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

Corporate political activity and firm outcomes: A meta-analysis

Using meta-analytic methods on a sample of 74 studies, we explore the links between CPA and public policy outcomes, and between CPA and firm outcomes. We find that CPA has at best a weak effect and that it appears to be better at maintaining public policy than changing them

Noise sensitivity of an atomic velocity sensor

We use Bloch oscillations to accelerate coherently Rubidium atoms. The variation of the velocity induced by this acceleration is an integer number times the recoil velocity due to the absorption of one photon. The measurement of the velocity variation is achieved using two velocity selective Raman pi-pulses: the first pulse transfers atoms from the hyperfine state 5S1/2 |F=2, mF=0> to 5S1/2, |F=1, mF = 0> into a narrow velocity class. After the acceleration of this selected atomic slice, we apply the second Raman pulse to bring the resonant atoms back to the initial state 5S1/2, |F=2, mF = 0>. The populations in (F=1 and F=2) are measured separately by using a one-dimensional time-of-flight technique. To plot the final velocity distribution we repeat this procedure by scanning the Raman beam frequency of the second pulse. This two pi-pulses system constitutes then a velocity sensor. Any noise in the relative phase shift of the Raman beams induces an error in the measured velocity. In this paper we present a theoretical and an experimental analysis of this velocity sensor, which take into account the phase fluctuations during the Raman pulses

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

Microstructured blood vessel surrogates reveal structural tropism of motile malaria parasites

Plasmodium sporozoites, the highly motile forms of the malaria parasite, are transmitted naturally by mosquitoes and traverse the skin to find, associate with, and enter blood capillaries. Research aimed at understanding how sporozoites select blood vessels is hampered by the lack of a suitable experimental system. Arrays of uniform cylindrical pillars can be used to study small cells moving in controlled environments. Here, an array system displaying a variety of pillars with different diameters and shapes is developed in order to investigate how Plasmodium sporozoites associate to the pillars as blood vessel surrogates. Investigating the association of sporozoites to pillars in arrays displaying pillars of different diameters reveals that the crescent-shaped parasites prefer to associate with and migrate around pillars with a similar curvature. This suggests that after transmission by a mosquito, malaria parasites may use a structural tropism to recognize blood capillaries in the dermis in order to gain access to the blood stream

An optical lattice on an atom chip

Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retro-reflected using the atom chip surface as a high-quality mirror, generating a vertical array of purely optical oblate traps. We load thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime where the thermal energy is smaller than a quantum of transverse excitation. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice.Comment: 3 pages, 2 figure

Second harmonic generating (SHG) nanoprobes for in vivo imaging

Fluorescence microscopy has profoundly changed cell and molecular biology studies by permitting tagged gene products to be followed as they function and interact. The ability of a fluorescent dye to absorb and emit light of different wavelengths allows it to generate startling contrast that, in the best cases, can permit single molecule detection and tracking. However, in many experimental settings, fluorescent probes fall short of their potential due to dye bleaching, dye signal saturation, and tissue autofluorescence. Here, we demonstrate that second harmonic generating (SHG) nanoprobes can be used for in vivo imaging, circumventing many of the limitations of classical fluorescence probes. Under intense illumination, such as at the focus of a laser-scanning microscope, these SHG nanocrystals convert two photons into one photon of half the wavelength; thus, when imaged by conventional two-photon microscopy, SHG nanoprobes appear to generate a signal with an inverse Stokes shift like a fluorescent dye, but with a narrower emission. Unlike commonly used fluorescent probes, SHG nanoprobes neither bleach nor blink, and the signal they generate does not saturate with increasing illumination intensity. The resulting contrast and detectability of SHG nanoprobes provide unique advantages for molecular imaging of living cells and tissues

Theoretical Analysis of a Large Momentum Beamsplitter using Bloch Oscillations

In this paper, we present the implementation of Bloch oscillations in an atomic interferometer to increase the separation of the two interfering paths. A numerical model, in very good agreement with the experiment, is developed. The contrast of the interferometer and its sensitivity to phase fluctuations and to intensity fluctuations are also calculated. We demonstrate that the sensitivity to phase fluctuations can be significantly reduced by using a suitable arrangement of Bloch oscillations pulses