1,336 research outputs found
Fixed point theorems for Boolean networks expressed in terms of forbidden subnetworks
We are interested in fixed points in Boolean networks, {\em i.e.} functions
from to itself. We define the subnetworks of as the
restrictions of to the subcubes of , and we characterizes a
class of Boolean networks satisfying the following property:
Every subnetwork of has a unique fixed point if and only if has no
subnetwork in . This characterization generalizes the fixed point
theorem of Shih and Dong, which asserts that if for every in
there is no directed cycle in the directed graph whose the adjacency matrix is
the discrete Jacobian matrix of evaluated at point , then has a
unique fixed point. Then, denoting by (resp. )
the networks whose the interaction graph is a positive (resp. negative) cycle,
we show that the non-expansive networks of are exactly the
networks of ; and for the class of
non-expansive networks we get a "dichotomization" of the previous forbidden
subnetwork theorem: Every subnetwork of has at most (resp. at least) one
fixed point if and only if has no subnetworks in (resp.
) subnetwork. Finally, we prove that if is a conjunctive
network then every subnetwork of has at most one fixed point if and only if
has no subnetwork in .Comment: 40 page
Learning and Interpreting Multi-Multi-Instance Learning Networks
We introduce an extension of the multi-instance learning problem where
examples are organized as nested bags of instances (e.g., a document could be
represented as a bag of sentences, which in turn are bags of words). This
framework can be useful in various scenarios, such as text and image
classification, but also supervised learning over graphs. As a further
advantage, multi-multi instance learning enables a particular way of
interpreting predictions and the decision function. Our approach is based on a
special neural network layer, called bag-layer, whose units aggregate bags of
inputs of arbitrary size. We prove theoretically that the associated class of
functions contains all Boolean functions over sets of sets of instances and we
provide empirical evidence that functions of this kind can be actually learned
on semi-synthetic datasets. We finally present experiments on text
classification, on citation graphs, and social graph data, which show that our
model obtains competitive results with respect to accuracy when compared to
other approaches such as convolutional networks on graphs, while at the same
time it supports a general approach to interpret the learnt model, as well as
explain individual predictions.Comment: JML
High performance graph analysis on parallel architectures
PhD ThesisOver the last decade pharmacology has been developing computational
methods to enhance drug development and testing. A computational
method called network pharmacology uses graph analysis
tools to determine protein target sets that can lead on better targeted
drugs for diseases as Cancer. One promising area of network-based
pharmacology is the detection of protein groups that can produce
better e ects if they are targeted together by drugs. However, the
e cient prediction of such protein combinations is still a bottleneck
in the area of computational biology.
The computational burden of the algorithms used by such protein
prediction strategies to characterise the importance of such proteins
consists an additional challenge for the eld of network pharmacology.
Such computationally expensive graph algorithms as the all pairs
shortest path (APSP) computation can a ect the overall drug discovery
process as needed network analysis results cannot be given on
time. An ideal solution for these highly intensive computations could
be the use of super-computing. However, graph algorithms have datadriven
computation dictated by the structure of the graph and this
can lead to low compute capacity utilisation with execution times
dominated by memory latency.
Therefore, this thesis seeks optimised solutions for the real-world
graph problems of critical node detection and e ectiveness characterisation
emerged from the collaboration with a pioneer company in the
eld of network pharmacology as part of a Knowledge Transfer Partnership
(KTP) / Secondment (KTS). In particular, we examine how
genetic algorithms could bene t the prediction of protein complexes
where their removal could produce a more e ective 'druggable' impact.
Furthermore, we investigate how the problem of all pairs shortest
path (APSP) computation can be bene ted by the use of emerging
parallel hardware architectures as GPU- and FPGA- desktop-based
accelerators.
In particular, we address the problem of critical node detection with
the development of a heuristic search method. It is based on a genetic
algorithm that computes optimised node combinations where their removal
causes greater impact than common impact analysis strategies.
Furthermore, we design a general pattern for parallel network analysis
on multi-core architectures that considers graph's embedded properties.
It is a divide and conquer approach that decomposes a graph
into smaller subgraphs based on its strongly connected components
and computes the all pairs shortest paths concurrently on GPU. Furthermore,
we use linear algebra to design an APSP approach based
on the BFS algorithm. We use algebraic expressions to transform the
problem of path computation to multiple independent matrix-vector
multiplications that are executed concurrently on FPGA. Finally, we
analyse how the optimised solutions of perturbation analysis and parallel
graph processing provided in this thesis will impact the drug
discovery process.This research was part of a Knowledge Transfer Partnership (KTP)
and Knowledge Transfer Secondment (KTS) between e-therapeutics
PLC and Newcastle University. It was supported as a collaborative
project by e-therapeutics PLC and Technology Strategy boar
Graph Kernels
We present a unified framework to study graph kernels, special cases of which include the random
walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004;
Mahé et al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time
complexity of kernel computation between unlabeled graphs with n vertices from O(n^6) to O(n^3).
We find a spectral decomposition approach even more efficient when computing entire kernel matrices.
For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn^3)
time per iteration, where d is the size of the label set. By extending the necessary linear algebra to
Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels,
and O(n^4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n^2)
time per iteration in all cases. Experiments on graphs from bioinformatics and other application
domains show that these techniques can speed up computation of the kernel by an order of magnitude
or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when
specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to
R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment
kernel of Fröhlich et al. (2006) yet provably positive semi-definite
Fundamentals
Volume 1 establishes the foundations of this new field. It goes through all the steps from data collection, their summary and clustering, to different aspects of resource-aware learning, i.e., hardware, memory, energy, and communication awareness. Machine learning methods are inspected with respect to resource requirements and how to enhance scalability on diverse computing architectures ranging from embedded systems to large computing clusters
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