Factorization of Width-two CSL Algebras and Nest Algebras

In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.

AN INFEASIBLE-INTERIOR-POINT PREDICTOR-CORRECTOR ALGORITHM FOR THE SECOND-ORDER CONE PROGRAM

A globally convergent infeasible-interior-point predictor-corrector algorithm is presented for the second-order cone programming （SOCP） by using the Alizadeh- Haeberly-Overton （AHO） search direction. This algorithm does not require the feasibility of the initial points and iteration points. Under suitable assumptions, it is shown that the algorithm can find an -approximate solution of an SOCP in at most O（√n ln（ε0/ε）） iterations. The iteration-complexity bound of our algorithm is almost the same as the best known bound of feasible interior point algorithms for the SOCP.

Bayesian network learning algorithm based on unconstrained optimization and ant colony optimization

Structure learning of Bayesian networks is a wellresearched but computationally hard task.For learning Bayesian networks,this paper proposes an improved algorithm based on unconstrained optimization and ant colony optimization（U-ACO-B） to solve the drawbacks of the ant colony optimization（ACO-B）.In this algorithm,firstly,an unconstrained optimization problem is solved to obtain an undirected skeleton,and then the ACO algorithm is used to orientate the edges,thus returning the final structure.In the experimental part of the paper,we compare the performance of the proposed algorithm with ACO-B algorithm.The experimental results show that our method is effective and greatly enhance convergence speed than ACO-B algorithm.

Fully Secure Identity-based Broadcast Encryption in the Subgroups

In this paper,we show how to use the dual techniques in the subgroups to give a secure identity-based broadcast encryption(IBBE) scheme with constant-size ciphertexts. Our scheme achieves the full security(adaptive security) under three static(i.e. non q-based) assumptions. It is worth noting that only recently Waters gives a short ciphertext broadcast encryption system that is even adaptively secure under the simple assumptions. One feature of our methodology is that it is relatively simple to leverage our techniques to get adaptive security.

Hooke and Jeeves algorithm for linear support vector machine

Coordinate descent method is a unconstrained optimization technique. When it is applied to support vector machine （SVM）, at each step the method updates one component of w by solving a one-variable sub-problem while fixing other components. All components of w update after one iteration. Then go to next iteration. Though the method converges and converges fast in the beginning, it converges slow for final convergence. To improve the speed of final convergence of coordinate descent method, Hooke and Jeeves algorithm which adds pattern search after every iteration in coordinate descent method was applied to SVM and a global Newton algorithm was used to solve one-variable subproblems. We proved the convergence of the algorithm. Experimental results show Hooke and Jeeves＇ method does accelerate convergence specially for final convergence and achieves higher testing accuracy more quickly in classification.

Graphical model construction based on evolutionary algorithms

Using Bayesian networks to model promising solutions from the current population of the evolutionary algorithms can ensure efficiency and intelligence search for the optimum. However, to construct a Bayesian network that fits a given dataset is a NP-hard problem, and it also needs consuming mass computational resources. This paper develops a methodology for constructing a graphical model based on Bayesian Dirichlet metric. Our approach is derived from a set of propositions and theorems by researching the local metric relationship of networks matching dataset. This paper presents the algorithm to construct a tree model from a set of potential solutions using above approach. This method is important not only for evolutionary algorithms based on graphical models, but also for machine learning and data mining. The experimental results show that the exact theoretical results and the approximations match very well.

Hypersphere support vector machines based on generalized multiplicative updates

This paper proposes a novel hypersphere support vector machines （HSVMs） based on generalized multiplicative updates. This algorithm can obtain the boundary of hypersphere containing one class of samples by the description of the training samples from one class and use this boundary to classify the test samples. The generalized multiplicative updates are applied to solving boundary optimization progranmning. Multiplicative updates available are suited for nonnegative quadratic convex programming. The generalized multiplicative updates are derived to box and sum constrained quadratic programming in this paper. They provide an extremely straightforward way to implement support vector machines （SVMs） where all variables are updated in parallel. The generalized multiplicative updates converge monotonically to the solution of the maximum margin hyperplane. The experiments show the superiority of our new algorithm.

New Constructions of Identity-Based Threshold Decryption

In this paper, based on the verifiable pair and identity-based threshold cryptography, a novel identity-based （ID-based） threshold decryption scheme （IDTDS） is proposed, which is provably secure against adaptive chosen cipbertext attack under the computational bilinear Diffie-Hellman （CBDH） problem assumption in the random oracle. The pubic cheekability of ciphertext in the IDTDS is given by simply creating a signed E1Gamal encryption instead of a noninteractive zero-knowledge proof. Furthermore, we introduce a modified verifiable pairing to ensure all decryption shares are consistent. Our scheme is more efficient in verification than the schemes considered previously.

Identity-based Broadcast Encryption with Shorter Transmissions

This paper describes two identity-based broadcast encryption （IBBE） schemes for mobile ad hoc networks. The first scheme proposed achieves sub-linear size cipertexts and the second scheme achieves O（1）- size ciphertexts. Furthermore, when the public keys are transmitted, the two schemes have short transmissions and achieve O（1） user storage cost, which are important for a mobile ad hoc network. Finally, the proposed schemes are provable security under the decision generalized bilinear Diffi-Hellman （GBDH） assumption in the random oracles model.

Nondifferentiable Multiobjective Programming under Generalized d-ρ-(η,θ)-Type I Univexity

In this puper, on the basis of notions of d-p-（η, θ）-invex function, type I function and univex function, we present new classes of generalized d-p-（η, θ）-type I univex functions. By using these new concepts, we obtain several sufficient optimality conditions for a feasible solution to be an efficient solution, and derive some Mond-Weir type duality results.