Quantum states for perfectly secure secret sharing

In this work, we investigate what kinds of quantum states are feasible to perform perfectly secure secret sharing, and present its necessary and sufficient conditions. We also show that the states are bipartite distillable for all bipartite splits, and hence the states could be distillable into the Greenberger-Horne-Zeilinger state. We finally exhibit a class of secret-sharing states, which have an arbitrarily small amount of bipartite distillable entanglement for a certain split.Comment: 4 page

Development of General Purpose Liquid Chromatography Simulator for the Exploration of Novel Liquid Chromatographic Strategies

The method development process in liquid chromatography (LC) involves optimization of a variety of method parameters including stationary phase chemistry, column temperature, initial and final mobile phase compositions, and gradient time when gradient mobile phases are used. Here, a general simulation program to predict the results (i.e., retention time, peak width and peak shape) of LC separations, with the ability to study various complex chromatographic conditions is described. The simulation program is based on the Craig distribution model where the column is divided into discrete distance (Δz) and time (Δt) segments in a grid and is based on parameterization with either the linear solvent strength or Neue-Kuss models for chromatographic retention. This algorithm is relatively simple to understand and produces results that agree well with closed form theory when available. The set of simulation programs allows for the use of any eluent composition profile (linear and nonlinear), any column temperature, any stationary phase composition (constant or non-constant), and any composition and shape of the injected sample profile. The latter addition to our program is particularly useful in characterizing the solvent mismatch effect in comprehensive two-dimensional liquid chromatography (2D-LC), in which there is a mismatch between the first dimension (1D) effluent and second dimension (2D) initial mobile phase composition. This solvent mismatch causes peak distortion and broadening. The use of simulations can provide a better understanding of this phenomenon and a guide for the method development for 2D-LC. Another development that is proposed to have a great impact on the enhancement of 2D-LC methods is the use of continuous stationary phase gradients. When using rapid mobile phase gradients in the second dimension separation with diode array detection (DAD), refractive index changes cause large backgrounds such as an injection ridge (from solvent mismatch) and sloping baselines which can be problematic for achieving accurate quantitation. Use of a stationary phase gradient may enable the use of an isocratic mobile phase in the 2D, thus minimizing these background signals. Finally, our simulator can be used as an educational tool. Unlike commercially available simulators, our program can capture the evolution of the chromatogram in the form of movies and/or snapshots of the analyte distribution over time and/or distance to facilitate a better understanding of the separation process under complicated circumstances. We plan to make this simulation program publically available to all chromatographers and educators to aid in more efficient method development and chromatographic training

Biological network comparison using graphlet degree distribution

Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics such as the degree distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions (GDDs) of graphlets with 2-5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets). Furthermore, we show a way to combine the 73 GDDs into a network 'agreement' measure. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, are better modeled by geometric random graphs than by Erdos-Reny, random scale-free, or Barabasi-Albert scale-free networks.Comment: Proceedings of the 2006 European Conference on Computational Biology, ECCB'06, Eilat, Israel, January 21-24, 200

Friction force microscopy : a simple technique for identifying graphene on rough substrates and mapping the orientation of graphene grains on copper

At a single atom thick, it is challenging to distinguish graphene from its substrate using conventional techniques. In this paper we show that friction force microscopy (FFM) is a simple and quick technique for identifying graphene on a range of samples, from growth substrates to rough insulators. We show that FFM is particularly effective for characterizing graphene grown on copper where it can correlate the graphene growth to the three-dimensional surface topography. Atomic lattice stick–slip friction is readily resolved and enables the crystallographic orientation of the graphene to be mapped nondestructively, reproducibly and at high resolution. We expect FFM to be similarly effective for studying graphene growth on other metal/locally crystalline substrates, including SiC, and for studying growth of other two-dimensional materials such as molybdenum disulfide and hexagonal boron nitride