This paper introduces a simple and very general theory of compressive sensing. In this theory, the sensing mechanism simply selects sensing vectors independently at random from a probability distribution F ; it includes all models — e.g. Gaussian, frequency measurements — discussed in the literature, but also provides a framework for new measurement strategies as well. We prove that if the prob...

In order to check finite propagation speed Fermi, in 1932, had considered two atoms A and B separated by some distance R. At time t = 0, A is in an excited state, B in its ground state, and no photons are present. Fermi’s idea was to calculate the excitation probability of B. In a model-independent way and with minimal assumptions – Hilbert space and positive energy only – it is proved, not jus...

In analogy with NP, a language L is in the class NQP if the strings in L are exactly those accepted by a polynomial-time quantum machine with non-zero probability. Previously, Adleman, Demarrais and Huang showed that NQP PP. The sharper upper bound NQP coC=P is implicit in Adleman et al. and results of Fortnow and Rogers. Here we prove that in fact NQP and coC=P are the same class, by showing t...

We develop an empirical Bayesian thresholding rule for the normal mean problem that adapts well to the sparsity of the signal. An key element is the use of a mixture loss function that combines both the Lp loss and the 0 − 1 loss function. The Bayes procedures under this loss are explicitly given as thresholding rules and are easy to compute. The prior on each mean is a mixture of an atom of pr...

We studied the effect of low-pass band filters on the dynamics of a nonisothermal autocatalator as seen through feedback on a system parameter. Filters were created by selecting Fourier coefficients for the modes in the pass band according to a uniform distribution. Numerical simulations over many realizations of feedback were compared to theoretical predictions for the feedback size as a funct...

We study a model of a nonlinear oscillator with a random frequency and derive the asymptotic behavior of the probability distribution function when the noise is white. In the small damping limit, we show that the physical observables grow algebraically with time before the dissipative time scale is reached, and calculate the associated anomalous diffusion exponents. In the case of colored noise...

The concept of scale-free network has emerged as a powerful unifying paradigm in the study of complex systems in biology and in physical and social studies. Metabolic, protein, and gene interaction networks have been reported to exhibit scale-free behavior based on the analysis of the distribution of the number of connections of the network nodes. Here we study 10 published datasets of various ...

A calculational framework is proposed for phylogenetics, using nonlocal quantum field theories in hypercubic geometry. Quadratic terms in the Hamiltonian give the underlying Markov dynamics, while higher degree terms represent branching events. The spatial dimension L is the number of leaves of the evolutionary tree under consideration. Momentum conservation modulo Z ×L 2 in L ← 1 scattering co...

In [1] a model was introduced for the creation of a class of random networks with nonzero clustering. Within this model the degree distribution and clustering spectrum of a network are prescribed, and as such can be fitted to given real-world data. Here we present an analytical approach to site percolation in these networks. Theoretical predictions for the critical site occupation probability a...

Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node one can be calculated using the flat boundary theory of Schwartz and Weiss [Large Deviations Performance Analysis (1994), Chapman and Hall, New York]. Surprisingly, however, these calculations show that the proportion ...