443 research outputs found
Overlap properties of geometric expanders
The {\em overlap number} of a finite -uniform hypergraph is
defined as the largest constant such that no matter how we map
the vertices of into , there is a point covered by at least a
-fraction of the simplices induced by the images of its hyperedges.
In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph
expansion for higher dimensional simplicial complexes, it was asked whether or
not there exists a sequence of arbitrarily large
-uniform hypergraphs with bounded degree, for which . Using both random methods and explicit constructions, we answer this
question positively by constructing infinite families of -uniform
hypergraphs with bounded degree such that their overlap numbers are bounded
from below by a positive constant . We also show that, for every ,
the best value of the constant that can be achieved by such a
construction is asymptotically equal to the limit of the overlap numbers of the
complete -uniform hypergraphs with vertices, as
. For the proof of the latter statement, we establish the
following geometric partitioning result of independent interest. For any
and any , there exists satisfying the
following condition. For any , for any point and
for any finite Borel measure on with respect to which
every hyperplane has measure , there is a partition into measurable parts of equal measure such that all but
at most an -fraction of the -tuples
have the property that either all simplices with
one vertex in each contain or none of these simplices contain
Superpatterns and Universal Point Sets
An old open problem in graph drawing asks for the size of a universal point
set, a set of points that can be used as vertices for straight-line drawings of
all n-vertex planar graphs. We connect this problem to the theory of
permutation patterns, where another open problem concerns the size of
superpatterns, permutations that contain all patterns of a given size. We
generalize superpatterns to classes of permutations determined by forbidden
patterns, and we construct superpatterns of size n^2/4 + Theta(n) for the
213-avoiding permutations, half the size of known superpatterns for
unconstrained permutations. We use our superpatterns to construct universal
point sets of size n^2/4 - Theta(n), smaller than the previous bound by a 9/16
factor. We prove that every proper subclass of the 213-avoiding permutations
has superpatterns of size O(n log^O(1) n), which we use to prove that the
planar graphs of bounded pathwidth have near-linear universal point sets.Comment: GD 2013 special issue of JGA
-free families in the Boolean lattice
For a family of subsets of [n]=\{1, 2, ..., n} ordered by
inclusion, and a partially ordered set P, we say that is P-free
if it does not contain a subposet isomorphic to P. Let be the
largest size of a P-free family of subsets of [n]. Let be the poset with
distinct elements a, b, c, d, a<b, c<d; i.e., the 2-dimensional Boolean
lattice. We show that where . We also prove that the largest -free
family of subsets of [n] having at most three different sizes has at most
2.20711N members.Comment: 18 pages, 2 figure
Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation
We study numerically the effects of time delay in networks of delay-coupled
excitable FitzHugh Nagumo systems with dissipation. The generation of periodic
self-sustained oscillations and its threshold are analyzed depending on the
dissipation of a single neuron, the delay time, and random initial conditions.
The peculiarities of spatiotemporal dynamics of time-delayed bidirectional
ring-structured FitzHugh-Nagumo neuronal systems are investigated in cases of
local and nonlocal coupling topology between the nodes, and a first-order
nonequilibrium phase transition to synchrony is established. It is shown that
the emergence of oscillatory activity in delay-coupled FitzHugh-Nagumo neurons
is observed for smaller values of the coupling strength as the dissipation
parameter decreases. This can provide the possibility of controlling the
spatiotemporal behavior of the considered neuronal networks. The observed
effects are quantified by plotting distributions of the maximal Lyapunov
exponent and the global order parameter in terms of delay and coupling
strength.Comment: 14 pages, 17 figure
Tur\'an numbers for -free graphs: topological obstructions and algebraic constructions
We show that every hypersurface in contains a large grid,
i.e., the set of the form , with . We use this to
deduce that the known constructions of extremal -free and
-free graphs cannot be generalized to a similar construction of
-free graphs for any . We also give new constructions of
extremal -free graphs for large .Comment: Fixed a small mistake in the application of Proposition
Proposed Revision to the Taxonomy of the Genus Pestivirus; Family Flaviviridae
We propose the creation of seven new species in the genus Pestivirus (family Flaviviridae) in addition to the four existing species, and naming species in a host-independent manner using the format Pestivirus X. Only the virus species names would change; virus isolates would still be referred to by their original names. The original species would be re-designated as Pestivirus A (original designation Bovine viral diarrhea virus 1), Pestivirus B (Bovine viral diarrhea virus 2), Pestivirus C (Classical swine fever virus) and Pestivirus D (Border disease virus). The seven new species (and example isolates) would be Pestivirus E (pronghorn pestivirus), Pestivirus F (Bungowannah virus), Pestivirus G (giraffe pestivirus), Pestivirus H (Hobi-like pestivirus), Pestivirus I (Aydin-like pestivirus), Pestivirus J (rat pestivirus) and Pestivirus K (atypical porcine pestivirus). A bat-derived virus and pestiviruses identified from sheep and goat (Tunisian sheep pestiviruses), which lack complete coding region sequences, may represent two additional species
Governance tools for board members : adapting strategy maps and balanced scorecards for directorial action
The accountability of members of the board of directors of publicly traded companies has increased over years. Corresponding to these developments, there has been an inadequate advancement of tools and frameworks to help directorial functioning. This paper provides an argument for design of the Balanced Scorecard and Strategy Maps made available to the directors as a means of influencing, monitoring, controlling and assisting managerial action. This paper examines how the Balanced Scorecard and Strategy Maps could be modified and used for this purpose. The paper suggests incorporating Balanced Scorecards in the Internal Process perspective, ‘internal’ implying here not just ‘internal to the firm’, but also ‘internal to the inter-organizational system’. We recommend that other such factors be introduced separately under a new ‘perspective’ depending upon what the board wants to emphasize without creating any unwieldy proliferation of measures. Tracking the Strategy Map over time by the board of directors is a way for the board to take responsibility for the firm’s performance. The paper makes a distinction between action variables and monitoring variables. Monitoring variables are further divided on the basis of two considerations: a) whether results have been met or not and b) whether causative factors have met the expected levels of performance or not. Based on directorial responsibilities and accountability, we take another look at how the variables could be specified more completely and accurately with directorial recommendations for executives
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