Balanced Allocation on Graphs: A Random Walk Approach

In this paper we propose algorithms for allocating $n$ sequential balls into $n$ bins that are interconnected as a $d$-regular $n$-vertex graph $G$, where $d\ge3$ can be any integer.Let $l$ be a given positive integer. In each round $t$, $1\le t\le n$, ball $t$ picks a node of $G$ uniformly at random and performs a non-backtracking random walk of length $l$ from the chosen node.Then it allocates itself on one of the visited nodes with minimum load (ties are broken uniformly at random). Suppose that $G$ has a sufficiently large girth and $d=\omega(\log n)$. Then we establish an upper bound for the maximum number of balls at any bin after allocating $n$ balls by the algorithm, called {\it maximum load}, in terms of $l$ with high probability. We also show that the upper bound is at most an $O(\log\log n)$ factor above the lower bound that is proved for the algorithm. In particular, we show that if we set $l=\lfloor(\log n)^{\frac{1+\epsilon}{2}}\rfloor$, for every constant $\epsilon\in (0, 1)$, and $G$ has girth at least $\omega(l)$, then the maximum load attained by the algorithm is bounded by $O(1/\epsilon)$ with high probability.Finally, we slightly modify the algorithm to have similar results for balanced allocation on $d$-regular graph with $d\in[3, O(\log n)]$ and sufficiently large girth

Matter-wave interferometry in periodic and quasi-periodic arrays

We calculate within a Bose-Hubbard tight-binding model the matter-wave flow driven by a constant force through a Bose-Einstein condensate of Rb 87 atoms in various types of quasi-onedimensional arrays of potential wells. Interference patterns are obtained when beam splitting is induced by creating energy minigaps either through period doubling or through quasi-periodicity governed by the Fibonacci series. The generation of such condensate modulations by means of optical-laser structures is also discussed.Comment: 11 pages, 6 figures. To appear in Opt. Com

Expression of TGFβ1 by Pulp Tissue of Human Permanent and Primary Teeth Capped by BiodentineTM

BiodentineTM,represented a novel bioactive tricalcium silicate cement ,that is introduced into dentistry. It was suggested to be biocompatible, having optimal working and setting time, excellent workability with superior adhesion to tooth structure. BiodentineTM was proved to maintain pulp as a vital tissue and enhance dentinal bridging, as alternative to Mineral trioxide aggregate that can be provided with a better handling characteristics and shorter working time. Moreover, dental pulp cells have the potential to differentiate into odontoblast-like cells and enhanced reparative dentine.In the present study "BiodentineTM" was directly applied on the dental pulp of cultured tooth of (36) human maxillary first premolars and (36) human maxillary first primary molar tooth . After various culture periods (2,14 and 28) days, the interaction of the material with dental pulp tissue was analyzed on tissue cultures. The effect of this material on TGFB1 expression on pulp tissue was studied by immunohistochemical investigation. The results illustrate that BiodentineTM" induced mineralized foci formation early after its application as direct pulp capping material in permanent and primary teeth. The mineralization appeared beneath the reparative dentine. BiodentineTM shows a highl significant increment of TGF- β1 expression by pulp cells (P< 0.01) in both permanent and primary teeth.Conclusions: When "BiodentineTM" was applied as direct pulp capping material for permanent and primary teeth, it induced an early form of reparative dentine synthesis, probably due to a modulation of pulp cell for expression TGF-β1. Keywords: Transforming growth factor(TGF), Biodentine, pulp cell

gp25L/emp24/p24 Protein Family Members of the cis-Golgi Network Bind Both COP I and II Coatomer

Abstract. Five mammalian members of the gp25L/ emp24/p24 family have been identified as major constituents of the cis-Golgi network of rat liver and HeLa cells. Two of these were also found in membranes of higher density (corresponding to the ER), and this correlated with their ability to bind COP I in vitro. This binding was mediated by a K(X)KXX-like retrieval motif present in the cytoplasmic domain of these two members. A second motif, double phenylalanine (FF), present in the cytoplasmic domain of all five members, was shown to participate in the binding of Sec23 (COP II). This motif is part of a larger one, similar to the F/YXXXXF/Y strong endocytosis and putative AP2 binding motif. In vivo mutational analysis confirmed the roles of both motifs so that when COP I binding was expected to be impaired, cell surface expression was observed, whereas mutation of the Sec23 binding motif resulted in a redistribution to the ER. Surprisingly, upon expression of mutated members, steady-state distribution of unmutated ones shifted as well, presumably as a consequence of their observed oligomeric properties

Quantum Field Theoretical Analysis on Unstable Behavior of Bose-Einstein Condensates in Optical Lattices

We study the dynamics of Bose-Einstein condensates flowing in optical lattices on the basis of quantum field theory. For such a system, a Bose-Einstein condensate shows a unstable behavior which is called the dynamical instability. The unstable system is characterized by the appearance of modes with complex eigenvalues. Expanding the field operator in terms of excitation modes including complex ones, we attempt to diagonalize the unperturbative Hamiltonian and to find its eigenstates. It turns out that although the unperturbed Hamiltonian is not diagonalizable in the conventional bosonic representation the appropriate choice of physical states leads to a consistent formulation. Then we analyze the dynamics of the system in the regime of the linear response theory. Its numerical results are consitent with as those given by the discrete nonlinear Schrodinger equation.Comment: 16pages, 4figure

Rotating BEC in an optical lattice in Uniformly frustrated Josephson Junction arrays regime: Vortex configuration formulation for ground state

We consider a rotating BEC in an optical lattices in a regime which can be mapped to the Joseohson junction arrays. In this regime, we formulate the ground state energy in terms of vortex configuration. This method give us the vortex lattice in the ground state in a natural way. We apply our result for an approximation scheme of the problem which we suppose that the coupling of the Josephson junctions are uniform. Application of method for ladder case presented and the results compared with Monte-Carlo method numerically.We discuss about restriction of method and suggest improvement for it.Comment: 6 pages, 7 figure

Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice

Dirac points lie at the heart of many fascinating phenomena in condensed matter physics, from massless electrons in graphene to the emergence of conducting edge states in topological insulators [1, 2]. At a Dirac point, two energy bands intersect linearly and the particles behave as relativistic Dirac fermions. In solids, the rigid structure of the material sets the mass and velocity of the particles, as well as their interactions. A different, highly flexible approach is to create model systems using fermionic atoms trapped in the periodic potential of interfering laser beams, a method which so far has only been applied to explore simple lattice structures [3, 4]. Here we report on the creation of Dirac points with adjustable properties in a tunable honeycomb optical lattice. Using momentum-resolved interband transitions, we observe a minimum band gap inside the Brillouin zone at the position of the Dirac points. We exploit the unique tunability of our lattice potential to adjust the effective mass of the Dirac fermions by breaking inversion symmetry. Moreover, changing the lattice anisotropy allows us to move the position of the Dirac points inside the Brillouin zone. When increasing the anisotropy beyond a critical limit, the two Dirac points merge and annihilate each other - a situation which has recently attracted considerable theoretical interest [5-9], but seems extremely challenging to observe in solids [10]. We map out this topological transition in lattice parameter space and find excellent agreement with ab initio calculations. Our results not only pave the way to model materials where the topology of the band structure plays a crucial role, but also provide an avenue to explore many-body phases resulting from the interplay of complex lattice geometries with interactions [11, 12]

Localized states in 2D semiconductors doped with magnetic impurities in quantizing magnetic field

A theory of magnetic impurities in a 2D electron gas quantized by a strong magnetic field is formulated in terms of Friedel-Anderson theory of resonance impurity scattering. It is shown that this scattering results in an appearance of bound Landau states with zero angular moment between the Landau subbands. The resonance scattering is spin selective, and it results in a strong spin polarization of Landau states, as well as in a noticeable magnetic field dependence of the $g$ factor and the crystal field splitting of the impurity $d$ levels.Comment: 12 pages, 4 figures Submitted to Physical Review B This version is edited and updated in accordance with recent experimental dat