Group testing with Random Pools: Phase Transitions and Optimal Strategy

The problem of Group Testing is to identify defective items out of a set of objects by means of pool queries of the form "Does the pool contain at least a defective?". The aim is of course to perform detection with the fewest possible queries, a problem which has relevant practical applications in different fields including molecular biology and computer science. Here we study GT in the probabilistic setting focusing on the regime of small defective probability and large number of objects, $p \to 0$ and $N \to \infty$. We construct and analyze one-stage algorithms for which we establish the occurrence of a non-detection/detection phase transition resulting in a sharp threshold, $\bar M$, for the number of tests. By optimizing the pool design we construct algorithms whose detection threshold follows the optimal scaling $\bar M\propto Np|\log p|$. Then we consider two-stages algorithms and analyze their performance for different choices of the first stage pools. In particular, via a proper random choice of the pools, we construct algorithms which attain the optimal value (previously determined in Ref. [16]) for the mean number of tests required for complete detection. We finally discuss the optimal pool design in the case of finite $p$

Escape from a zero current state in a one dimensional array of Josephson junctions

A long one dimensional array of small Josephson junctions exhibits Coulomb blockade of Cooper pair tunneling. This zero current state exists up to a switching voltage, Vsw, where there is a sudden onset of current. In this paper we present histograms showing how Vsw changes with temperature for a long array and calculations of the corresponding escape rates. Our analysis of the problem is based on the existence of a voltage dependent energy barrier and we do not make any assumptions about its shape. The data divides up into two temperature regimes, the higher of which can be explained with Kramers thermal escape model. At low temperatures the escape becomes independent of temperature.Comment: 4 pages 5 figure

Palette-colouring: a belief-propagation approach

We consider a variation of the prototype combinatorial-optimisation problem known as graph-colouring. Our optimisation goal is to colour the vertices of a graph with a fixed number of colours, in a way to maximise the number of different colours present in the set of nearest neighbours of each given vertex. This problem, which we pictorially call "palette-colouring", has been recently addressed as a basic example of problem arising in the context of distributed data storage. Even though it has not been proved to be NP complete, random search algorithms find the problem hard to solve. Heuristics based on a naive belief propagation algorithm are observed to work quite well in certain conditions. In this paper, we build upon the mentioned result, working out the correct belief propagation algorithm, which needs to take into account the many-body nature of the constraints present in this problem. This method improves the naive belief propagation approach, at the cost of increased computational effort. We also investigate the emergence of a satisfiable to unsatisfiable "phase transition" as a function of the vertex mean degree, for different ensembles of sparse random graphs in the large size ("thermodynamic") limit.Comment: 22 pages, 7 figure

Voltage rectification by a SQUID ratchet

We argue that the phase across an asymmetric dc SQUID threaded by a magnetic flux can experience an effective ratchet (periodic and asymmetric) potential. Under an external ac current, a rocking ratchet mechanism operates whereby one sign of the time derivative of the phase is favored. We show that there exists a range of parameters in which a fixed sign (and, in a narrower range, even a fixed value) of the average voltage across the ring occurs, regardless of the sign of the external current dc component.Comment: 4 pages, 4 EPS figures, uses psfig.sty. Revised version, to appear in Physical Review Letters (26 August 1996

Metal-insulator Crossover Behavior at the Surface of NiS_2

We have performed a detailed high-resolution electron spectroscopic investigation of NiS$_2$ and related Se-substituted compounds NiS$_{2-x}$Se$_x$, which are known to be gapped insulators in the bulk at all temperatures. A large spectral weight at the Fermi energy of the room temperature spectrum, in conjunction with the extreme surface sensitivity of the experimental probe, however, suggests that the surface layer is metallic at 300 K. Interestingly, the evolution of the spectral function with decreasing temperature is characterized by a continuous depletion of the single-particle spectral weight at the Fermi energy and the development of a gap-like structure below a characteristic temperature, providing evidence for a metal-insulator crossover behavior at the surfaces of NiS$_2$ and of related compounds. These results provide a consistent description of the unusual transport properties observed in these systems.Comment: 12 pages, 3 figure

Superselectors: Efficient Constructions and Applications

We introduce a new combinatorial structure: the superselector. We show that superselectors subsume several important combinatorial structures used in the past few years to solve problems in group testing, compressed sensing, multi-channel conflict resolution and data security. We prove close upper and lower bounds on the size of superselectors and we provide efficient algorithms for their constructions. Albeit our bounds are very general, when they are instantiated on the combinatorial structures that are particular cases of superselectors (e.g., (p,k,n)-selectors, (d,\ell)-list-disjunct matrices, MUT_k(r)-families, FUT(k, a)-families, etc.) they match the best known bounds in terms of size of the structures (the relevant parameter in the applications). For appropriate values of parameters, our results also provide the first efficient deterministic algorithms for the construction of such structures

Untersuchung der Wurzel-Boden Grenzfläche im Unterboden mit Hilfe der Röntgenstrahl Computertomographie und Endoskopie

Transportprozesse von Luft, Wasser und gelösten Stoffen haben erheblichen Einfluss in Hinblick auf die Erzeugung von Kulturpflanzen. Diese Transportprozesse wiederum, stehen in Abhängigkeit zu der Struktur des Bodens. Besonders für den Unterboden stellen Bioporen eine Möglichkeit als Wurzel-Boden Grenzfläche dar, die erheblich durch die Aktivität von Flora und Fauna beeinflusst wird. Mit X-ray CT, Bildauswertung und Endoskopie wurden mit Regenwürmern besetzte Bodensäulen untersucht. Es wurde der Frage nachgegangen, welchen Einfluss die Aktivität von Wurzeln und Regenwürmern auf die Wurzel-Boden Grenzfläche hat und inwiefern Eigenschaften und Charakteristik von Bioporen verändert werden. Es hat sich gezeigt, dass die vorhandenen Strukturen eines etablierten Biopore-Netzwerkes in hohem Maße wiederverwendet und somit in ihrer Struktur verändert wurden

Determining intended evidence relations in natural language arguments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72555/1/j.1467-8640.1991.tb00386.x.pd

Appearance and Stability of Anomalously Fluctuating States in Shor's Factoring Algorithm

We analyze quantum computers which perform Shor's factoring algorithm, paying attention to asymptotic properties as the number L of qubits is increased. Using numerical simulations and a general theory of the stabilities of many-body quantum states, we show the following: Anomalously fluctuating states (AFSs), which have anomalously large fluctuations of additive operators, appear in various stages of the computation. For large L, they decohere at anomalously great rates by weak noises that simulate noises in real systems. Decoherence of some of the AFSs is fatal to the results of the computation, whereas decoherence of some of the other AFSs does not have strong influence on the results of the computation. When such a crucial AFS decoheres, the probability of getting the correct computational result is reduced approximately proportional to L^2. The reduction thus becomes anomalously large with increasing L, even when the coupling constant to the noise is rather small. Therefore, quantum computations should be improved in such a way that all AFSs appearing in the algorithms do not decohere at such great rates in the existing noises.Comment: 11 figures. A few discussions were added in verion 2. Version 3 is the SAME as version 2; only errors during the Web-upload were fixed. Version 4 is the publised version, in which several typos are fixed and the reference list is update