1,402 research outputs found
Structurally robust biological networks
Background:
The molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.
Results:
In this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.
Conclusions:
The impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters
Dengue disease, basic reproduction number and control
Dengue is one of the major international public health concerns. Although
progress is underway, developing a vaccine against the disease is challenging.
Thus, the main approach to fight the disease is vector control. A model for the
transmission of Dengue disease is presented. It consists of eight mutually
exclusive compartments representing the human and vector dynamics. It also
includes a control parameter (insecticide) in order to fight the mosquito. The
model presents three possible equilibria: two disease-free equilibria (DFE) and
another endemic equilibrium. It has been proved that a DFE is locally
asymptotically stable, whenever a certain epidemiological threshold, known as
the basic reproduction number, is less than one. We show that if we apply a
minimum level of insecticide, it is possible to maintain the basic reproduction
number below unity. A case study, using data of the outbreak that occurred in
2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has
appeared in International Journal of Computer Mathematics (2011), DOI:
10.1080/00207160.2011.55454
Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil
We propose a new mathematical model for the spread of Zika virus. Special
attention is paid to the transmission of microcephaly. Numerical simulations
show the accuracy of the model with respect to the Zika outbreak occurred in
Brazil.Comment: This is a preprint of a paper whose final and definite form is with
'Mathematical Methods in the Applied Sciences', ISSN 0170-4214. Submitted Aug
10, 2017; Revised Nov 13, 2017; accepted for publication Nov 14, 201
Completeness of Lyapunov Abstraction
In this work, we continue our study on discrete abstractions of dynamical
systems. To this end, we use a family of partitioning functions to generate an
abstraction. The intersection of sub-level sets of the partitioning functions
defines cells, which are regarded as discrete objects. The union of cells makes
up the state space of the dynamical systems. Our construction gives rise to a
combinatorial object - a timed automaton. We examine sound and complete
abstractions. An abstraction is said to be sound when the flow of the time
automata covers the flow lines of the dynamical systems. If the dynamics of the
dynamical system and the time automaton are equivalent, the abstraction is
complete.
The commonly accepted paradigm for partitioning functions is that they ought
to be transversal to the studied vector field. We show that there is no
complete partitioning with transversal functions, even for particular dynamical
systems whose critical sets are isolated critical points. Therefore, we allow
the directional derivative along the vector field to be non-positive in this
work. This considerably complicates the abstraction technique. For
understanding dynamical systems, it is vital to study stable and unstable
manifolds and their intersections. These objects appear naturally in this work.
Indeed, we show that for an abstraction to be complete, the set of critical
points of an abstraction function shall contain either the stable or unstable
manifold of the dynamical system.Comment: In Proceedings HAS 2013, arXiv:1308.490
Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation
In this paper we provide rigorous proof for the convergence of an iterative
voting-based image segmentation algorithm called Active Masks. Active Masks
(AM) was proposed to solve the challenging task of delineating punctate
patterns of cells from fluorescence microscope images. Each iteration of AM
consists of a linear convolution composed with a nonlinear thresholding; what
makes this process special in our case is the presence of additive terms whose
role is to "skew" the voting when prior information is available. In real-world
implementation, the AM algorithm always converges to a fixed point. We study
the behavior of AM rigorously and present a proof of this convergence. The key
idea is to formulate AM as a generalized (parallel) majority cellular
automaton, adapting proof techniques from discrete dynamical systems
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Towards integrated neural-symbolic systems for human-level AI: Two research programs helping to bridge the gaps
After a human-level AI-oriented overview of the status quo in neural-symbolic integration, two research programs aiming at overcoming long-standing challenges in the field are suggested to the community: The first program targets a better understanding of foundational differences and relationships on the level of computational complexity between symbolic and subsymbolic computation and representation, potentially providing explanations for the empirical differences between the paradigms in application scenarios and a foothold for subsequent attempts at overcoming these. The second program suggests a new approach and computational architecture for the cognitively-inspired anchoring of an agent's learning, knowledge formation, and higher reasoning abilities in real-world interactions through a closed neural-symbolic acting/sensing-processing-reasoning cycle, potentially providing new foundations for future agent architectures, multi-agent systems, robotics, and cognitive systems and facilitating a deeper understanding of the development and interaction in human-technological settings
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