计量经济分析 = Econometric analysis

We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

1980 Preface * 1999 Preface * 1999 Acknowledgements * Introduction * 1 Circular Logic * 2 Phase Singularities (Screwy Results of Circular Logic) * 3 The Rules of the Ring * 4 Ring Populations * 5 Getting Off the Ring * 6 Attracting Cycles and Isochrons * 7 Measuring the Trajectories of a Circadian Clock * 8 Populations of Attractor Cycle Oscillators * 9 Excitable Kinetics and Excitable Media * 10 The Varieties of Phaseless Experience: In Which the Geometrical Orderliness of Rhythmic Organization Breaks Down in Diverse Ways * 11 The Firefly Machine 12 Energy Metabolism in Cells * 13 The Malonic Acid Reagent ('Sodium Geometrate') * 14 Electrical Rhythmicity and Excitability in Cell Membranes * 15 The Aggregation of Slime Mold Amoebae * 16 Numerical Organizing Centers * 17 Electrical Singular Filaments in the Heart Wall * 18 Pattern Formation in the Fungi * 19 Circadian Rhythms in General * 20 The Circadian Clocks of Insect Eclosion * 21 The Flower of Kalanchoe * 22 The Cell Mitotic Cycle * 23 The Female Cycle * References * Index of Names * Index of Subjects

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/596B270197FE27DE5FABB598B6210622/S0025557200150892a.pdf/div-class-title-span-class-italic-the-geometry-of-biological-time-span-by-a-t-winfree-pp-544-dm68-corrected-second-printing-1990-isbn-3-540-52528-9-springer-div.pdf

The geometry of biological time , by A. T. Winfree. Pp 544. DM68. Corrected Second Printing 1990. ISBN 3-540-52528-9 (Springer)

The diverse microbial community that inhabits the human gut has an extensive metabolic repertoire that is distinct from, but complements the activity of mammalian enzymes in the liver and gut mucosa and includes functions essential for host digestion. As such, the gut microbiota is a key factor in shaping the biochemical profile of the diet and, therefore, its impact on host health and disease. The important role that the gut microbiota appears to play in human metabolism and health has stimulated research into the identification of specific microorganisms involved in different processes, and the elucidation of metabolic pathways, particularly those associated with metabolism of dietary components and some host-generated substances. In the first part of the review, we discuss the main gut microorganisms, particularly bacteria, and microbial pathways associated with the metabolism of dietary carbohydrates (to short chain fatty acids and gases), proteins, plant polyphenols, bile acids, and vitamins. The second part of the review focuses on the methodologies, existing and novel, that can be employed to explore gut microbial pathways of metabolism. These include mathematical models, omics techniques, isolated microbes, and enzyme assays.

/pdf/gut-microbiota-functions-metabolism-of-nutrients-and-other-2k42y77a1n.pdf

Gut microbiota functions: metabolism of nutrients and other food components

The geometry. of numbers can be traced back at least to Lagrange [1773], who proved important results about quadratic forms in two variables. The proofs as well as the formulations of results were purely arithmetic. Reviewing a book of Seeber [1831B] on ternary quadratic forms, Gaus [1831] introduced for the first time geometric methods. Geometric methods were predominant in the work of Dirichlet [1850]. On the other hand Hermite [1850] and Korkine and Zolotareff [1872], [1873], [1877] gave arithmetic proofs for their results on quadratic forms in more than three variables. Finally Minkowski [1891] noticed that a simple geometric argument which he used to give a new proof of a theorem of Hermite could be adapted to much more general situations. Then Minkowski [1896B], [7B], [11B] started a systematic study of geometric methods in number theory and called this new branch of number theory geometry of numbers. Many results and most concepts of modern geometry of numbers have their origin in the work of Minkowski. After Minkowski many eminent mathematicians made contributions to this field. In order to avoid controversies I will not mention any of them. Geometry of numbers is closely related to other branches of number theory such as algebraic number theory and Diophantine approximation. A flourishing offspring is discrete geometry, developed mainly by Fejes Toth and his school.

Geometry of Numbers

A detailed survey is given of various results pertaining to two well-known problems of combinatorial geometry: Borsuk's problem on partitions of an arbitrary bounded d-dimensional set of non-zero diameter into parts of smaller diameter, and the problem of finding chromatic numbers of some metric spaces. Furthermore, a general method is described for obtaining good lower bounds for the minimum number of parts of smaller diameter into which an arbitrary non-singleton set of dimension d can be divided as well as for the chromatic numbers of various metric spaces, in particular, and . Finally, some new lower bounds are proved for chromatic numbers in low dimensions, and new natural generalizations of the notion of chromatic number are proposed.

Borsuk's problem and the chromatic numbers of some metric spaces

/pdf/problema-borsuka-i-khromaticheskie-chisla-nekotorykh-1qyqkj8h57.pdf

Проблема Борсука и хроматические числа некоторых метрических пространств@@@Borsuk's problem and the chromatic numbers of some metric spaces

On the chromatic number of a space

In this chapter, we discuss two classical problems lying on the edge of graph theory and combinatorial geometry. The first problem is due to E. Nelson. It consists of coloring metric spaces in such a way that pairs of points at some prescribed distances receive different colors. The second problem is attributed to K. Borsuk and involves finding the minimum number of parts of smaller diameter into which an arbitrary bounded nonsingleton point set in a metric space can be partitioned. Both problems are easily translated into the language of graph theory, provided we consider, instead of the whole space, any (finite) distance graph or any (finite) graph of diameters. During the last decades, a huge number of ideas have been proposed for solving both problems, and many results in both directions have been obtained. In the survey below, we try to give an entire picture of this beautiful area of geometric combinatorics.

Coloring Distance Graphs and Graphs of Diameters

/pdf/o-khromaticheskom-chisle-prostranstva-on-the-chromatic-1tyg9oojn3.pdf

Andrei Mikhailovich Raigorodskii

Papers

Borsuk's problem and the chromatic numbers of some metric spaces

Проблема Борсука и хроматические числа некоторых метрических пространств@@@Borsuk's problem and the chromatic numbers of some metric spaces

On the chromatic number of a space

Coloring Distance Graphs and Graphs of Diameters

О хроматическом числе пространства@@@On the chromatic number of a space