On the intersection of tolerance and cocomparability graphs.

Tolerance graphs have been extensively studied since their introduction, due to their interesting structure and their numerous applications, as they generalize both interval and permutation graphs in a natural way. It has been conjectured by Golumbic, Monma, and Trotter in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocomparability graphs can be efficiently recognized, a positive answer to this conjecture in the general case would enable us to efficiently distinguish between tolerance and bounded tolerance graphs, although it is NP-complete to recognize each of these classes of graphs separately. This longstanding conjecture has been proved under some – rather strong – structural assumptions on the input graph; in particular, it has been proved for complements of trees, and later extended to complements of bipartite graphs, and these are the only known results so far. Furthermore, it is known that the intersection of tolerance and cocomparability graphs is contained in the class of trapezoid graphs. Our main result in this article is that the above conjecture is true for every graph G that admits a tolerance representation with exactly one unbounded vertex; note that this assumption concerns only the given tolerance representation R of G, rather than any structural property of G. Moreover, our results imply as a corollary that the conjecture of Golumbic, Monma, and Trotter is true for every graph G = (V,E) that has no three independent vertices a, b, c ∈ V such that N(a) ⊂ N(b) ⊂ N(c), where N(v) denotes the set of neighbors of a vertex v ∈ V ; this is satisfied in particular when G is the complement of a triangle-free graph (which also implies the above-mentioned correctness for complements of bipartite graphs). Our proofs are constructive, in the sense that, given a tolerance representation R of a graph G, we transform R into a bounded tolerance representation R of G. Furthermore, we conjecture that any minimal tolerance graph G that is not a bounded tolerance graph, has a tolerance representation with exactly one unbounded vertex. Our results imply the non-trivial result that, in order to prove the conjecture of Golumbic, Monma, and Trotter, it suffices to prove our conjecture

The role of markets in food availability and market integration among smallholder farmers: the case of Western Kenya [Poster]

Poster presented at Tropentag 2013. International Research on Food Security, Natural Resource Management and Rural Development. "Agricultural development within the rural-urban continuum". Stuttgart-Hohenheim (Germany), Sep 17-19 2013

Crop species diversity in smallholder farms in Western Kenya and their contribution to food security

Poster presented at First International Conference on Global Food Security. Noordwijkerhout (The Netherlands), 29 Sep - 02 Oct 2013

Assessment of on-farm, market and wild food diversity in three agro-ecological zones of Western Kenya

Poster presented at Tropentag 2014. International Conference on Research on Food Security, Natural Resource Management and Rural Development. "Bridging the Gap between Increasing Knowledge and Decreasing Resources" Prague (Czech Republic) Sep 17-19 2014

On the intersection of tolerance and cocomparability graphs.

It has been conjectured by Golumbic and Monma in 1984 that the intersection of tolerance and cocomparability graphs coincides with bounded tolerance graphs. Since cocomparability graphs can be efficiently recognized, a positive answer to this conjecture in the general case would enable us to efficiently distinguish between tolerance and bounded tolerance graphs, although it is NP-complete to recognize each of these classes of graphs separately. The conjecture has been proved under some – rather strong – structural assumptions on the input graph; in particular, it has been proved for complements of trees, and later extended to complements of bipartite graphs, and these are the only known results so far. Furthermore, it is known that the intersection of tolerance and cocomparability graphs is contained in the class of trapezoid graphs. In this article we prove that the above conjecture is true for every graph G, whose tolerance representation satisfies a slight assumption; note here that this assumption concerns only the given tolerance representation R of G, rather than any structural property of G. This assumption on the representation is guaranteed by a wide variety of graph classes; for example, our results immediately imply the correctness of the conjecture for complements of triangle-free graphs (which also implies the above-mentioned correctness for complements of bipartite graphs). Our proofs are algorithmic, in the sense that, given a tolerance representation R of a graph G, we describe an algorithm to transform R into a bounded tolerance representation R  ∗  of G. Furthermore, we conjecture that any minimal tolerance graph G that is not a bounded tolerance graph, has a tolerance representation with exactly one unbounded vertex. Our results imply the non-trivial result that, in order to prove the conjecture of Golumbic and Monma, it suffices to prove our conjecture. In addition, there already exists evidence in the literature that our conjecture is true

On the Possibility of Optical Unification in Heterotic Strings

Recently J. Giedt discussed a mechanism, entitled optical unification, whereby string scale unification is facilitated via exotic matter with intermediate scale mass. This mechanism guarantees that a virtual MSSM unification below the string scale is extrapolated from the running of gauge couplings upward from M_Z^o when an intermediate scale desert is assumed. In this letter we explore the possibility of optical unification within the context of weakly coupled heterotic strings. In particular, we investigate this for models of free fermionic construction containing the NAHE set of basis vectors. This class is of particular interest for optical unification, because it provides a standard hypercharge embedding within SO(10), giving the standard k_Y = 5/3 hypercharge level, which was shown necessary for optical unification. We present a NAHE model for which the set of exotic SU(3)_C triplet/anti-triplet pairs, SU(2)_L doublets, and non-Abelian singlets with hypercharge offers the possibility of optical unification. Whether this model can realize optical unification is conditional upon these exotics not receiving Fayet-Iliopoulos (FI) scale masses when a flat direction of scalar vacuum expectation values is non-perturbatively chosen to cancel the FI D-term, xi, generated by the anomalous U(1)-breaking Green-Schwarz-Dine-Seiberg-Wittten mechanism. A study of perturbative flat directions and their phenomenological implications for this model is underway. This paper is a product of the NFS Research Experiences for Undergraduates and the NSF High School Summer Science Research programs at Baylor University.Comment: 16 pages. Standard Late

Flowmeter and Ground Penetrating Radar: comparison between hydrogeological and geophysical methods

We discuss a comparison between saturated hydraulic conductivity calculated with Electromagnetic Borehole Flowmeter (EBF) and water content obtained by Ground Penetrating Radar (GPR) Zero Offset Profile (ZOP

Delineation of RAID1, the RACK1 interaction domain located within the unique N-terminal region of the cAMP-specific phosphodiesterase, PDE4D5

Background The cyclic AMP specific phosphodiesterase, PDE4D5 interacts with the β-propeller protein RACK1 to form a signaling scaffold complex in cells. Two-hybrid analysis of truncation and mutant constructs of the unique N-terminal region of the cAMP-specific phosphodiesterase, PDE4D5 were used to define a domain conferring interaction with the signaling scaffold protein, RACK1. Results Truncation and mutagenesis approaches showed that the RACK1-interacting domain on PDE4D5 comprised a cluster of residues provided by Asn-22/Pro-23/Trp-24/Asn-26 together with a series of hydrophobic amino acids, namely Leu-29, Val-30, Leu-33, Leu-37 and Leu-38 in a 'Leu-Xaa-Xaa-Xaa-Leu' repeat. This was done by 2-hybrid analyses and then confirmed in biochemical pull down analyses using GST-RACK1 and mutant PDE4D5 forms expressed in COS cells. Mutation of Arg-34, to alanine, in PDE4D5 attenuated its interaction with RACK1 both in 2-hybrid screens and in pull down analyses. A 38-mer peptide, whose sequence reflected residues 12 through 49 of PDE4D5, bound to RACK1 with similar affinity to native PDE4D5 itself (Ka circa 6 nM). Conclusions The RACK1 Interaction Domain on PDE4D5, that we here call RAID1, is proposed to form an amphipathic helical structure that we suggest may interact with the C-terminal β-propeller blades of RACK1 in a manner akin to the interaction of the helical G-γ signal transducing protein with the β-propeller protein, G-β

Comparing initial-data sets for binary black holes

We compare the results of constructing binary black hole initial data with three different decompositions of the constraint equations of general relativity. For each decomposition we compute the initial data using a superposition of two Kerr-Schild black holes to fix the freely specifiable data. We find that these initial-data sets differ significantly, with the ADM energy varying by as much as 5% of the total mass. We find that all initial-data sets currently used for evolutions might contain unphysical gravitational radiation of the order of several percent of the total mass. This is comparable to the amount of gravitational-wave energy observed during the evolved collision. More astrophysically realistic initial data will require more careful choices of the freely specifiable data and boundary conditions for both the metric and extrinsic curvature. However, we find that the choice of extrinsic curvature affects the resulting data sets more strongly than the choice of conformal metric.Comment: 18 pages, 12 figures, accepted for publication in Phys. Rev.

Recognition models of alphanumeric characters

Several methods to study the recognition and similarity of alphanumeric characters are briefly discussed and evaluated. In particular, the application of the choice-model (Luce, 1959, 1963) to recognition of letters is criticized. A feature analytic model for recognition of alphanumeric characters based on Tversky's (1977) features of similarity is proposed and tested. It is argued that the proposed model: (a) is parsimonious in that it utilizes a relatively small number of parameters, (b) is psychologically more meaningful compared with other approaches in that it is attempting to study underlying processes rather than just reveal a similarity structure, (c) yields predictions that have a high level of fit with the observed data. Possible implications from the use of the model for future research are briefly discussed