On the number of matroids

We consider the problem of determining $m_n$, the number of matroids on $n$ elements. The best known lower bound on $m_n$ is due to Knuth (1974) who showed that $\log \log m_n$ is at least $n-3/2\log n-1$. On the other hand, Piff (1973) showed that $\log\log m_n\leq n-\log n+\log\log n +O(1)$, 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 $\log\log m_n$ that is within an additive $1+o(1)$ 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 $n$ elements.Comment: Short note, 4 page

Streaming Algorithms for Submodular Function Maximization

We consider the problem of maximizing a nonnegative submodular set function $f:2^{\mathcal{N}} \rightarrow \mathbb{R}^+$ subject to a $p$-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 $\Omega(\frac{1}{p})$-approximation using $O(k \log k)$-space, where $k$ is an upper bound on the cardinality of the desired set. The model assumes value oracle access to $f$ and membership oracles for the matroids defining the $p$-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.% H$_2$O.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$_2$ 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