Neutral losses: A type of important variables in prediction of branching degree for acyclic alkenes from mass spectra

Neutral losses are a type of important variables in mass spectral interpretation. Since it is hard to calculate or extract neutral losses from mass spectra, they are usually discarded. In this study, dissimilarity analysis was employed to extract mass spectral characteristics for predicting branching degree of acyclic alkenes. The relationships between branching degree and neutral loss were constructed under direction of experimental observation and mass spectral fragmentations. A branching degree predictor of acyclic alkenes was subsequently built based on the above relationships. After tested by the experimental data in previous studies, the predictor could correctly provide the branching degree from abundant ions of mass spectra. More importantly, this predictor was able to point out which acyclic alkenes could be predicted correctly or not.     

Data Visualization With Multidimensional Scaling

We discuss methodology for multidimensional scaling (MDS) and its implementation in two software systems, GGvis and XGvis. MDS is a visualization technique for proximity data, that is, data in the form of N × N dissimilarity matrices. MDS constructs maps (“configurations,” “embeddings”) in IR^k by interpreting the dissimilarities as distances. Two frequent sources of dissimilarities are high-dimensional data and graphs. When the dissimilarities are distances between high-dimensional objects, MDS acts as a (often nonlinear) dimension-reduction technique. When the dissimilarities are shortest-path distances in a graph, MDS acts as a graph layout technique. MDS has found recent attention in machine learning motivated by image databases (“Isomap”). MDS is also of interest in view of the popularity of “kernelizing” approaches inspired by Support Vector Machines (SVMs; “kernel PCA”).

This article discusses the following general topics: (1) the stability and multiplicity of MDS solutions; (2) the analysis of structure within and between subsets of objects with missing value schemes in dissimilarity matrices; (3) gradient descent for optimizing general MDS loss functions (“Strain” and “Stress”); (4) a unification of classical (Strain-based) and distance (Stress-based) MDS.

Particular topics include the following: (1) blending of automatic optimization with interactive displacement of configuration points to assist in the search for global optima; (2) forming groups of objects with interactive brushing to create patterned missing values in MDS loss functions; (3) optimizing MDS loss functions for large numbers of objects relative to a small set of anchor points (“external unfolding”); and (4) a non-metric version of classical MDS.

We show applications to the mapping of computer usage data, to the dimension reduction of marketing segmentation data, to the layout of mathematical graphs and social networks, and finally to the spatial reconstruction of molecules.     

A perceptual space for underwater man-made sounds towards target classification

This work is the second part in a series of studies about the auditory features for underwater target classification, focusing on man-made vehicle targets (i.e. submarines, patrol boats and large surface ships). A psychoacoustic method, which is suitable for a small number of samples, was used. An optimal model with three common dimensions, specificities and latent classes was selected on the basis of the dissimilarity ratings among representative sounds and with the use of an extended version of the multidimensional scaling algorithm CLASCAL. However, such a three-dimensional space could not absolutely separate targets, whereas the first dimension in the four-dimensional space discriminated the submarines, patrol boats and ships; thus, the four-dimensional space was superior in target classification. The stepwise regression method was used to establish the relationships between individual dimensions and typical auditory features. Results showed that the first dimension was represented by the linear combination of zero-crossing rate and spectral variation, whereas the second dimension was described by attack slope. The last two dimensions were not associated with any features, and they were proved to include meaningless data noises. Finally, through a contrastive analysis, the perceptual space obtained in this study was found to be a good ‘local’ representation of the space in the first part of the study series.     

Embedding complex networks in a low dimensional Euclidean space based on vertex dissimilarities

We propose a method for representing vertices of a complex network as points in a Euclidean space of an appropriate dimension. To this end, we first adopt two widely used quantities as the measures for the dissimilarity between vertices. The dissimilarity is then transformed into its corresponding distance in a Euclidean space via the non-metric multidimensional scaling. We applied the proposed method to real-world as well as models of complex networks. We empirically found that real-world complex networks were embedded in a Euclidean space of relatively lower dimensions and the configuration of vertices in the space was mostly characterized by the self-similarity of a multifractal. In contrast, by applying the same scheme to the network models, we found that, in general, higher dimensions were needed to embed the networks into a Euclidean space and the embedding results usually did not exhibit the self-similar property. From the analysis, we learn that the proposed method serves a way not only to visualize the complex networks in a Euclidean space but to characterize the complex networks in a different manner from conventional ways.     

Distances in evidence theory: Comprehensive survey and generalizations

The purpose of the present work is to survey the dissimilarity measures defined so far in the mathematical framework of evidence theory, and to propose a classification of these measures based on their formal properties. This research is motivated by the fact that while dissimilarity measures have been widely studied and surveyed in the fields of probability theory and fuzzy set theory, no comprehensive survey is yet available for evidence theory. The main results presented herein include a synthesis of the properties of the measures defined so far in the scientific literature; the generalizations proposed naturally lead to additions to the body of the previously known measures, leading to the definition of numerous new measures. Building on this analysis, we have highlighted the fact that Dempster’s conflict cannot be considered as a genuine dissimilarity measure between two belief functions and have proposed an alternative based on a cosine function. Other original results include the justification of the use of two-dimensional indexes as (cosine; distance) couples and a general formulation for this class of new indexes. We base our exposition on a geometrical interpretation of evidence theory and show that most of the dissimilarity measures so far published are based on inner products, in some cases degenerated. Experimental results based on Monte Carlo simulations illustrate interesting relationships between existing measures.     

Macrocyclic‐ligand Induced Synthesis of Aryl Ethynides with Divergent Silver(I) Clusters

Two structurally characterized metal‐cluster‐centered supramolecular architectures named [Ag₈(1,2‐(C ≡ C)₂‐C₆H₄ )( Py[6] )(CF₃CO₂ )₆] · 2.5MeOH ( 1 ) and [Ag₁₂(1,2,4,5‐(C ≡ C)₄C₆H₂ )( Py[6] )₂(CF₃SO₃ )₈]·4MeOH ·3H₂O ( 2 ) are synthesized through the interaction with a bowl‐shaped macrocyclic ligand Py[6] . Particularly, two dissimilar silver(I) clusters are resulted in 2 within the structure under the influence of the macrocyclic ligand Py[6] . Such dissimilarity of the silver(I) cluster is also reflected on the structural and photophysical differences between 1 and 2 .     

Dissimilar chromatographic systems to indicate and identify antioxidants from Mallotus species

The genus of Mallotus contains several species commonly used as traditional medicines in oriental countries. A data set containing 39 Mallotus samples, differing in species, cultivation conditions, harvest season and/or part of the plant was used to develop fingerprints on two dissimilar chromatographic systems. An exploratory analysis with principal component analysis (PCA) was performed on both data sets individually. The results were also combined to obtain additional information on the unknown samples included in the data set. Furthermore, the antioxidant activity of the samples was measured and modelled as a function of the fingerprints using the orthogonal projections to latent structures (O-PLS) technique. The regression coefficients of the models were studied to indicate the peaks potentially responsible for the antioxidant activity. The indicated peaks were analyzed and identified by HPLC coupled to mass spectrometry (HPLC-MS). Because of the complexity of biological samples, it was aspired to separate co-eluting components based on the significant difference in chromatographic selectivity on the dissimilar systems and consequently obtain additional, complementary information on the contribution of the individual components to the antioxidant activity. The results illustrate the potential use of dissimilar chromatographic systems. Several initially co-eluting compounds could be separated on the dissimilar system. The corresponding regression coefficients provided complementary information on the potential antioxidant activity of the separated compounds.     

Dissimilarity analysis and automatic identification of monomethylalkanes from gas chromatography mass spectrometry data 1. Principle and protocols

Monomethylalkanes are common but important components in many naturally occurring and synthetic organic materials. Generally, this kind of compounds is routinely analyzed by gas chromatography mass spectrometry (GC–MS) and identified by the retention pattern or similarity matching to the reference mass spectral library. However, these identification approaches rely on the limited standard database or costly standard compounds. When unknown monomethylalkane is absent from the reference library, these approaches might be less useful. In this study, based on the fragmentation rules and empirical observation, many interesting mass spectral characteristics of monomethylalkanes were discovered and employed to infer the number of carbon atoms and methylated position. Combined with the retention pattern, a protocol was described for the identification of monomethylalkane analyzed by GC–MS. After tested by simulated data and GC–MS data of the gasoline sample, it was demonstrated that the developing approach could automatically and correctly identify monomethylalkanes in complicated GC–MS data.     

Fuzzy set approach to the utility,preference relations,and aggregation operators

Score x = (x₁, … , x_n) describing an alternative α is modelled by means of a continuous quasi-convex fuzzy quantity μ_α = μ_x, thus allowing to compare alternatives (scores) by means of fuzzy ordering (comparison) methods. Applying some defuzzification method leads to the introduction of operators acting on scores. A special stress is put on the Mean of Maxima defuzzification method allowing to introduce several averaging aggregation operators. Moreover, our approach allows to introduce weights into above mentioned aggregation, even in the non-anonymous (non-symmetric) case. Finally, Ordered Weighted Aggregation Operators (OWAO) are introduced, generalizing the standard OWA operators.