Principles of Discrete Time Mechanics: I. Particle Systems

We discuss the principles to be used in the construction of discrete time classical and quantum mechanics as applied to point particle systems. In the classical theory this includes the concept of virtual path and the construction of system functions from classical Lagrangians, Cadzow's variational principle applied to the action sum, Maeda-Noether and Logan invariants of the motion, elliptic and hyperbolic harmonic oscillator behaviour, gauge invariant electrodynamics and charge conservation, and the Grassmannian oscillator. First quantised discrete time mechanics is discussed via the concept of system amplitude, which permits the construction of all quantities of interest such as commutators and scattering amplitudes. We discuss stroboscopic quantum mechanics, or the construction of discrete time quantum theory from continuous time quantum theory and show how this works in detail for the free Newtonian particle. We conclude with an application of the Schwinger action principle to the important case of the quantised discrete time inhomogeneous oscillator.Comment: 35 pages, LateX, To be published in J.Phys.A: Math.Gen. Basic principles stated: applications to field theory in subsequent papers of series contact email address: [email protected]

Gourds and squashes (Cucurbita spp.) adapted to megafaunal extinction and ecological anachronism through domestication.

The genus Cucurbita (squashes, pumpkins, gourds) contains numerous domesticated lineages with ancient New World origins. It was broadly distributed in the past but has declined to the point that several of the crops' progenitor species are scarce or unknown in the wild. We hypothesize that Holocene ecological shifts and megafaunal extinctions severely impacted wild Cucurbita, whereas their domestic counterparts adapted to changing conditions via symbiosis with human cultivators. First, we used high-throughput sequencing to analyze complete plastid genomes of 91 total Cucurbita samples, comprising ancient (n = 19), modern wild (n = 30), and modern domestic (n = 42) taxa. This analysis demonstrates independent domestication in eastern North America, evidence of a previously unknown pathway to domestication in northeastern Mexico, and broad archaeological distributions of taxa currently unknown in the wild. Further, sequence similarity between distant wild populations suggests recent fragmentation. Collectively, these results point to wild-type declines coinciding with widespread domestication. Second, we hypothesize that the disappearance of large herbivores struck a critical ecological blow against wild Cucurbita, and we take initial steps to consider this hypothesis through cross-mammal analyses of bitter taste receptor gene repertoires. Directly, megafauna consumed Cucurbita fruits and dispersed their seeds; wild Cucurbita were likely left without mutualistic dispersal partners in the Holocene because they are unpalatable to smaller surviving mammals with more bitter taste receptor genes. Indirectly, megafauna maintained mosaic-like landscapes ideal for Cucurbita, and vegetative changes following the megafaunal extinctions likely crowded out their disturbed-ground niche. Thus, anthropogenic landscapes provided favorable growth habitats and willing dispersal partners in the wake of ecological upheaval.Research was supported by The Pennsylvania State University Huck Institutes of the Life Sciences and College of the Liberal Arts (G.H.P.), Wenner–Gren post-PhD Research Grant 8770 and Natural Environment Research Council Independent Research Fellowship NE/L012030/1 (to L.K.), and the Smithsonian Institution (B.D.S.). Instrumentation was funded by the National Science Foundation through Grant OCI–0821527.This is the author accepted manuscript. The final version is available from PNAS via http://dx.doi.org/10.1073/pnas.151610911

A Simple Two-Dimensional Model System to Study Electrostatic-Self-Assembly

This paper surveys the variables controlling the lattice structure and charge in macroscopic Coulombic crystals made from electrically charged, millimeter-sized polymer objects (spheres, cubes, and cylinders). Mechanical agitation of these objects inside planar, bounded containers caused them to charge electrically through contact electrification, and to self-assemble. The processes of electrification and self-assembly, and the characteristics of the assemblies, depended on the type of motion used for agitation, on the type of materials used for the objects and the dish, on the size and shape of the objects and the dish, and on the number of objects. Each of the three different materials in the system (of the dish and of the two types of spheres) influenced the electrification. Three classes of structures formed by self-assembly, depending on the experimental conditions: two-dimensional lattices, one-dimensional chains, and zero-dimensional ‘rosettes’. The lattices were characterized by their structure (disordered, square, rhombic, or hexagonal) and by the electrical charges of individual objects; the whole lattices were approximately electrically neutral. The lattices observed in this study were qualitatively different from ionic crystals; the charge of objects had practically continuous values which changed during agitation and self-assembly, and depended on experimental conditions which included the lattice structure itself. The relationship between charge and structure led to the coexistence of regions with different lattice structures within the same assembly, and to transformations between different lattice structures during agitation.Chemistry and Chemical Biolog

Synthesis of a large communications aperture using small antennas

In this report we compare the cost of an array of small antennas to that of a single large antenna assuming both the array and single large antenna have equal performance and availability. The single large antenna is taken to be one of the 70-m antennas of the Deep Space Network. The cost of the array is estimated as a function of the array element diameter for three different values of system noise temperature corresponding to three different packaging schemes for the first amplifier. Array elements are taken to be fully steerable paraboloids and their cost estimates were obtained from commercial vendors. Array loss mechanisms and calibration problems are discussed. For array elements in the range 3 - 35 m there is no minimum in the cost versus diameter curve for the three system temperatures that were studied

Euarchontan opsin variation brings new focus to primate origins

Debate on the adaptive origins of primates has long focused on the functional ecology of the primate visual system. For example, it is hypothesized that variable expression of short- (SWS1) and middle-to-long-wavelength sensitive (M/LWS) opsins, which confer color vision, can be used to infer ancestral activity patterns and therefore selective ecological pressures. A problem with this approach is that opsin gene variation is incompletely known in the grandorder Euarchonta, i.e., the orders Scandentia (treeshrews), Dermoptera (colugos), and Primates. The ancestral state of primate color vision is therefore uncertain. Here we report on the genes (OPN1SW and OPN1LW) that encode SWS1 and M/LWS opsins in seven species of treeshrew, including the sole nocturnal scandentian Ptilocercus lowii. In addition, we examined the opsin genes of the Central American woolly opossum (Caluromys derbianus), an enduring ecological analogue in the debate on primate origins. Our results indicate: 1) retention of ultraviolet (UV) sensitivity in C. derbianus and a shift from UV to blue spectral sensitivities at the base of Euarchonta; 2) ancient pseudogenization of OPN1SW in the ancestors of P. lowii, but a signature of purifying selection in those of C. derbianus; and, 3) the absence of OPN1LW polymorphism among diurnal treeshrews. These findings suggest functional variation in color vision of nocturnal mammals and a distinctive visual ecology of early primates, perhaps one that demanded greater spatial resolution under light levels that could support cone-mediated color discrimination

Cross-Regional Gradient of Dendritic Morphology in Isochronically-Sourced Mouse Supragranular Pyramidal Neurons

Architectonic heterogeneity in neurons is thought to be important for equipping the mammalian cerebral cortex with an adaptable network that can organize the manifold totality of information it receives. To this end, the dendritic arbors of supragranular pyramidal neurons, even those of the same class, are known to vary substantially. This diversity of dendritic morphology appears to have a rostrocaudal configuration in some brain regions of various species. For example, in humans and non-human primates, neurons in more rostral visual association areas (e.g., V4) tend to have more complex dendritic arbors than those in the caudal primary visual cortex. A rostrocaudal configuration is not so clear in any region of the mouse, which is increasingly being used as a model for neurodevelopmental disorders that arise from dysfunctional cerebral cortical circuits. Therefore, in this study we investigated the complexity of dendritic arbors of neurons distributed throughout a broad area of the mouse cerebral cortex. We reduced selection bias by labeling neurons restricted to become supragranular pyramidal neurons using in utero electroporation. While we observed that the simple rostrocaudal position, cortical depth, or even functional region of a neuron was not directly related to its dendritic morphology, a model that instead included a caudomedial-to-rostrolateral gradient accounted for a significant amount of the observed dendritic morphological variance. In other words, rostrolateral neurons from our data set were generally more complex when compared to caudomedial neurons. Furthermore, dividing the cortex into a visual area and a non-visual area maintained the power of the relationship between caudomedial-to-rostrolateral position and dendritic complexity. Our observations therefore support the idea that dendritic morphology of mouse supragranular excitatory pyramidal neurons across much of the tangential plane of the cerebral cortex is partly shaped by a developmental gradient spanning several functional regions

Author Correction: A consensus-based transparency checklist.

An amendment to this paper has been published and can be accessed via a link at the top of the paper

1963: Abilene Christian College Bible Lectures - Full Text

THE CHRISTIAN AND MORALITY” Being the Abilene Christian College Annual Bible Lectures 1963 Price: $3.95 Published by ABILENE CHRISTIAN COLLEGE STUDENTS EXCHANGE ACC Station Abilene, Texa

Scaffolding development and the human condition

This paper addresses the concept of semiotic scaffolding by considering it in light of questions arising from the contemporary challenge to the humanities. This challenge comes from a mixture of scientistic demands, opportunism on the part of Western governments in thrall to neo-liberalism, along with crass economic utilitarianism. In this paper we attempt to outline what a theory of semiotic scaffolding may offer to an understanding of the humanities’ contemporary role, as well as what the humanities might offer to the elucidation of semiotic scaffolding. We argue that traditional humanist positions adopted in defence of the humanities fail to articulate the enhancement of humanity that semiotic scaffolding represents. At the same time, we note that the concept of scaffolding is sometimes in danger of taking on a functionalist perspective which understanding the humanities modus operandi is likely to dispel. Putting forward these arguments, we draw on the work of Peirce, Cassirer and Sebeok in elucidating the structural and ‘future-orientated’ benefits of the scaffolding process as it suffuses the humanities