A Contour Integral Representation for the Dual Five-Point Function and a Symmetry of the Genus Four Surface in R6

The invention of the "dual resonance model" N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation formulas such as the contour-integral representation obtained by Pochhammer in 1890. Here we explore the geometry underlying the dual five-point function B5, the simplest generalization of the Euler Beta function. Analyzing the B5 integrand leads to a polyhedral structure for the five-crosscap surface, embedded in RP5, that has 12 pentagonal faces and a symmetry group of order 120 in PGL(6). We find a Pochhammer-like representation for B5 that is a contour integral along a surface of genus five. The symmetric embedding of the five-crosscap surface in RP5 is doubly covered by a symmetric embedding of the surface of genus four in R6 that has a polyhedral structure with 24 pentagonal faces and a symmetry group of order 240 in O(6). The methods appear generalizable to all N, and the resulting structures seem to be related to associahedra in arbitrary dimensions.Comment: 43 pages and 44 figure

Nested reconfigurable robots: theory, design, and realization

Rather than the conventional classification method, we propose to divide modular and reconfigurable robots into intra-, inter-, and nested reconfigurations. We suggest designing the robot with nested reconfigurability, which utilizes individual robots with intra-reconfigurability capable of combining with other homogeneous/heterogeneous robots (inter-reconfigurability). The objective of this approach is to generate more complex morphologies for performing specific tasks that are far from the capabilities of a single module or to respond to programmable assembly requirements. In this paper, we discuss the theory, concept, and initial mechanical design of Hinged-Tetro, a self-reconfigurable module conceived for the study of nested reconfiguration. Hinged-Tetro is a mobile robot that uses the principle of hinged dissection of polyominoes to transform itself into any of the seven one-sided tetrominoes in a straightforward way. The robot can also combine with other modules for shaping complex structures or giving rise to a robot with new capabilities. Finally, the validation experiments verify the nested reconfigurability of Hinged-Tetro. Extensive tests and analyses of intra-reconfiguration are provided in terms of energy and time consumptions. Experiments using two robots validate the inter-reconfigurability of the proposed module

Excitonic Funneling in Extended Dendrimers with Non-Linear and Random Potentials

The mean first passage time (MFPT) for photoexcitations diffusion in a funneling potential of artificial tree-like light-harvesting antennae (phenylacetylene dendrimers with generation-dependent segment lengths) is computed. Effects of the non-linearity of the realistic funneling potential and slow random solvent fluctuations considerably slow down the center-bound diffusion beyond a temperature-dependent optimal size. Diffusion on a disordered Cayley tree with a linear potential is investigated analytically. At low temperatures we predict a phase in which the MFPT is dominated by a few paths.Comment: 4 pages, 4 figures, To be published in Phys. Rev. Let

Disorder and Funneling Effects on Exciton Migration in Tree-Like Dendrimers

The center-bound excitonic diffusion on dendrimers subjected to several types of non-homogeneous funneling potentials, is considered. We first study the mean-first passage time (MFPT) for diffusion in a linear potential with different types of correlated and uncorrelated random perturbations. Increasing the funneling force, there is a transition from a phase in which the MFPT grows exponentially with the number of generations $g$, to one in which it does so linearly. Overall the disorder slows down the diffusion, but the effect is much more pronounced in the exponential compared to the linear phase. When the disorder gives rise to uncorrelated random forces there is, in addition, a transition as the temperature $T$ is lowered. This is a transition from a high-$T$ regime in which all paths contribute to the MFPT to a low-$T$ regime in which only a few of them do. We further explore the funneling within a realistic non-linear potential for extended dendrimers in which the dependence of the lowest excitonic energy level on the segment length was derived using the Time-Dependent Hatree-Fock approximation. Under this potential the MFPT grows initially linearly with $g$ but crosses-over, beyond a molecular-specific and $T$-dependent optimal size, to an exponential increase. Finally we consider geometrical disorder in the form of a small concentration of long connections as in the {\it small world} model. Beyond a critical concentration of connections the MFPT decreases significantly and it changes to a power-law or to a logarithmic scaling with $g$, depending on the strength of the funneling force.Comment: 13 pages, 9 figure

An U.S. Export Disposal Policy for Wheat and Corn Stocks: A Quantitative Analysis for 1977/78 to 1984/85

Over the past decade the operation of the commodity loan programs and since 1977 the farmer-owned reserve (FOR) programs, has resulted in the accumulation of large quantities of grain stocks both in the hands of the government and in the hands of farmers, sealed under the reserve program. Government and farmer-owned reserve (FOR) stocks for wheat exceeded a billion bushels several times in recent years and for corn reached two and a half billion bushels in 1982/83. The build-up of these stocks in 1982/83 led to the implementation of the massive acreage reduction under the Payment-in-Kind (PIK) program. Government-owned (CCC) and FOR stocks were used in this program as payment to farmers for idling cropland

The World Soybean Trade Model: Specification, Estimation, and Validation

The soybean trade model is one of the three models in the trade modeling system developed, updated, and maintained by the Center for Agricultural and Rural Development (CARD). The other two commodity trade models are for wheat and the feed-grains complex. The three trade models are linked through cross-price linkages in the supply and demand components of these models, yet each model can be solved independently. In general, however, all three trade models are solved iteratively to obtain a simultaneous solution. Equilibrium price, quantities of supply and demand, and net trade are determined by equating excess demands and supplies across regions and explicitly linking prices in each region to a world reference price

The World Feed-Grains Trade Model: Specification, Estimation, and Validation

The feed-grains trade model is one of the three models in the world trade modeling system developed, updated, and maintained by the Center for Agricultural and Rural Development (CARD). The other two commodity trade models are for wheat and the soybeans complex. The three world models are related through cross-price linkages in the supply and demand components of these models, yet each model can be solved independently. In general, however, all three trade models are solved iteratively to obtain a simultaneous solution. Equilibrium prices, quantities of supply and demand, and net trade are determined by equating excess demands and supplies across regions and explicitly linking prices in each region to a world reference price

FAPRI Trade Model for the Soybean Sector: Specification, Estimation, and Validation

The international components and the overall structure of this model are based on recent work by Huyser (1983). The U.S. Structure and components of the model are based on recent work by Ash (1984) and earlier work by Baumes and Meyers (1980) and Meyers and Hacklander (1979). The roots of all these models trace back to the seminal work on the soybean industry by Houck, Ryan, and Subotnik (1972). A review of related modeling work in the soybean sector can be found in Huyser and Ash