Affine insertion and Pieri rules for the affine Grassmannian

We study combinatorial aspects of the Schubert calculus of the affine Grassmannian Gr associated with SL(n,C). Our main results are: 1) Pieri rules for the Schubert bases of H^*(Gr) and H_*(Gr), which expresses the product of a special Schubert class and an arbitrary Schubert class in terms of Schubert classes. 2) A new combinatorial definition for k-Schur functions, which represent the Schubert basis of H_*(Gr). 3) A combinatorial interpretation of the pairing between homology and cohomology of the affine Grassmannian. These results are obtained by interpreting the Schubert bases of Gr combinatorially as generating functions of objects we call strong and weak tableaux, which are respectively defined using the strong and weak orders on the affine symmetric group. We define a bijection called affine insertion, generalizing the Robinson-Schensted Knuth correspondence, which sends certain biwords to pairs of tableaux of the same shape, one strong and one weak. Affine insertion offers a duality between the weak and strong orders which does not seem to have been noticed previously. Our cohomology Pieri rule conjecturally extends to the affine flag manifold, and we give a series of related combinatorial conjectures.Comment: 98 page

Neuroinformatics: From Bioinformatics to Databasing the Brain

Neuroinformatics seeks to create and maintain web-accessible databases of experimental and computational data, together with innovative software tools, essential for understanding the nervous system in its normal function and in neurological disorders. Neuroinformatics includes traditional bioinformatics of gene and protein sequences in the brain; atlases of brain anatomy and localization of genes and proteins; imaging of brain cells; brain imaging by positron emission tomography (PET), functional magnetic resonance imaging (fMRI), electroencephalography (EEG), magnetoencephalography (MEG) and other methods; many electrophysiological recording methods; and clinical neurological data, among others. Building neuroinformatics databases and tools presents difficult challenges because they span a wide range of spatial scales and types of data stored and analyzed. Traditional bioinformatics, by comparison, focuses primarily on genomic and proteomic data (which of course also presents difficult challenges). Much of bioinformatics analysis focus on sequences (DNA, RNA, and protein molecules), as the type of data that are stored, compared, and sometimes modeled. Bioinformatics is undergoing explosive growth with the addition, for example, of databases that catalog interactions between proteins, of databases that track the evolution of genes, and of systems biology databases which contain models of all aspects of organisms. This commentary briefly reviews neuroinformatics with clarification of its relationship to traditional and modern bioinformatics

A planned program for speech education in a secondary school

Thesis (M.S.)--Boston Universit

A Description and Analysis of Behavior Patterns Among Uinta Ground Squirrels

This research describes and analyzes the behavior of free-living Uinta ground squirrels (Spermophilus armatus) temporally, spatially and with reference to differences in sex, age, population density and habitat. In addition, the relationships between local meteorological parameters and time spent above ground are described and analyzed. The frequency of eight behaviors, feeding, moving, encounters, upright, motionless, grooming, nest gathering and calling, among ground squirrels was found to be labile, varying in frequency with time of day, period of the season, sex, age, population density and habitat, and varying in spatial distribution within the home range. The dominant behavior, feeding, was most frequent during the first and last two hours of the day and tended to occur within the home range core during these hours. During the midday periods home range use became more general and the frequency of the other behaviors increased as feeding frequency decreased. During periods of sexual activity (the beginning and end of the homeothermic season), male ground squirrels displayed high frequencies of encounters, moving and calling behaviors

kk-Schur functions and affine Schubert calculus

This book is an exposition of the current state of research of affine Schubert calculus and $k$-Schur functions. This text is based on a series of lectures given at a workshop titled "Affine Schubert Calculus" that took place in July 2010 at the Fields Institute in Toronto, Ontario. The story of this research is told in three parts: 1. Primer on $k$-Schur Functions 2. Stanley symmetric functions and Peterson algebras 3. Affine Schubert calculusComment: 213 pages; conference website: http://www.fields.utoronto.ca/programs/scientific/10-11/schubert/, updates and corrections since v1. This material is based upon work supported by the National Science Foundation under Grant No. DMS-065264

Division I Female Cross-Country Runners’ Perception of Eating Behaviors and Attitudes Toward Health: A Pilot Study

International Journal of Exercise Science 11(3): 941-956, 2018.The complexity behind nutritional decisions and the impact of these decisions on overall health (both physical and emotional) in the Division I female runner is not yet well understood. Thus, the purpose of this study was to explore the perspectives of female collegiate cross-country runners from a Division I school on eating behaviors and attitudes toward health. In this qualitative study, six NCAA Division I female collegiate cross-country runners participated in individual interviews. Through qualitative analysis, three themes (Nutritional Views, Identity as a Runner, and Psychological Factors) and 11 subthemes emerged. The interactions that occurred between the subthemes and themes demonstrated that there were multiple interacting factors influencing the athletes’ nutritional behaviors. Intrinsic factors consisted of maintaining self-control, perception of trust and available time. Extrinsic factors included availability of a nutritionist, family and team support, and availability of nutritious food. These findings give some insight into the nutritional decisions in female runners, but it is a complex issue. It is evident that individualized education regarding eating behavior is needed for the female athlete

Supersymmetric Biorthogonal Quantum Systems

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.Comment: Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-1