A Class of Feature Spaces and Violation of the Triangle Inequality

A class of feature spaces that can violate the triangle inequality is proposed. The theory states that arbitrary N samples, in which all the distances between any pair of samples are given but their coordinates are unknown,can always assign the coordinates in the defined feature space after eigenvalue decomposition

POWER-LAW DISTRIBUTION OF RATE-OF-RETURN DEVIATION AND EVALUATION OF CASH FLOW IN A CONTROL EQUIPMENT MANUFACTURING COMPANY

Although it is well known that power-law distribution appears in stock price fluctuation models and the like and theoretical analytic methods by mathematical finance has made progress, there are not many examples where such theoretical analysis has been performed for manufacturing industries. Therefore, we collected data about a rate of return and its deviation in a certain control equipment manufacturing company for about 10 years, and analyzed the both by applying methods of mathematical finance. Regarding rate-of-return deviation, it was found that it conforms to log-normal distribution. From analysis of mathematical models about rate-of-return deviation, we obtained the following conclusion. If an amount of money of order entries and an amount of money of production are stochastic, accumulated excessive order entries become of Brownian motion, and thus a random "fluctuation" occurs in hour to hour order entries and production even though it might be of a small degree. In comparison with a case where production is made to conform to the average order entry, pro t can be increased in a case where strategy to purposefully lead to excessive production or excessive order entries state is adopted. Regarding rate of return, analysis of characteristics of power-law distribution was made. As a result of analysis of mathematical models for a rate of return, the followings are reported. A cash ow of a target company is log-normally distributed. With regard to equipment manufacturing, whether a value after a repayment of a loan is changed or not in the case where a guaranty by a company president is required is reported. In addition, how a value of manufacturing equipment (remaining value) changes after a repayment of a loan relative to a repayment period is reported. Finally, a degree (sensitivity) of influence of parameters, an initial plan money amount, a repaid money amount and a repayment period, on a remaining value and a result of risk analysis is also reported

ECOMICS: A Web-Based Toolkit for Investigating the Biomolecular Web in Ecosystems Using a Trans-omics Approach

Ecosystems can be conceptually thought of as interconnected environmental and metabolic systems, in which small molecules to macro-molecules interact through diverse networks. State-of-the-art technologies in post-genomic science offer ways to inspect and analyze this biomolecular web using omics-based approaches. Exploring useful genes and enzymes, as well as biomass resources responsible for anabolism and catabolism within ecosystems will contribute to a better understanding of environmental functions and their application to biotechnology. Here we present ECOMICS, a suite of web-based tools for ECosystem trans-OMICS investigation that target metagenomic, metatranscriptomic, and meta-metabolomic systems, including biomacromolecular mixtures derived from biomass. ECOMICS is made of four integrated webtools. E-class allows for the sequence-based taxonomic classification of eukaryotic and prokaryotic ribosomal data and the functional classification of selected enzymes. FT2B allows for the digital processing of NMR spectra for downstream metabolic or chemical phenotyping. Bm-Char allows for statistical assignment of specific compounds found in lignocellulose-based biomass, and HetMap is a data matrix generator and correlation calculator that can be applied to trans-omics datasets as analyzed by these and other web tools. This web suite is unique in that it allows for the monitoring of biomass metabolism in a particular environment, i.e., from macromolecular complexes (FT2DB and Bm-Char) to microbial composition and degradation (E-class), and makes possible the understanding of relationships between molecular and microbial elements (HetMap). This website is available to the public domain at: https://database.riken.jp/ecomics/

Evaluation and Characterization of Bacterial Metabolic Dynamics with a Novel Profiling Technique, Real-Time Metabolotyping

BACKGROUND: Environmental processes in ecosystems are dynamically altered by several metabolic responses in microorganisms, including intracellular sensing and pumping, battle for survival, and supply of or competition for nutrients. Notably, intestinal bacteria maintain homeostatic balance in mammals via multiple dynamic biochemical reactions to produce several metabolites from undigested food, and those metabolites exert various effects on mammalian cells in a time-dependent manner. We have established a method for the analysis of bacterial metabolic dynamics in real time and used it in combination with statistical NMR procedures. METHODOLOGY/PRINCIPAL FINDINGS: We developed a novel method called real-time metabolotyping (RT-MT), which performs sequential (1)H-NMR profiling and two-dimensional (2D) (1)H, (13)C-HSQC (heteronuclear single quantum coherence) profiling during bacterial growth in an NMR tube. The profiles were evaluated with such statistical methods as Z-score analysis, principal components analysis, and time series of statistical TOtal Correlation SpectroScopY (TOCSY). In addition, using 2D (1)H, (13)C-HSQC with the stable isotope labeling technique, we observed the metabolic kinetics of specific biochemical reactions based on time-dependent 2D kinetic profiles. Using these methods, we clarified the pathway for linolenic acid hydrogenation by a gastrointestinal bacterium, Butyrivibrio fibrisolvens. We identified trans11, cis13 conjugated linoleic acid as the intermediate of linolenic acid hydrogenation by B. fibrisolvens, based on the results of (13)C-labeling RT-MT experiments. In addition, we showed that the biohydrogenation of polyunsaturated fatty acids serves as a defense mechanism against their toxic effects. CONCLUSIONS: RT-MT is useful for the characterization of beneficial bacterium that shows potential for use as probiotic by producing bioactive compounds

Systematic NMR Analysis of Stable Isotope Labeled Metabolite Mixtures in Plant and Animal Systems: Coarse Grained Views of Metabolic Pathways

BACKGROUND: Metabolic phenotyping has become an important 'bird's-eye-view' technology which can be applied to higher organisms, such as model plant and animal systems in the post-genomics and proteomics era. Although genotyping technology has expanded greatly over the past decade, metabolic phenotyping has languished due to the difficulty of 'top-down' chemical analyses. Here, we describe a systematic NMR methodology for stable isotope-labeling and analysis of metabolite mixtures in plant and animal systems. METHODOLOGY/PRINCIPAL FINDINGS: The analysis method includes a stable isotope labeling technique for use in living organisms; a systematic method for simultaneously identifying a large number of metabolites by using a newly developed HSQC-based metabolite chemical shift database combined with heteronuclear multidimensional NMR spectroscopy; Principal Components Analysis; and a visualization method using a coarse-grained overview of the metabolic system. The database contains more than 1000 (1)H and (13)C chemical shifts corresponding to 142 metabolites measured under identical physicochemical conditions. Using the stable isotope labeling technique in Arabidopsis T87 cultured cells and Bombyx mori, we systematically detected >450 HSQC peaks in each (13)C-HSQC spectrum derived from model plant, Arabidopsis T87 cultured cells and the invertebrate animal model Bombyx mori. Furthermore, for the first time, efficient (13)C labeling has allowed reliable signal assignment using analytical separation techniques such as 3D HCCH-COSY spectra in higher organism extracts. CONCLUSIONS/SIGNIFICANCE: Overall physiological changes could be detected and categorized in relation to a critical developmental phase change in B. mori by coarse-grained representations in which the organization of metabolic pathways related to a specific developmental phase was visualized on the basis of constituent changes of 56 identified metabolites. Based on the observed intensities of (13)C atoms of given metabolites on development-dependent changes in the 56 identified (13)C-HSQC signals, we have determined the changes in metabolic networks that are associated with energy and nitrogen metabolism

FoodPro: A Web-Based Tool for Evaluating Covariance and Correlation NMR Spectra Associated with Food Processes

Foods from agriculture and fishery products are processed using various technologies. Molecular mixture analysis during food processing has the potential to help us understand the molecular mechanisms involved, thus enabling better cooking of the analyzed foods. To date, there has been no web-based tool focusing on accumulating Nuclear Magnetic Resonance (NMR) spectra from various types of food processing. Therefore, we have developed a novel web-based tool, FoodPro, that includes a food NMR spectrum database and computes covariance and correlation spectra to tasting and hardness. As a result, FoodPro has accumulated 236 aqueous (extracted in D2O) and 131 hydrophobic (extracted in CDCl3) experimental bench-top 60-MHz NMR spectra, 1753 tastings scored by volunteers, and 139 hardness measurements recorded by a penetrometer, all placed into a core database. The database content was roughly classified into fish and vegetable groups from the viewpoint of different spectrum patterns. FoodPro can query a user food NMR spectrum, search similar NMR spectra with a specified similarity threshold, and then compute estimated tasting and hardness, covariance, and correlation spectra to tasting and hardness. Querying fish spectra exemplified specific covariance spectra to tasting and hardness, giving positive covariance for tasting at 1.31 ppm for lactate and 3.47 ppm for glucose and a positive covariance for hardness at 3.26 ppm for trimethylamine N-oxide