979 research outputs found

    Combinatorial properties of finite geometric lattices

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    Let L be a finite geometric lattice of dimension n, and let w(k) denote the number of elements in L of rank k. Two theorems about the numbers w(k) are proved: first, w(k) ≥ w(1) for k = 2, 3, ..., n-1. Second, w(k) = w(1) if and only if k = n-1 and L is modular. Several corollaries concerning the "matching" of points and dual points are derived from these theorems. Both theorems can be regarded as a generalization of a theorem of de Bruijn and Erdös concerning ʎ= 1 designs. The second can also be considered as the converse to a special case of Dilworth's theorem on finite modular lattices. These results are related to two conjectures due to G. -C. Rota. The "unimodality" conjecture states that the w(k)'s form a unimodal sequence. The "Sperner" conjecture states that a set of non-comparable elements in L has cardinality at most max/k {w(k)}. In this thesis, a counterexample to the Sperner conjecture is exhibited.</p

    Closed form summation of C-finite sequences

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    We consider sums of the form ∑j=0n−1F1(a1n+b1j+c1)F2(a2n+b2j+c2)...Fk(akn+bkj+ck),\sum_{j=0}^{n-1}F_1(a_1n+b_1j+c_1)F_2(a_2n+b_2j+c_2)... F_k(a_kn+b_kj+c_k), in which each {Fi(n)}\{F_i(n)\} is a sequence that satisfies a linear recurrence of degree D(i)<∞D(i)<\infty, with constant coefficients. We assume further that the aia_i's and the ai+bia_i+b_i's are all nonnegative integers. We prove that such a sum always has a closed form, in the sense that it evaluates to a linear combination of a finite set of monomials in the values of the sequences {Fi(n)}\{F_i(n)\} with coefficients that are polynomials in nn. We explicitly describe two different sets of monomials that will form such a linear combination, and give an algorithm for finding these closed forms, thereby completely automating the solution of this class of summation problems. We exhibit tools for determining when these explicit evaluations are unique of their type, and prove that in a number of interesting cases they are indeed unique. We also discuss some special features of the case of ``indefinite summation," in which a1=a2=...=ak=0a_1=a_2=... = a_k = 0

    Closed form summation of C-finite sequences

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    Discrete Cubical and Path Homologies of Graphs

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    In this paper we study and compare two homology theories for (simple and undirected) graphs. The first, which was developed by Barcelo, Caprano, and White, is based on graph maps from hypercubes to the graph. The second theory was developed by Grigor'yan, Lin, Muranov, and Yau, and is based on paths in the graph. Results in both settings imply that the respective homology groups are isomorphic in homological dimension one. We show that, for several infinite classes of graphs, the two theories lead to isomorphic homology groups in all dimensions. However, we provide an example for which the homology groups of the two theories are not isomorphic at least in dimensions two and three. We establish a natural map from the cubical to the path homology groups which is an isomorphism in dimension one and surjective in dimension two. Again our example shows that in general the map is not surjective in dimension three and not injective in dimension two. In the process we develop tools to compute the homology groups for both theories in all dimensions

    On the vanishing of discrete singular cubical homology for graphs

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    We prove that if G is a graph without 3-cycles and 4-cycles, then the discrete cubical homology of G is trivial in dimension d, for all d\ge 2. We also construct a sequence { G_d } of graphs such that this homology is non-trivial in dimension d for d\ge 1. Finally, we show that the discrete cubical homology induced by certain coverings of G equals the ordinary singular homology of a 2-dimensional cell complex built from G, although in general it differs from the discrete cubical homology of the graph as a whole.Comment: Minor changes, background information adde

    Spatial Ecology and Habitat Selection of Montezuma Quail in Texas

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    Montezuma quail (Cyrtonyx montezumae) occur throughout desert mountain ranges in the southwestern United States and northern Mexico. Considered a popular game bird in Arizona and New Mexico, they are not hunted in Texas. A hunting season was proposed for the species in 1997 but met with strong objections, most citing the dearth of information about the species. Much of the literature on Montezuma quail ecology is anecdotal or outdated. Previous researchers had problems capturing birds for marking and, once captured, keeping radio-marked birds alive. We used trained pointing dogs and conducted a radiotelemetry study on Montezuma quail in the Davis Mountains of Texas from January 2009 through September 2010. We captured 72 birds and recorded 966 locations. Home ranges were calculated for 13 individuals which had at least 25 locations. A 95% fixed kernel was calculated on each individual giving a mean 6 SD home range of 2,149.4 6 4,736.8 ha. Movements varied widely by individuals and the greatest straight-line movement was 12.7 km. We also performed habitat selection analysis. Mountain savannah ecological sites were preferred across all 3 spatial scales. Our results confirm that home range size and movements by Montezuma quail occur at a much larger scale than previously reported. Thus, managing lands on a larger scale and targeting mountain savannah ecological sites should be considered

    Small ring metallocycles : V. Crystal and molecular structure of hydrido-1,3-(1,1,3,3-tetramethyldisiloxanediyl)carbonylbis(triphenylphosphine)iridium(III), Me2SiOSiMe2Ir(H)(CO)(PPh3)2 [middle dot] EtOH

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    The structure of the cyclo-metalladisiloxane, Me2SiOSiMe2Ir(H)(CO)(PPh3)2, has been determined by single crystal X-ray diffraction using Mo-K[alpha] radiation. Data were collected to 20 = 45 [deg] giving 6060 unique reflections,of which 4582 had I [ges]3[sigma](I). The latter were used in the full-matrix refinement. Crystallographic data: space group, P; cell constants: 12.604(7),12.470(4), 15.821(6) A, 66.93(6)[deg], 105.34(7)[deg], 112.41(8)[deg];V 2095(3) A3; p(obs) 1.45 g/cm3; p(calc) 1.46g/cm3 (Z=2). The asymmetric unit consists of one iridium complex and one molecule of ethanol of salvation. The structure was solved by standard heavy atom methods and refined with all non-hydrogen atoms anisotrophic to final R factors, R1 0.034 and R2 0.042. The iridium metallocycle has approximate Cs symmetry with the mirror plane passing through the four-membered IrSiOSi ring. The average Ir---P, Ir---Si and Si---O bond lengths are 2.38, 2.41, and 1.68 A, respectively. The Ir---CO and C---O bond lengths are 1.903(8) and 1.133(8). The H atom bonded to Ir was not located.The Ir atom is raised out of the basal, P2Si2 plane toward the carbonyl by about 0.26 A. The most striking feature of the structure is the strain apparent in the four-membered ring. The internal angels are: 64.7 (Si---Ir---Si), 96.8 (Ir---Si---O), 97.8 (Ir---Si---O), and 99.8 (Si---O---Si). In an unstrained molecule, the Si---O---Si angle is normally in the 130-150[deg] range. It is proposed that the strain in the ring is consistent with the catalytic activity of the metallocycle.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/23652/1/0000618.pd

    IgG4 antibodies to the recombinant filarial antigen Wb-Bhp-1 decrease dramatically following treatment of lymphatic filariasis

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    BACKGROUND: Lymphatic filariasis (LF) is a neglected tropical disease and a major cause of chronic disability. Improved diagnostic tests are needed because of long-term persistence of anti-filarial antibodies or circulating filarial antigenemia after treatments that clear microfilaremia. Here, we assess changes in levels of antibodies to the recombinant filarial antigens Wb-Bhp-1, Wb123, and Bm14 after anti-filarial treatment. METHODOLOGY/PRINCIPAL FINDINGS: IgG4 antibodies to recombinant filarial antigens were assessed by ELISA. We tested serial plasma samples from a clinical trial in Papua New Guinea. Before treatment, 90%, 71% and 99% of participants had antibodies to Wb-Bhp-1, Wb123, and Bm14, respectively. Antibodies to Wb-Bhp-1 and Wb123, but not Bm14, were significantly higher in participants with persistent microfilaremia 24 months after treatment. Antibodies to all three antigens declined significantly by 60 months after treatment with ivermectin, diethylcarbamazine and albendazole despite circulating filarial antigen in 76% of participants. By 60 months follow up, antibodies to Wb-Bhp-1, Wb123, and Bm14 were detected in 17%, 7% and 90% of participants, respectively. Antibodies to Wb-Bhp-1 also declined more rapidly after treatment than antibodies to Bm14 in samples from a clinical trial conducted in Sri Lanka. We also tested archived serum samples from people living in filariasis-endemic communities in Egypt with different infection profiles. Antibodies to Wb-Bhp-1 were detected in 73% of microfilaremic people, 53% of amicrofilaremic people with circulating filarial antigen, and 17.5% of endemic individuals without microfilaria or circulating filarial antigen. Tests performed with legacy samples from India showed that few people with filarial lymphedema had antibodies to these recombinant antigens. CONCLUSIONS: Antibodies to Wb-Bhp-1 and Wb123 are more closely correlated with persistent microfilaremia than circulating filarial antigenemia or antibodies to Bm14, and they clear more rapidly after anti-filarial treatment. Additional studies are needed to assess the value of Wb-Bhp-1 serology as a tool for determining the success of LF elimination efforts

    Predicting live weight of rural African goats using body measurements

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    The goal of the current study was to develop simple regression-based equations that allow small-scale producers to use simple body measurements to accurately predict live weight of typical African goats. The data used in this study were recorded in five African countries, and was composed of 814 individuals of 40 indigenous breeds or populations and crosses that included 158 males and 656 females. Records included the live weight measured with a hanging scale, linear body measurements, country, breed, owner, and age. Country, breed, age, chest girth, height at withers, body length, and shoulder width had large effects (p76 cm, the prediction model selected that included linear terms for chest girth, body length, shoulder width and height at withers plus a quadratic term for chest girth was selected as the most accurate. When analyzed within country from Uganda and Zimbabwe, animals with chest girth \u3c 55cm the linear model with additional quadratic terms for chest girth and body length was selected. For animals with chest girth 55-75cm the linear model with the added quadratic terms for chest girth and body length was selected for animals from Malawi and Zimbabwe while the linear model with a quadratic term for chest girth was selected for Mozambique, Tanzania and Uganda. For animals with chest girth of \u3e76 cm the linear model with a quadratic term for chest girth was chosen for Tanzania, while for the other countries the linear model with quadratic terms for chest girth and body length was most accurate. In all cases, the models produced smaller mean prediction errors than the BM method
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