Sources of areographic coordinates, 1909-1954

Prepared for Air Force Cambridge Research Laboratories, Air Research and Development Command, U.S. Air Force.

An introduction to the use of generalized coordinates in mechanics and physics,

Mode of access: Internet.

The Rab5 effector rabankyrin-5 regulates and coordinates different endocytic mechanisms

The small GTPase Rab5 is a key regulator of clathrin-mediated endocytosis. On early endosomes, within a spatially restricted domain enriched in phosphatydilinositol-3-phosphate [PI(3)P], Rab5 coordinates a complex network of effectors that functionally cooperate in membrane tethering, fusion, and organelle motility. Here we discovered a novel PI(3)P-binding Rab5 effector, Rabankyrin-5, which localises to early endosomes and stimulates their fusion activity. In addition to early endosomes, however, Rabankyrin-5 localises to large vacuolar structures that correspond to macropinosomes in epithelial cells and fibroblasts. Overexpression of Rabankyrin-5 increases the number of macropinosomes and stimulates fluid-phase uptake, whereas its downregulation inhibits these processes. In polarised epithelial cells, this function is primarily restricted to the apical membrane. Rabankyrin-5 localises to large pinocytic structures underneath the apical surface of kidney proximal tubule cells, and its overexpression in polarised Madin-Darby canine kidney cells stimulates apical but not basolateral, non-clathrin-mediated pinocytosis. in demonstrating a regulatory role in endosome fusion and (macro) pinocytosis, our studies suggest that Rab5 regulates and coordinates different endocytic mechanisms through its effector Rabankyrin-5. Furthermore, its active role in apical pinocytosis in epithelial cells suggests an important function of Rabankyrin-5 in the physiology of polarised cells.

Rank test of location optimal for hyperbolic secant distribution

There are at least two reasons for a symmetric, unimodal, diffuse tailed hyperbolic secant distribution to be interesting in real-life applications. It displays one of the common types of non normality in natural data and is closely related to the logistic and Cauchy distributions that often arise in practice. To test the difference in location between two hyperbolic secant distributions, we develop a simple linear rank test with trigonometric scores. We investigate the small-sample and asymptotic properties of the test statistic and provide tables of the exact null distribution for small sample sizes. We compare the test to the Wilcoxon two-sample test and show that, although the asymptotic powers of the tests are comparable, the present test has certain practical advantages over the Wilcoxon test.

Bounds on integrals of the Wigner function: The hyperbolic case

Wigner functions play a central role in the phase space formulation of quantum mechanics. Although closely related to classical Liouville densities, Wigner functions are not positive definite and may take negative values on subregions of phase space. We investigate the accumulation of these negative values by studying bounds on the integral of an arbitrary Wigner function over noncompact subregions of the phase plane with hyperbolic boundaries. We show using symmetry techniques that this problem reduces to computing the bounds on the spectrum associated with an exactly solvable eigenvalue problem and that the bounds differ from those on classical Liouville distributions. In particular, we show that the total "quasiprobability" on such a region can be greater than 1 or less than zero. (C) 2005 American Institute of Physics.

R-estimator of location of the generalized secant hyperbolic distribution

The generalized secant hyperbolic distribution (GSHD) proposed in Vaughan (2002) includes a wide range of unimodal symmetric distributions, with the Cauchy and uniform distributions being the limiting cases, and the logistic and hyperbolic secant distributions being special cases. The current article derives an asymptotically efficient rank estimator of the location parameter of the GSHD and suggests the corresponding one- and two-sample optimal rank tests. The rank estimator derived is compared to the modified MLE of location proposed in Vaughan (2002). By combining these two estimators, a computationally attractive method for constructing an exact confidence interval of the location parameter is developed. The statistical procedures introduced in the current article are illustrated by examples.

OntoRama: Browsing RDF ontologies using a hyperbolic-style browser

This paper presents a Java-based hyperbolic-style browser designed to render RDF files as structured ontological maps. The program was motivated by the need to browse the content of a web-accessible ontology server: WEB KB-2. The ontology server contains descriptions of over 74,500 object types derived from the WordNet 1.7 lexical database and can be accessed using RDF syntax. Such a structure creates complications for hyperbolic-style displays. In WEB KB-2 there are 140 stable ontology link types and a hyperbolic display needs to filter and iconify the view so different link relations can be distinguished in multi-link views. Our browsing tool, OntoRama, is therefore motivated by two possibly interfering aims: the first to display up to 10 times the number of nodes in a hyperbolic-style view than using a conventional graphics display; secondly, to render the ontology with multiple links comprehensible in that view.

The retromer coat complex coordinates endosomal sorting and dynein-mediated transport, with carrier recognition by the trans-Golgi network

Early endosome-to-trans-Golgi network (TGN) transport is organized by the retromer complex. Consisting of cargo-selective and membrane-bound subcomplexes, retromer coordinates sorting with membrane deformation and carrier formation. Here, we describe four mammalian retromers whose membrane-bound subcomplexes contain specific combinations of the sorting nexins (SNX), SNX1, SNX2, SNX5, and SNX6. We establish that retromer requires a dynamic spatial organization of the endosomal network, which is regulated through association of SNX5/SNX6 with the p150(glued) component of dynactin, an activator of the minus-end directed microtubule motor dynein; an association further defined through genetic studies in C. elegans. Finally, we also establish that the spatial organization of the retromer pathway is mediated through the association of SNX1 with the proposed TGN-localized tether Rab6-interacting protein-1. These interactions describe fundamental steps in retromer-mediated transport and establish that the spatial organization of the retromer network is a critical element required for efficient retromer-mediated sorting.

A study of the aerodynamic characteristics of captor hoods in local exhaust ventilation systems

The research objectives were:- 1.To review the literature to establish the factors which have traditionally been regarded as most crucial to the design of effectlve exhaust ventilation systems. 2. To design, construct, install and calibrate a wind tunnel. 3. To develop procedures for air velocity measurement followed by a comprehensive programme of aerodvnamic data collection and data analysis for a variety of conditions. The major research findings were:- a) The literature in the subject is inadequate. There is a particular need for a much greater understanding of the aerodynamics of the suction flow field. b) The discrepancies between the experimentally observed centre-line velocities and those predicted by conventional formulae are unacceptably large. c) There was little agreement between theoretically calculated and observed velocities in the suction zone of captor hoods. d) Improved empirical formulae for the prediction of centre-line velocity applicable to the classical geometrically shaped suction openings and the flanged condition could be (and were) derived. Further analysis of data revealed that: - i) Point velocity is directly proportional to the suction. flow rate and the ratio of the point velocity to the average face velocity is constant. ii) Both shape, and size of the suction opening are significant factors as the coordinates of their points govern the extent of the effect of the suction flow field. iii) The hypothetical ellipsoidal potential function and hyperbolic streamlines were found experimentally to be correct. iv) The effect of guide plates depends on the size, shape and the angle of fitting. The effect was to very approximately double the suction velocity but the exact effect is difficult to predict. v) The axially symmetric openings produce practically symmetric flow fields. Similarity of connection pieces between the suction opening and the main duct in each case is essential in order to induce a similar suction flow field. Additionally a pilot study was made in which an artificial extraneous air flow was created, measured and its interaction with the suction flow field measured and represented graphically.

SNX4 coordinates endosomal sorting of TfnR with dynein-mediated transport into the endocytic recycling compartment

SNX-BAR proteins are a sub-family of sorting nexins implicated in endosomal sorting. Here, we establish that through its phox homology (PX) and Bin-Amphiphysin-Rvs (BAR) domains, sorting nexin-4 (SNX4) is associated with tubular and vesicular elements of a compartment that overlaps with peripheral early endosomes and the juxtanuclear endocytic recycling compartment (ERC). Suppression of SNX4 perturbs transport between these compartments and causes lysosomal degradation of the transferrin receptor (TfnR). Through an interaction with KIBRA, a protein previously shown to bind dynein light chain 1, we establish that SNX4 associates with the minus end-directed microtubule motor dynein. Although suppression of KIBRA and dynein perturbs early endosome-to-ERC transport, TfnR sorting is maintained. We propose that by driving membrane tubulation, SNX4 coordinates iterative, geometric-based sorting of the TfnR with the long-range transport of carriers from early endosomes to the ERC. Finally, these data suggest that by associating with molecular motors, SNX-BAR proteins may coordinate sorting with carrier transport between donor and recipient membranes.

A Differential Game Described by a Hyperbolic System

An antagonistic differential game of hyperbolic type with a separable linear vector pay-off function is considered. The main result is the description of all ε-Slater saddle points consisting of program strategies, program ε-Slater maximins and minimaxes for each ε ∈ R^N > for this game. To this purpose, the considered differential game is reduced to find the optimal program strategies of two multicriterial problems of hyperbolic type. The application of approximation enables us to relate these problems to a problem of optimal program control, described by a system of ordinary differential equations, with a scalar pay-off function. It is found that the result of this problem is not changed, if the players use positional or program strategies. For the considered differential game, it is interesting that the ε-Slater saddle points are not equivalent and there exist two ε-Slater saddle points for which the values of all components of the vector pay-off function at one of them are greater than the respective components of the other ε-saddle point.

Formation of Singularities for Weakly Non-Linear N×N Hyperbolic Systems

We present some results on the formation of singularities for C^1 - solutions of the quasi-linear N × N strictly hyperbolic system Ut + A(U )Ux = 0 in [0, +∞) × Rx . Under certain weak non-linearity conditions (weaker than genuine non-linearity), we prove that the first order derivative of the solution blows-up in finite time.

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Time-spatial drift of decelerating electromagnetic pulses

A time dependent electromagnetic pulse generated by a current running laterally to the direction of the pulse propagation is considered in paraxial approximation. It is shown that the pulse envelope moves in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. These pulses propagate in time with deceleration along the dominant propagation direction and drift uniformly in the lateral direction. The Airy pulse stops at infinity while the asymptotic velocity of the Gaussian is nonzero. © 2013 Optical Society of America.