12,956 research outputs found
On the number of matroids
We consider the problem of determining , the number of matroids on
elements. The best known lower bound on is due to Knuth (1974) who showed
that is at least . On the other hand, Piff
(1973) showed that , and it has
been conjectured since that the right answer is perhaps closer to Knuth's
bound.
We show that this is indeed the case, and prove an upper bound on that is within an additive term of Knuth's lower bound. Our proof
is based on using some structural properties of non-bases in a matroid together
with some properties of independent sets in the Johnson graph to give a
compressed representation of matroids.Comment: Final version, 17 page
An entropy argument for counting matroids
We show how a direct application of Shearers' Lemma gives an almost optimum
bound on the number of matroids on elements.Comment: Short note, 4 page
Targeting the STAT6 pathway to inhibit tumor-associated macrophages-induced tumor growth and metastasis in breast cancer
Streaming Algorithms for Submodular Function Maximization
We consider the problem of maximizing a nonnegative submodular set function
subject to a -matchoid
constraint in the single-pass streaming setting. Previous work in this context
has considered streaming algorithms for modular functions and monotone
submodular functions. The main result is for submodular functions that are {\em
non-monotone}. We describe deterministic and randomized algorithms that obtain
a -approximation using -space, where is
an upper bound on the cardinality of the desired set. The model assumes value
oracle access to and membership oracles for the matroids defining the
-matchoid constraint.Comment: 29 pages, 7 figures, extended abstract to appear in ICALP 201
First-principles molecular-dynamics simulations of a hydrous silica melt: Structural properties and hydrogen diffusion mechanism
We use {\it ab initio} molecular dynamics simulations to study a sample of
liquid silica containing 3.84 wt.% HO.We find that, for temperatures of
3000 K and 3500 K,water is almost exclusively dissolved as hydroxyl groups, the
silica network is partially broken and static and dynamical properties of the
silica network change considerably upon the addition of water.Water molecules
or free O-H groups occur only at the highest temperature but are not stable and
disintegrate rapidly.Structural properties of this system are compared to those
of pure silica and sodium tetrasilicate melts at equivalent temperatures. These
comparisons confirm the picture of a partially broken tetrahedral network in
the hydrous liquid and suggest that the structure of the matrix is as much
changed by the addition of water than it is by the addition of the same amount
(in mole %) of sodium oxide. On larger length scales, correlations are
qualitatively similar but seem to be more pronounced in the hydrous silica
liquid. Finally, we study the diffusion mechanisms of the hydrogen atoms in the
melt. It turns out that HOSi triclusters and SiO dangling bonds play a
decisive role as intermediate states for the hydrogen diffusion.Comment: 25 pages, 18 figures. submitte
Revisiting the Training of Logic Models of Protein Signaling Networks with a Formal Approach based on Answer Set Programming
A fundamental question in systems biology is the construction and training to
data of mathematical models. Logic formalisms have become very popular to model
signaling networks because their simplicity allows us to model large systems
encompassing hundreds of proteins. An approach to train (Boolean) logic models
to high-throughput phospho-proteomics data was recently introduced and solved
using optimization heuristics based on stochastic methods. Here we demonstrate
how this problem can be solved using Answer Set Programming (ASP), a
declarative problem solving paradigm, in which a problem is encoded as a
logical program such that its answer sets represent solutions to the problem.
ASP has significant improvements over heuristic methods in terms of efficiency
and scalability, it guarantees global optimality of solutions as well as
provides a complete set of solutions. We illustrate the application of ASP with
in silico cases based on realistic networks and data
Effects of Scalar Dissipation Rate Fluctuations on Autoignition of Hydrogen/Air Mixture
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76071/1/AIAA-38665-294.pd
Packing sporadic real-time tasks on identical multiprocessor systems
In real-time systems, in addition to the functional correctness recurrent tasks must fulfill timing constraints to ensure the correct behavior of the system. Partitioned scheduling is widely used in real-time systems, i.e., the tasks are statically assigned onto processors while ensuring that all timing constraints are met. The decision version of the problem, which is to check whether the deadline constraints of tasks can be satisfied on a given number of identical processors, has been known NP-complet
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