Peregrinations from Physics to Phylogeny

The following sections are included:

• Photos
• Foreword
• Table of Content
• Brief Chronology of Hao Bailin
• List of English Publications of Hao Bailin

Professor Hao Bailin is one of China's most talented and most versatile theoretical physicists. He has made important contributions to a wide variety of research fields, including biology in which he pioneered a multidimensional method for studying the evolutionary pathways of bacteria. Indeed he calls himself, appreciatively I believe, a guerrilla fighter…

Kenneth Wilson's Nobel Prize winning breakthrough in the renormalization group theory of phase transition and critical phenomena almost overlapped with the violent “cultural revolution” years (1966–1976) in China. An unexpected chance in 1972 brought the author of these lines close to the Wilson–Fisher є-expansion of critical exponents and eventually led to a joint paper with Lu Yu published entirely in Chinese without any English title and abstract. Even the original acknowledgment was deleted because of mentioning foreign names like Kenneth Wilson and Kerson Huang. In this article I will tell the 40-year old story as a much belated tribute to Kenneth Wilson and to reproduce the essence of our work in English. At the end, I give an elementary derivation of the Callan–Symanzik equation without referring to field theory.

A central topic in statistical mechanics, a research area Professor Hao Bailin devoted himself throughout the years, is the study of the state of matter. For a gas system the study begins with an understanding of the equation of state relating the pressure P, volume V and the temperature T. In 1901 Onnes introduced the virial expansion

The dynamics of reacting chemical systems is governed by typically polynomial differential equations that may contain nonlinear terms and/or embedded feedback loops. Thus the dynamics of such systems may exhibit features associated with nonlinear dynamical systems, including (among others): temporal oscillations, excitability, multistability, reaction-diffusion-driven formation of spatial patterns, and deterministic chaos. These behaviors are exhibited in the concentrations of intermediate chemical species. Bifurcations occur between particular dynamic behaviors as system parameters are varied. The governing differential equations of reacting chemical systems have as variables the concentrations of all chemical species involved, as well as controllable parameters, including temperature, the initial concentrations of all chemical species, and fixed reaction-rate constants. A discussion is presented of the kinetics of chemical reactions as well as some thermodynamic considerations important to the appearance of temporal oscillations and other nonlinear dynamic behaviors, e.g., deterministic chaos. The behavior, chemical details, and mechanism of the oscillatory Belousov-Zhabotinsky Reaction (BZR) are described. Furthermore, experimental and mathematical evidence is presented that the BZR does indeed exhibit deterministic chaos when run in a flow reactor. The origin of this chaos seems to be in toroidal dynamics in which flow-driven oscillations in the control species bromomalonic acid couple with the BZR limit cycle…

The concept of resonance has been instrumental to the study of Hamiltonian systems with divided phase space. One can also define such systems over discrete spaces, which have a finite or countable number of points, but in this new setting the notion of resonance must be re-considered from scratch. I review some recent developments in the area of arithmetic dynamics which outline some salient features of linear and nonlinear stable (elliptic) orbits over a discrete space, and also underline the difficulties that emerge in their analysis.

We give an exact quantitative solution for the motion of three vortices of any strength, which Poincaré showed to be integrable. The absolute motion of one vortex is generally biperiodic: in uniformly rotating axes, the motion is periodic. There are two kinds of relative equilibrium configuration: two equilateral triangles and one or three colinear configurations, their stability conditions split the strengths space into three domains in which the sets of trajectories are topologically distinct.

According to the values of the strengths and the initial positions, all the possible motions are classified. Two sets of strengths lead to generic motions other than biperiodic. First, when the angular momentum vanishes, besides the biperiodic regime there exists an expansion spiral motion and even a triple collision in a finite time, but the latter motion is nongeneric. Second, when two strengths are opposite, the system also exhibits the elastic diffusion of a vortex doublet by the third vortex.

For given values of the invariants, the volume of the phase space of this Hamiltonian system is proportional to the period of the reduced motion, a well known result of the theory of adiabatic invariants. We then formally examine the behaviour of the quantities that Onsager defined only for a large number of interacting vortices.

This paper is dedicated to HAO Bailin on the occasion of his eighties birthday, the great scholar and very good friend who never tired to introduce us to the wonderful and complex intricacies of Chinese culture and history. In this paper, we present an analysis of oracle-bone characters for animals from a ‘cognitive’ point of view. After some general remarks on oraclebone characters presented in Section 1 and a short outline of the paper in Section 2, we collect various oracle-bone characters for animals from published resources in Section 3. In the next section, we begin analysing a group of 60 ancient animal characters from www.zdic.net, a highly acclaimed internet dictionary of Chinese characters that is strictly based on historical sources, and introduce five categories of specific features regarding their (graphical) structure that will be used in Section 5 to associate corresponding feature vectors to these characters. In Section 6, these feature vectors will be used to investigate their dissimilarity in terms of a family of parameterised distance measures. And in the last section, we apply the SplitsTree method as encoded in the NeighbourNet algorithms to construct a corresponding family of dissimilarity-based networks with the intention of elucidating how the ancient Chinese might have perceived the ‘animal world’ in the late bronze age and to demonstrate that these pictographs reflect an intuitive understanding of this world and its inherent structure that predates its classification in the oldest surviving Chinese encyclopedia from approximately the 3rd century BC, the ErYa, as well as similar classification systems in the West by one to two millennia. We also present an English dictionary of 70 oracle-bone characters for animals in Appendix 1. In Appendix 2, we list various variants of animal characters that were published in the Jia Gu Wen Bian (cf. , A Complete Collection of Oracle Bone Characters, edited by the Institute of Archaeology of the Chinese Academy of Social Sciences, published by the Zhonghua Book Company in 1965). We recall the frequencies of the 521 most frequent oracle-bone characters in Appendix 3 as reported in [7, 8]. And in Appendix 4, we list the animals registered in the last five chapters of the ErYa.

We study the organization of stability phases in the control parameter space of a periodically driven Brusselator. Specifically, we report high-resolution stability diagrams classifying periodic phases in terms of the number of spikes per period of their regular oscillations. Such diagrams contain accumulations of periodic oscillations with an apparently unbounded growth in the number of their spikes. In addition to the entrainment horns, we investigate the organization of oscillations in the limit of small frequencies and amplitudes of the drive. We find this limit to be free from chaotic oscillations and to display an extended and regular tiling of periodic phases. The Brusselator contains also several features discovered recently in more complex scenarios like, e.g. in lasers and in biochemical reactions, and exhibits properties which are helpful in the generic classification of entrainment in driven systems. Our stability diagrams reveal snippets of how the full classification of oscillations might look like for a wide class of flows.

We propose an order index, ϕ, which quantifies the notion of “life at the edge of chaos” when applied to genome sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length and base composition. The 786 complete genomic sequences in GenBank were found to have ϕ values in a very narrow range, 0.037 ± 0.027. We show this implies that genomes are halfway towards being completely random, namely, at the edge of chaos. We argue that this narrow range represents the neighborhood of a fixed-point in the space of sequences, and genomes are driven there by the dynamics of a robust, predominantly neutral evolution process…

Jamming of hard spheres is a new critical phenomenon whose exponents are different from those of the other known transitions. These exponents have been recently computed in a mean field approximation whose limits of validity are not known. Even if their values are in very good agreement with the ones obtained by accurate numerical simulations, the deep reasons for this success are not understood.

In this paper, after a brief presentation of the state of the art on the glass transition and jamming, I will discuss how this breakthrough can be the starting point of possible progresses in the following directions: the computation of the upper critical dimension for jamming, harmonic oscillations for soft spheres at low temperature, off-equilibrium behavior and quantum glassy effects

CV stands for Composition Vector. CVTree is an alignment-free method to infer phylogenetic trees from prokaryote whole genomes by using CVs after a subtraction procedure. CVTree is the name of a public domain Web Server that implements the method. The results obtained by this method or by the Web Server are also sometimes called CVTrees. The branchings in CVTrees are verified by direct comparison with the Bergey's Systematics and agree well with the latter at all taxonomic ranks from phylum down to species with a few exceptions which in most cases correspond to long-debated problems and may hint on possible taxonomic revisions. Moreover, CVTrees provide higher strain resolution at species level and below. In this mini-review we shall describe briefly the CVTree method and show some of its results.

In 1982 I graduated from Peking University with a bachelor's degree in astrophysics. Passing the entrance exam the same year I became a graduate student in the Institute of Theoretical Physics (ITP), Chinese Academy of Sciences, with Prof. Hao Bailin as my advisor. More than 30 years have gone by. I often recall the days I spent at the ITP with great fondness. Classmates have become life-long friends. The lessons we have learned from Prof. Hao about research, scholarship and life continue to influence us today…

This is a collection of my memories of personal experience with Professor Bailin Hao, in celebration of his 80th birthday.