THE SOLUTION OF RANDOM EIGENVALUE PROBLEM WITH SMALL STOCHASTIC PROCESSES

This paper considers an eigenvalue problem containing small stochastic processes. For every fixed is, we can use the Prufer substitution to prove the existence of the random solutions lambda(n) and u(n) in the meaning of large probability. These solutions can be expanded in epsilon regularly, and their correction terms can be obtained by solving some random linear differential equations.

Generalized mixed equilibrium problem in Banach spaces

This paper uses a hybrid algorithm to find a common element of the set of solutions to a generalized mixed equilibrium problem, the set of solutions to variational inequality problems, and the set of common fixed points for a finite family of quasi-C- nonexpansive mappings in a uniformly smooth and strictly convex Banach space. As applications, we utilize our results to study the optimization problem. It shows that our results improve and extend the corresponding results announced by many others recently.

A DUAL COUPLED METHOD FOR BOUNDARY VALUE PROBLEMS OF PDE WITH COEFFICIENTS OF SMALL PERIOD

In this paper the homogenization method is improved to develop one kind of dual coupled approximate method, which reflects both the macro-scope properties of whole structure and its loadings, and micro-scope configuration properties of composite materials. The boundary value problem of woven membrane is considered, the dual asymptotic expression of the exact solution is given, and its approximation and error estimation are discussed. Finally the numerical example shows the effectiveness of this dual coupled method.

Avoiding Small Denominator Problems by Means of the Homotopy Analysis Method

The so-called“small denominator problem”was a fundamental problem of dynamics,as pointed out by Poincar´e.Small denominators appear most commonly in perturbative theory.The Duffing equation is the simplest example of a non-integrable system exhibiting all problems due to small denominators.In this paper,using the forced Duffing equation as an example,we illustrate that the famous“small denominator problems”never appear if a non-perturbative approach based on the homotopy analysis method(HAM),namely“the method of directly defining inverse mapping”(MDDiM),is used.The HAM-based MDDiM provides us great freedom to directly define the inverse operator of an undetermined linear operator so that all small denominators can be completely avoided and besides the convergent series of multiple limit-cycles of the forced Duffing equation with high nonlinearity are successfully obtained.So,from the viewpoint of the HAM,the famous“small denominator problems”are only artifacts of perturbation methods.Therefore,completely abandoning perturbation methods but using the HAM-based MDDiM,one would be never troubled by“small denominators”.The HAM-based MDDiM has general meanings in mathematics and thus can be used to attack many open problems related to the so-called“small denominators”.

A New Intramedulary Locking Plate for the Osteotomy of the V. Metatarsal in the Correction of the Tailors Bunion. Midterm Results of 21 Patients

Background: Since we are very successful in the operation of hallux valgus using a transverse sub-capital osteotomy fixated with an intramedullary angle-stable locking plate, and a tailors bunion is understood as a reversed hallux valgus, we have applied the operation also for such indication. Method: The osteotomy was carried out at a straight V. metatarsal subcapitally, and in case of an outwardly curved V. metatarsal at the bending location. The intramedullary plates are available in different designs and the plate and screws disappear completely in the bone, so the soft tissues are not disturbed. The head of the plate is either straight or curved in order to shift the distal fragment sufficiently. Results: 26 patients were operated within a period of 5 years (2008-2012). 21 patients were followed up after an average of 34.4 months. The IM angle IV/V could be improved by an average of 11.76 to an average of 4.10. This is a highliy significant pre- to postoperative difference of 7.66 (t = 15.07, p < 0.001). The AOFAS score was improved by an average of 42.24 points from 55.76 points preoperatively to 98.00 points postoperative. There was no pseudo-arthrosis and no wound healing impairment. All patients were either satisfied or very satisfied with the surgery. Conclusion: This method does not have the disadvantages of the other common operations of the Tailors bunion and is applied now as a standard method in this deformity.

A lattice-based signcryption scheme without random oracles

In order to achieve secure signcryption schemes in the quantum era, Li Fagen et al. [Concurrency and Computation： Practice and Experience, 2012, 25（4）： 2112-2122] and Wang Fenghe et al. [Applied Mathematics ＆ Information Sciences, 2012, 6（1）： 23-28] have independently extended the concept of signcryption to lattice-based cryptography. However, their schemes are only secure under the random or- acle model. In this paper, we present a lattice-based signcryp- tion scheme which is secure under the standard model. We prove that our scheme achieves indistinguishability against adaptive chosen-ciphertext attacks （IND-CCA2） under the learning with errors （LWE） assumption and existential unforgeability against adaptive chosen-message attacks （EUF- CMA） under the small integer solution （SIS） assumption.

Discovery of marageing steels: machine learning vs. physical metallurgical modelling

Physical metallurgical(PM)and data-driven approaches can be independently applied to alloy design.Steel technology is a field of physical metallurgy around which some of the most comprehensive understanding has been developed,with vast models on the relationship between composition,processing,microstructure and properties.They have been applied to the design of new steel alloys in the pursuit of grades of improved properties.With the advent of rapid computing and low-cost data storage,a wealth of data has become available to a suite of modelling techniques referred to as machine learning(ML).ML is being emergingly applied in materials discovery while it requires data mining with its adoption being limited by insufficient high-quality datasets,often leading to unrealistic materials design predictions outside the boundaries of the intended properties.It is therefore required to appraise the strength and weaknesses of PM and ML approach,to assess the real design power of each towards designing novel steel grades.This work incorporates models and datasets from well-established literature on marageing steels.Combining genetic algorithm(GA)with PM models to optimise the parameters adopted for each dataset to maximise the prediction accuracy of PM models,and the results were compared with ML models.The results indicate that PM approaches provide a clearer picture of the overall composition-microstructureproperties relationship but are highly sensitive to the alloy system and hence lack on exploration ability of new domains.ML conversely provides little explicit physical insight whilst yielding a stronger prediction accuracy for large-scale data.Hybrid PM/ML approaches provide solutions maximising accuracy,while leading to a clearer physical picture and the desired properties.

A generic high-throughput microstructure classification and quantification method for regular SEM images of complex steel microstructures combining EBSD labeling and deep learning

We present an electron backscattered diffraction(EBSD)-trained deep learning(DL)method integrating traditional material characterization informatics and artificial intelligence for a more accurate classification and quantification of complex microstructures using only regular scanning electron microscope(SEM)images.In this method,EBSD analysis is applied to produce accurate ground truth data for guiding the DL model training.An U-Net architecture is used to establish the correlation between SEM input images and EBSD ground truth data using only small experimental datasets.The proposed method is successfully applied to two engineering steels with complex microstructures,i.e.,a dual-phase(DP)steel and a quenching and partitioning(Q&P)steel,to segment different phases and quantify phase content and grain size.Alternatively,once properly trained the method can also produce quasi-EBSD maps by inputting regular SEM images.The good generality of the trained models is demonstrated by using DP and Q&P steels not associated with the model training.Finally,the method is applied to SEM images with various states,i.e.,different imaging modes,image qualities and magnifications,demonstrating its good robustness and strong application ability.Furthermore,the visualization of feature maps during the segmenting process is utilised to explain the mechanism of this method’s good performance.

Attribute-Based Signature on Lattices

Attribute-based signature is a versatile class of digital signatures. In attribute-based signature, a signer obtains his private key corresponding to the set of his attributes from a trusted authority, and then he can sign a message with any predicate that is satisfied by his attributes set. Unfortunately, there does not exist an attributebased signature which is resistance to the quantum attacks. This means we do not have secure attribute-based signature schemes in a post-quantum world. Based on this consideration, an attribute-based signature on lattices,which could resist quantum attacks, is proposed. This scheme employs "bonsai tree" techniques, and could be proved secure under the hardness assumption of small integer solution problem.

Improved authenticated key agreement protocol based on Bi-ISIS problem

In the post quantum era,public key cryptographic scheme based on lattice is considered to be the most promising cryptosystem that can resist quantum computer attacks.However,there are still few efficient key agreement protocols based on lattice up to now.To solve this issue,an improved key agreement protocol with post quantum security is proposed.Firstly,by analyzing the Wess-Zumino model+(WZM+)key agreement protocol based on small integer solution(SIS)hard problem,it is found that there are fatal defects in the protocol that cannot resist man-in-the-middle attack.Then based on the bilateral inhomogeneous small integer solution(Bi-ISIS)problem,a mutual authenticated key agreement(AKA)protocol with key confirmation is proposed and designed.Compared with Diffie-Hellman(DH)protocol,WZM+key agreement protocol,and the AKA agreement based on the ideal lattice protocol,the improved protocol satisfies the provable security under the extend Canetti-Krawczyk(eCK)model and can resist man-in-the-middle attack,replay attack and quantum computing attack.

Generating labeled samples for hyperspectral image classification using correlation of spectral bands

Because the labor needed to manually label a huge training sample set is usually not available, the problem of hyperspectral image classification often suffers from a lack of labeled training samples. At the same time, hyperspectral data represented in a large number of bands are usually highly correlated. In this paper, to overcome the small sample problem in hyperspectral image classification, correlation of spectral bands is fully utilized to generate multiple new sub-samples from each original sample. The number of labeled training samples is thus increased several times. Experiment results demonstrate that the proposed method has an obvious advantage when the number of labeled samples is small.

An Algorithm Substitution Attack on Fiat-Shamir Signatures Based on Lattice

Many evidences have showed that some intelligence agencies(often called big brother)attempt to monitor citizens’communication by providing coerced citizens a lot of subverted cryptographic algorithms and coercing them to adopt these algorithms.Since legalized services on large number of various applications and system architectures depend on digital signature techniques,in the context some coerced users who use double authentication preventing signatures to design some novel digital signature techniques,have some convincing dissertations to defuse requests from authorities and big brothers creating some corresponding subverted signatures.As rapid progress in quantum computers,National Security Agency advisory memorandum and announcement of National Institute of Standards and Technology procedures from standardization focus on some cryptographic algorithms which are post quantum secure.Motivated by these issues,we design an algorithm substitution attack against Fiat-Shamir family based on lattices(e.g.,BLISS,BG,Ring-TESLA,PASSSign and GLP)that are proven post-quantum computational secure.We also show an efficient deterable way to eliminate big brother’s threat by leaking signing keys from signatures on two messages to be public.Security proof shows that our schemes satisfy key extraction,undetectability and deterability.Through parameters analysis and performance evaluation,we demonstrate that our deterring subverted Fiat-Shamir signature is practical,which means that it can be applied to privacy and protection in some system architectures.