5,866 research outputs found
Assisted Common Information: Further Results
We presented assisted common information as a generalization of
G\'acs-K\"orner (GK) common information at ISIT 2010. The motivation for our
formulation was to improve upperbounds on the efficiency of protocols for
secure two-party sampling (which is a form of secure multi-party computation).
Our upperbound was based on a monotonicity property of a rate-region (called
the assisted residual information region) associated with the assisted common
information formulation. In this note we present further results. We explore
the connection of assisted common information with the Gray-Wyner system. We
show that the assisted residual information region and the Gray-Wyner region
are connected by a simple relationship: the assisted residual information
region is the increasing hull of the Gray-Wyner region under an affine map.
Several known relationships between GK common information and Gray-Wyner system
fall out as consequences of this. Quantities which arise in other source coding
contexts acquire new interpretations. In previous work we showed that assisted
common information can be used to derive upperbounds on the rate at which a
pair of parties can {\em securely sample} correlated random variables, given
correlated random variables from another distribution. Here we present an
example where the bound derived using assisted common information is much
better than previously known bounds, and in fact is tight. This example
considers correlated random variables defined in terms of standard variants of
oblivious transfer, and is interesting on its own as it answers a natural
question about these cryptographic primitives.Comment: 8 pages, 3 figures, 1 appendix; to be presented at the IEEE
International Symposium on Information Theory, 201
Detection Limit for Optically Sensing Specific Protein Interactions in Free-solution
Optical molecular sensing techniques are often limited by the refractive
index change associated with the probed interactions. In this work, we present
a closed form analytical model to estimate the magnitude of optical refractive
index change arising from protein-protein interactions. The model, based on the
Maxwell Garnett effective medium theory and first order chemical kinetics
serves as a general framework for estimating the detection limits of optical
sensing of molecular interactions. The model is applicable to situations where
one interacting species is immobilized to a surface, as commonly done, or to
emerging techniques such as Back-Scattering Interferometry (BSI) where both
interacting species are un-tethered. Our findings from this model point to the
strong role of as yet unidentified factors in the origin of the BSI signal
resulting in significant deviation from linear optical response.Comment: 7 Page Manuscript + 14 Page Supplementary Informatio
Projective modules over overrings of polynomial rings
Let A be a commutative Noetherian ring of dimension d and let P be a
projective R=A[X_1,\ldots,X_l,Y_1,\ldots,Y_m,\frac {1}{f_1\ldots f_m}]-module
of rank r\geq max {2,dim A+1, where f_i\in A[Y_i]. Then
(i) \EL^1(R\op P) acts transitively on Um(R\oplus P). In particular, P is
cancellative.
(ii) If A is an affine algebra over a field, then P has a unimodular element.
(iii) The natural map \Phi_r : GL_r(R)/EL^1_r(R) \ra K_1(R) is surjective.
(iv) Assume f_i is a monic polynomial. Then \Phi_{r+1} is an isomorphism.
In the case of Laurent polynomial ring (i.e. f_i=Y_i), (i) is due to Lindel,
(ii) is due to Bhatwadekar, Lindel and Rao and (iii, iv) is due to Suslin
Cosmology and thermodynamics of FRW universe with bulk viscous stiff fluid
We consider a cosmological model dominated by stiff fluid with a constant
bulk viscosity. We classify all the possible cases of the universe predicted by
the model and analyzing the scale factor, density as well as the curvature
scalar. We find that when the dimensionless constant bulk viscous parameter is
in the range the model began with a Big Bang, and make a
transition form the decelerating expansion epoch to an accelerating epoch, then
tends to the de Sitter phase as . The transition into the
accelerating epoch would be in the recent past, when For
the model doesn't have a Big Bang and suffered an increase in the
fluid density and scalar curvature as the universe expands, which are
eventually saturates as the scale factor in the future. We have
analyzed the model with statefinder diagnostics and find that the model is
different from CDM model but approaches CDM point as We have also analyzed the status of the generalized second law of
thermodynamics with apparent horizon as the boundary of the universe and found
that the law is generally satisfied when and for
the law is satisfied when the scale factor is larger than a
minimum value
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