The Riemann zeta function is a meromorphic functionon the whole complex plane. It has infinitely many zeros and aunique pole at s = 1. Those zeros at s = −2,−4,−6, . . . areknown as trivial zeros. The Riemann hypothesis, conjectured byBernhard Riemann in 1859, claims that all non-trivial zeros of ζ(s)lie on the line R(s) =12 . The density hypothesis is a conjecturede...

The estimation of probability densities from data is widely used as an intermediate step in the estimation of entropy, Kullback-Leibler (KL) divergence, and mutual information, and for statistical tasks such as hypothesis testing. We propose an alternative to density estimation– partitioning a space into regions whose approximate probability mass is known–that can be used for the same purposes....

More measurements are generated by the target per observation interval, when the target is detected by a high resolution sensor, or there are more measurement sources on the target surface. Such a target is referred to as an extended target. The probability hypothesis density filter is considered an efficient method for tracking multiple extended targets. However, the crucial problem of how to ...

If equipped with several radar emitters, a target will produce more than one measurement per time step and is denoted as an extended target. However, due to the requirement of all possible measurement set partitions, the exact probability hypothesis density filter for extended target tracking is computationally intractable. To reduce the computational burden, a fast partitioning algorithm based...

We continue to explore the hypothesis that neuronal populations represent and process analog variables in terms of probability density functions (PDFs). A neural assembly encoding the joint probability density over relevant analog variables can in principle answer any meaningful question about these variables by implementing the Bayesian rules of inference. Aided by an intermediate representati...