Related papers: Monotone Property Thresholds
This paper has been withdrawn by the author and it is published in AGAG
Discrete Morse theory has recently been applied in metric graph reconstruction from a given density function concentrated around an (unknown) underlying embedded graph. We propose a new noise model for the density function to reconstruct a…
Sparsity and entropy are pillar notions of modern theories in signal processing and information theory. However, there is no clear consensus among scientists on the characterization of these notions. Previous efforts have contributed to…
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review…
The amount of training-data is one of the key factors which determines the generalization capacity of learning algorithms. Intuitively, one expects the error rate to decrease as the amount of training-data increases. Perhaps surprisingly,…
This article proposes a unified framework for portfolio optimization (PO), recognizing an object called the `gain probability density function (PDF)' as the fundamental object of the problem from which any objective function could be…
This is a (mostly expository) paper on Reidemeister classes, twisted Burnside-Frobenius theory, congruences, R-infinity property and all that. It was written in 2005 and published in 2008. We post it as it was, only the bibliography data is…
Property testers are fast, randomized "election polling"-type algorithms that determine if an input (e.g., graph or hypergraph) has a certain property or is $\varepsilon$-far from the property. In the dense graph model of property testing,…
There have been recent debates about whether $\overline{\text{MS}}$ parton densities exactly obey positivity bounds (including the Soffer bound), and whether the bounds should be applied as a constraint on global fits to parton densities…
We prove new results on upper and lower limits of real-valued functions by means of $\psi$-densities introduced by P. D. Barry in 1962. This allows us to improve several existing results on the growth of non-decreasing and unbounded…
A Boolean $k$-monotone function defined over a finite poset domain ${\cal D}$ alternates between the values $0$ and $1$ at most $k$ times on any ascending chain in ${\cal D}$. Therefore, $k$-monotone functions are natural generalizations of…
This paper is withdrawn by the authors, a better version is available as hep-ph/0505139.
In this paper, we introduce a noisy framework for SFTs, allowing some amount of forbidden patterns to appear. Using the Besicovitch distance, which permits a global comparison of configurations, we then study the closeness of noisy measures…
The generalized Marcum functions $Q_{\mu}(x,y)$ and $P_{\mu}(x,y)$ have as particular cases the non-central $\chi^2$ and gamma cumulative distributions, which become central distributions (incomplete gamma function ratios) when the…
The goal of property testing is to quickly distinguish between objects which satisfy a property and objects that are $\epsilon$-far from satisfying the property. There are now several general results in this area which show that natural…
This article has been withdrawn because it has been merged with the earlier article GCT3 (arXiv: CS/0501076 [cs.CC]) in the series. The merged article is now available as: Geometric Complexity Theory III: on deciding nonvanishing of a…
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…
The notion of probability density for a random function is not as straightforward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we show that it is possible to develop the…
The connection between monotonicity formulas and the (S$_+$)-property is that, for some popular differential operators, the former is used to prove the latter. The purpose of this paper is to explore this connection, remark how in the past…