1,875 research outputs found
Chemosensing in microorganisms to practical biosensors
Microorganisms like bacteria can sense concentration of chemo-attractants in
its medium very accurately. They achieve this through interaction between the
receptors on their cell surface and the chemo-attractant molecules (like
sugar). But the physical processes like diffusion set some limits on the
accuracy of detection which was discussed by Berg and Purcell in the late
seventies. We have a re-look at their work in order to assess what insight it
may offer towards making efficient, practical biosensors. We model the
functioning of a typical biosensor as a reaction-diffusion process in a
confined geometry. Using available data first we characterize the system by
estimating the kinetic constants for the binding/unbinding reactions between
the chemo-attractants and the receptors. Then we compute the binding flux for
this system which Berg and Purcell had discussed. But unlike in microorganisms
where the interval between successive measurements determines the efficiency of
the nutrient searching process, it turns out that biosensors depend on long
time properties like signal saturation time which we study in detail. We also
develop a mean field description of the kinetics of the system.Comment: 6 pages, 7 figure
Studies on the SJ Vacuum in de Sitter Spacetime
In this work we study the Sorkin-Johnston (SJ) vacuum in de Sitter spacetime
for free scalar field theory. For the massless theory we find that the SJ
vacuum can neither be obtained from the Fock vacuum of Allen and Folacci
nor from the non-Fock de Sitter invariant vacuum of Kirsten and Garriga. Using
a causal set discretisation of a slab of 2d and 4d de Sitter spacetime, we find
the causal set SJ vacuum for a range of masses of the free scalar
field. While our simulations are limited to a finite volume slab of global de
Sitter spacetime, they show good convergence as the volume is increased. We
find that the 4d causal set SJ vacuum shows a significant departure from the
continuum Motolla-Allen -vacua. Moreover, the causal set SJ vacuum is
well-defined for both the minimally coupled massless and the conformally
coupled massless cases. This is at odds with earlier work on the
continuum de Sitter SJ vacuum where it was argued that the continuum SJ vacuum
is ill-defined for these masses. Our results hint at an important tension
between the discrete and continuum behaviour of the SJ vacuum in de Sitter and
suggest that the former cannot in general be identified with the Mottola-Allen
-vacua even for .Comment: 43 pages, 25 figure
3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction
These are notes of introductory lectures on (a) elements of 2+1 dimensional
gravity, (b) some aspects of its relation to Chern-Simons theory, (c) its
generalization to couple higher spins, and (d) cosmic singularity resolution as
an application in the context of flat space higher spin theory. A knowledge of
the Einstein-Hilbert action, classical non-Abelian gauge theory and some
(negotiable amount of) maturity are the only pre-requisites.Comment: 23 pages, Based on talks/lectures by CK at Goteborg, Tehran and
Bangkok. v2:acknowledgments and references added, v3:published versio
A comparison of the Benjamini-Hochberg procedure with some Bayesian rules for multiple testing
In the spirit of modeling inference for microarrays as multiple testing for
sparse mixtures, we present a similar approach to a simplified version of
quantitative trait loci (QTL) mapping. Unlike in case of microarrays, where the
number of tests usually reaches tens of thousands, the number of tests
performed in scans for QTL usually does not exceed several hundreds. However,
in typical cases, the sparsity of significant alternatives for QTL mapping
is in the same range as for microarrays. For methodological interest, as well
as some related applications, we also consider non-sparse mixtures. Using
simulations as well as theoretical observations we study false discovery rate
(FDR), power and misclassification probability for the Benjamini-Hochberg (BH)
procedure and its modifications, as well as for various parametric and
nonparametric Bayes and Parametric Empirical Bayes procedures. Our results
confirm the observation of Genovese and Wasserman (2002) that for small p the
misclassification error of BH is close to optimal in the sense of attaining the
Bayes oracle. This property is shared by some of the considered Bayes testing
rules, which in general perform better than BH for large or moderate 's.Comment: Published in at http://dx.doi.org/10.1214/193940307000000158 the IMS
Collections (http://www.imstat.org/publications/imscollections.htm) by the
Institute of Mathematical Statistics (http://www.imstat.org
Consistency of a recursive estimate of mixing distributions
Mixture models have received considerable attention recently and Newton
[Sankhy\={a} Ser. A 64 (2002) 306--322] proposed a fast recursive algorithm for
estimating a mixing distribution. We prove almost sure consistency of this
recursive estimate in the weak topology under mild conditions on the family of
densities being mixed. This recursive estimate depends on the data ordering and
a permutation-invariant modification is proposed, which is an average of the
original over permutations of the data sequence. A Rao--Blackwell argument is
used to prove consistency in probability of this alternative estimate. Several
simulations are presented, comparing the finite-sample performance of the
recursive estimate and a Monte Carlo approximation to the permutation-invariant
alternative along with that of the nonparametric maximum likelihood estimate
and a nonparametric Bayes estimate.Comment: Published in at http://dx.doi.org/10.1214/08-AOS639 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Fast generation of stability charts for time-delay systems using continuation of characteristic roots
Many dynamic processes involve time delays, thus their dynamics are governed
by delay differential equations (DDEs). Studying the stability of dynamic
systems is critical, but analyzing the stability of time-delay systems is
challenging because DDEs are infinite-dimensional. We propose a new approach to
quickly generate stability charts for DDEs using continuation of characteristic
roots (CCR). In our CCR method, the roots of the characteristic equation of a
DDE are written as implicit functions of the parameters of interest, and the
continuation equations are derived in the form of ordinary differential
equations (ODEs). Numerical continuation is then employed to determine the
characteristic roots at all points in a parametric space; the stability of the
original DDE can then be easily determined. A key advantage of the proposed
method is that a system of linearly independent ODEs is solved rather than the
typical strategy of solving a large eigenvalue problem at each grid point in
the domain. Thus, the CCR method significantly reduces the computational effort
required to determine the stability of DDEs. As we demonstrate with several
examples, the CCR method generates highly accurate stability charts, and does
so up to 10 times faster than the Galerkin approximation method.Comment: 12 pages, 6 figure
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