The JNR Property and the Borel Structure of a Banach Space

Research partially supported by a grant of Caja de Ahorros del Mediterraneo.

On the Structure of Spatial Branching Processes

The paper is a contribution to the theory of branching processes with discrete time and a general phase space in the sense of [2]. We characterize the class of regular, i.e. in a sense sufficiently random, branching processes (Φk) k∈Z by almost sure properties of their realizations without making any assumptions about stationarity or existence of moments. This enables us to classify the clans of (Φk) into the regular part and the completely non-regular part. It turns out that the completely non-regular branching processes are built up from single-line processes, whereas the regular ones are mixtures of left-tail trivial processes with a Poisson family structure.

Survey of Existing Services in the Mathematical Digital Libraries and Repositories in the EuDML Project

This paper presents a survey of the existing services provided by the digital libraries and repositories on mathematics of the content provider partners in the EuDML project. The purpose is to support the development of the concepts, criteria and methods for the continuous evaluation of these and new relevant existing services. The work was concentrated on the classification of the relevant services in order to specify a common evaluating structure.

Mathematical Modeling, Music Literacy and Their Transmission in Fine Arts Education

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Structure of the Unit Group of FD10

2000 Mathematics Subject Classification: 16U60, 20C05.

Multi-objective optimization of the molecular structure of refrigerants

The aim of this work was to develop a new methodology, which can be used to design new refrigerants that are better than the currently used refrigerants. The methodology draws some parallels with the general approach of computer aided molecular design. However, the mathematical way of representing the molecular structure of an organic compound and the use of meta models during the optimization process make it different. In essence, this approach aimed to generate molecules that conform to various property requirements that are known and specified a priori. A modified way of mathematically representing the molecular structure of an organic compound having up to four carbon atoms, along with atoms of other elements such as hydrogen, oxygen, fluorine, chlorine and bromine, was developed. The normal boiling temperature, enthalpy of vaporization, vapor pressure, tropospheric lifetime and biodegradability of 295 different organic compounds, were collected from open literature and data bases or estimated. Surrogate models linking the previously mentioned quantities with the molecular structure were developed. Constraints ensuring the generation of structurally feasible molecules were formulated and used in commercially available optimization algorithms to generate molecular structures of promising new refrigerants. This study was intended to serve as a proof-of-concept of designing refrigerants using the newly developed methodology.

Structure and mechanics of active colloids

11 pages Acknowledgments MCM thanks Xingbo Yang and Lisa Manning for their contribution to some aspects of the work reviewed here and for fruitful discussions. MCM was supported by NSF-DMR-305184. MCM and AP acknowledge support by the NSF IGERT program through award NSF-DGE-1068780. MCM, AP and DY were additionally supported by the Soft Matter Program at Syracuse University. AP acknowledges use of the Syracuse University HTC Campus Grid which is supported by NSF award ACI-1341006. YF was supported by NSF grant DMR-1149266 and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR-1420382.

Structure and mechanics of active colloids

11 pages Acknowledgments MCM thanks Xingbo Yang and Lisa Manning for their contribution to some aspects of the work reviewed here and for fruitful discussions. MCM was supported by NSF-DMR-305184. MCM and AP acknowledge support by the NSF IGERT program through award NSF-DGE-1068780. MCM, AP and DY were additionally supported by the Soft Matter Program at Syracuse University. AP acknowledges use of the Syracuse University HTC Campus Grid which is supported by NSF award ACI-1341006. YF was supported by NSF grant DMR-1149266 and the Brandeis Center for Bioinspired Soft Materials, an NSF MRSEC, DMR-1420382.

Investigating practitioner self-efficacy in an era of mathematical reform

The purpose of this study is to explore teacher self-efficacy at a time of radical mathematical reform. Project Maths – the new initiative which was rolled out nationwide in 2010 differs from previous attempts at innovation in that it targets a much closer connection between curriculum and pedagogy. Gone are the days of well-rehearsed routines where the role of the mathematician was essentially that of demonstrator. Teaching for understanding is now the main ‘official’ pedagogical focus, with emphasis on the practitioner playing the part of mediator between subject-matter and student. Mathematical instruction is not merely concerned with the transmission of knowledge and skills which is a particular pedagogical position to take. It is also an emotional practice (Hargreaves, 1998) that colours and expresses the feelings and actions of practitioners. While emotion plays a key role in teachers’ commitment to curricular reform, it is also shaped by the social and cultural contexts of mathematical change, alongside with the attitudes and beliefs of the mathematical teaching community. Inspired by Bandura’s theory of learning (1986), this investigation aims to shed light on the complex interplay between so-called mastery and vicarious experiences, social persuasion and physiological states. Vygotsky’s view of learning (1978) as a socio-cultural process is also drawn upon, as it provides a useful structure against which teacher self-efficacy and professional development can be examined. Finally, Hiebert’s theory (1986) is used to examine mathematics teaching self-efficacy and mathematics self-efficacy.

The Control of a Mathematical Analog of a Tentacle

A 2-dimensional dynamic analog of squid tentacles was presented. The tentacle analog consists of a multi-cell structure, which can be easily replicated to a large scale. Each cell of the model is a quadrilateral with unit masses at the corners. Each side of the quadrilateral is a spring-damper system in parallel. The spring constants are the controls for the system. The dynamics are subject to the constraint that the area of each quadrilateral must remain constant. The system dynamics was analyzed, and various equilibrium points were found with different controls. Then these equilibrium points were further determined experimentally, demonstrated to be asymptotically stable. A simulation built in MATLAB was used to find the convergence rates under different controls and damping coefficients. Finally, a control scheme was developed and used to drive the system to several configurations observed in real tentacle.

On the critical point structure of eigenfunctions belonging to the first nonzero eigenvalue of a genus two closed hyperbolic surface

We develop a method based on spectral graph theory to approximate the eigenvalues and eigenfunctions of the Laplace-Beltrami operator of a compact riemannian manifold -- The method is applied to a closed hyperbolic surface of genus two -- The results obtained agree with the ones obtained by other authors by different methods, and they serve as experimental evidence supporting the conjectured fact that the generic eigenfunctions belonging to the first nonzero eigenvalue of a closed hyperbolic surface of arbitrary genus are Morse functions having the least possible total number of critical points among all Morse functions admitted by such manifolds

Zig-zagging in geometrical reasoning in technological collaborative environments: a Mathematical Working Space-framed study concerning cognition and affect

This study highlights the importance of cognition-affect interaction pathways in the construction of mathematical knowledge. Scientific output demands further research on the conceptual structure underlying such interaction aimed at coping with the high complexity of its interpretation. The paper discusses the effectiveness of using a dynamic model such as that outlined in the Mathematical Working Spaces (MWS) framework, in order to describe the interplay between cognition and affect in the transitions from instrumental to discursive geneses in geometrical reasoning. The results based on empirical data from a teaching experiment at a middle school show that the use of dynamic geometry software favours students’ attitudinal and volitional dimensions and helps them to maintain productive affective pathways, affording greater intellectual independence in mathematical work and interaction with the context that impact learning opportunities in geometric proofs. The reflective and heuristic dimensions of teacher mediation in students’ learning is crucial in the transition from instrumental to discursive genesis and working stability in the Instrumental-Discursive plane of MWS.

Analysis of a stochastic SIR epidemic on a random network incorporating household structure

This paper is concerned with a stochastic SIR (susceptible-infective-removed) model for the spread of an epidemic amongst a population of individuals, with a random network of social contacts, that is also partitioned into households. The behaviour of the model as the population size tends to infinity in an appropriate fashion is investigated. A threshold parameter which determines whether or not an epidemic with few initial infectives can become established and lead to a major outbreak is obtained, as are the probability that a major outbreak occurs and the expected proportion of the population that are ultimately infected by such an outbreak, together with methods for calculating these quantities. Monte Carlo simulations demonstrate that these asymptotic quantities accurately reflect the behaviour of finite populations, even for only moderately sized finite populations. The model is compared and contrasted with related models previously studied in the literature. The effects of the amount of clustering present in the overall population structure and the infectious period distribution on the outcomes of the model are also explored.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

Changes In Chromatin Structure In Nih 3t3 Cells Induced By Valproic Acid And Trichostatin A.

Valproic acid (VPA) and trichostatin A (TSA) are known histone deacetylase inhibitors (HDACIs) with epigenetic activity that affect chromatin supra-organization, nuclear architecture, and cellular proliferation, particularly in tumor cells. In this study, chromatin remodeling with effects extending to heterochromatic areas was investigated by image analysis in non-transformed NIH 3T3 cells treated for different periods with different doses of VPA and TSA under conditions that indicated no loss of cell viability. Image analysis revealed chromatin decondensation that affected not only euchromatin but also heterochromatin, concomitant with a decreased activity of histone deacetylases and a general increase in histone H3 acetylation. Heterochromatin protein 1-α (HP1-α), identified immunocytochemically, was depleted from the pericentromeric heterochromatin following exposure to both HDACIs. Drastic changes affecting cell proliferation and micronucleation but not alteration in CCND2 expression and in ratios of Bcl-2/Bax expression and cell death occurred following a 48-h exposure of the NIH 3T3 cells particularly in response to higher doses of VPA. Our results demonstrated that even low doses of VPA (0.05 mM) and TSA (10 ng/ml) treatments for 1 h can affect chromatin structure, including that of the heterochromatin areas, in non-transformed cells. HP1-α depletion, probably related to histone demethylation at H3K9me3, in addition to the effect of VPA and TSA on histone H3 acetylation, is induced on NIH 3T3 cells. Despite these facts, alterations in cell proliferation and micronucleation, possibly depending on mitotic spindle defects, require a longer exposure to higher doses of VPA and TSA.