335 research outputs found
Universal Nonlinear Filtering Using Feynman Path Integrals II: The Continuous-Continuous Model with Additive Noise
In this paper, the Feynman path integral formulation of the
continuous-continuous filtering problem, a fundamental problem of applied
science, is investigated for the case when the noise in the signal and
measurement model is additive. It is shown that it leads to an independent and
self-contained analysis and solution of the problem. A consequence of this
analysis is Feynman path integral formula for the conditional probability
density that manifests the underlying physics of the problem. A corollary of
the path integral formula is the Yau algorithm that has been shown to be
superior to all other known algorithms. The Feynman path integral formulation
is shown to lead to practical and implementable algorithms. In particular, the
solution of the Yau PDE is reduced to one of function computation and
integration.Comment: Interdisciplinary, 41 pages, 5 figures, JHEP3 class; added more
discussion and reference
Euclidean Quantum Mechanics and Universal Nonlinear Filtering
An important problem in applied science is the continuous nonlinear filtering
problem, i.e., the estimation of a Langevin state that is observed indirectly.
In this paper, it is shown that Euclidean quantum mechanics is closely related
to the continuous nonlinear filtering problem. The key is the configuration
space Feynman path integral representation of the fundamental solution of a
Fokker-Planck type of equation termed the Yau Equation of continuous-continuous
filtering. A corollary is the equivalence between nonlinear filtering problem
and a time-varying Schr\"odinger equation.Comment: 19 pages, LaTeX, interdisciplinar
On the Gaussian Many-to-One X Channel
In this paper, the Gaussian many-to-one X channel, which is a special case of
general multiuser X channel, is studied. In the Gaussian many-to-one X channel,
communication links exist between all transmitters and one of the receivers,
along with a communication link between each transmitter and its corresponding
receiver. As per the X channel assumption, transmission of messages is allowed
on all the links of the channel. This communication model is different from the
corresponding many-to-one interference channel (IC). Transmission strategies
which involve using Gaussian codebooks and treating interference from a subset
of transmitters as noise are formulated for the above channel. Sum-rate is used
as the criterion of optimality for evaluating the strategies. Initially, a many-to-one X channel is considered and three transmission strategies
are analyzed. The first two strategies are shown to achieve sum-rate capacity
under certain channel conditions. For the third strategy, a sum-rate outer
bound is derived and the gap between the outer bound and the achieved rate is
characterized. These results are later extended to the case. Next,
a region in which the many-to-one X channel can be operated as a many-to-one IC
without loss of sum-rate is identified. Further, in the above region, it is
shown that using Gaussian codebooks and treating interference as noise achieves
a rate point that is within bits from the sum-rate capacity.
Subsequently, some implications of the above results to the Gaussian
many-to-one IC are discussed. Transmission strategies for the many-to-one IC
are formulated and channel conditions under which the strategies achieve
sum-rate capacity are obtained. A region where the sum-rate capacity can be
characterized to within bits is also identified.Comment: Submitted to IEEE Transactions on Information Theory; Revised and
updated version of the original draf
Almost Budget Balanced Mechanisms with Scalar Bids For Allocation of a Divisible Good
This paper is about allocation of an infinitely divisible good to several
rational and strategic agents. The allocation is done by a social planner who
has limited information because the agents' valuation functions are taken to be
private information known only to the respective agents. We allow only a scalar
signal, called a bid, from each agent to the social planner. Yang and Hajek
[Jour. on Selected Areas in Comm., 2007] as well as Johari and Tsitsiklis
[Jour. of Oper. Res., 2009] proposed a scalar strategy Vickrey-Clarke-Groves
(SSVCG) mechanism with efficient Nash equilibria. We consider a setting where
the social planner desires minimal budget surplus. Example situations include
fair sharing of Internet resources and auctioning of certain public goods where
revenue maximization is not a consideration. Under the SSVCG framework, we
propose a mechanism that is efficient and comes close to budget balance by
returning much of the payments back to the agents in the form of rebates. We
identify a design criterion for {\em almost budget balance}, impose feasibility
and voluntary participation constraints, simplify the constraints, and arrive
at a convex optimization problem to identify the parameters of the rebate
functions. The convex optimization problem has a linear objective function and
a continuum of linear constraints. We propose a solution method that involves a
finite number of constraints, and identify the number of samples sufficient for
a good approximation.Comment: Accepted for publication in the European Journal of Operational
Research (EJOR
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