The effective symmetry and material properties of twinned ferroelectric crystals with perovskite structure were analyzed. The twins or twinbands studied here were formed during ferroelectric phase transitions, which resulted in one of the following symmetry changes: m3m → 3m, m3m → 4mm, and m3m → mm2. It was found that the volume ratios of the two domains in a twin structure were not always equ...

B. Szegedy [Edge coloring models and reflection positivity, Journal of the American Mathematical Society 20 (2007) 969–988] showed that the number of homomorphisms into a weighted graph is equal to the partition function of a complex edge-coloring model. Using some results in geometric invariant theory, we characterize for which weighted graphs the edge-coloring model can be taken to be real va...

Given a large and complex network, we would like to find the partition of this network into a small number of clusters. This question has been addressed in many different ways. In a previous paper, we proposed a deterministic framework for an optimal partition of a network as well as the associated algorithms. In this paper, we extend this framework to a probabilistic setting, in which each nod...

By calculating the evolution of surface energies and surface stress tensors of Ge-covered Si(001) with increasing Ge coverage, we derive the most probable Ge stoichiometry in the subsurface regions beyond 1 monolayer coverage. We compare the calculated surface reconstruction and surface stress at the thermodynamic and kinetic limits to experiment to provide a quantitative understanding of the r...

We give a new version of the Shannon-McMillan-Breiman theorem in the case of a bijective action. For a finite partition α of a compact set X and a measurable action T on X, we denote by CT n,m,α(x) the element of the partition α ∨ T 1α ∨ . . . ∨ Tmα ∨ T−1α ∨ . . . ∨ T−nα which contains a point x. We prove that for μ-almost all x, lim n+m→∞ ( −1 n+m ) logμ(C n,m,α(x)) = hμ(T, α), where μ is a T ...

“Control” studies attempts to set the outcome of elections through the addition, deletion, or partition of voters or candidates. The set of benchmark control types was largely set in the seminal 1992 paper by Bartholdi, Tovey, and Trick that introduced control, and there now is a large literature studying how many of the benchmark types various election systems are vulnerable to, i.e., have pol...

We consider multistage stochastic programming problems in which the random parameters have finite support, leading to optimization over a finite scenario set. We propose a hierarchy of bounds based on partitions of the scenario set into subsets of (nearly) equal cardinality. These expected partition (EP) bounds coincide with EGSO bounds provided by Sandıkçı et al. (2013) in the case that the su...

Recently, a one-parameter deformation of the Maldacena-Núñez background was constructed in hep-th/0505100. According to the Lunin-Maldacena conjecture, the background is dual to pure N = 1 SYM in the IR coupled to a KK sector whose dynamics is altered by a dipole deformation that is proportional to the deformation parameter γ. Thus, the deformation serves to identify the aspects of the gravity ...