128 research outputs found
The Separatrix Algorithm for Synthesis and Analysis of Stochastic Simulations with Applications in Disease Modeling
Decision makers in epidemiology and other disciplines are faced with the daunting challenge of designing interventions that will be successful with high probability and robust against a multitude of uncertainties. To facilitate the decision making process in the context of a goal-oriented objective (e.g., eradicate polio by ), stochastic models can be used to map the probability of achieving the goal as a function of parameters. Each run of a stochastic model can be viewed as a Bernoulli trial in which “success” is returned if and only if the goal is achieved in simulation. However, each run can take a significant amount of time to complete, and many replicates are required to characterize each point in parameter space, so specialized algorithms are required to locate desirable interventions. To address this need, we present the Separatrix Algorithm, which strategically locates parameter combinations that are expected to achieve the goal with a user-specified probability of success (e.g. 95%). Technically, the algorithm iteratively combines density-corrected binary kernel regression with a novel information-gathering experiment design to produce results that are asymptotically correct and work well in practice. The Separatrix Algorithm is demonstrated on several test problems, and on a detailed individual-based simulation of malaria
Mathematics for modern biology
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student-submitted PDF version of thesis.Includes bibliographical references (p. 115-124).In recent years there has been a great deal of new activity at the interface of biology and computation. This has largely been driven by the massive in flux of data from new experimental technologies, particularly high-throughput sequencing and array-based data. These new data sources require both computational power and new mathematics to properly piece them apart. This thesis discusses two problems in this field, network reconstruction and multiple network alignment, and draws the beginnings of a connection between information theory and population genetics. The first section addresses cellular signaling network inference. A central challenge in systems biology is the reconstruction of biological networks from high-throughput data sets, We introduce a new method based on parameterized modeling to infer signaling networks from perturbation data. We use this on Microarray data from RNAi knockout experiments to reconstruct the Rho signaling network in Drosophila. The second section addresses information theory and population genetics. While much has been proven about population genetics, a connection with information theory has never been drawn. We show that genetic drift is naturally measured in terms of the entropy of the allele distribution. We further sketch a structural connection between the two fields. The final section addresses multiple network alignment. With the increasing availability of large protein-protein interaction networks, the question of protein network alignment is becoming central to systems biology.(cont.) We introduce a new algorithm, IsoRankN to compute a global alignment of multiple protein networks. We test this on the five known eukaryotic protein-protein interaction (PPI) networks and show that it outperforms existing techniques.by Michael Hartmann Baym.Ph.D
From non-degenerate conducting polymers to dense matter in the massive Gross-Neveu model
Using results from the theory of non-degenerate conducting polymers like
cis-polyacetylene, we generalize our previous work on dense baryonic matter and
the soliton crystal in the massless Gross-Neveu model to finite bare fermion
mass. In the large N limit, the exact crystal ground state can be constructed
analytically, in close analogy to the bipolaron lattice in polymers. These
findings are contrasted to the standard scenario with homogeneous phases only
and a first order phase transition at a critical chemical potential.Comment: 12 pages, 7 figures, revtex; v2: improved readability, following
advice of PRD referee; accepted for publicatio
Flexible rule use: Common neural substrates in children and adults
AbstractFlexible rule-guided behavior develops gradually, and requires the ability to remember the rules, switch between them as needed, and implement them in the face of competing information. Our goals for this study were twofold: first, to assess whether these components of rule-guided behavior are separable at the neural level, and second, to identify age-related differences in one or more component that could support the emergence of increasingly accurate and flexible rule use over development. We collected event-related fMRI data while 36 children aged 8–13 and adults aged 20–27 performed a task that manipulated rule representation, rule switching, and stimulus incongruency. Several regions – left dorsolateral prefrontal cortex (DLPFC), left posterior parietal cortex, and pre-supplementary motor area – were engaged by both the rule representation and the rule-switching manipulations. These regions were engaged similarly across age groups, though contrasting timecourses of activation in left DLPFC suggest that children updated task rules more slowly than did adults. These findings support the idea that common networks can contribute to a variety of executive functions, and that some developmental changes take the form of changes in temporal dynamics rather than qualitative changes in the network of brain regions engaged
Correlators and fractional statistics in the quantum Hall bulk
We derive single-particle and two-particle correlators of anyons in the
presence of a magnetic field in the lowest Landau level. We show that the
two-particle correlator exhibits signatures of fractional statistics which can
distinguish anyons from their fermionic and bosonic counterparts. These
signatures include the zeroes of the two-particle correlator and its exclusion
behavior. We find that the single-particle correlator in finite geometries
carries valuable information relevant to experiments in which quasiparticles on
the edge of a quantum Hall system tunnel through its bulk.Comment: 4 pages, 3 figures, RevTe
Femtoscopy in Relativistic Heavy Ion Collisions: Two Decades of Progress
Analyses of two-particle correlations have provided the chief means for
determining spatio-temporal characteristics of relativistic heavy ion
collisions. We discuss the theoretical formalism behind these studies and the
experimental methods used in carrying them out. Recent results from RHIC are
put into context in a systematic review of correlation measurements performed
over the past two decades. The current understanding of these results is
discussed in terms of model comparisons and overall trends.Comment: 49 pages, 16 figures; to appear in Annual Review of Nuclear and
Particle Science; final version includes minor updates in text, a few
references added, and two figures updated; Figures and numerical data tables
available at http://www.physics.ohio-state.edu/~lisa/FemtoscopyReview2005
Ultracold atomic quantum gases far from equilibrium
We calculate the time evolution of a far-from-equilibrium initial state of a
non-relativistic ultracold Bose gas in one spatial dimension. The
non-perturbative approximation scheme is based on a systematic expansion of the
two-particle irreducible effective action in powers of the inverse number of
field components. This yields dynamic equations which contain direct
scattering, memory and off-shell effects that are not captured in mean-field
theory.Comment: 4 pages, Proc. Int. Conf. Strong and Electroweak Matter, SEWM 2006;
Nucl. Phys. A, to be publishe
Comparison of Boltzmann Equations with Quantum Dynamics for Scalar Fields
Boltzmann equations are often used to study the thermal evolution of particle
reaction networks. Prominent examples are the computation of the baryon
asymmetry of the universe and the evolution of the quark-gluon plasma after
relativistic heavy ion collisions. However, Boltzmann equations are only a
classical approximation of the quantum thermalization process which is
described by the so-called Kadanoff-Baym equations. This raises the question
how reliable Boltzmann equations are as approximations to the full
Kadanoff-Baym equations. Therefore, we present in this paper a detailed
comparison between the Kadanoff-Baym and Boltzmann equations in the framework
of a scalar Phi^4 quantum field theory in 3+1 space-time dimensions. The
obtained numerical solutions reveal significant discrepancies in the results
predicted by both types of equations. Apart from quantitative discrepancies, on
a qualitative level the universality respected by the Kadanoff-Baym equations
is severely restricted in the case of Boltzmann equations. Furthermore, the
Kadanoff-Baym equations strongly separate the time scales between kinetic and
chemical equilibration. This separation of time scales is absent for the
Boltzmann equation.Comment: text and figures revised, references added, results unchanged, 21
pages, 10 figures, published in Phys. Rev. D73 (2006) 12500
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