121,436 research outputs found
Nonlinear Markov Processes in Big Networks
Big networks express various large-scale networks in many practical areas
such as computer networks, internet of things, cloud computation, manufacturing
systems, transportation networks, and healthcare systems. This paper analyzes
such big networks, and applies the mean-field theory and the nonlinear Markov
processes to set up a broad class of nonlinear continuous-time block-structured
Markov processes, which can be applied to deal with many practical stochastic
systems. Firstly, a nonlinear Markov process is derived from a large number of
interacting big networks with symmetric interactions, each of which is
described as a continuous-time block-structured Markov process. Secondly, some
effective algorithms are given for computing the fixed points of the nonlinear
Markov process by means of the UL-type RG-factorization. Finally, the Birkhoff
center, the Lyapunov functions and the relative entropy are used to analyze
stability or metastability of the big network, and several interesting open
problems are proposed with detailed interpretation. We believe that the results
given in this paper can be useful and effective in the study of big networks.Comment: 28 pages in Special Matrices; 201
Refining interaction search through signed iterative Random Forests
Advances in supervised learning have enabled accurate prediction in
biological systems governed by complex interactions among biomolecules.
However, state-of-the-art predictive algorithms are typically black-boxes,
learning statistical interactions that are difficult to translate into testable
hypotheses. The iterative Random Forest algorithm took a step towards bridging
this gap by providing a computationally tractable procedure to identify the
stable, high-order feature interactions that drive the predictive accuracy of
Random Forests (RF). Here we refine the interactions identified by iRF to
explicitly map responses as a function of interacting features. Our method,
signed iRF, describes subsets of rules that frequently occur on RF decision
paths. We refer to these rule subsets as signed interactions. Signed
interactions share not only the same set of interacting features but also
exhibit similar thresholding behavior, and thus describe a consistent
functional relationship between interacting features and responses. We describe
stable and predictive importance metrics to rank signed interactions. For each
SPIM, we define null importance metrics that characterize its expected behavior
under known structure. We evaluate our proposed approach in biologically
inspired simulations and two case studies: predicting enhancer activity and
spatial gene expression patterns. In the case of enhancer activity, s-iRF
recovers one of the few experimentally validated high-order interactions and
suggests novel enhancer elements where this interaction may be active. In the
case of spatial gene expression patterns, s-iRF recovers all 11 reported links
in the gap gene network. By refining the process of interaction recovery, our
approach has the potential to guide mechanistic inquiry into systems whose
scale and complexity is beyond human comprehension
On Orthogonal Band Allocation for Multi-User Multi-Band Cognitive Radio Networks: Stability Analysis
In this work, we study the problem of band allocation of buffered
secondary users (SUs) to primary bands licensed to (owned by)
buffered primary users (PUs). The bands are assigned to SUs in an orthogonal
(one-to-one) fashion such that neither band sharing nor multi-band allocations
are permitted. In order to study the stability region of the secondary network,
the optimization problem used to obtain the stability region's envelope
(closure) is established and is shown to be a linear program which can be
solved efficiently and reliably. We compare our orthogonal allocation system
with two typical low-complexity and intuitive band allocation systems. In one
system, each cognitive user chooses a band randomly in each time slot with some
assignment probability designed such that the system maintained stable, while
in the other system fixed (deterministic) band assignment is adopted throughout
the lifetime of the network. We derive the stability regions of these two
systems. We prove mathematically, as well as through numerical results, the
advantages of our proposed orthogonal system over the other two systems.Comment: Conditional Acceptance in IEEE Transactions on Communication
Inference and learning in sparse systems with multiple states
We discuss how inference can be performed when data are sampled from the
non-ergodic phase of systems with multiple attractors. We take as model system
the finite connectivity Hopfield model in the memory phase and suggest a cavity
method approach to reconstruct the couplings when the data are separately
sampled from few attractor states. We also show how the inference results can
be converted into a learning protocol for neural networks in which patterns are
presented through weak external fields. The protocol is simple and fully local,
and is able to store patterns with a finite overlap with the input patterns
without ever reaching a spin glass phase where all memories are lost.Comment: 15 pages, 10 figures, to be published in Phys. Rev.
An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System
We report constraints on the three-dimensional orbital architecture for all
four planets known to orbit the nearby M dwarf Gliese 876 based solely on
Doppler measurements and demanding long-term orbital stability. Our dataset
incorporates publicly available radial velocities taken with the ELODIE and
CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished
HIRES velocities. We first quantitatively assess the validity of the planets
thought to orbit GJ 876 by computing the Bayes factors for a variety of
different coplanar models using an importance sampling algorithm. We find that
a four-planet model is preferred over a three-planet model. Next, we apply a
Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses
and orbits using an n-body model in three-dimensional space. Based on the
radial velocities alone, we find that a 99% credible interval provides upper
limits on the mutual inclinations for the three resonant planets
( for the "c" and "b" pair and for
the "b" and "e" pair). Subsequent dynamical integrations of our posterior
sample find that the GJ 876 planets must be roughly coplanar
( and ), suggesting the amount of
planet-planet scattering in the system has been low. We investigate the
distribution of the respective resonant arguments of each planet pair and find
that at least one argument for each planet pair and the Laplace argument
librate. The libration amplitudes in our three-dimensional orbital model
supports the idea of the outer-three planets having undergone significant past
disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples
available at https://github.com/benelson/GJ87
Evolutionary Poisson Games for Controlling Large Population Behaviors
Emerging applications in engineering such as crowd-sourcing and
(mis)information propagation involve a large population of heterogeneous users
or agents in a complex network who strategically make dynamic decisions. In
this work, we establish an evolutionary Poisson game framework to capture the
random, dynamic and heterogeneous interactions of agents in a holistic fashion,
and design mechanisms to control their behaviors to achieve a system-wide
objective. We use the antivirus protection challenge in cyber security to
motivate the framework, where each user in the network can choose whether or
not to adopt the software. We introduce the notion of evolutionary Poisson
stable equilibrium for the game, and show its existence and uniqueness. Online
algorithms are developed using the techniques of stochastic approximation
coupled with the population dynamics, and they are shown to converge to the
optimal solution of the controller problem. Numerical examples are used to
illustrate and corroborate our results
Multi-TGDR: a regularization method for multi-class classification in microarray experiments
Background
With microarray technology becoming mature and popular, the selection and use
of a small number of relevant genes for accurate classification of samples is a
hot topic in the circles of biostatistics and bioinformatics. However, most of
the developed algorithms lack the ability to handle multiple classes, which
arguably a common application. Here, we propose an extension to an existing
regularization algorithm called Threshold Gradient Descent Regularization
(TGDR) to specifically tackle multi-class classification of microarray data.
When there are several microarray experiments addressing the same/similar
objectives, one option is to use meta-analysis version of TGDR (Meta-TGDR),
which considers the classification task as combination of classifiers with the
same structure/model while allowing the parameters to vary across studies.
However, the original Meta-TGDR extension did not offer a solution to the
prediction on independent samples. Here, we propose an explicit method to
estimate the overall coefficients of the biomarkers selected by Meta-TGDR. This
extension permits broader applicability and allows a comparison between the
predictive performance of Meta-TGDR and TGDR using an independent testing set.
Results
Using real-world applications, we demonstrated the proposed multi-TGDR
framework works well and the number of selected genes is less than the sum of
all individualized binary TGDRs. Additionally, Meta-TGDR and TGDR on the
batch-effect adjusted pooled data approximately provided same results. By
adding Bagging procedure in each application, the stability and good predictive
performance are warranted.
Conclusions
Compared with Meta-TGDR, TGDR is less computing time intensive, and requires
no samples of all classes in each study. On the adjusted data, it has
approximate same predictive performance with Meta-TGDR. Thus, it is highly
recommended
Transit Timing Observations from Kepler: III. Confirmation of 4 Multiple Planet Systems by a Fourier-Domain Study of Anti-correlated Transit Timing Variations
We present a method to confirm the planetary nature of objects in systems
with multiple transiting exoplanet candidates. This method involves a
Fourier-Domain analysis of the deviations in the transit times from a constant
period that result from dynamical interactions within the system. The
combination of observed anti-correlations in the transit times and mass
constraints from dynamical stability allow us to claim the discovery of four
planetary systems Kepler-25, Kepler-26, Kepler-27, and Kepler-28, containing
eight planets and one additional planet candidate.Comment: Accepted to MNRA
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