Geometric combinatorial algebras: cyclohedron and simplex

In this paper we report on results of our investigation into the algebraic structure supported by the combinatorial geometry of the cyclohedron. Our new graded algebra structures lie between two well known Hopf algebras: the Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of binary trees. Connecting algebra maps arise from a new generalization of the Tonks projection from the permutohedron to the associahedron, which we discover via the viewpoint of the graph associahedra of Carr and Devadoss. At the same time that viewpoint allows exciting geometrical insights into the multiplicative structure of the algebras involved. Extending the Tonks projection also reveals a new graded algebra structure on the simplices. Finally this latter is extended to a new graded Hopf algebra (one-sided) with basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices, with journal correction

Elasmobranch resources of India

Available information on the length-weight relationship, age and growth for some elasmobranch species was compiled and growth parameters discussed. Food and feeding habits studied for some species indicated preferences, except tiger shark, for certain food. In some cases there is shifting of food habits as the young shark grows to adulthood. Starvation of female sharks is a notable feature during advanced stage of pregnancy. The three types of development exhibited by different species are discussed. The size of litter, the relationship between the length of mother and litter size and fecundity are dealt with. Landings of elasmobranchs over the years were steadily increasing. There was spurt in landings during mid seventies. In recent years the elasmobranch production appeared to be stabilizing and a sign of stagnation in the landings is evident. Group wise, reqion wise and gear wise landings are discussed

Distribution, abundance and biology of unicorn cod, Bregmaceros mcclellandi in the deep scattering layers of Indian Exclusive Economic Zone

In the deep scattering layer (DSL) the fishes have accounted for 5.4 % of the total (numerical) biomass. Juvenile fish belonging to different families were the most abundant component followed by Vinciguerria, myctophids, leptocephali, stomiforms, and unicorn cod. The "unicorn cod is represented by a single species, Bregmaceros mcclellandi (2.4%) in the total fish biomass. It occurred in 52 stations out of 445 IKMT stations. During day time the average number per haul was 21 where as in night hauls it was 29. The resource was fairly abundant along the northwest coast within the depth belt of 200 m. Biological studies on the size composition, feeding habits, and reproductive biology of the species were also carried out. The length ranged from 10-65 mm. The major diet consists of copepods, euphausiids, cheatognaths, ostracods and decapod larvae. Invariably the feeding intensity was low. The catch was composed of mostly females in maturity stages IV-V. The species spawns only once in a year. The fecundity ranged from 530 - 980 in fishes of 42 - 50 mm in total length

The impacts of monetary policies on US agriculture

The increased integration of the U.S. farm sector with the nonfarm sector, during the past decade, both domestically and internationally, led to significant implications for farm product prices, input costs, and farm income from developments in international and/or domestic economies. This is true, especially in light of the effects of exchange rates, interest rates, and inflation, all of which are influenced by macroeconomic policies and capital markets, on the farm sector. However, much of the literature in the area of macroeconomics of agriculture mainly focused on the linkage between exchange rates and agricultural commodity trade; relatively little attention has been given to other macrointerconnections such as interest rates, inflation, and income linkages;This study examines the interrelationships between the macrosector and agriculture by incorporating exchange rates, interest rates, inflation, and income linkages in a general equilibrium macroeconometric model. Using this model, the effects of changes in U.S. monetary policies on the U.S. farm sector (particularly on crop prices, livestock product prices, crop production and demand, exports, inventories, livestock production and demand, and farm incomes) are examined through these four linkages;Since the exchange rate is an important monetary factor that influences the agricultural commodity trade, in this study, the exchange rate is endogenized by following the monetary approach to exchange rate determination. The sample period of the study is 1950-1982. The estimated model has good statistical properties. In particular, all the coefficients related to the four macrolinkages are consistent with a priori expectations and, thus, provide evidence for the hypothesis that macroeconomic developments are very important for the hypothesis that macroeconomic developments are very important for U.S. agriculture;The results indicate that the effect of money supply changes on agricultural trade and prices would be magnified if a more complete set of linkages are specified rather than specifying only the exchange rate linkage. Furthermore, the simulation results show that an expansionary monetary policy has a positive impact on the farm sector, since such a policy increases the farm prices and income through the above-mentioned four linkages. On the other hand, a contractionary monetary policy has an adverse effect on the farm sector by decreasing farm prices and incomes

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

Flatfishes, goatfishes and whitefishes

Although in order to exploit these minor demersal resources there are no specialised fishing efforts, their contribution to demersal Jinjish production is substantial, mostly exploited by bottom trawling in recent years. The annual flat fish production has been amounting upto 63,344 t in 1992, that of goatfishes upto 33,300 t in 1991 and of whitefish to 25,340 t in 1985. Of late, Kerala has accounted for 47% flatfish production, followed by Karnataka-Goa 23% and Maharashtra 14%. For goatfishes, Tamilnadu-Pondicherry is responsible for 41% followed by Kerala 30% and Andhra Pradesh 13%. Gujarat has been harvesting 49% of the Whitefish yield, followed by Karnataka-Goa 18 % and Maharashtra 13%. The present paper brings together all the available data published and unpublished on the fishery and biology of various species contributing to the fisheries in different parts of the country. Based on these it is seen that the catch of the Malabar sole can be marginally increased in Calicut but not in Mangalore. In the case of the whitefish, there is an all-India decline in production in all the states due to indiscriminate exploitation of juveniles by considerably small cod end mesh size of bottom trawls. The present paper draws attention to the gaps still existing in our knowledge and the future research need on the fishery and biology of the important species, stock assessment estimates, relationships between the parental stocks and the progeny: the bottom hydrological conditions and the biological characteristics of the various populations in space and time, for realising the Maximum Sustainable Yield and for implementing their management and conservation

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

Nonneutral Effects of Money Supply on Farm and Industrial Product Prices

Changes in relative prices or terms of trade, i.e., the ratio of farm output to farm input or nonfarm output prices, have significant implications for the farm economy. If the prices farmers receive for their outputs increase (decrease) relative to the prices they pay for their inputs, the economic well being of farmers is enhanced (diminished). The terms of trade are likely to change if general price inflation changes. Thus, movements in general price inflation can affect farm income significantly. Recent macroeconomics literature postulates that to the extent that general inflation can in and of itself generate relative price changes, it is only the unanticipated inflation can do so. And, fully anticipated inflation has no effect on relative prices. This study examines the effect of unanticipated inflation generated by unanticipated changes in the money supply\u27s growth rate on relative prices, and derives the implications for farm income. Section II presents a brief survey of past studies on this issue. Section III explains the Vector Autoregression (VAR) technique, developed and popularized by Sims, which is used for the analysis. Section IF discusses empirical results obtained from the VAR methods. Finally, Section V sets forth the conclusions