Almost uniform sampling via quantum walks

Many classical randomized algorithms (e.g., approximation algorithms for #P-complete problems) utilize the following random walk algorithm for {\em almost uniform sampling} from a state space $S$ of cardinality $N$: run a symmetric ergodic Markov chain $P$ on $S$ for long enough to obtain a random state from within $\epsilon$ total variation distance of the uniform distribution over $S$. The running time of this algorithm, the so-called {\em mixing time} of $P$, is $O(\delta^{-1} (\log N + \log \epsilon^{-1}))$, where $\delta$ is the spectral gap of $P$. We present a natural quantum version of this algorithm based on repeated measurements of the {\em quantum walk} $U_t = e^{-iPt}$. We show that it samples almost uniformly from $S$ with logarithmic dependence on $\epsilon^{-1}$ just as the classical walk $P$ does; previously, no such quantum walk algorithm was known. We then outline a framework for analyzing its running time and formulate two plausible conjectures which together would imply that it runs in time $O(\delta^{-1/2} \log N \log \epsilon^{-1})$ when $P$ is the standard transition matrix of a constant-degree graph. We prove each conjecture for a subclass of Cayley graphs.Comment: 13 pages; v2 added NSF grant info; v3 incorporated feedbac

Role of electromagnetically induced transparency in resonant four-wave-mixing schemes.

Published versio

Exit and Occupation times for Brownian Motion on Graphs with General Drift and Diffusion Constant

We consider a particle diffusing along the links of a general graph possessing some absorbing vertices. The particle, with a spatially-dependent diffusion constant D(x) is subjected to a drift U(x) that is defined in every point of each link. We establish the boundary conditions to be used at the vertices and we derive general expressions for the average time spent on a part of the graph before absorption and, also, for the Laplace transform of the joint law of the occupation times. Exit times distributions and splitting probabilities are also studied and several examples are discussed.Comment: Accepted for publication in J. Phys.

Major Cellular and Physiological Impacts of Ocean Acidification on a Reef Building Coral

As atmospheric levels of CO2 increase, reef-building corals are under greater stress from both increased sea surface temperatures and declining sea water pH. To date, most studies have focused on either coral bleaching due to warming oceans or declining calcification due to decreasing oceanic carbonate ion concentrations. Here, through the use of physiology measurements and cDNA microarrays, we show that changes in pH and ocean chemistry consistent with two scenarios put forward by the Intergovernmental Panel on Climate Change (IPCC) drive major changes in gene expression, respiration, photosynthesis and symbiosis of the coral, Acropora millepora, before affects on biomineralisation are apparent at the phenotype level. Under high CO2 conditions corals at the phenotype level lost over half their Symbiodinium populations, and had a decrease in both photosynthesis and respiration. Changes in gene expression were consistent with metabolic suppression, an increase in oxidative stress, apoptosis and symbiont loss. Other expression patterns demonstrate upregulation of membrane transporters, as well as the regulation of genes involved in membrane cytoskeletal interactions and cytoskeletal remodeling. These widespread changes in gene expression emphasize the need to expand future studies of ocean acidification to include a wider spectrum of cellular processes, many of which may occur before impacts on calcification

Local political marketing in the context of the conservative party

Local political marketing can be defined as marketing related strategy, activities, and tactics implemented by a political party in a local geographic constituency, in order to attempt to maximise aggregate potential voter satisfaction, and therefore maximise total number of votes and electoral support in the constituency. Through 12 in-depth interviews with Local Constituency Party representatives from the Conservative Party, the study found that local political marketing was acknowledged by a majority of respondents although this was not unequivocal, and was frequently conflated with campaigning. Local political marketing was associated with: visual identity, language/messages, values, image, communication devices, awareness raising, data management and targeting, and simplification. The support from higher levels of the party in local political marketing was varied across constituencies. There was evidence of growing coordination /influence by higher levels of the party in local political marketing. However, this tended to be in seats judged as ‘winnable’

Identification of Intracellular and Plasma Membrane Calcium Channel Homologues in Pathogenic Parasites

Ca2+ channels regulate many crucial processes within cells and their abnormal activity can be damaging to cell survival, suggesting that they might represent attractive therapeutic targets in pathogenic organisms. Parasitic diseases such as malaria, leishmaniasis, trypanosomiasis and schistosomiasis are responsible for millions of deaths each year worldwide. The genomes of many pathogenic parasites have recently been sequenced, opening the way for rational design of targeted therapies. We analyzed genomes of pathogenic protozoan parasites as well as the genome of Schistosoma mansoni, and show the existence within them of genes encoding homologues of mammalian intracellular Ca2+ release channels: inositol 1,4,5-trisphosphate receptors (IP3Rs), ryanodine receptors (RyRs), two-pore Ca2+ channels (TPCs) and intracellular transient receptor potential (Trp) channels. The genomes of Trypanosoma, Leishmania and S. mansoni parasites encode IP3R/RyR and Trp channel homologues, and that of S. mansoni additionally encodes a TPC homologue. In contrast, apicomplexan parasites lack genes encoding IP3R/RyR homologues and possess only genes encoding TPC and Trp channel homologues (Toxoplasma gondii) or Trp channel homologues alone. The genomes of parasites also encode homologues of mammalian Ca2+ influx channels, including voltage-gated Ca2+ channels and plasma membrane Trp channels. The genome of S. mansoni also encodes Orai Ca2+ channel and STIM Ca2+ sensor homologues, suggesting that store-operated Ca2+ entry may occur in this parasite. Many anti-parasitic agents alter parasite Ca2+ homeostasis and some are known modulators of mammalian Ca2+ channels, suggesting that parasite Ca2+ channel homologues might be the targets of some current anti-parasitic drugs. Differences between human and parasite Ca2+ channels suggest that pathogen-specific targeting of these channels may be an attractive therapeutic prospect