Quantum Measurement and the Aharonov-Bohm Effect with Superposed Magnetic Fluxes

We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized superposed currents in a superconducting ring and discuss broader implications.Comment: 6 pages, 4 figures; Changes from version 3: corrected typo (not present in versions 1 and 2) in Eq. 8; Changes from version 2: shortened abstract; added refs and material in Section IV. The final publication is available at: http://link.springer.com/article/10.1007/s11128-013-0652-

Oblivious tight compaction in O(n) time with smaller constant

Oblivious compaction is a crucial building block for hash-based oblivious RAM. Asharov et al. recently gave a O(n) algorithm for oblivious tight compaction. Their algorithm is deterministic and asymptotically optimal, but it is not practical to implement because the implied constant is $\gg 2^{38}$. We give a new algorithm for oblivious tight compaction that runs in time $< 16014.54n$. As part of our construction, we give a new result in the bootstrap percolation of random regular graphs

Outbreak of Infectious Diseases through the Weighted Random Connection Model

When modeling the spread of infectious diseases, it is important to incorporate risk behavior of individuals in a considered population. Not only risk behavior, but also the network structure created by the relationships among these individuals as well as the dynamical rules that convey the spread of the disease are the key elements in predicting and better understanding the spread. In this work we propose the weighted random connection model, where each individual of the population is characterized by two parameters: its position and risk behavior. A goal is to model the effect that the probability of transmissions among individuals increases in the individual risk factors, and decays in their Euclidean distance. Moreover, the model incorporates a combined risk behavior function for every pair of the individuals, through which the spread can be directly modeled or controlled. We derive conditions for the existence of an outbreak of infectious diseases in this model. Our main result is the almost sure existence of an infinite component in the weighted random connection model. We use results on the random connection model and site percolation in Z2

Isolation and Connectivity in Random Geometric Graphs with Self-similar Intensity Measures

Random geometric graphs consist of randomly distributed nodes (points), with pairs of nodes within a given mutual distance linked. In the usual model the distribution of nodes is uniform on a square, and in the limit of infinitely many nodes and shrinking linking range, the number of isolated nodes is Poisson distributed, and the probability of no isolated nodes is equal to the probability the whole graph is connected. Here we examine these properties for several self-similar node distributions, including smooth and fractal, uniform and nonuniform, and finitely ramified or otherwise. We show that nonuniformity can break the Poisson distribution property, but it strengthens the link between isolation and connectivity. It also stretches out the connectivity transition. Finite ramification is another mechanism for lack of connectivity. The same considerations apply to fractal distributions as smooth, with some technical differences in evaluation of the integrals and analytical arguments