2,623 research outputs found
Informational Divergence Approximations to Product Distributions
The minimum rate needed to accurately approximate a product distribution
based on an unnormalized informational divergence is shown to be a mutual
information. This result subsumes results of Wyner on common information and
Han-Verd\'{u} on resolvability. The result also extends to cases where the
source distribution is unknown but the entropy is known
Measuring Shared Information and Coordinated Activity in Neuronal Networks
Most nervous systems encode information about stimuli in the responding
activity of large neuronal networks. This activity often manifests itself as
dynamically coordinated sequences of action potentials. Since multiple
electrode recordings are now a standard tool in neuroscience research, it is
important to have a measure of such network-wide behavioral coordination and
information sharing, applicable to multiple neural spike train data. We propose
a new statistic, informational coherence, which measures how much better one
unit can be predicted by knowing the dynamical state of another. We argue
informational coherence is a measure of association and shared information
which is superior to traditional pairwise measures of synchronization and
correlation. To find the dynamical states, we use a recently-introduced
algorithm which reconstructs effective state spaces from stochastic time
series. We then extend the pairwise measure to a multivariate analysis of the
network by estimating the network multi-information. We illustrate our method
by testing it on a detailed model of the transition from gamma to beta rhythms.Comment: 8 pages, 6 figure
Resolvability on Continuous Alphabets
We characterize the resolvability region for a large class of point-to-point
channels with continuous alphabets. In our direct result, we prove not only the
existence of good resolvability codebooks, but adapt an approach based on the
Chernoff-Hoeffding bound to the continuous case showing that the probability of
drawing an unsuitable codebook is doubly exponentially small. For the converse
part, we show that our previous elementary result carries over to the
continuous case easily under some mild continuity assumption.Comment: v2: Corrected inaccuracies in proof of direct part. Statement of
Theorem 3 slightly adapted; other results unchanged v3: Extended version of
camera ready version submitted to ISIT 201
Measurement uncertainty relations for position and momentum: Relative entropy formulation
Heisenberg's uncertainty principle has recently led to general measurement
uncertainty relations for quantum systems: incompatible observables can be
measured jointly or in sequence only with some unavoidable approximation, which
can be quantified in various ways. The relative entropy is the natural
theoretical quantifier of the information loss when a `true' probability
distribution is replaced by an approximating one. In this paper, we provide a
lower bound for the amount of information that is lost by replacing the
distributions of the sharp position and momentum observables, as they could be
obtained with two separate experiments, by the marginals of any smeared joint
measurement. The bound is obtained by introducing an entropic error function,
and optimizing it over a suitable class of covariant approximate joint
measurements. We fully exploit two cases of target observables: (1)
-dimensional position and momentum vectors; (2) two components of position
and momentum along different directions. In (1), we connect the quantum bound
to the dimension ; in (2), going from parallel to orthogonal directions, we
show the transition from highly incompatible observables to compatible ones.
For simplicity, we develop the theory only for Gaussian states and
measurements.Comment: 33 page
Information processing and the second law of thermodynamics: an inclusive, Hamiltonian approach
We obtain generalizations of the Kelvin-Planck, Clausius, and Carnot
statements of the second law of thermodynamics, for situations involving
information processing. To this end, we consider an information reservoir
(representing, e.g. a memory device) alongside the heat and work reservoirs
that appear in traditional thermodynamic analyses. We derive our results within
an inclusive framework in which all participating elements -- the system or
device of interest, together with the heat, work and information reservoirs --
are modeled explicitly by a time-independent, classical Hamiltonian. We place
particular emphasis on the limits and assumptions under which cyclic motion of
the device of interest emerges from its interactions with work, heat, and
information reservoirs.Comment: 14 pages, 4 figure
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