Constructive Membership Predicates as Index Types

In the constructive setting, membership predicates over recursive types are inhabited by terms indexing the elements that satisfy the criteria for membership. In this paper, we motivate and explore this idea in the concrete setting of lists and trees. We show that the inhabitants of membership predicates are precisely the inhabitants of a generic shape type. We show that membership of x (of type T) in structure S, (x_TS) can not, in general, index all parts of a structure S and we generalize to a form ρS where ρ is a predicate over S. Under this scheme, (λx.True)S is the set of all indexes into S, but we show that not all subsets of indexes are expressible by strictly local predicates. Accordingly, we extend our membership predicates to predicates that retain state “from above” as well as allow “looking below”. Predicates of this form are complete in the sense that they can express every subset of indexes in S. These ideas are motivated by experience programming in Nuprl's constructive type theory and examining the constructive content of mechanically checked formal proofs involving membership predicates.     

Obituary

RILEM Bulletin

Obituary     

Inverse random under sampling for class imbalance problem and its application to multi-label classification

In this paper, a novel inverse random under sampling (IRUS) method is proposed for the class imbalance problem. The main idea is to severely under sample the majority class thus creating a large number of distinct training sets. For each training set we then find a decision boundary which separates the minority class from the majority class. By combining the multiple designs through fusion, we construct a composite boundary between the majority class and the minority class. The proposed methodology is applied on 22 UCI data sets and experimental results indicate a significant increase in performance when compared with many existing class-imbalance learning methods. We also present promising results for multi-label classification, a challenging research problem in many modern applications such as music, text and image categorization.     

Consensus in the presence of mortal Byzantine faulty processes

We consider the problem of reaching agreement in distributed systems in which some processes may deviate from their prescribed behavior before they eventually crash. We call this failure model “mortal Byzantine”. After discussing some application examples where this model is justified, we provide matching upper and lower bounds on the number of faulty processes, and on the required number of rounds in synchronous systems. We then continue our study by varying different system parameters. On the one hand, we consider the failure model under weaker timing assumptions, namely for partially synchronous systems and asynchronous systems with unreliable failure detectors. On the other hand, we vary the failure model in that we limit the occurrences of faulty steps that actually lead to a crash in synchronous systems.     

MPTP 0.1 - System Description

MPTP (Mizar Problems for Theorem Proving) is a system for translating the Mizar Mathematical Library (MML) into untyped first order format suitable for automated theorem provers, allowing generating theorem proving problems corresponding to MML. The first version generates about 30000 problems from complete proofs of Mizar theorems, and about 630000 problems from the simple (one-step) justifications done by the Mizar checker. We describe the design and structure of the system, some limitations, and planned future extensions.     

General view on current conveyors

We propose a new current conveyor terminology and explain how these terms are coined. Copyright © 2004 John Wiley & Sons, Ltd.     

统计不相关最佳鉴别矢量集的本质研究

对统计不相关最佳鉴别矢量集的本质进行研究，在基于总体散布矩阵特征分解的基础上，构造了一种白化变换，使得变换后的样本空间中的总体散布矩阵为单位矩阵，这样使得传统的最佳鉴别矢量集算法得到的均是具有统计不相关的最佳鉴别矢量集，从而揭示了统计不相关最佳鉴别变换的本质——白化变换加普通的线性鉴别变换。该方法的最大优点在于所获得的最优鉴别矢量同时具有正交性和统计不相关性。该方法对代数特征抽取具有普遍适用性。用ORL人脸数据库的数值实验，验证了该方法的有效性。     

Chemistry towards Biology—Instruct: Snapshot

The knowledge of interactions between different molecules is undoubtedly the driving force of all contemporary biomedical and biological sciences. Chemical biology/biological chemistry has become an important multidisciplinary bridge connecting the perspectives of chemistry and biology to the study of small molecules/peptidomimetics and their interactions in biological systems. Advances in structural biology research, in particular linking atomic structure to molecular properties and cellular context, are essential for the sophisticated design of new medicines that exhibit a high degree of druggability and very importantly, druglikeness. The authors of this contribution are outstanding scientists in the field who provided a brief overview of their work, which is arranged from in silico investigation through the characterization of interactions of compounds with biomolecules to bioactive materials.     

A comparative study of the purification of betanin

Betanin is a natural pigment with antioxidant properties used as a food colourant. This work describes the spectrophotometric and chromatographic quantification of betanin (2S/15S) and its epimer isobetanin (2S/15R) in fresh beetroot juice, food-grade beetroot powder and betanin standard diluted in dextrin. Absorption spectra of all three samples were deconvoluted using a mixed three-function model. Food-grade beetroot powder has the largest amount of violet-red impurities, probably formed during processing. The purification of betanin from these complex matrices was carried out by seven different methods. Ion exchange chromatography was the most efficient method for the purification of betanin from all samples; however, fractions contain high amounts of salt. Reversed-phase HPLC as well as reversed-phase column chromatography also produced good results at a much faster rate. The longer retention time of isobetanin when compared to betanin in reversed-phase conditions has been investigated by means of quantum-mechanical methods.