Code2vect: An efficient heterogenous data classifier and nonlinear regression technique

The aim of this paper is to present a new classification and regression algorithm based on Artificial Intelligence. The main feature of this algorithm, which will be called Code2Vect, is the nature of the data to treat: qualitative or quantitative and continuous or discrete. Contrary to other artificial intelligence techniques based on the “Big-Data,” this new approach will enable working with a reduced amount of data, within the so-called “Smart Data” paradigm. Moreover, the main purpose of this algorithm is to enable the representation of high-dimensional data and more specifically grouping and visualizing this data according to a given target. For that purpose, the data will be projected into a vectorial space equipped with an appropriate metric, able to group data according to their affinity (with respect to a given output of interest). Furthermore, another application of this algorithm lies on its prediction capability. As it occurs with most common data-mining techniques such as regression trees, by giving an input the output will be inferred, in this case considering the nature of the data formerly described. In order to illustrate its potentialities, two different applications will be addressed, one concerning the representation of high-dimensional and categorical data and another featuring the prediction capabilities of the algorithm.     

Reduction of fourth order ordinary differential equations to second and third order Lie linearizable forms

Meleshko presented a new method for reducing third order autonomous ordinary differential equations (ODEs) to Lie linearizable second order ODEs. We extended his work by reducing fourth order autonomous ODEs to second and third order linearizable ODEs and then applying the Ibragimov and Meleshko linearization test for the obtained ODEs. The application of the algorithm to several ODEs is also presented.     

On classification of four-dimensional nilpotent Leibniz algebras

Leibniz algebras are certain generalization of Lie algebras. In this paper, we give the classification of four-dimensional non-Lie nilpotent Leibniz algebras. We use the canonical forms for the congruence classes of matrices of bilinear forms and some other techniques to obtain our result.     

Identification of key classification features of early cervical squamous cell carcinoma

Despite the tremendous progress in molecular analysis of pan-cancer, little is known regarding molecular classification of cervical squamous cell carcinoma. In this study, we adopted a multi-omics approach to identify potential key classification features of cervical squamous cell carcinoma. Specifically, we analyzed mRNA, and microRNA (miRNA) expression data, as well as DNA methylation and copy number variation in cervical squamous cell carcinoma cases, using datasets obtained from The Cancer Genome Atlas (TCGA). Moreover, we identified molecules in each dimension, as well as integrated and clustered filtered classification features, and used them to distinguish different subtypes. The resulting key classification features were used to establish a classification model for cervical squamous cell carcinoma. Our results revealed two cervical squamous cell carcinoma subtypes, with significant differences across clinical survival levels, as well as 8 key classification features of cervical squamous cell carcinomas. These findings are expected to provide important references for early classification of cervical squamous cell carcinoma and identification of classification markers.     

Data fusion methodologies for food and beverage authentication and quality assessment – A review

The ever increasing interest of consumers for safety, authenticity and quality of food commodities has driven the attention towards the analytical techniques used for analyzing these commodities. In recent years, rapid and reliable sensor, spectroscopic and chromatographic techniques have emerged that, together with multivariate and multiway chemometrics, have improved the whole control process by reducing the time of analysis and providing more informative results. In this progression of more and better information, the combination (fusion) of outputs of different instrumental techniques has emerged as a means for increasing the reliability of classification or prediction of foodstuff specifications as compared to using a single analytical technique. Although promising results have been obtained in food and beverage authentication and quality assessment, the combination of data from several techniques is not straightforward and represents an important challenge for chemometricians. This review provides a general overview of data fusion strategies that have been used in the field of food and beverage authentication and quality assessment.     

On Dual Configurational Forces

The dual conservation laws of elasticity are systematically re-examined by using both Noether's variational approach and Coleman–Noll–Gurtin's thermodynamics approach. These dual conservation laws can be interpreted as the dual configurational force, and therefore they provide the dual energy–momentum tensor. Some previously unknown and yet interesting results in elasticity theory have been discovered. As an example, we note the following duality condition between the configuration force (energy–momentum tensor) and the dual configuration force (dual energy–momentum tensor) ,

The Order of Automorphisms of Quasigroups

We prove quadratic upper bounds on the order of any autotopism of a quasigroup or Latin square, and hence also on the order of any automorphism of a Steiner triple system or 1‐factorization of a complete graph. A corollary is that a permutation σ chosen uniformly at random from the symmetric group will almost surely not be an automorphism of a Steiner triple system of order n, a quasigroup of order n or a 1‐factorization of the complete graph . Nor will σ be one component of an autotopism for any Latin square of order n. For groups of order n it is known that automorphisms must have order less than n, but we show that quasigroups of order n can have automorphisms of order greater than n. The smallest such quasigroup has order 7034. We also show that quasigroups of prime order can possess autotopisms that consist of three permutations with different cycle structures. Our results answer three questions originally posed by D.  Stones.     

Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.     

论滑坡分类

在广泛查阅和总结国内外滑坡分类基础上 ,以滑坡监测预报与防治为目的 ,遵从滑坡活动各要素的地位与作用 ,根据分类体系的完备性需要 ,理清了已有各种滑坡分类的性质及其彼此间的关系 ,并对之进行了科学归纳、取舍和补充 ,建立了具有层次系统性的综合性滑坡分类体系。为建立滑坡监测预报地质模型体系奠定了基础 ,并有助于对滑坡活动的全面研究。