Improved Lower Bounds for Constant GC-Content DNA Codes

The design of large libraries of oligonucleotides having constant GC-content and satisfying Hamming distance constraints between oligonucleotides and their Watson-Crick complements is important in reducing hybridization errors in DNA computing, DNA microarray technologies, and molecular bar coding. Various techniques have been studied for the construction of such oligonucleotide libraries, ranging from algorithmic constructions via stochastic local search to theoretical constructions via coding theory. We introduce a new stochastic local search method which yields improvements up to more than one third of the benchmark lower bounds of Gaborit and King (2005) for n-mer oligonucleotide libraries when n <= 14. We also found several optimal libraries by computing maximum cliques on certain graphs.Comment: 4 page

MEMS-based Speckle Spectrometer

We describe a new concept for a MEMS-based active spatial filter for astronomical spectroscopy. The goal of this device is to allow the use of a diffraction-limited spectrometer on a seeing limited observation at improved throughput over a comparable seeing-limited spectrometer, thus reducing the size and cost of the spectrometer by a factor proportional to r0/D (For the case of a 10 meter telescope this size reduction will be approximately a factor of 25 to 50). We use a fiber-based integral field unit (IFU) that incorporates an active MEMS mirror array to feed an astronomical spectrograph. A fast camera is used in parallel to sense speckle images at a spatial resolution of lambda/D and at a temporal frequency greater than that of atmospheric fluctuations. The MEMS mirror-array is used as an active shutter to feed speckle images above a preset intensity threshold to the spectrometer, thereby increasing the signal-to-noise ratio (SNR) of the spectrogram. Preliminary calculations suggests an SNR improvement of a factor of about 1.4. Computer simulations have shown an SNR improvement of 1.1, but have not yet fully explored the parameter space.Comment: 11 pages, 5 figures, presented at SPIE Astronomical Telescopes and Instrumentation, 24 - 31 May 2006, Orlando, Florida US

Quantum State Tomography and Quantum Games

We develop a technique for single qubit quantum state tomography using the mathematical setup of generalized quantization scheme for games. In our technique Alice sends an unknown pure quantum state to Bob who appends it with |0><0| and then applies the unitary operators on the appended quantum state and finds the payoffs for Alice and himself. It is shown that for a particular set of unitary operators these elements become equal to Stokes parameters for an unknown quantum state. In this way an unknown quantum state can be measured and reconstructed. Strictly speaking this technique is not a game as no strategic competitions are involved.Comment: 9 pages, 3 figure

A novel configuration model for random graphs with given degree sequence

Recently, random graphs in which vertices are characterized by hidden variables controlling the establishment of edges between pairs of vertices have attracted much attention. Here, we present a specific realization of a class of random network models in which the connection probability between two vertices (i,j) is a specific function of degrees ki and kj. In the framework of the configuration model of random graphs, we find analytical expressions for the degree correlation and clustering as a function of the variance of the desired degree distribution. The expressions obtained are checked by means of numerical simulations. Possible applications of our model are discussed.Comment: 7 pages, 3 figure

Solving the Uncapacitated Single Allocation p-Hub Median Problem on GPU

A parallel genetic algorithm (GA) implemented on GPU clusters is proposed to solve the Uncapacitated Single Allocation p-Hub Median problem. The GA uses binary and integer encoding and genetic operators adapted to this problem. Our GA is improved by generated initial solution with hubs located at middle nodes. The obtained experimental results are compared with the best known solutions on all benchmarks on instances up to 1000 nodes. Furthermore, we solve our own randomly generated instances up to 6000 nodes. Our approach outperforms most well-known heuristics in terms of solution quality and time execution and it allows hitherto unsolved problems to be solved

Retrieving the Size of Deep-subwavelength Objects via Tunable Optical Spin-Orbit Coupling

We propose a scheme to retrieve the size parameters of a nano-particle on a glass substrate at a scale much smaller than the wavelength. This is achieved by illuminating the particle using two plane waves to create rich and non-trivial local polarization distributions, and observing the far-field scattering pattern into the substrate. A simple dipole model which exploits tunneling effect of evanescent field into regions beyond the critical angle, as well as directional scattering due to spin-orbit coupling is developed, to relate the particle's shape, size and position to the far-field scattering with remarkable sensitivity. Our method brings about a far-field super-resolution imaging scheme based on the interaction of vectorial light with nanoparticles