447 research outputs found
Maximum Shallow Clique Minors in Preferential Attachment Graphs Have Polylogarithmic Size
No full textPreferential attachment graphs are random graphs designed to mimic properties of real word networks. They are constructed by a random process that iteratively adds vertices and attaches them preferentially to vertices that already have high degree. We prove various structural asymptotic properties of this graph model. In particular, we show that the size of the largest r-shallow clique minor in Gⁿ_m is at most log(n)^{O(r²)}m^{O(r)}. Furthermore, there exists a one-subdivided clique of size log(n)^{1/4}. Therefore, preferential attachment graphs are asymptotically almost surely somewhere dense and algorithmic techniques developed for structurally sparse graph classes are not directly applicable. However, they are just barely somewhere dense. The removal of just slightly more than a polylogarithmic number of vertices asymptotically almost surely yields a graph with locally bounded treewidth
Evaluating Restricted First-Order Counting Properties on Nowhere Dense Classes and Beyond
No full textIt is known that first-order logic with some counting extensions can be efficiently evaluated on graph classes with bounded expansion, where depth-r minors have constant density. More precisely, the formulas are ∃ x₁… x_k#y φ(x_1,…,x_k, y) > N, where φ is an FO-formula. If φ is quantifier-free, we can extend this result to nowhere dense graph classes with an almost linear FPT run time. Lifting this result further to slightly more general graph classes, namely almost nowhere dense classes, where the size of depth-r clique minors is subpolynomial, is impossible unless FPT = W[1]. On the other hand, in almost nowhere dense classes we can approximate such counting formulas with a small additive error. Note those counting formulas are contained in FOC({>}) but not FOC₁().
In particular, it follows that partial covering problems, such as partial dominating set, have fixed parameter algorithms on nowhere dense graph classes with almost linear running time
Endogenous regulation of the GnRH receptor by GnRH in the human placenta
No full textGonadotrophin releasing hormone (GnRH) plays an important regulatory role in the function and growth of human placenta, but its placental expression sites and co-localization with GnRH receptor (GnRH-R) are not well known, GnRH and GnRH-R expression has been found in both placenta and cultured trophoblasts; however, cultured trophoblastic cells very quickly lose GnRH-R message and subsequently receptor protein. Speculating that endogenously released GnRH induced this down-regulation, we determined GnRH-R in cultures of trophoblastic cells in the presence of a neutralizing anti-GnRH antibody, Cells incubated with this antibody showed a strong signal for the GnRH-R, while those cultured without did not las analysed by immunofluorescence, reverse transcription-polymerase chain reaction, protein 'dot blot' and Western blotting), Furthermore, addition of the GnRH agonist buserelin led to a reduction of the receptor protein. We have therefore shown that GnRH released from trophoblastic cells down-regulates GnRH-R in these trophoblastic cells. Having previously shown that trophoblast layers were synchronously positive for GnRH and GnRH-R, these new findings support the hypothesis of an ultrashort feedback regulation of trophoblasts by GnRH involving autocrine regulation of GnRH-R
Smaller kernels for hitting set problems of constant arity
No full textWe demonstrate a kernel of size O(k^2) for 3-HITTING SET
when all subsets in the collection to be hit are of size at most
three), giving a partial answer to an open question of Niedermeier by
improving on the O(k^3) kernel of Niedermeier and Rossmanith. Our
technique uses the Nemhauser-Trotter linear-size kernel for vc, and
generalizes to demonstrating a kernel of size O(k^{r-1}) for r- HITTING SET (for fixed r).Postprint (published version
Smaller kernels for hitting set problems of constant arity
No full textWe demonstrate a kernel of size O(k^2) for 3-HITTING SET
when all subsets in the collection to be hit are of size at most
three), giving a partial answer to an open question of Niedermeier by
improving on the O(k^3) kernel of Niedermeier and Rossmanith. Our
technique uses the Nemhauser-Trotter linear-size kernel for vc, and
generalizes to demonstrating a kernel of size O(k^{r-1}) for r- HITTING SET (for fixed r).Postprint (published version
Remorse, probation and the state
No full textPhilosophical debate on the role of remorse in criminal justice has largely focused on whether remorse should play a role in sentencing decisions. In this chapter, the author argues that this focus is unhelpfully narrow. Even though there are, the author believes, good reasons to think that remorse should not influence sentencing, there are other valuable roles for remorse in a well-designed and well-functioning criminal justice system. In defending this conclusion, the chapter looks at the nature and value of probation. In particular, it looks at the role that the encouragement of remorse might have in a well-structured and open probationary relationship. It is not always inappropriate, the chapter concludes, for state officials to take an interest in whether offenders are remorseful for what they have done
Smaller kernels for hitting set problems of constant arity
No full textWe demonstrate a kernel of size O(k^2) for 3-HITTING SET
when all subsets in the collection to be hit are of size at most
three), giving a partial answer to an open question of Niedermeier by
improving on the O(k^3) kernel of Niedermeier and Rossmanith. Our
technique uses the Nemhauser-Trotter linear-size kernel for vc, and
generalizes to demonstrating a kernel of size O(k^{r-1}) for r- HITTING SET (for fixed r)
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