Approximation of Sums of Locally Dependent Random Variables via Perturbation of Stein Operator

Let $(X_i, i\in J)$ be a family of locally dependent non-negative integer-valued random variables, and consider the sum $W=\sum_{i\in J}X_i$. We establish general error upper bounds for $d_{TV}(W, M)$ using the three-parametric perturbation form of Stein operator, where the target variable $M$ is either the mixture of Poisson distribution and binomial or negative binomial distribution, and the three parameters are delicately determined by guaranteeing $M$ and $W$ are identical in the first three factorial cumulants. As applications, we discuss in detail the classic local dependence structure examples like $(1, 1)$-runs, ($k_{1},k_{2}$)-runs and $k$-runs, and attain $O(|J|^{-1})$ error bounds under some special cases by exactly figuring out the smoothness of the conditional distributions of $W$ upon partial sums. The obtained result is to some extent a significant improvement of Pek\"{o}z [Bernoulli, 19 (2013)] and Upadhye, et al. [Bernoulli, 23 (2017)]

Tail Bounds on the Spectral Norm of Sub-Exponential Random Matrices

Let $X$ be an $n\times n$ symmetric random matrix with independent but non-identically distributed entries. The deviation inequalities of the spectral norm of $X$ with Gaussian entries have been obtained by using the standard concentration of Gaussian measure results. This paper establishes an upper tail bound of the spectral norm of $X$ with sub-Exponential entries. Our method relies upon a crucial ingredient of a novel chaining argument that essentially involves both the particular structure of the sets used for the chaining and the distribution of coordinates of a point on the unit sphere.Comment: 18page

Deviation Inequalities on the Spectral Norm of Products of Random and Deterministic Matrices

We study the spectral norm of matrices $BA$, where $A$ is a random matrix with independent mean zero subexponential entries, and $B$ is a fixed matrix. We show that the spectral norm of such an $m\times n$ matrix $BA$ exceeds $\sqrt{n}+\sqrt{m}$ with an exponential decay probability. Applying this result, we prove an estimate of the smallest singular value of a random subexponential matrix using an argument in the previous work of Rudelson and Vershynin.Comment: arXiv admin note: text overlap with arXiv:0812.2432, arXiv:0802.3956 by other author

A Modular Framework of Distributed Hydrological Modeling System: Hydroinformatic Modeling System, HIMS

Distributed hydrological models have been shown high light on because of the spatial variability of hydrological processes. On the other hand, the complexity of the hydrological processes, the multi-purposes of hydrological modeling and the availability of observed data have made it difficult to bring forward a hydrological model system for general use. It is always confused and time consumed to find a model of most fit to practical application because of the variety types of hydrological models. In this paper, the framework of a modular based distributed hydrological modeling system has been discussed. The system was so called Hydroinformatic Modeling System (HIMS), include hydroinformatic management system, data pre- and post-processing system, and hydrological model & function library. For the management and processing of spatial information, basic GIS functions have been integrated into system on the basis of SUPERMAP, which is component based GIS software. The hydrological function library (HFL), which represents different processes of hydrological cycle, was the core of the entire system. Distributed hydrological models of different scale were all established on the HFL. The HIMS has been applied to hydrological research in the Yellow River Basin and has reached to some success. However, since it is still in its trial version, much more work need to be done to improve it

A Monopole UWB Antenna for WIFI 7/Bluetooth and Satellite Communication

In this paper, a monopole UWB broadband antenna is designed, fabricated, and measured for wireless communication networks. The initial radiator model of the proposed antenna has a short-sleeve shape, and to expand the impedance bandwidth, the right and left angles are subtracted symmetrically from the lower half of the radiator. The impedance matching is improved by etching slots in the feed line and adding L-shaped patches symmetrically on both sides of the feed line. The results show that the proposed miniaturized antenna system can cover WiFi 7(2.4–2.484 GHz, 5.15–5.35 GHz, 5.725–5.825 GHz, 5.925–7.125 GHz), 4G LTE (2.3–2.39 GHz, 2.555–2.655 GHz), 5G (4.8–5.0 GHz), X-band (7–12.4 GHz), Ku-band (10.7–14.59 GHz), and C-band uplink bands (5.925–6.425 GHz). Moreover, the antenna is found to be omnidirectional at low frequencies, with a maximum peak gain of 5.43 dBi. The antenna can be used for multi-frequency wireless communication applications

Discretized Normal Approximation of Sums of Locally Dependent Random Variables via Stein's Method

Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectation and variance. We consider the sum $W=\sum_{i\in J}X_i$ and establish general error upper bounds for the total variation distance $d_{TV}(W, Y^{d})$, where $Y^{d}$ is the discretized normal distribution. The major ingredient of the proof is to approximate $W$ by a three-parametric intermediate random variable $M$ based on Stein's method. As applications, we study in detail four well-known examples, which are counting vertices of all edges point inward, birthday problem, counting monochromatic edges in uniformly colored graphs, and triangles in the Erd\H{o}s-R\'{e}nyi random graph. Through delicate analysis and computations we obtain sharper upper error bounds than existing results

Design of a Dual-Band WiFi Antenna Using the Theory of Characteristic Modes and Nested Chinese Characters

In this paper, a dual-band WiFi antenna and its Multiple Input Multiple Output (MIMO) system application is designed, fabricated, and measured based on the Chinese characters “Men” and “Wei”. The antenna uses a 40 × 40 × 1.6 mm3 FR4 substrate to analyze the combinatorial structure of Chinese characters using the theory of characteristic modes, to optimize the antenna dimensions by analyzing the mode current distribution, and to broaden the antenna bandwidth by etching rectangular slots on the ground. The measured and simulated results show that the four-element MIMO antenna covers 5.68–8.01 GHz, the isolation between the antennas is higher than 20 dB in the working band, the envelope correlation coefficient and the channel capacity losses of the simulation are lower than 0.001 and 0.18 bits/s/HZ, respectively. The efficiency of the antenna is higher than 90%, and it can be used for WiFi communication bands (5.8 GHz and 6 GHz)