A correspondence between rooted planar maps and normal planar lambda terms

A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no beta-redexes, and planar if it is linear and the use of variables moreover follows a deterministic stack discipline. We begin by showing that the sequence counting normal planar lambda terms by a natural notion of size coincides with the sequence (originally computed by Tutte) counting rooted planar maps by number of edges. Next, we explain how to apply the machinery of string diagrams to derive a graphical language for normal planar lambda terms, extracted from the semantics of linear lambda calculus in symmetric monoidal closed categories equipped with a linear reflexive object or a linear reflexive pair. Finally, our main result is a size-preserving bijection between rooted planar maps and normal planar lambda terms, which we establish by explaining how Tutte decomposition of rooted planar maps (into vertex maps, maps with an isthmic root, and maps with a non-isthmic root) may be naturally replayed in linear lambda calculus, as certain surgeries on the string diagrams of normal planar lambda terms.Comment: Corrected title field in metadat

Determining Sex And Ancestry Of The Hyoid From The Robert J. Terry Anatomical Collection

One of the basic goals of the physical anthropologist is to create a biological profile, consisting of sex, ancestry, age, and stature, from the skeletal material that they are presented with. This thesis seeks to explore size and shape differences related to sex and ancestry from the hyoid bones of the Robert J. Terry Anatomical Collection in order to gauge its usefulness in the process of developing a biological profile. A series of measurements were taken from 398 hyoids and analysis was conducted using a number of statistical methods. Independent samples t-tests were used to examine size differences between sexes and ancestries, while linear regression analysis and principle component analysis were used to examine shape differences. Discriminant function analysis was employed to test the ability of the hyoids to be classified by sex or ancestry. The ultimate goal of the thesis is to provide physical anthropologists with a series of discriminant function equations that can be used to estimate the sex and ancestry of a hyoid. Five equations ranging in accuracy from 83-88% were developed to determine sex of a hyoid, while four equations ranging in accuracy from 70-89% can be used to determine ancestry. In addition, the t-tests, regression analyses, and principle component analysis have identified several variations in size and shape between sexes and ancestries. These analyses have provided further knowledge as to the morphological form of the hyoid, as well as a method that can be easily used by physical anthropologists to assess sex and ancestry

Spartan Daily, November 23, 1959

Volume 47, Issue 43https://scholarworks.sjsu.edu/spartandaily/3959/thumbnail.jp

Cellulose Filaments for Responsive and Functional Materials

Cellulosic filaments, found in plants, are crucial structural elements for their survival and are a great source of inspiration to obtain new functional materials. The work performed out in this thesis aimed for the isolation, physical characterization, study of the morphology and shape, as well as the mechanical behaviour of cellulosic filaments obtained from the leaves of Agapanthus africanus and Ornithogalum thyrsoides and from the filaments that form the ribbons existing on the awns of the Erodium plants. These cellulosic filaments and filament networks were chosen due to the fundamental role that they play in the plant kingdom and their ability to change shape in the presence of an external stimuli. The study of the chosen systems served as an inspiration for the preparation and production of new membranes formed by non-woven networks of micro/nano filaments. A prototype, which allows for the selective removal of oil micro droplets from aqueous emulsions, was developed. This dissertation begins with a general introduction, based on two review papers, which the author of this thesis is the first author, in which the main concepts used in the following chapters are addressed and interconnected. The original part of the work is in chapters II, III and IV. In chapter II, the study of microfilaments from the leaves tracheary of two plants, Agapanthus africanus and Ornithogalum thyrsoides, is made. These microfilaments belong to plants of the same order and have identical shapes (left helices), chemical composition and skeletons, but different mechanical properties. For the first time, micrometric droplets of a nematic liquid crystal were used as sensors to reveal the morphology of the filaments. In order to obtain quantitative characteristics on the surface of the microfilaments, photos of the textures of pierced droplets were obtained by Polarized Optical Microscopy (POM). These textures were compared with simulated optical microphotographs obtained by numerical modelling for the nematic droplets. Homeotropic anchoring at the air, and different anchoring conditions, at the interfaces with the filaments were considered for the nematic structure. This study allowed the establishment of relationships between the physical properties/morphology of the filaments and to determine their interactions with other filaments and with the environment. In chapter III, cellulosic networks existing on dead tissues of the Erodium awns were isolated and characterized. An interesting feature of these cellulosic networks is that they form ribbons that change reversibly the shape in the presence of moisture. When dried these ribbons are right-handed helices, that uncoil remaining taut, in the presence of moisture. The work performed allowed the preparation of helical ribbons that can change the shape from right- to lefthanded helices in the presence of moisture. The behaviour observed was explained using computational simulations, considering filaments that contract and expand asymmetrically. Birefringent transparent ribbons were also isolated. The asymmetric arrangement of cellulosic fibres allows the material to be stimuli-responsive without the use of complicated lithography and intricate deposition techniques, making it suitable for a diverse range of applications, such as the production of intelligent textiles and environmental friendly micro components. In chapter IV, non-woven membranes obtained from cellulosic materials and cellulose nanocrystals were prepared and characterized. Different patterns were designed using the screenprinting technique. The adhesion between the different types of cellulosic fibres was promoted through a heat treatment. The non-woven membranes produced allowed the development of a prototype that selectively removes oil droplets from aqueous emulsions with an efficiency of approximately 80%. Throughout this thesis (chapters II and III), the complexity of the systems increases. The work begins by studying the morphology of a filament and its mechanical behaviour in the presence of other filaments. After a much more complex system, in which anisotropic filament networks, produced by the Erodium plant were addressed. The stimuli-responsive behaviour of these anisotropic networks was investigated after being released by the plant. Based on the understanding of the systems formed by cellulosic filaments, studied in chapters II and III, functional non-woven membranes were produced, printed, and characterized. The non-woven membranes led to the development of a prototype, which allows the selective removal of micro droplets of oil form aqueous emulsions. At the end, a summary of the main scientific results and future work including a technological application, which was developed in the framework of this thesis, are presented.Os filamentos celulósicos, existentes nas plantas, são elementos estruturais cruciais para a sua sobrevivência e fontes de inspiração para a obtenção de novos materiais funcionais. O trabalho realizado nesta tese visou o isolamento, caracterização física, estudo da morfologia e forma, assim como do comportamento mecânico de filamentos celulósicos obtidos a partir das folhas das plantas Agapanthus africanus e Ornithogalum thyrsoides e de filamentos que formam fitas existentes nas hastes da planta Erodium. Estes filamentos e redes de filamentos celulósicos foram escolhidos devido ao papel fundamental que desempenham no reino vegetal e à resposta que podem apresentar na presença de estímulos externos. O estudo dos sistemas escolhidos serviu de inspiração para a preparação e fabrico de novas membranas formadas por redes não tecidas de filamentos micro/nanométricos e o desenvolvimento de um protótipo, que permite a remoção seletiva de microgotas de óleo de emulsões aquosas. Inicia-se com uma introdução de caracter geral, baseada em dois artigos de revisão, dos quais a autora desta tese é primeira autora, na qual se abordam e interligam os conceitos principais, que são utilizados nos capítulos seguintes. A parte original do trabalho reparte-se pelos capítulos II, III e IV. No capítulo II é feito o estudo de microfilamentos existentes nos sistemas vasculares das folhas de duas plantas, Agaphantus africanus e Ornithogalum thyrsoides. Estes microfilamentos pertencem a plantas da mesma ordem e possuem formas (hélices esquerdas), composições químicas e esqueletos idênticos, mas apresentam propriedades mecânicas distintas. Pela primeira vez foram utilizadas gotas micrométricas de um cristal líquido nemático como sensores da morfologia dos filamentos isolados. De modo a obter características quantitativas sobre a superfície dos microfilamentos, fotos de texturas obtidas por microscopia com luz polarizada foram comparadas com microfotografias óticas simuladas a partir de modelação numérica de um meio contínuo das estruturas das gotas nemáticas, com ancoragem homeotrópica na superfície com o ar suspensas nos microfilamentos com diferentes ancoragens. O estudo realizado permitiu estabelecer relações entre as propriedades físicas/morfologia dos filamentos e determinar as suas interações com outros filamentos e com o meio ambiente. No capítulo III foram isoladas e caracterizadas redes celulósicas existentes nas hastes de tecidos mortos da planta Erodium. Uma característica interessante destas redes celulósicas é a de formarem fitas que mudam reversivelmente de conformação na presença de humidade. Quando secas estas fitas são hélices direitas, que na presença de humidade desenrolam para fitas esticadas, sem torção nem flexão. Este trabalho permitiu induzir uma inversão de quiralidade nas fitas que foi explicada pelo uso de simulações computacionais considerando que as fitas contraem e esticam de modo assimétrico. Fitas birrefringentes transparentes também foram isoladas. A disposição assimétrica das fibras celulósicas permite a resposta do material não envolvendo o uso de técnicas complicadas de litografia nem de deposição, podendo ser aplicado, por exemplo, no fabrico de têxteis inteligentes e de microcomponentes amigos do ambiente. No capítulo IV foram preparadas e caracterizadas membranas não tecidas obtidas a partir de soluções de derivados celulósicos e de celulose nano cristalina. Foram desenhadas diferentes geometrias pela utilização da técnica de “screenprinting” e promovida a adesão entre os diferentes tipos de fibras celulósicas através de tratamento térmico. As membranas não tecidas produzidas permitiram o desenvolvimento de um protótipo que remove, de forma seletiva, microgotas de óleo de emulsões aquosas com uma eficiência de cerca de 80%. Ao longo desta tese (capítulo II e III), a complexidade dos sistemas estudados aumenta, isto é, começa-se por estudar a morfologia de um filamento e o seu comportamento mecânico na presença de outros filamentos, para depois se passar para um sistema muito mais complexo em que redes anisotrópicas de filamentos, impressas pela planta Erodium, permitem a resposta a estímulos externos da estrutura formada, mesmo após esta ter abandonado a planta. Tendo por base a compreensão dos sistemas formados por filamentos celulósicos, estudados nos capítulos II e III, foram produzidas, impressas e caracterizadas, no laboratório, membranas funcionais tecidas de filamentos micro/nano celulósicos. As membranas não tecidas originaram o desenvolvimento de um protótipo, que permite a remoção seletiva de micro gotas de óleo existentes em emulsões aquosas. No final é apresentado um sumário dos principais resultados científicos e perspetivas de avanço tecnológico alcançadas por este trabalho