Counting the number of social media posts on a target phenomenon has become a popular method to monitor a spatiotemporal signal. However, such counting is plagued by biased, missing, or scarce data. We address these issues by formulating signal recovery as a Poisson point process estimation problem. We explicitly incorporate human population bias, time delays and spatial distortions, and spatio...

In the measurement of the amplitude of vibration of objects, holographic imaging techniques usually involve fringe counting; because of the limited resolution of the images, measurements of large amplitudes are not accessible. We demonstrate a technique that suppresses the necessity of fringe counting--frequency sideband imaging--where the order of the sideband is considered a marker of the amp...

The large-Nc consistency conditions for axial vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of lowenergy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial vector and isovector magnetic coupling constants get corrections only at the order 1/N2 c follows from the Nc-counting...

low density polyethylene films incorporating different types of organically modified nanoclays were prepared. physical, surface morphology and mechanical properties of the films were analyzed by x-ray diffraction pattern, scanning electron microscopy and tensile strength (ts) and length increase until fracture point (e) parameters, respectively. colony counting method was used to investigate an...

Given a combinatorial decomposition for a counting problem, we resort to the simplescheme of approximating large numbers by floating-point representations in order to obtainefficient Fully Polynomial Time Approximation Schemes (FPTASes) for it. The numberof bits employed for the exponent and the mantissa will depend on the error parameter0 < ε ≤ 1 and on the characteristics ...

We derive a stochastic path integral representation of counting statistics in semiclassical systems. The formalism is introduced on the simple case of a single chaotic cavity with two quantum point contacts, and then further generalized to find the propagator for charge distributions with an arbitrary number of counting fields and generalized charges. The counting statistics is given by the sad...

We describe an algorithm, AGM-X0(N), for point counting on elliptic curves of small characteristic p using p-adic lifts of their invariants associated to modular curves X0(N). The algorithm generalizes the contruction of Satoh [10], SST [11], and Mestre [9]. We describe this method and give details of its implementation for characteristics 2, 3, 5, 7, and 13.

We discuss a method for computing ∑ p≤x 1/p, using time about x2/3 and space about x1/3. It is based on the Meissel-Lehmer algorithm for computing the prime-counting function π(x), which was adapted and improved by Lagarias, Miller, and Odlyzko. We used this algorithm to determine the first point at which the prime harmonic sum first crosses 4.

We report on our project to find explicit examples of K3 surfaces having real or complex multiplication. Our strategy is to search through the arithmetic consequences of RM and CM. In order to do this, an efficient method is needed for point counting on surfaces defined over finite fields. For this, we describe algorithms that are p-adic in nature.