45,846 research outputs found
Dynamical Behavior of a stochastic SIRS epidemic model
In this paper we study the Kernack - MacKendrick model under telegraph noise.
The telegraph noise switches at random between two SIRS models. We give out
conditions for the persistence of the disease and the stability of a disease
free equilibrium. We show that the asymptotic behavior highly depends on the
value of a threshold which is calculated from the intensities of
switching between environmental states, the total size of the population as
well as the parameters of both SIRS systems. According to the value of
, the system can globally tend towards an endemic case or a disease
free case. The aim of this work is also to describe completely the omega-limit
set of all positive solutions to the model. Moreover, the attraction of the
omega-limit set and the stationary distribution of solutions will be pointed
out.Comment: 16 page
Sketch-based Influence Maximization and Computation: Scaling up with Guarantees
Propagation of contagion through networks is a fundamental process. It is
used to model the spread of information, influence, or a viral infection.
Diffusion patterns can be specified by a probabilistic model, such as
Independent Cascade (IC), or captured by a set of representative traces.
Basic computational problems in the study of diffusion are influence queries
(determining the potency of a specified seed set of nodes) and Influence
Maximization (identifying the most influential seed set of a given size).
Answering each influence query involves many edge traversals, and does not
scale when there are many queries on very large graphs. The gold standard for
Influence Maximization is the greedy algorithm, which iteratively adds to the
seed set a node maximizing the marginal gain in influence. Greedy has a
guaranteed approximation ratio of at least (1-1/e) and actually produces a
sequence of nodes, with each prefix having approximation guarantee with respect
to the same-size optimum. Since Greedy does not scale well beyond a few million
edges, for larger inputs one must currently use either heuristics or
alternative algorithms designed for a pre-specified small seed set size.
We develop a novel sketch-based design for influence computation. Our greedy
Sketch-based Influence Maximization (SKIM) algorithm scales to graphs with
billions of edges, with one to two orders of magnitude speedup over the best
greedy methods. It still has a guaranteed approximation ratio, and in practice
its quality nearly matches that of exact greedy. We also present influence
oracles, which use linear-time preprocessing to generate a small sketch for
each node, allowing the influence of any seed set to be quickly answered from
the sketches of its nodes.Comment: 10 pages, 5 figures. Appeared at the 23rd Conference on Information
and Knowledge Management (CIKM 2014) in Shanghai, Chin
Assessment of treatment response in tuberculosis
Antibiotic treatment of tuberculosis has a duration of several months. There is significant variability of the host immune response and the pharmacokinetic-pharmacodynamic properties of Mycobacterium tuberculosis sub-populations at the site of disease. A limitation of sputum-based measures of treatment response may be sub-optimal detection and monitoring of Mycobacterium tuberculosis sub-populations. Potential biomarkers and surrogate endpoints should be benchmarked against hard clinical outcomes (failure/relapse/death) and may need tailoring to specific patient populations. Here, we assess the evidence supporting currently utilized and future potential host and pathogen-based models and biomarkers for monitoring treatment response in active and latent tuberculosis. Biomarkers for monitoring treatment response in extrapulmonary, pediatric and drug resistant tuberculosis are research priorities
An interior point algorithm for minimum sum-of-squares clustering
Copyright @ 2000 SIAM PublicationsAn exact algorithm is proposed for minimum sum-of-squares nonhierarchical clustering, i.e., for partitioning a given set of points from a Euclidean m-space into a given number of clusters in order to minimize the sum of squared distances from all points to the centroid of the cluster to which they belong. This problem is expressed as a constrained hyperbolic program in 0-1 variables. The resolution method combines an interior point algorithm, i.e., a weighted analytic center column generation method, with branch-and-bound. The auxiliary problem of determining the entering column (i.e., the oracle) is an unconstrained hyperbolic program in 0-1 variables with a quadratic numerator and linear denominator. It is solved through a sequence of unconstrained quadratic programs in 0-1 variables. To accelerate resolution, variable neighborhood search heuristics are used both to get a good initial solution and to solve quickly the auxiliary problem as long as global optimality is not reached. Estimated bounds for the dual variables are deduced from the heuristic solution and used in the resolution process as a trust region. Proved minimum sum-of-squares partitions are determined for the rst time for several fairly large data sets from the literature, including Fisher's 150 iris.This research was supported by the Fonds
National de la Recherche Scientifique Suisse, NSERC-Canada, and FCAR-Quebec
An optimal linear solver for the Jacobian system of the extreme type-II Ginzburg--Landau problem
This paper considers the extreme type-II Ginzburg--Landau equations, a
nonlinear PDE model for describing the states of a wide range of
superconductors. Based on properties of the Jacobian operator and an AMG
strategy, a preconditioned Newton--Krylov method is constructed. After a
finite-volume-type discretization, numerical experiments are done for
representative two- and three-dimensional domains. Strong numerical evidence is
provided that the number of Krylov iterations is independent of the dimension
of the solution space, yielding an overall solver complexity of O(n)
Robust Lattice Alignment for K-user MIMO Interference Channels with Imperfect Channel Knowledge
In this paper, we consider a robust lattice alignment design for K-user
quasi-static MIMO interference channels with imperfect channel knowledge. With
random Gaussian inputs, the conventional interference alignment (IA) method has
the feasibility problem when the channel is quasi-static. On the other hand,
structured lattices can create structured interference as opposed to the random
interference caused by random Gaussian symbols. The structured interference
space can be exploited to transmit the desired signals over the gaps. However,
the existing alignment methods on the lattice codes for quasi-static channels
either require infinite SNR or symmetric interference channel coefficients.
Furthermore, perfect channel state information (CSI) is required for these
alignment methods, which is difficult to achieve in practice. In this paper, we
propose a robust lattice alignment method for quasi-static MIMO interference
channels with imperfect CSI at all SNR regimes, and a two-stage decoding
algorithm to decode the desired signal from the structured interference space.
We derive the achievable data rate based on the proposed robust lattice
alignment method, where the design of the precoders, decorrelators, scaling
coefficients and interference quantization coefficients is jointly formulated
as a mixed integer and continuous optimization problem. The effect of imperfect
CSI is also accommodated in the optimization formulation, and hence the derived
solution is robust to imperfect CSI. We also design a low complex iterative
optimization algorithm for our robust lattice alignment method by using the
existing iterative IA algorithm that was designed for the conventional IA
method. Numerical results verify the advantages of the proposed robust lattice
alignment method
Identification of nonlinear lateral flow immunoassay state-space models via particle filter approach
This is the post-print of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, the particle filtering approach is used, together with the kernel smoothing method, to identify the state-space model for the lateral flow immunoassay through available but short time-series measurement. The lateral flow immunoassay model is viewed as a nonlinear dynamic stochastic model consisting of the equations for the biochemical reaction system as well as the measurement output. The renowned extended Kalman filter is chosen as the importance density of the particle filter for the purpose of modeling the nonlinear lateral flow immunoassay. By using the developed particle filter, both the states and parameters of the nonlinear state-space model can be identified simultaneously. The identified model is of fundamental significance for the development of lateral flow immunoassay quantification. It is shown that the proposed particle filtering approach works well for modeling the lateral flow immunoassay.This work was supported in part by the International Science and Technology
Cooperation Project of China under Grant 2009DFA32050, Natural Science Foundation of China under Grants 61104041, International Science and Technology Cooperation Project of Fujian Province of China under Grant
2009I0016
- ā¦