1,204 research outputs found
Glueability of Resource Proof-Structures: Inverting the Taylor Expansion
A Multiplicative-Exponential Linear Logic (MELL) proof-structure can be expanded into a set of resource proof-structures: its Taylor expansion. We introduce a new criterion characterizing those sets of resource proof-structures that are part of the Taylor expansion of some MELL proof-structure, through a rewriting system acting both on resource and MELL proof-structures
Unifying Sparsest Cut, Cluster Deletion, and Modularity Clustering Objectives with Correlation Clustering
Graph clustering, or community detection, is the task of identifying groups
of closely related objects in a large network. In this paper we introduce a new
community-detection framework called LambdaCC that is based on a specially
weighted version of correlation clustering. A key component in our methodology
is a clustering resolution parameter, , which implicitly controls the
size and structure of clusters formed by our framework. We show that, by
increasing this parameter, our objective effectively interpolates between two
different strategies in graph clustering: finding a sparse cut and forming
dense subgraphs. Our methodology unifies and generalizes a number of other
important clustering quality functions including modularity, sparsest cut, and
cluster deletion, and places them all within the context of an optimization
problem that has been well studied from the perspective of approximation
algorithms. Our approach is particularly relevant in the regime of finding
dense clusters, as it leads to a 2-approximation for the cluster deletion
problem. We use our approach to cluster several graphs, including large
collaboration networks and social networks
Quasi-stationary distributions
This paper contains a survey of results related to quasi-stationary distributions, which arise in the setting of stochastic dynamical systems that eventually evanesce, and which may be useful in describing the long-term behaviour of such systems before evanescence. We are concerned mainly with continuous-time Markov chains over a finite or countably infinite state space, since these processes most often arise in applications, but will make reference to results for other processes where appropriate. Next to giving an historical account of the subject, we review the most important results on the existence and identification of quasi-stationary distributions for general Markov chains, and give special attention to birth-death processes and related models. Results on the question of whether a quasi-stationary distribution, given its existence, is indeed a good descriptor of the long-term behaviour of a system before evanescence, are reviewed as well. The paper is concluded with a summary of recent developments in numerical and approximation methods
Encrypted statistical machine learning: new privacy preserving methods
We present two new statistical machine learning methods designed to learn on
fully homomorphic encrypted (FHE) data. The introduction of FHE schemes
following Gentry (2009) opens up the prospect of privacy preserving statistical
machine learning analysis and modelling of encrypted data without compromising
security constraints. We propose tailored algorithms for applying extremely
random forests, involving a new cryptographic stochastic fraction estimator,
and na\"{i}ve Bayes, involving a semi-parametric model for the class decision
boundary, and show how they can be used to learn and predict from encrypted
data. We demonstrate that these techniques perform competitively on a variety
of classification data sets and provide detailed information about the
computational practicalities of these and other FHE methods.Comment: 39 page
On Some Dynamical Systems in Finite Fields and Residue Rings
We use character sums to confirm several recent conjectures of V. I. Arnold
on the uniformity of distribution properties of a certain dynamical system in a
finite field. On the other hand, we show that some conjectures are wrong. We
also analyze several other conjectures of V. I. Arnold related to the orbit
length of similar dynamical systems in residue rings and outline possible ways
to prove them. We also show that some of them require further tuning
The Surface Laplacian Technique in EEG: Theory and Methods
This paper reviews the method of surface Laplacian differentiation to study
EEG. We focus on topics that are helpful for a clear understanding of the
underlying concepts and its efficient implementation, which is especially
important for EEG researchers unfamiliar with the technique. The popular
methods of finite difference and splines are reviewed in detail. The former has
the advantage of simplicity and low computational cost, but its estimates are
prone to a variety of errors due to discretization. The latter eliminates all
issues related to discretization and incorporates a regularization mechanism to
reduce spatial noise, but at the cost of increasing mathematical and
computational complexity. These and several others issues deserving further
development are highlighted, some of which we address to the extent possible.
Here we develop a set of discrete approximations for Laplacian estimates at
peripheral electrodes and a possible solution to the problem of multiple-frame
regularization. We also provide the mathematical details of finite difference
approximations that are missing in the literature, and discuss the problem of
computational performance, which is particularly important in the context of
EEG splines where data sets can be very large. Along this line, the matrix
representation of the surface Laplacian operator is carefully discussed and
some figures are given illustrating the advantages of this approach. In the
final remarks, we briefly sketch a possible way to incorporate finite-size
electrodes into Laplacian estimates that could guide further developments.Comment: 43 pages, 8 figure
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