2,827 research outputs found
Unifying Structured Recursion Schemes
AbstractFolds and unfolds have been understood as fundamental building blocks for total programming, and have been extended to form an entire zoo of specialised structured recursion schemes. A great number of these schemes were unified by the introduction of adjoint folds, but more exotic beasts such as recursion schemes from comonads proved to be elusive. In this paper, we show how the two canonical derivations of adjunctions from (co)monads yield recursion schemes of significant computational importance: monadic catamorphisms come from the Kleisli construction, and more astonishingly, the elusive recursion schemes from comonads come from the Eilenberg–Moore construction. Thus, we demonstrate that adjoint folds are more unifying than previously believed.</jats:p
Kernel-based Inference of Functions over Graphs
The study of networks has witnessed an explosive growth over the past decades
with several ground-breaking methods introduced. A particularly interesting --
and prevalent in several fields of study -- problem is that of inferring a
function defined over the nodes of a network. This work presents a versatile
kernel-based framework for tackling this inference problem that naturally
subsumes and generalizes the reconstruction approaches put forth recently by
the signal processing on graphs community. Both the static and the dynamic
settings are considered along with effective modeling approaches for addressing
real-world problems. The herein analytical discussion is complemented by a set
of numerical examples, which showcase the effectiveness of the presented
techniques, as well as their merits related to state-of-the-art methods.Comment: To be published as a chapter in `Adaptive Learning Methods for
Nonlinear System Modeling', Elsevier Publishing, Eds. D. Comminiello and J.C.
Principe (2018). This chapter surveys recent work on kernel-based inference
of functions over graphs including arXiv:1612.03615 and arXiv:1605.07174 and
arXiv:1711.0930
Highly optimized tolerance and power laws in dense and sparse resource regimes
Power law cumulative frequency vs. event size distributions
are frequently cited as evidence for complexity and
serve as a starting point for linking theoretical models and mechanisms with
observed data. Systems exhibiting this behavior present fundamental
mathematical challenges in probability and statistics. The broad span of length
and time scales associated with heavy tailed processes often require special
sensitivity to distinctions between discrete and continuous phenomena. A
discrete Highly Optimized Tolerance (HOT) model, referred to as the
Probability, Loss, Resource (PLR) model, gives the exponent as a
function of the dimension of the underlying substrate in the sparse
resource regime. This agrees well with data for wildfires, web file sizes, and
electric power outages. However, another HOT model, based on a continuous
(dense) distribution of resources, predicts . In this paper we
describe and analyze a third model, the cuts model, which exhibits both
behaviors but in different regimes. We use the cuts model to show all three
models agree in the dense resource limit. In the sparse resource regime, the
continuum model breaks down, but in this case, the cuts and PLR models are
described by the same exponent.Comment: 19 pages, 13 figure
An introduction to Graph Data Management
A graph database is a database where the data structures for the schema
and/or instances are modeled as a (labeled)(directed) graph or generalizations
of it, and where querying is expressed by graph-oriented operations and type
constructors. In this article we present the basic notions of graph databases,
give an historical overview of its main development, and study the main current
systems that implement them
A Unifying Framework for Type Inhabitation
In this paper we define a framework to address different kinds of problems related to type inhabitation, such as type checking, the emptiness problem, generation of inhabitants and counting, in a uniform way. Our framework uses an alternative representation for types, called the pre-grammar of the type, on which different methods for these problems are based. Furthermore, we define a scheme for a decision algorithm that, for particular instantiations of the parameters, can be used to show different inhabitation related problems to be in PSPACE
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