as possible. Using this technique introduces errors in the calculated cost C(S) of a particular state S used by the annealing process. Analytically derived bounds are placed on this error in order to assure convergence to the correct result. The resulting parallel simulated annealing algorithm dynamically changes the frequency of global updates as a function of the annealing control parameter, i.e., temperature. Implementation results on the Intel iPSC/2 are reporte

Relaxing Synchronization in Distributed Simulated Annealing

This paper presents a cost error measurement scheme and relaxed synchronization method, for simulated annealing on a distributed memory multicomputer, which predicts the amount of cost error that an algorithm will tolerate. An adaptive error control method is developed and implemented on an Intel iPSC/

Uterine and placental expression of TRPV6 gene is regulated via progesterone receptor- or estrogen receptor-mediated pathways during pregnancy in rodents

Transient receptor potential cation channel, subfamily V, member 6 (TRPV6) is an epithelial Ca2+ channel protein expressed in calcium absorbing organs. In the present study, we investigated the expression and regulation of uterine and placental TRPV6 during gestation in rodents. Uterine TRPV6 peaked at pregnancy day (P) 0.5, P5.5 and, P13.5 and was detected in uterine epithelium and glands of rats, while placental TRPV6 mRNA levels increased in mid-gestation. Uterine and placental TRPV6 mRNA levels in rats appear to cyclically change during pregnancy, suggesting that TRPV6 may participate in the implantation process. In addition, uterine TRPV6 mRNA is only expressed in placenta-unattached areas of the uterus, and uterine TRPV6 immunoreactivity was observed in luminal and glandular epithelial cells. In the placenta, TRPV6 was detected in the labyrinth and spongy zone. These results may indicate that TRPV6 has at least two functions: implantation of the embryo and maintenance of pregnancy. To investigate the pathway(s) mediating TRPV6 expression in rodents, anti-steroid hormone antagonists were injected prior to maximal TRPV6 expression. In rats, TRPV6 expression was reduced by RU486 (an anti-progesterone) through progesterone receptors, and ICI 182,780 (an anti-estrogen) blocked TRPV6 expression via estrogen receptors in mice. The juxtaposition of uterine and placental TRPV6 expressed in these tissues supports the notion that TRPV6 participates in transferring calcium ions between the maternal and fetal compartments. Taken together, TRPV6 gene may function as a key element in controlling calcium transport in the uterus between the embryo and the placenta during pregnancy

Proposal of a New Scenario Composition Method for Escape Room Game Design

리얼 방탈출 게임은 (이하 방탈출 게임) 관찰력과 창의력을 발취하여 팀원 간의 상호작용을 통해 실제 공간에서 진행할 수 있는 게임으로서 전 세계적으로 많은 인기를 얻고 있다. 본 논문은 방탈출 게임 디자인의 기반이 되는 시나리오 구성 방법을 제안하고자 한다. 이를 위해 방탈출 게임의 체험 및 관찰 통해 사람들이 즐거움을 느끼는 과정을 이해하고 시나리오 구성 과정을 정의한 뒤 시나리오 초안을 작성하여 스토리라인을 강조하는 방탈출 게임의 시나리오 기본 요소와 구성 원칙을 제안하였다.OAIID:RECH_ACHV_DSTSH_NO:A201701934RECH_ACHV_FG:RR00200003ADJUST_YN:EMP_ID:A080155CITE_RATE:FILENAME:hci2017_방탈출 게임 디자인을 위한 시나리오 구성방법 제안.pdfDEPT_NM:디자인학부EMAIL:[email protected]_YN:FILEURL:https://srnd.snu.ac.kr/eXrepEIR/fws/file/977abf52-2a2d-4bec-8817-4fb7e3ef54d7/linkCONFIRM: