156,569 research outputs found
Feasible Interpolation for QBF Resolution Calculi
In sharp contrast to classical proof complexity we are currently short of lower bound techniques for QBF proof systems. In this paper we establish the feasible interpolation technique for all resolution-based QBF systems, whether modelling CDCL or expansion-based solving. This both provides the first general lower bound method for QBF proof systems as well as largely extends the scope of classical feasible interpolation. We apply our technique to obtain new exponential lower bounds to all resolution-based QBF systems for a new class of QBF formulas based on the clique problem. Finally, we show how feasible interpolation relates to the recently established lower bound method based on strategy extraction
The quantum Bell-Ziv-Zakai bounds and Heisenberg limits for waveform estimation
We propose quantum versions of the Bell-Ziv-Zakai lower bounds on the error
in multiparameter estimation. As an application we consider measurement of a
time-varying optical phase signal with stationary Gaussian prior statistics and
a power law spectrum , with . With no other
assumptions, we show that the mean-square error has a lower bound scaling as
, where is the time-averaged mean photon
flux. Moreover, we show that this accuracy is achievable by sampling and
interpolation, for any . This bound is thus a rigorous generalization of
the Heisenberg limit, for measurement of a single unknown optical phase, to a
stochastically varying optical phase.Comment: 18 pages, 6 figures, comments welcom
A feasible interpolation for random resolution
Random resolution, defined by Buss, Kolodziejczyk and Thapen (JSL, 2014), is
a sound propositional proof system that extends the resolution proof system by
the possibility to augment any set of initial clauses by a set of randomly
chosen clauses (modulo a technical condition). We show how to apply the general
feasible interpolation theorem for semantic derivations of Krajicek (JSL, 1997)
to random resolution. As a consequence we get a lower bound for random
resolution refutations of the clique-coloring formulas.Comment: Preprint April 2016, revised September and October 201
DIGITAL SIGNAL PROCESSING FOR RADIO MONITORING
A radio monitoring system based on a receiver, interfaces and FFT analyzer is described. The
controller of the system evaluates spectra and the frequencies and levels of sinusoid signals (carriers)
are accurately measured by interpolation of spectral values. The interpolation procedure and a new
interpolation algorithm is described. The Cramer-Rao Lower Bound is also calculated for real-
and complex-valued input data. Real-life measurement results are also presented
Sharp Bounds for Optimal Decoding of Low Density Parity Check Codes
Consider communication over a binary-input memoryless output-symmetric
channel with low density parity check (LDPC) codes and maximum a posteriori
(MAP) decoding. The replica method of spin glass theory allows to conjecture an
analytic formula for the average input-output conditional entropy per bit in
the infinite block length limit. Montanari proved a lower bound for this
entropy, in the case of LDPC ensembles with convex check degree polynomial,
which matches the replica formula. Here we extend this lower bound to any
irregular LDPC ensemble. The new feature of our work is an analysis of the
second derivative of the conditional input-output entropy with respect to
noise. A close relation arises between this second derivative and correlation
or mutual information of codebits. This allows us to extend the realm of the
interpolation method, in particular we show how channel symmetry allows to
control the fluctuations of the overlap parameters.Comment: 40 Pages, Submitted to IEEE Transactions on Information Theor
Convexity-preserving Bernstein–Be´ zier quartic scheme
A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Be´ zier quartic function is used for interpolation. Lower bound of the boundary and inner Be´zier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints
The Gaussian core model in high dimensions
We prove lower bounds for energy in the Gaussian core model, in which point
particles interact via a Gaussian potential. Under the potential function with , we show that no point
configuration in of density can have energy less than
as with and
fixed. This lower bound asymptotically matches the upper bound of obtained as the expectation in the Siegel mean value
theorem, and it is attained by random lattices. The proof is based on the
linear programming bound, and it uses an interpolation construction analogous
to those used for the Beurling-Selberg extremal problem in analytic number
theory. In the other direction, we prove that the upper bound of is no longer asymptotically sharp when . As
a consequence of our results, we obtain bounds in for the
minimal energy under inverse power laws with , and
these bounds are sharp to within a constant factor as with
fixed.Comment: 30 pages, 1 figur
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