Periodicity and criticality in the Olami-Feder-Christensen model of earthquakes

Characteristic versus critical features of earthquakes are studied on the basis of the Olami-Feder-Christensen model. It is found that the local recurrence-time distribution exhibits a sharp $\delta$-function-like peak corresponding to rhythmic recurrence of events with a fixed ``period'' uniquely determined by the transmission parameter of the model, together with a power-law-like tail corresponding to scale-free recurrence of events. The model exhibits phenomena closely resembling the asperity known in seismology

Zone diagrams in Euclidean spaces and in other normed spaces

Zone diagrams are a variation on the classical concept of Voronoi diagrams. Given n sites in a metric space that compete for territory, the zone diagram is an equilibrium state in the competition. Formally it is defined as a fixed point of a certain "dominance” map. Asano, Matoušek, and Tokuyama proved the existence and uniqueness of a zone diagram for point sites in the Euclidean plane, and Reem and Reich showed existence for two arbitrary sites in an arbitrary metric space. We establish existence and uniqueness for n disjoint compact sites in a Euclidean space of arbitrary (finite) dimension, and more generally, in a finite-dimensional normed space with a smooth and rotund norm. The proof is considerably simpler than that of Asano etal. We also provide an example of non-uniqueness for a norm that is rotund but not smooth. Finally, we prove existence and uniqueness for two point sites in the plane with a smooth (but not necessarily rotund) nor

Equivalence Classes of Boundary Conditions in Gauge Theory on Z3Z_3 Orbifold

We study equivalence classes of boundary conditions in gauge theory on the orbifold $T^2/Z_3$. Orbifold conditions and those gauge transformation properties are given and the gauge equivalence is understood by the Hosotani mechanism. Mode expansions are carried out for six-dimensional $Z_3$ singlet fields and a $Z_3$ triplet field, and the one-loop effective potential for Wilson line phases is calculated.Comment: PTPTEX,17 page

Search for a Realistic Orbifold Grand Unification

We review the prototype model of a grand unified theory on the orbifold $S^1/Z_2$ and discuss topics related to the choice of boundary conditions; the dynamical rearrangement of gauge symmetry and the equivalence classes of BCs. We explore a family unification scenario by orbifolding.Comment: 19 pages, 4 figures, to appear in the proceeding of International Workshop on Grand Unified Theories: Current Status and Future Prospects (GUT07), December 17-19 2007, Kusatsu, Japa

Distance k-Sectors Exist

The bisector of two nonempty sets P and Q in a metric space is the set of all points with equal distance to P and to Q. A distance k-sector of P and Q, where k is an integer, is a (k-1)-tuple (C_1, C_2, ..., C_{k-1}) such that C_i is the bisector of C_{i-1} and C_{i+1} for every i = 1, 2, ..., k-1, where C_0 = P and C_k = Q. This notion, for the case where P and Q are points in Euclidean plane, was introduced by Asano, Matousek, and Tokuyama, motivated by a question of Murata in VLSI design. They established the existence and uniqueness of the distance trisector in this special case. We prove the existence of a distance k-sector for all k and for every two disjoint, nonempty, closed sets P and Q in Euclidean spaces of any (finite) dimension, or more generally, in proper geodesic spaces (uniqueness remains open). The core of the proof is a new notion of k-gradation for P and Q, whose existence (even in an arbitrary metric space) is proved using the Knaster-Tarski fixed point theorem, by a method introduced by Reem and Reich for a slightly different purpose.Comment: 10 pages, 5 figure

Asperity characteristics of the Olami-Feder-Christensen model of earthquakes

Properties of the Olami-Feder-Christensen (OFC) model of earthquakes are studied by numerical simulations. The previous study indicated that the model exhibits ``asperity''-like phenomena, {\it i.e.}, the same region ruptures many times near periodically [T.Kotani {\it et al}, Phys. Rev. E {\bf 77}, 010102 (2008)]. Such periodic or characteristic features apparently coexist with power-law-like critical features, {\it e.g.}, the Gutenberg-Richter law observed in the size distribution. In order to clarify the origin and the nature of the asperity-like phenomena, we investigate here the properties of the OFC model with emphasis on its stress distribution. It is found that the asperity formation is accompanied by self-organization of the highly concentrated stress state. Such stress organization naturally provides the mechanism underlying our observation that a series of asperity events repeat with a common epicenter site and with a common period solely determined by the transmission parameter of the model. Asperity events tend to cluster both in time and in space

ABO-incompatible living-donor pediatric kidney transplantation in Japan

The Japanese ABO-Incompatible Transplantation Committee officially collected and analyzed data on pediatric ABO-incompatible living-donor kidney transplantation in July 2012. The age of a child was defined a

Physically Consistent Preferential Bayesian Optimization for Food Arrangement

This paper considers the problem of estimating a preferred food arrangement for users from interactive pairwise comparisons using Computer Graphics (CG)-based dish images. As a foodservice industry requirement, we need to utilize domain rules for the geometry of the arrangement (e.g., the food layout of some Japanese dishes is reminiscent of mountains). However, those rules are qualitative and ambiguous; the estimated result might be physically inconsistent (e.g., each food physically interferes, and the arrangement becomes infeasible). To cope with this problem, we propose Physically Consistent Preferential Bayesian Optimization (PCPBO) as a method that obtains physically feasible and preferred arrangements that satisfy domain rules. PCPBO employs a bi-level optimization that combines a physical simulation-based optimization and a Preference-based Bayesian Optimization (PbBO). Our experimental results demonstrated the effectiveness of PCPBO on simulated and actual human users.Comment: 8 pages, 10 figures, accepted by IEEE Robotics and Automation Letters (RA-L) 202

Finite spin-glass transition of the ±J\pm J XY model in three dimensions

A three-dimensional $\pm J$ XY spin-glass model is investigated by a nonequilibrium relaxation method. We have introduced a new criterion for the finite-time scaling analysis. A transition temperature is obtained by a crossing point of obtained data. The scaling analysis on the relaxation functions of the spin-glass susceptibility and the chiral-glass susceptibility shows that both transitions occur simultaneously. The result is checked by relaxation functions of the Binder parameters and the glass correlation lengths of the spin and the chirality. Every result is consistent if we consider that the transition is driven by the spin degrees of freedom.Comment: 11 pages, 8 figures, incorrect arguments are delete