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

Extended Theories of Gravity

中枢神経系疾患の治療は正常細胞（ニューロン）の機能維持を目的とするが，脳血管障害のように機能障害の原因が細胞の死滅に基づくことは多い．一方，脳腫瘍の治療においては薬物療法や放射線療法といった腫瘍細胞の死滅を目標とするものが大きな位置を占める．いずれの場合にも，細胞死の機序を理解することは各種病態や治療法の理解のうえで重要である．現在のところ最も研究の進んでいる細胞死の型はアポトーシスである．そのなかで重要な位置を占めるミトコンドリアにおける反応および抗アポトーシス因子について概要を紹介する．

Neuroscience 細胞死：最近の知見

IN two previous notes1, Prof. Max Born and I have shown that one can obtain a theory of superconductivity by taking account of the fact that the interaction of the electrons with the ionic lattice is appreciable only near the boundaries of Brillouin zones, and particularly strong near the corners of these. This leads to the criterion that the metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.

On the theory of superconductivity

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

We show that the usually neglected interaction between the electric dipole of the water molecule and the quantized electromagnetic radiation field can be treated in the context of a recent quantum field theoretical formulation of collective dynamics. We find the emergence of collective modes and the appearance of permanent electric polarization around any electrically polarized impurity.

Water as a Free Electric Dipole Laser

This introduction to the dissipative quantum model of brain and to its possible implications for consciousness studies is addressed to a broad interdisciplinary audience. Memory and consciousness are approached from the physicist point of view focusing on the basic observation that the brain is an open system continuously interacting with its environment. The unavoidable dissipative character of the brain functioning turns out to be the root of the brain’s large memory capacity and of other memory features such as memory association, memory confusion, duration of memory. The openness of the brain implies a formal picture of the world which is modeled on the same brain image: a sort of brain copy or “Double”, where world objectiveness and the brain implicit subjectivity are conjugated. Consciousness is seen to arise from the permanent “dialogue” of the brain with its Double. The author’s narration of his (re-)search gives a cross-over of the physics of elementary particles and condensed matter, and the brain’s basic dynamics. This dynamic interplay makes for a “satisfying feeling of the unity of knowledge”. (Series A)

My double unveiled

http://www.stoqatpul.org/lat/materials/freeman_neurodynamcs_many_body_dynamics.pdf

Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics

Quantum Field Theory of Fermion Mixing

The quantum model of the brain proposed by Ricciardi and Umezawa is extended to dissipative dynamics in order to study the problem of memory capacity. It is shown that infinitely many vacua are accessible to memory printing in a way that in sequential information recording the storage of a new information does not destroy the previously stored ones, thus allowing a huge memory capacity. The mechanism of information printing is shown to induce breakdown of time-reversal symmetry. Thermal properties of the memory states, as well as their relation with squeezed coherent states, are finally discussed.

Giuseppe Vitiello

Papers

Water as a Free Electric Dipole Laser

My double unveiled

Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics

Quantum Field Theory of Fermion Mixing

Dissipation and memory capacity in the quantum brain model