6,062 research outputs found
Numerical algebraic geometry for model selection and its application to the life sciences
Researchers working with mathematical models are often confronted by the
related problems of parameter estimation, model validation, and model
selection. These are all optimization problems, well-known to be challenging
due to non-linearity, non-convexity and multiple local optima. Furthermore, the
challenges are compounded when only partial data is available. Here, we
consider polynomial models (e.g., mass-action chemical reaction networks at
steady state) and describe a framework for their analysis based on optimization
using numerical algebraic geometry. Specifically, we use probability-one
polynomial homotopy continuation methods to compute all critical points of the
objective function, then filter to recover the global optima. Our approach
exploits the geometric structures relating models and data, and we demonstrate
its utility on examples from cell signaling, synthetic biology, and
epidemiology.Comment: References added, additional clarification
Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks
Future wireless networks have a substantial potential in terms of supporting
a broad range of complex compelling applications both in military and civilian
fields, where the users are able to enjoy high-rate, low-latency, low-cost and
reliable information services. Achieving this ambitious goal requires new radio
techniques for adaptive learning and intelligent decision making because of the
complex heterogeneous nature of the network structures and wireless services.
Machine learning (ML) algorithms have great success in supporting big data
analytics, efficient parameter estimation and interactive decision making.
Hence, in this article, we review the thirty-year history of ML by elaborating
on supervised learning, unsupervised learning, reinforcement learning and deep
learning. Furthermore, we investigate their employment in the compelling
applications of wireless networks, including heterogeneous networks (HetNets),
cognitive radios (CR), Internet of things (IoT), machine to machine networks
(M2M), and so on. This article aims for assisting the readers in clarifying the
motivation and methodology of the various ML algorithms, so as to invoke them
for hitherto unexplored services as well as scenarios of future wireless
networks.Comment: 46 pages, 22 fig
A Novel Multiobjective Cell Switch-Off Framework for Cellular Networks
Cell Switch-Off (CSO) is recognized as a promising approach to reduce the
energy consumption in next-generation cellular networks. However, CSO poses
serious challenges not only from the resource allocation perspective but also
from the implementation point of view. Indeed, CSO represents a difficult
optimization problem due to its NP-complete nature. Moreover, there are a
number of important practical limitations in the implementation of CSO schemes,
such as the need for minimizing the real-time complexity and the number of
on-off/off-on transitions and CSO-induced handovers. This article introduces a
novel approach to CSO based on multiobjective optimization that makes use of
the statistical description of the service demand (known by operators). In
addition, downlink and uplink coverage criteria are included and a comparative
analysis between different models to characterize intercell interference is
also presented to shed light on their impact on CSO. The framework
distinguishes itself from other proposals in two ways: 1) The number of
on-off/off-on transitions as well as handovers are minimized, and 2) the
computationally-heavy part of the algorithm is executed offline, which makes
its implementation feasible. The results show that the proposed scheme achieves
substantial energy savings in small cell deployments where service demand is
not uniformly distributed, without compromising the Quality-of-Service (QoS) or
requiring heavy real-time processing
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Combinatorial optimization and metaheuristics
Today, combinatorial optimization is one of the youngest and most active areas of discrete mathematics. It is a branch of optimization in applied mathematics and computer science, related to operational research, algorithm theory and computational complexity theory. It sits at the intersection of several fields, including artificial intelligence, mathematics and software engineering. Its increasing interest arises for the fact that a large number of scientific and industrial problems can be formulated as abstract combinatorial optimization problems, through graphs and/or (integer) linear programs. Some of these problems have polynomial-time (“efficient”) algorithms, while most of them are NP-hard, i.e. it is not proved that they can be solved in polynomial-time. Mainly, it means that it is not possible to guarantee that an exact solution to the problem can be found and one has to settle for an approximate solution with known performance guarantees. Indeed, the goal of approximate methods is to find “quickly” (reasonable run-times), with “high” probability, provable “good” solutions (low error from the real optimal solution). In the last 20 years, a new kind of algorithm commonly called metaheuristics have emerged in this class, which basically try to combine heuristics in high level frameworks aimed at efficiently and effectively exploring the search space. This report briefly outlines the components, concepts, advantages and disadvantages of different metaheuristic approaches from a conceptual point of view, in order to analyze their similarities and differences. The two very significant forces of intensification and diversification, that mainly determine the behavior of a metaheuristic, will be pointed out. The report concludes by exploring the importance of hybridization and integration methods
Perfect Sampling of the Master Equation for Gene Regulatory Networks
We present a Perfect Sampling algorithm that can be applied to the Master
Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's
Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo
methods and combines it with the Dominated Coupling From The Past (DCFTP)
algorithm to provide guaranteed sampling from the stationary distribution. We
show how the DCFTP-SSA can be generically applied to genetic networks with
feedback formed by the interconnection of linear enzymatic reactions and
nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the
error and convergence of the DCFTP-SSA, as compared to the standard SSA,
through a set of increasingly complex examples. Once the building blocks for
GRNs have been introduced, the algorithm is applied to study properly averaged
dynamic properties of two experimentally relevant genetic networks: the toggle
switch, a two-dimensional bistable system, and the repressilator, a
six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa
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