Regression Analysis of the Number of Association Rules

The typical model, which involves the measures： support, confidence, and interest, is often adapted to mining association rules. In the model, the related parameters are usually chosen by experience; consequently, the number of useful rules is hard to estimate. If the number is too large, we cannot effectively extract the meaningful rules. This paper analyzes the meanings of the parameters and designs a variety of equations between the number of rules and the parameters by using regression method. Finally, we experimentally obtain a preferable regression equation. This paper uses multiple correlation coeficients to test the fitting efiects of the equations and uses significance test to verify whether the coeficients of parameters are significantly zero or not. The regression equation that has a larger multiple correlation coeficient will be chosen as the optimally fitted equation. With the selected optimal equation, we can predict the number of rules under the given parameters and further optimize the choice of the three parameters and determine their ranges of values.

REAL-TIME ASSESSMENT OF MICROWAVE ABLATION EFFICACY BY NIR SPECTROSCOPIC TECHNIQUE

Microwave ablation(MWA)status monitoring in real time plays a key role in assessment of therapeutic fectiveness.As a novel realtime assessment method,near infrared spectroscopy(NIRs)was used to evaluate the ablation eficacy.MWA experiments were carried out on in vitroporcine livers.An optical measurement system for biological tissue is developed by our lab tomonitor reduced scattering coefficient(μ')at 690 nm of the coagulation zones.It is noted that p's of liver tissue,which increases as the liver tissue being ablated,is clearly related with the co-agulation status.μ's of normal tissue and coagulated tissue is 3-5 and 17-19 cm-1,respectively.Continuous changes ofμ's demonstrate that optical parameter can be used as an efficacy evaluation factor because it essentially indicates the degree of thermal damage.Compared withtemperat ure,optical parameter is more sensitive and accurate,which is promising for real-timetherapeutic eficacy assessment in MWA.

Markovian Quadratic BSDEs with an Unbounded Sub-quadratic Growth

This paper is devoted to the solvability of Markovian quadratic backward stochastic differential equations(BSDEs for short)with bounded terminal conditions.The generator is allowed to have an unbounded sub-quadratic growth in the second unknown variable z.The existence and uniqueness results are given to these BSDEs.As an application,an existence result is given to a system of coupled forward-backward stochastic differential equations with measurable coefficients.

Error estimate of the homogenization solution for elliptic problems with small periodic coefficients on L~∞(Ω)

In this paper,we discuss the multi-scale homogenization theory for the second order elliptic problems with small periodic coefficients of the form xi(aij(xε) uεx(jx)) = f(x).Assuming n = 2 and u0 ∈ W 1,∞(Ω),we present an error estimate between the homogenization solution u0(x) and the exact solution uε(x) on the Sobolev space L∞(Ω).

On an open problem of Sankaranarayanan

Let λ(n) be the n-th normalized Fourier coeficient of a holomorphic Hecke eigenform f(z) ∈ Sk(Γ) for the full modular group.In one of his papers,Sankaranarayanan mentioned that it is an open problem to give a non-trivial estimate for the sum of λ(n) over cubes,i.e.n x λ(n3).In this paper,we are able to use the analytic properties of symmetric power L-functions to solve his problem.More precisely,we prove that Σn≤zλ(n3)<< x(3/4 +ε),Σn≤zλ(n4)<< x(97+ε).

Some non-trivial Kazhdan-Lusztig coefficients of an affine Weyl group of type _n

In this paper we show that the leading coeficient μ(y,w) of some Kazhdan-Lusztig polynomials Py,w with y,w in an affine Weyl group of type n is n + 2.This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.