200 research outputs found
Optimal Grid Drawings of Complete Multipartite Graphs and an Integer Variant of the Algebraic Connectivity
How to draw the vertices of a complete multipartite graph on different
points of a bounded -dimensional integer grid, such that the sum of squared
distances between vertices of is (i) minimized or (ii) maximized? For both
problems we provide a characterization of the solutions. For the particular
case , our solution for (i) also settles the minimum-2-sum problem for
complete bipartite graphs; the minimum-2-sum problem was defined by Juvan and
Mohar in 1992. Weighted centroidal Voronoi tessellations are the solution for
(ii). Such drawings are related with Laplacian eigenvalues of graphs. This
motivates us to study which properties of the algebraic connectivity of graphs
carry over to the restricted setting of drawings of graphs with integer
coordinates.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
Estimation of a probability in inverse binomial sampling under normalized linear-linear and inverse-linear loss
Sequential estimation of the success probability in inverse binomial
sampling is considered in this paper. For any estimator , its quality
is measured by the risk associated with normalized loss functions of
linear-linear or inverse-linear form. These functions are possibly asymmetric,
with arbitrary slope parameters and for
respectively. Interest in these functions is motivated by their significance
and potential uses, which are briefly discussed. Estimators are given for which
the risk has an asymptotic value as tends to , and which guarantee that,
for any in , the risk is lower than its asymptotic value. This
allows selecting the required number of successes, , to meet a prescribed
quality irrespective of the unknown . In addition, the proposed estimators
are shown to be approximately minimax when does not deviate too much from
, and asymptotically minimax as tends to infinity when .Comment: 4 figure
A new method to quantify and compare the multiple components of fitness-A study case with kelp niche partition by divergent microstage adaptations to Temperature
Point 1 Management of crops, commercialized or protected species, plagues or life-cycle evolution are subjects requiring comparisons among different demographic strategies. The simpler methods fail in relating changes in vital rates with changes in population viability whereas more complex methods lack accuracy by neglecting interactions among vital rates. Point 2 The difference between the fitness (evaluated by the population growth rate.) of two alternative demographies is decomposed into the contributions of the differences between the pair-wised vital rates and their interactions. This is achieved through a full Taylor expansion (i.e. remainder = 0) of the demographic model. The significance of each term is determined by permutation tests under the null hypothesis that all demographies come from the same pool. Point 3 An example is given with periodic demographic matrices of the microscopic haploid phase of two kelp cryptic species observed to partition their niche occupation along the Chilean coast. The method provided clear and synthetic results showing conditional differentiation of reproduction is an important driver for their differences in fitness along the latitudinal temperature gradient. But it also demonstrated that interactions among vital rates cannot be neglected as they compose a significant part of the differences between demographies. Point 4 This method allows researchers to access the effects of multiple effective changes in a life-cycle from only two experiments. Evolutionists can determine with confidence the effective causes for changes in fitness whereas population managers can determine best strategies from simpler experimental designs.CONICYT-FRENCH EMBASSADY Ph.D. gran
Modular differential equations for characters of RCFT
We discuss methods, based on the theory of vector-valued modular forms, to
determine all modular differential equations satisfied by the conformal
characters of RCFT; these modular equations are related to the null vector
relations of the operator algebra. Besides describing effective algorithmic
procedures, we illustrate our methods on an explicit example.Comment: 13 page
Interpolated sequences and critical -values of modular forms
Recently, Zagier expressed an interpolated version of the Ap\'ery numbers for
in terms of a critical -value of a modular form of weight 4. We
extend this evaluation in two directions. We first prove that interpolations of
Zagier's six sporadic sequences are essentially critical -values of modular
forms of weight 3. We then establish an infinite family of evaluations between
interpolations of leading coefficients of Brown's cellular integrals and
critical -values of modular forms of odd weight.Comment: 23 pages, to appear in Proceedings for the KMPB conference: Elliptic
Integrals, Elliptic Functions and Modular Forms in Quantum Field Theor
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