Testing Algorithms for Identifying Source Confusion in the H i-MaNGA Survey

Astronomical observations of neutral atomic hydrogen (H i) are an important tracer of several key processes of galaxy evolution, but face significant difficulties with terrestrial telescopes. Among these is source confusion, or the inability to distinguish between emission from multiple nearby sources separated by distances smaller than the telescope’s spatial resolution. Confusion can compromise the data for the primary target if the flux from the secondary galaxy is sufficient. This paper presents an assessment of the confusion-flagging methods of the H i-MaNGA survey, using higher-resolution H i data from the Westorbork Synthesis Radio Telescope-Apertif survey. We find that removing potentially confused observations using a confusion probability metric—calculated from the relationship between galaxy color, surface brightness, and H i content—successfully eliminates all significantly confused observations in our sample, although roughly half of the eliminated observations are not significantly confused.

Asymptotic behaviors with convergence rates of distributions of negative-binomial sums

The negative-binomial sum is an extension of a geometric sum. It has been arisen from the necessity to resolve practical problems in telecommunications, network analysis, stochastic finance and insurance mathematics, etc. Up to the present, the topics related to negative-binomial sums like asymptotic distributions and rates of convergence have been investigated by many mathematicians. However, in a lot of various situations, the results concerned the rates of convergence for negative-binomial sums are still restrictive. The main purpose of this paper is to establish some weak limit theorems for negative-binomial sums of independent, identically distributed (i.i.d.) random variables via Gnedenko's Transfer Theorem originated by Gnedenko and Fahim (1969). Using Zolotarev's probability metric, the rate of convergence in weak limit theorems for negativebinomial sum are established. The received results are the rates of convergence in weak limit theorem for partial sum of i.i.d random variables related to symmetric stable distribution (Theorem 1), and asymptotic distribution together with the convergence rates for negative-binomial sums of i.i.d. random variables concerning to symmetric Linnik laws and Generalized Linnik distribution (Theorem 2 and Theorem 3). Based on the results of this paper, the analogous results for geometric sums of i.i.d. random variables will be concluded as direct consequences. However, the article has just been solved for the case of 1 <a < 2; it is quite hard to estimate in the case of a 2 (0;1) via the Zolotarev's probability metric. Mathematics Subject Classification 2010: 60G50; 60F05; 60E07.

Explaining Scales and Statistics of Tropical Precipitation Clusters with a Stochastic Model

Precipitation clusters are contiguous raining regions characterized by a precipitation threshold, size, and the total rainfall contained within—termed the cluster power. Tropical observations suggest that the probability distributions of both cluster size and power contain a power-law range (with slope ~ −1.5) bounded by a large-event “cutoff.” Events with values beyond the cutoff signify large, powerful clusters and represent extreme events. A two-dimensional stochastic model is introduced to reproduce the observed cluster distributions, including the slope and the cutoff. The model is equipped with coupled moisture and weak temperature gradient (WTG) energy equations, empirically motivated precipitation parameterization, temporally persistent noise, and lateral mixing processes, all of which collectively shape the model cluster distributions. Moisture–radiative feedbacks aid clustering, but excessively strong feedbacks push the model into a self-aggregating regime. The power-law slope is stable in a realistic parameter range. The cutoff is sensitive to multiple model parameters including the stochastic forcing amplitude, the threshold moisture value that triggers precipitation, and the lateral mixing efficiency. Among the candidates for simple analogs of precipitation clustering, percolation models are ruled out as unsatisfactory, but the stochastic branching process proves useful in formulating a neighbor probability metric. This metric measures the average number of nearest neighbors that a precipitating entity can spawn per time interval and captures the cutoff parameter sensitivity for both cluster size and power. The results here suggest that the clustering tendency and the horizontal scale limiting large tropical precipitating systems arise from aggregate effects of multiple moist processes, which are encapsulated in the neighbor probability metric.

Mining the Key Nodes from Software Network Based on Fault Accumulation and Propagation

The increasement of software complexity directly results in the augment of software fault and costs a lot in the process of software development and maintenance. The complex network model is used to study the accumulation and accumulation of faults in complex software as a whole. Then key nodes with high fault probability and powerful fault propagation capability can be found, and the faults can be discovered as soon as possible and the severity of the damage to the system can be reduced effectively. In this paper, the algorithm MFS_AN (mining fault severity of all nodes) is proposed to mine the key nodes from software network. A weighted software network model is built by using functions as nodes, call relationships as edges, and call times as weight. Exploiting recursive method, a fault probability metric FP of a function, is defined according to the fault accumulation characteristic, and a fault propagation capability metric FPC of a function is proposed according to the fault propagation characteristic. Based on the FP and FPC, the fault severity metric FS is put forward to obtain the function nodes with larger fault severity in software network. Experimental results on two real software networks show that the algorithm MFS_AN can discover the key function nodes correctly and effectively.

On the rates of convergence to symmetric stable laws for distributions of normalized geometric random sums

Let X1,X2,... be a sequence of independent, identically distributed random variables. Let ?p be a geometric random variable with parameter p?(0,1), independent of all Xj, j ? 1: Assume that ? : N ? R+ is a positive normalized function such that ?(n) = o(1) when n ? +?. The paper deals with the rate of convergence for distributions of randomly normalized geometric random sums ?(?p) ??p,j=1 Xj to symmetric stable laws in term of Zolotarev?s probability metric.