Molecular set theory: II. An aspect of the biomathematical theory of sets

In an earlier paper (Molecular Set Theory: I.Bull. Math. Biophysics,22, 285–307, 1960) the author proposed a “Molecular Set Theory” as a formal mathematical meta-theoretic system for representing complex reactions not only of biological interest, but also of general chemical interest. The present paper is a refinement and extension of the earlier work along more formal algebraic lines. For example the beginnings of an algebra of molecular transformations is presented. It also emphasizes that this development, together with the genetical set theory of Woodger's and Rashevsky's set-theoretic contributions to Relational Biology, points to the existence of a biomathematical theory of sets which is not deducible from the general mathematical, abstract theory of sets.     

Making Illuminated Parchments

The author describes how contemporary music education at the secondary level has fallen short of Dr. Charles Leonhard's vision for developing musical understanding and musical responsiveness in all students and cites several historical events as pivotal in promoting the profession's current path. The author then challenges this generalization by describing the professional practices of a forward-thinking high school band director who epitomizes Leonhard's ideal of a music teacher and serves as a model for professional dispositions. The author also offers social interaction theory as a promising foundation on which to assemble a music teacher education program capable of producing teachers with dispositions that serve the highest goals of the music education profession.     

Molecular set theory: A mathematical representation for chemical reaction mechanisms

The present investigation is part of a program aimed at examining the mathematical basis of reaction rate theory (Bartholomay,Bull. Math. Biophys. 20, 1958) from the point of view of individual molecular events. Certain inconsistencies resulting from the classical procedure of using stoichiometric “chemical equations” to represent the kinds of mechanisms involved are pointed out and remedies are suggested by the introduction of set-theoretic notation within the framework of a so-calledMolecular Set Theory. It is concluded that whereas ordinary algebra is a suitable basis for stoichiometry, in discussing mechanisms of chemical reactions,molecular set theory is more appropriate. This is a theory of material transformations which is patterned afterabstract set theory: the individual molecules of a chemical species and chemical transformations from one species to another correspond to the abstract concepts of elements or points of a set and their mappings into other sets respectively. The new notions ofexact molecular sequences andequivalence classes of molecules arising from this study of chemical reactions may be of purely mathematical interest when referred back to the context of abstract set theory.     

Fostering Formal Commutativity Knowledge with Approximate Arithmetic

How can we enhance the understanding of abstract mathematical principles in elementary school? Different studies found out that nonsymbolic estimation could foster subsequent exact number processing and simple arithmetic. Taking the commutativity principle as a test case, we investigated if the approximate calculation of symbolic commutative quantities can also alter the access to procedural and conceptual knowledge of a more abstract arithmetic principle. Experiment 1 tested first graders who had not been instructed about commutativity in school yet. Approximate calculation with symbolic quantities positively influenced the use of commutativity-based shortcuts in formal arithmetic. We replicated this finding with older first graders (Experiment 2) and third graders (Experiment 3). Despite the positive effect of approximation on the spontaneous application of commutativity-based shortcuts in arithmetic problems, we found no comparable impact on the application of conceptual knowledge of the commutativity principle. Overall, our results show that the usage of a specific arithmetic principle can benefit from approximation. However, the findings also suggest that the correct use of certain procedures does not always imply conceptual understanding. Rather, the conceptual understanding of commutativity seems to lag behind procedural proficiency during elementary school.     

Natural selection. IV. The Price equation

The Price equation partitions total evolutionary change into two components. The first component provides an abstract expression of natural selection. The second component subsumes all other evolutionary processes, including changes during transmission. The natural selection component is often used in applications. Those applications attract widespread interest for their simplicity of expression and ease of interpretation. Those same applications attract widespread criticism by dropping the second component of evolutionary change and by leaving unspecified the detailed assumptions needed for a complete study of dynamics. Controversies over approximation and dynamics have nothing to do with the Price equation itself, which is simply a mathematical equivalence relation for total evolutionary change expressed in an alternative form. Disagreements about approach have to do with the tension between the relative valuation of abstract versus concrete analyses. The Price equation's greatest value has been on the abstract side, particularly the invariance relations that illuminate the understanding of natural selection. Those abstract insights lay the foundation for applications in terms of kin selection, information theory interpretations of natural selection and partitions of causes by path analysis. I discuss recent critiques of the Price equation by Nowak and van Veelen.     

原木锯割弦切板材板面尺寸的数学描述理论

为船舶、乐器等特殊行业需要的弦切板数控加工提供数学描述理论,提出的这些理论将为数控加工的数学模型建立提供基础理论,为板材纹理的视频再现提供数学方法．本文提出的理论还将为三角形下锯法提供理论依据,与制材工艺结合起来,将使传统加工工艺数学化,为科学管理和数字化控制提供了理论．本文是木材工业中用数学描述加工过程的开始,可以推进木材工业加工过程数学描述研究的开展．     

Dance and Music in “Gangnam Style”: How Dance Observation Affects Meter Perception

Dance and music often co-occur as evidenced when viewing choreographed dances or singers moving while performing. This study investigated how the viewing of dance motions shapes sound perception. Previous research has shown that dance reflects the temporal structure of its accompanying music, communicating musical meter (i.e. a hierarchical organization of beats) via coordinated movement patterns that indicate where strong and weak beats occur. Experiments here investigated the effects of dance cues on meter perception, hypothesizing that dance could embody the musical meter, thereby shaping participant reaction times (RTs) to sound targets occurring at different metrical positions.In experiment 1, participants viewed a video with dance choreography indicating 4/4 meter (dance condition) or a series of color changes repeated in sequences of four to indicate 4/4 meter (picture condition). A sound track accompanied these videos and participants reacted to timbre targets at different metrical positions. Participants had the slowest RT’s at the strongest beats in the dance condition only. In experiment 2, participants viewed the choreography of the horse-riding dance from Psy’s “Gangnam Style” in order to examine how a familiar dance might affect meter perception. Moreover, participants in this experiment were divided into a group with experience dancing this choreography and a group without experience. Results again showed slower RTs to stronger metrical positions and the group with experience demonstrated a more refined perception of metrical hierarchy. Results likely stem from the temporally selective division of attention between auditory and visual domains. This study has implications for understanding: 1) the impact of splitting attention among different sensory modalities, and 2) the impact of embodiment, on perception of musical meter. Viewing dance may interfere with sound processing, particularly at critical metrical positions, but embodied familiarity with dance choreography may facilitate meter awareness. Results shed light on the processing of multimedia environments.     

Dance and early childhood cognition: The Isadora Effect

ABSTRACT

This article proposes the existence of an Isadora Effect: the propositions that motor development plays a primal role in brain development, and the first understanding of symbolic meaning among young children occurs from an understanding of movement and gesture. Anecdotal evidence for the past few decades has demonstrated that dance education and the early use of symbolic movement greatly enhance cognitive development in young children. The author presents (a) background and historical information about dance in early childhood in the United States; (b) research in which physical, emotional, and social development has served the backbone for rationalizing inclusion of dance in early education; (c) The Isadora Effect in early childhood dance education and its relationship to cognitive development, brain development, and intelligence; (d) the 21st Century Skills in relation to early childhood development and dance education; and (e) early childhood dance education and the National Core Arts Standards. The author makes three recommendations for improving the development of American youth relative to early childhood dance education: increased inclusion of creative movement and dance in early childhood curricula, scientific study by the pediatric and neurological communities to investigate effects of motor development and early symbolic movement on brain development and cognitive growth, and ways dance educators can communicate with policy makers about the kinds of support needed to make the first two recommendations a reality.     

The proteomics of feather development in pied flycatchers (Ficedula hypoleuca) with different plumage coloration

The genetic theory of morphological evolution postulates that form evolves largely by changing the expression proteins that are functionally conserved. It follows that understanding the function of proteins during different phases of development as well as the mechanisms by which the functions are modified is a prerequisite for understanding evolutionary change. Male pied flycatchers exhibit marked phenotypic variation in their breeding plumage. This variation has repeatedly been shown to have adaptive significance, but the molecular basis of this variation is not known. Here, we characterize the proteome of developing pied flycatcher feathers from differently pigmented males and also introduce a new method for examining the effect sizes of expression differences in protein interaction networks. Approximately 300 proteins were identified in the developing feathers of males. Gene products associated with cellular transport, cell metabolism and protein synthesis formed a large part of the developing feather proteome. Sixty‐five proteins associated with the development of the epidermis and/or pigmentation were detected in the data. The examination of expression level differences of protein–protein interaction networks revealed an immunological signalling–related network to exhibit significantly higher expression in black compared to brown males. Additionally, indications of differences in energy balance and oxidative stress related characteristics were detected. Together, these results provide new insight into the molecular mechanisms and evolutionary significance of plumage colour variation.     

Review and application of group theory to molecular systems biology

In this paper we provide a review of selected mathematical ideas that can help us better understand the boundary between living and non-living systems. We focus on group theory and abstract algebra applied to molecular systems biology. Throughout this paper we briefly describe possible open problems. In connection with the genetic code we propose that it may be possible to use perturbation theory to explore the adjacent possibilities in the 64-dimensional space-time manifold of the evolving genome. With regards to algebraic graph theory, there are several minor open problems we discuss. In relation to network dynamics and groupoid formalism we suggest that the network graph might not be the main focus for understanding the phenotype but rather the phase space of the network dynamics. We show a simple case of a C ₆ network and its phase space network. We envision that the molecular network of a cell is actually a complex network of hypercycles and feedback circuits that could be better represented in a higher-dimensional space. We conjecture that targeting nodes in the molecular network that have key roles in the phase space, as revealed by analysis of the automorphism decomposition, might be a better way to drug discovery and treatment of cancer.     

A 2-dimensional geometry for biological time

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal …) and properly biological (heart beating, respiration, metabolic …). In particular, the role of biological rhythms do not seem to have any counterpart in mathematical formalization of physical clocks, which are based on frequencies along the usual (possibly thermodynamical, thus oriented) time. We then suggest a functional representation of biological time by a 2-dimensional manifold as a mathematical frame for accommodating autonomous biological rhythms. The “visual” representation of rhythms so obtained, in particular heart beatings, will provide, by a few examples, hints towards possible applications of our approach to the understanding of interspecific differences or intraspecific pathologies. The 3-dimensional embedding space, needed for purely mathematical reasons, allows to introduce a suitable extra-dimension for “representation time”, with a cognitive significance.     

Syncopation,Body-Movement and Pleasure in Groove Music

Moving to music is an essential human pleasure particularly related to musical groove. Structurally, music associated with groove is often characterised by rhythmic complexity in the form of syncopation, frequently observed in musical styles such as funk, hip-hop and electronic dance music. Structural complexity has been related to positive affect in music more broadly, but the function of syncopation in eliciting pleasure and body-movement in groove is unknown. Here we report results from a web-based survey which investigated the relationship between syncopation and ratings of wanting to move and experienced pleasure. Participants heard funk drum-breaks with varying degrees of syncopation and audio entropy, and rated the extent to which the drum-breaks made them want to move and how much pleasure they experienced. While entropy was found to be a poor predictor of wanting to move and pleasure, the results showed that medium degrees of syncopation elicited the most desire to move and the most pleasure, particularly for participants who enjoy dancing to music. Hence, there is an inverted U-shaped relationship between syncopation, body-movement and pleasure, and syncopation seems to be an important structural factor in embodied and affective responses to groove.     

BacterialLectinDb: An integrated bacterial lectin database

Studies of various diversified bacterial lectins/ lectin data may serve as a tool with enormous promise to help biotechnologists/ geneticists in their innovative technology to explore a deeper understanding in proteomics/ genomics research for finding the molecular basis of infectious diseases and also to new approaches for their prevention and in development of new bacterial vaccines. Hence we developed a bacterial lectin database named 'BacterialLectinDb'. An organized database schema for BacterialLectinDb was designed to collate all the available information about all bacterial lectins as a central repository. The database was designed using HTML, XML. AVAILABILITY: The database is available for free at http://www.research-bioinformatics.in.     

Provisional evidence that the arginine vasopressin 1a receptor gene is associated with musical memory

In a preliminary pilot study, 82 university students were administered an extensive battery of musical and phonological memory tasks; their scores were examined for an association with promoter repeats in the arginine vasopressin 1a receptor and serotonin transporter genes. We previously showed that these genes were associated with another music-related phenotype, creative dance. Highly significant Gene×Gene epistatic interactions were observed between promoter region polymorphisms and musical as well as phonological memory using family-based and population-based tests. Given the prominent role of vasopressin in social behavior, the preliminary association found in our study between musical memory and vasopressin could serve to support evolutionary accounts postulating a social adaptive role in music, such as mother–infant communication, sexual selection, group cohesion, and even early protolanguage.     

Art Comes to Life in a Steel Mill Town

In this article, the authors investigate how Korea's current educational policy's emphasis on artistic expression, and therefore music education, has been realized in the praxis of early childhood education. The authors view policy as discourses and texts that early childhood educators interpret and reinterpret within specific contexts. Policy rhetoric and practice fail to recognize the integration of musical conceptual development, expressive ability, creativity, and communication. The musical development of a child should be viewed as his or her right to nurture a musical self in a meaningful musical context.     

Spatial Representations Are Specific to Different Domains of Knowledge

There is evidence that many abstract concepts are represented cognitively in a spatial format. However, it is unknown whether similar spatial processes are employed in different knowledge domains, or whether individuals exhibit similar spatial profiles within and across domains. This research investigated similarities in spatial representation in two knowledge domains – mathematics and music. Sixty-one adults completed analogous number magnitude and pitch discrimination tasks: the Spatial-Numerical Association of Response Codes and Spatial-Musical Association of Response Codes tasks. Subgroups of individuals with different response patterns were identified through cluster analyses. For both the mathematical and musical tasks, approximately half of the participants showed the expected spatial judgment effect when explicitly cued to focus on the spatial properties of the stimuli. Despite this, performances on the two tasks were largely independent. Consistent with previous research, the study provides evidence for the spatial representation of number and pitch in the majority of individuals. However, there was little evidence to support the claim that the same spatial representation processes underpin mathematical and musical judgments.     

From presentation to representation in E. B. Wilson'sThe Cell

Diagrams make it possible to present scientific facts in more abstract and generalized form. While some detail is lost, simplified and accessible knowledge is gained. E. B. Wilson's work in cytology provides a case study of changing uses of diagrams and accompanying abstraction. In his early work, Wilson presented his data in photographs, which he saw as coming closest to “fact.” As he gained confidence in his interpretations, and as he sought to provide a generalized textbook account of cell development, he relied on increasingly abstract diagrams. In addition, he came to see that highly abstract and even schematic drawings could provide more than pictures directly from life.     

The role of ethylene in the development of plant form

Ethylene is a gaseous growth factor involved in a diverse arrayof cellular, developmental and stress-related processes in plants.A number of examples of the role played by ethylene in the developmentof form in plants are described; reaction wood formation, floralinduction, sex determination, flooding-induced shoot elongation,and leaf abscission. Recent advances in the understanding ofthe molecular mechanism under-pinning post-pollination perianthwilting in orchids is reviewed. This study indicates that theprocess of post-pollination perianth wilting involves an earlyincrease in sensitivity to endogenous levels of ethylene whichset in motion a chain of events in which ethylene autocatalyticallyinduces its own synthesis in the pistil. Ethylene also inducesthe expression of ACO in the perianth which converts pistil-derivedACC into ethylene which drives the wilting process. Conceptsdrawn from this system are then applied to the Arabidopsis rootepidermis in which ethylene is a positive regulator of roothair development in an effort to come to a mechanistic understandingof the process of pattern formation in this system. Understandingthe molecular basis of the role of ethylene in these model systemswill provide useful paradigms for examining the part playedby ethylene in the diverse array of processes in which thisgrowth factor is involved. Key words: Ethylene, development, plant form