We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussia...

We present new, deep, narrow- and broad-band Hubble Space Telescope observations of seven the most star-forming brightest cluster galaxies (BCGs). Continuum-subtracted [O II] maps reveal detailed, complex structure warm ($T \sim 10^4$ K) ionized gas filaments in these BCGs, allowing us to measure spatially-resolved star formation rates (SFRs) ~60-600 Msun/yr. compare SFRs systems others from li...

An asymptotic formula for the sum of reciprocals of π(n) is derived, where π(x) is the number of primes not exceeding x. This result improves the previous results of De Koninck-Ivi´c and L. Panaitopol. Let, as usual, π(x) = px 1 denote the number of primes not exceeding x. The prime number theorem (see e.g., [2, Chapter 12]) in its strongest known form states that (1) π(x) = li x + R(x), with (...

The ever-increasing demand for new energy sources witnessed at present is leading to a shortage of oil and gas resources throughout the world. At same time, polluting such as coal are being gradually replaced by gas, fuel types electricity produced renewable methods. Unconventional shale reserves, relying on presence substantial volumes good quality, thermally mature organic matter, therefore c...

Supporting data applications over networks comprising both wireless and wireline links is of increasing importance for both military and commercial systems. Many standard data applications on current wireline networks are based on TCP/IP, the end-to-end ow and congestion control protocol widely used on the Internet, so that it is of crucial importance to devise network level controls that enabl...

In this article, we study the problem of changes of sign of π(x)− li(x). We provide three improvements. First, we give better esimates of error term for Lehman’s theorem. Second, we rigorously prove the positivity of this difference for a region formerly conjectured by Patrick Demichel. Third, we improve the estimates for regions of positivity by using number theoretic results. 1. Previous work...

The CTMC log-likelihood component is in the curved exponential family, with natural parameters log(λij) and ∑ i 6=j λij corresponding to sufficient statistics nT (i, j) and dT (i). Individual level baseline covariates wh are added via log(λij) = β T ijw h, where h denotes the individual and wh and βij are p-dimensional vectors corresponding to p covariates. For convenience, we list the intensit...

, where C0 = ∫ 1 0 f(t)dt. j ∼ scale, k ∼ position. Key properties: 1. vanishing moments: We say ψ has M vanishing moments when ∫ 1 0 tψj,k(t)dt = 0 form = 0, 1, . . . ,M− 1 This means the wavelet is “blind” to polynomial segment with degree α ≤M − 1 2. compact support: a daubechies wavelet with M vanishing moments has support ∝ 2M. Together, these properties imply that only O(l log n) nonzero ...

We study the basic preferential attachment process, which generates a sequence of random trees, each obtained from the previous one by introducing a new vertex and joining it to one existing vertex, chosen with probability proportional to its degree. We investigate the number Dt(`) of vertices of each degree ` at each time t, focussing particularly on the case where ` is a growing function of t...

Let G = (V; E; w) be an undirected graph with positive edge lengths and S ⊂ V a set of k speci0ed sources. The k-source maximum eccentricity spanning tree is a spanning tree T minimizing the maximum distance from a source to a vertex, i.e., maxs∈S {maxv∈V{dT (s; v)}}, where dT (s; v) is the length of the path between s and v in T . In this paper, we propose an O(|V |2 log |V |+ |V | |E|) time a...