There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

This is a review of Collected Works of John Tate. Parts I, II, edited by Barry Mazur and Jean-Pierre Serre. American Mathematical Society, Providence, Rhode Island, 2016. For several decades it has been clear to the friends and colleagues of John Tate that a “Collected Works” was merited. The award of the Abel Prize to Tate in 2010 added impetus, and finally, in Tate’s ninety-second year we have these two magnificent volumes, edited by Barry Mazur and Jean-Pierre Serre. Beyond Tate’s published articles, they include five unpublished articles and a selection of his letters, most accompanied by Tate’s comments, and a collection of photographs of Tate. For an overview of Tate’s work, the editors refer the reader to [4]. Before discussing the volumes, I describe some of Tate’s work. 1. Hecke L-series and Tate’s thesis Like many budding number theorists, Tate’s favorite theorem when young was Gauss’s law of quadratic reciprocity. When he arrived at Princeton as a graduate student in 1946, he was fortunate to find there the person, Emil Artin, who had discovered the most general reciprocity law, so solving Hilbert’s ninth problem. By 1920, the German school of algebraic number theorists (Hilbert, Weber, . . .) together with its brilliant student Takagi had succeeded in classifying the abelian extensions of a number field K: to each group I of ideal classes in K, there is attached an extension L of K (the class field of I); the group I determines the arithmetic of the extension L/K, and the Galois group of L/K is isomorphic to I. Artin’s contribution was to prove (in 1927) that there is a natural isomorphism from I to the Galois group of L/K. When the base field contains an appropriate root of 1, Artin’s isomorphism gives a reciprocity law, and all possible reciprocity laws arise this way. In the 1930s, Chevalley reworked abelian class field theory. In particular, he replaced “ideals” with his “idèles” which greatly clarified the relation between the local and global aspects of the theory. For his thesis, Artin suggested that Tate do the same for Hecke L-series. When Hecke proved that the abelian L-functions of number fields (generalizations of Dirichlet’s L-functions) have an analytic continuation throughout the plane with a functional equation of the expected type, he saw that his methods applied even to a new kind of L-function, now named after him. Once Tate had developed his harmonic analysis of local fields and of the idèle group, he was able prove analytic continuation and functional equations for all the relevant L-series without Hecke’s complicated theta-formulas. Received by the editors September 5, 2016. 2010 Mathematics Subject Classification. Primary 01A75, 11-06, 14-06. c ©2017 American Mathematical Society

The collected works

Child psychiatrists, pediatricians, and other child clinicians need to have a solid understanding of child language development. There are at least four important reasons that make this necessary. First, slowing, arrest, and deviation of language development are highly associated with, and complicate the course of, child psychopathology. Second, language competence plays a crucial role in emotional and mood regulation, evaluation, and therapy. Third, language deficits are the most frequent underpinning of the learning disorders, ubiquitous in our clinical populations. Fourth, clinicians should not confuse the rich linguistic and dialectal diversity of our clinical populations with abnormalities in child language development. The challenge for the clinician becomes, then, how to get immersed in the captivating field of child language acquisition without getting overwhelmed by its conceptual and empirical complexity. In the past 50 years and since the seminal works of Roger Brown, Jerome Bruner, and Catherine Snow, child language researchers (often known as developmental psycholinguists) have produced a remarkable body of knowledge. Linguists such as Chomsky and philosophers such as Grice have strongly influenced the science of child language. One of the major tenets of Chomskian linguistics (known as generative grammar) is that children’s capacity to acquire language is “hardwired” with “universal grammar”—an innate language acquisition device (LAD), a language “instinct”—at its core. This view is in part supported by the assertion that the linguistic input that children receive is relatively dismal and of poor quality relative to the high quantity and quality of output that they manage to produce after age 2 and that only an advanced, innate capacity to decode and organize linguistic input can enable them to “get from here (prelinguistic infant) to there (linguistic child).” In “Constructing a Language,” Tomasello presents a contrasting theory of how the child acquires language: It is not a universal grammar that allows for language development. Rather, human cognition universals of communicative needs and vocal-auditory processing result in some language universals, such as nouns and verbs as expressions of reference and predication (p. 19). The author proposes that two sets of cognitive skills resulting from biological/phylogenetic adaptations are fundamental to the ontogenetic origins of language. These sets of inherited cognitive skills are intentionreading on the one hand and pattern-finding, on the other. Intention-reading skills encompass the prelinguistic infant’s capacities to share attention to outside events with other persons, establishing joint attentional frames, to understand other people’s communicative intentions, and to imitate the adult’s communicative intentions (an intersubjective form of imitation that requires symbolic understanding and perspective-taking). Pattern-finding skills include the ability of infants as young as 7 months old to analyze concepts and percepts (most relevant here, auditory or speech percepts) and create concrete or abstract categories that contain analogous items. Tomasello, a most prominent developmental scientist with research foci on child language acquisition and on social cognition and social learning in children and primates, succinctly and clearly introduces the major points of his theory and his views on the origins of language in the initial chapters. In subsequent chapters, he delves into the details by covering most language acquisition domains, namely, word (lexical) learning, syntax, and morphology and conversation, narrative, and extended discourse. Although one of the remaining domains (pragmatics) is at the core of his theory and permeates the text throughout, the relative paucity of passages explicitly devoted to discussing acquisition and proBOOK REVIEWS

Constructing a language: A usage-based theory of language acquisition

I. Measurements and Numbers. II. Fundamentals. III. Non-Archimedean Analysis. IV. The Ultrametric Hilbert Space Description of Quantum Measurements with a Finite Exactness. V. Non-Kolmogorov Probability Theory. VI. Non-Kolmogorov Probability and Quantum Physics. VII. Position and Momentum Representations. VIII. p-adic Dynamical Systems with Applications to Biology and Social Sciences. Open Problems. Appendix. Bibliography. Index.

Non-Archimedean analysis : quantum paradoxes, dynamical systems and biological models

Preface Part I. Physics Concepts in Social Science? A Discussion: 1. Classical, statistical and quantum mechanics: all in one 2. Econophysics: statistical physics and social science 3. Quantum social science: a non-mathematical motivation Part II. Mathematics and Physics Preliminaries: 4. Vector calculus and other mathematical preliminaries 5. Basic elements of quantum mechanics 6. Basic elements of Bohmian mechanics Part III. Quantum Probabilistic Effects in Psychology: Basic Questions and Answers: 7. A brief overview 8. Interference effects in psychology - an introduction 9. A quantum-like model of decision making Part IV. Other Quantum Probabilistic Effects in Economics, Finance and Brain Sciences: 10. Financial/economic theory in crisis 11. Bohmian mechanics in finance and economics 12. The Bohm-Vigier Model and path simulation 13. Other applications to economic/financial theory 14. The neurophysiological sources of quantum-like processing in the brain Conclusion Glossary Index.

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Quantum Social Science

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Ubiquitous Quantum Structure

Quantum-like Paradigm- Classical (Kolmogorovian) and Quantum (Born) Probability- Contextual Probabilistic Model #x2013 V#x00E4 xj#x00F6 Model- Quantum-like Representation Algorithm #x002D QLRA- The Quantum-like Brain- Experimental Tests of Quantum-like Behavior of the Mind- Quantum-like Decision Making and Disjunction Effect- Macroscopic Games and Quantum Logic- Contextual Approach to Quantum-like Macroscopic Games- Psycho-financial Model- The Problem of Smoothness of Bohmian Trajectories

Ubiquitous quantum structure : from psychology to finance

Introduction. I. First Steps to Non-Archimedean Fields. II. The Gauss, Lebesgue and Feynman Distributions over Non-Archimedean Fields. III. The Gauss and Feynman Distributions on Infinite-Dimensional Spaces over Non-Archimedean Fields. IV. Quantum Mechanics for Non-Archimedean Wave Functions. V. Functional Integrals and the Quantization of Non-Archimedean Models with an Infinite Number of Degrees of Freedom. VI. The p-Adic-Valued Probability Measures. VII. Statistical Stabilization with Respect to p-Adic and Real Metrics. VIII. The p-Adic Valued Probability Distributions (Generalized Functions). IX. p-Adic Superanalysis. Bibliographical Remarks. Open Problems. Appendix: 1. Expansion of Numbers on a Given Scale. 2. An Analogue of Newton's Method. 3. Non-Existence of Differential Maps from Qp to R. Bibliography. Index.

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Andrei Khrennikov

Papers

Non-Archimedean analysis : quantum paradoxes, dynamical systems and biological models

Quantum Social Science

Ubiquitous Quantum Structure

Ubiquitous quantum structure : from psychology to finance

p-Adic Valued Distributions in Mathematical Physics