70,534 research outputs found
Logspace computations in graph products
We consider three important and well-studied algorithmic problems in group
theory: the word, geodesic, and conjugacy problem. We show transfer results
from individual groups to graph products. We concentrate on logspace complexity
because the challenge is actually in small complexity classes, only. The most
difficult transfer result is for the conjugacy problem. We have a general
result for graph products, but even in the special case of a graph group the
result is new. Graph groups are closely linked to the theory of Mazurkiewicz
traces which form an algebraic model for concurrent processes. Our proofs are
combinatorial and based on well-known concepts in trace theory. We also use
rewriting techniques over traces. For the group-theoretical part we apply
Bass-Serre theory. But as we need explicit formulae and as we design concrete
algorithms all our group-theoretical calculations are completely explicit and
accessible to non-specialists
Graphs, Matrices, and the GraphBLAS: Seven Good Reasons
The analysis of graphs has become increasingly important to a wide range of
applications. Graph analysis presents a number of unique challenges in the
areas of (1) software complexity, (2) data complexity, (3) security, (4)
mathematical complexity, (5) theoretical analysis, (6) serial performance, and
(7) parallel performance. Implementing graph algorithms using matrix-based
approaches provides a number of promising solutions to these challenges. The
GraphBLAS standard (istc- bigdata.org/GraphBlas) is being developed to bring
the potential of matrix based graph algorithms to the broadest possible
audience. The GraphBLAS mathematically defines a core set of matrix-based graph
operations that can be used to implement a wide class of graph algorithms in a
wide range of programming environments. This paper provides an introduction to
the GraphBLAS and describes how the GraphBLAS can be used to address many of
the challenges associated with analysis of graphs.Comment: 10 pages; International Conference on Computational Science workshop
on the Applications of Matrix Computational Methods in the Analysis of Modern
Dat
Multi-task Neural Network for Non-discrete Attribute Prediction in Knowledge Graphs
Many popular knowledge graphs such as Freebase, YAGO or DBPedia maintain a
list of non-discrete attributes for each entity. Intuitively, these attributes
such as height, price or population count are able to richly characterize
entities in knowledge graphs. This additional source of information may help to
alleviate the inherent sparsity and incompleteness problem that are prevalent
in knowledge graphs. Unfortunately, many state-of-the-art relational learning
models ignore this information due to the challenging nature of dealing with
non-discrete data types in the inherently binary-natured knowledge graphs. In
this paper, we propose a novel multi-task neural network approach for both
encoding and prediction of non-discrete attribute information in a relational
setting. Specifically, we train a neural network for triplet prediction along
with a separate network for attribute value regression. Via multi-task
learning, we are able to learn representations of entities, relations and
attributes that encode information about both tasks. Moreover, such attributes
are not only central to many predictive tasks as an information source but also
as a prediction target. Therefore, models that are able to encode, incorporate
and predict such information in a relational learning context are highly
attractive as well. We show that our approach outperforms many state-of-the-art
methods for the tasks of relational triplet classification and attribute value
prediction.Comment: Accepted at CIKM 201
Towards a fully automated computation of RG-functions for the 3- O(N) vector model: Parametrizing amplitudes
Within the framework of field-theoretical description of second-order phase
transitions via the 3-dimensional O(N) vector model, accurate predictions for
critical exponents can be obtained from (resummation of) the perturbative
series of Renormalization-Group functions, which are in turn derived
--following Parisi's approach-- from the expansions of appropriate field
correlators evaluated at zero external momenta.
Such a technique was fully exploited 30 years ago in two seminal works of
Baker, Nickel, Green and Meiron, which lead to the knowledge of the
-function up to the 6-loop level; they succeeded in obtaining a precise
numerical evaluation of all needed Feynman amplitudes in momentum space by
lowering the dimensionalities of each integration with a cleverly arranged set
of computational simplifications. In fact, extending this computation is not
straightforward, due both to the factorial proliferation of relevant diagrams
and the increasing dimensionality of their associated integrals; in any case,
this task can be reasonably carried on only in the framework of an automated
environment.
On the road towards the creation of such an environment, we here show how a
strategy closely inspired by that of Nickel and coworkers can be stated in
algorithmic form, and successfully implemented on the computer. As an
application, we plot the minimized distributions of residual integrations for
the sets of diagrams needed to obtain RG-functions to the full 7-loop level;
they represent a good evaluation of the computational effort which will be
required to improve the currently available estimates of critical exponents.Comment: 54 pages, 17 figures and 4 table
Toward a multilevel representation of protein molecules: comparative approaches to the aggregation/folding propensity problem
This paper builds upon the fundamental work of Niwa et al. [34], which
provides the unique possibility to analyze the relative aggregation/folding
propensity of the elements of the entire Escherichia coli (E. coli) proteome in
a cell-free standardized microenvironment. The hardness of the problem comes
from the superposition between the driving forces of intra- and inter-molecule
interactions and it is mirrored by the evidences of shift from folding to
aggregation phenotypes by single-point mutations [10]. Here we apply several
state-of-the-art classification methods coming from the field of structural
pattern recognition, with the aim to compare different representations of the
same proteins gathered from the Niwa et al. data base; such representations
include sequences and labeled (contact) graphs enriched with chemico-physical
attributes. By this comparison, we are able to identify also some interesting
general properties of proteins. Notably, (i) we suggest a threshold around 250
residues discriminating "easily foldable" from "hardly foldable" molecules
consistent with other independent experiments, and (ii) we highlight the
relevance of contact graph spectra for folding behavior discrimination and
characterization of the E. coli solubility data. The soundness of the
experimental results presented in this paper is proved by the statistically
relevant relationships discovered among the chemico-physical description of
proteins and the developed cost matrix of substitution used in the various
discrimination systems.Comment: 17 pages, 3 figures, 46 reference
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