A RANDOM FUNCTIONAL CENTRAL LIMIT THEOREM FOR PROCESSES OF PRODUCT SUMS OF LINEAR PROCESSES GENERATED BY MARTINGALE DIFFERENCES

A random functional central limit theorem is obtained for processes of partial sums andproduct sums of linear processes generated by non-stationary martingale differences. It devel-ops and improves some corresponding results on processes of partial sums of linear processesgenerated by strictly stationary martingale differences, which can be found in [5].

Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

Nullors, and Nullor Circuits;There Applications in Symbolic Circuit Analysis and Design

The objective in this presentation is to introduce some of the unique properties and applications of nullors in active circuit analysis and designs. The emphasis is to discuss the role nullors can play in symbolic representation of transfer functions. To show this we adopt the topological platform for the circuit analysis and use a recently developed Admittance Method (AM) to achieve the Sum of Tree Products (STP), replacing the determinant and cofactors of the Nodal Admittance Matrix (NAM) of the circuit. To construct a transfer function, we start with a given active circuit and convert all its controlled sources and I/O-ports to nullors. Now, with a solid nullor circuit (passive elements and nullors) we first eliminate the passive elements through AM operations. This produces the STPs. Second, the all-nullor circuit is then used to find the signs or the STPs. Finally, the transfer function (in symbolic, if chosen) is obtained from the ratio between the STPs.

Parallel Computation of Disjoint Products Approach

In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.

A General Law of Precise Asymptotics for Products of Sums under Dependence

Let {Xn,n ≥ 1} be a strictly stationary LNQD （LPQD） sequence of positive random variables with EX1 = μ 〉 0, and VarX1 = σ^2 〈 ∞. Denote by Sn = ∑i=1^n Xi and γ = σ/μ the coefficients of variation. In this paper, under some suitable conditions, we show that a general law of precise asymptotics for products of sums holds. It can describe the relations among the boundary function, weighted function, convergence rate and limit value in the study of complete convergence.

An Improved Result in Almost Sure Central Limit Theory for Products of Partial Sums with Stable Distribution

Consider a sequence of i.i.d.positive random variables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (1,2].A universal result in the almost sure limit theorem for products of partial sums is established. Our results significantly generalize and improve those on the almost sure central limit theory previously obtained by Gonchigdanzan and Rempale and by Gonchigdanzan.In a sense,our results reach the optimal form.

Moderate deviations principle for products of sums of random variables

Let(Xn)n≥1 be a sequence of independent identically distributed(i.i.d.) positive random variables with EX1 = μ,Var(X1) = σ2.In the present paper,we establish the moderate deviations principle for the products of partial sums(πnk=1Sk/n!μn)1/(γbn√(2n))1where γ = σ/μ denotes the coefficient of variation and(bn) is the moderate deviations scale.

A CLASS OF LDPC CODE'S CONSTRUCTION BASED ON AN ITERATIVE RANDOM METHOD

This letter gives a random construction for Low Density Parity Check (LDPC) codes, which uses an iterative algorithm to avoid short cycles in the Tanner graph. The construction method has great flexible choice in LDPC code's parameters including codelength, code rate, the least girth of the graph, the weight of column and row in the parity check matrix. The method can be applied to the irregular LDPC codes and strict regular LDPC codes. Systemic codes have many applications in digital communication, so this letter proposes a construction of the generator matrix of systemic LDPC codes from the parity check matrix. Simulations show that the method performs well with iterative decoding.

Approximate Processing Element Design and Analysis for the Implementation of CNN Accelerators

As a primary computation unit,a processing element(PE)is key to the energy efficiency of a convolutional neural network(CNN)accelerator.Taking advantage of the inherent error tolerance of CNNs,approximate computing with high hardware efficiency has been considered for implementing the computation units of CNN accelerators.However,individual approximate designs such as multipliers and adders can only achieve limited accuracy and hardware improvements.In this paper,an approximate PE is dedicatedly devised for CNN accelerators by synergistically considering the data representation,multiplication and accumulation.An approximate data format is defined for the weights using stochastic rounding.This data format enables a simple implementation of multiplication by using small lookup tables,an adder and a shifter.Two approximate accumulators are further proposed for the product accumulation in the PE.Compared with the exact 8-bit fixed-point design,the proposed PE saves more than 29%and 20%in power-delay product for 3×3 and 5×5 sum of products,respectively.Also,compared with the PEs consisting of state-of-the-art approximate multipliers,the proposed design shows significantly smaller error bias with lower hardware overhead.Moreover,the application of the approximate PEs in CNN accelerators is analyzed by implementing a multi-task CNN for face detection and alignment.We conclude that 1)an approximate PE is more effective for face detection than for alignment,2)an approximate PE with high statistically-measured accuracy does not necessarily result in good quality in face detection,and 3)properly increasing the number of PEs in a CNN accelerator can improve its power and energy efficiency.

A Note on the ASCLT for Triangular Arrays of Random Variables with an Extension to U-statistics

In this paper, we obtain an almost sure central limit theorem for products of independent sums of positive random variables. An extension of the result gives an ASCLT for the U-statistics.

A New Improved Method for Symbolic Reliability Analysis

This paper describes a method for finding the terminal pair reliability expression of communication networks.This method incorporates bit manipulation and Boolean operations for generating the sum of disjointed products(SDP) expression in which each term has 1 to 1 correspondence with respective minimal path(or cut).This method is convenient and efficient. An example illustrates the method.

Exact Reliability Formulas for Linear Consecutive-k-out-of-n: F Systems

A consecutive k out of n: F System, with n linearly arranged i. i. d. components, is examined. This paper gives an exact formula for computing the system's reliability directly. Complexity of this algorithm is an O(n k). Further more, the system's reliability can be computed more quickly and more effectively from this formula than those previously given.