68,300 research outputs found
All Classical Adversary Methods are Equivalent for Total Functions
We show that all known classical adversary lower bounds on randomized query complexity are equivalent for total functions, and are equal to the fractional block sensitivity fbs(f). That includes the Kolmogorov complexity bound of Laplante and Magniez and the earlier relational adversary bound of Aaronson. For partial functions, we show unbounded separations between fbs(f) and other adversary bounds, as well as between the relational and Kolmogorov complexity bounds.
We also show that, for partial functions, fractional block sensitivity cannot give lower bounds larger than sqrt(n * bs(f)), where n is the number of variables and bs(f) is the block sensitivity. Then we exhibit a partial function f that matches this upper bound, fbs(f) = Omega(sqrt(n * bs(f)))
Low-Sensitivity Functions from Unambiguous Certificates
We provide new query complexity separations against sensitivity for total
Boolean functions: a power separation between deterministic (and even
randomized or quantum) query complexity and sensitivity, and a power
separation between certificate complexity and sensitivity. We get these
separations by using a new connection between sensitivity and a seemingly
unrelated measure called one-sided unambiguous certificate complexity
(). We also show that is lower-bounded by fractional block
sensitivity, which means we cannot use these techniques to get a
super-quadratic separation between and . We also provide a
quadratic separation between the tree-sensitivity and decision tree complexity
of Boolean functions, disproving a conjecture of Gopalan, Servedio, Tal, and
Wigderson (CCC 2016).
Along the way, we give a power separation between certificate
complexity and one-sided unambiguous certificate complexity, improving the
power separation due to G\"o\"os (FOCS 2015). As a consequence, we
obtain an improved lower-bound on the
co-nondeterministic communication complexity of the Clique vs. Independent Set
problem.Comment: 25 pages. This version expands the results and adds Pooya Hatami and
Avishay Tal as author
Current mode fractional order filters using VDTAs with Grounded capacitors
In this work, the design of current mode Fractional order filter using VDTAs (Voltage differencing trans-conductance amplifier) as an active element with grounded capacitors has been proposed. The approximate transfer functions of low and high pass filters of fractional order on the basis of the integer order transfer has been shown and the form of those functions of filters is also implemented using VDTA as an active building block. In this work, filters of the different sequence have been realized. The frequency domain simulation results of the proposed filters are obtained on Matlab and PSPICE with TSMC CMOS 180 nm technology parameters. Stability and sensitivity is also verifie
Certificate games
We introduce and study Certificate Game complexity, a measure of complexity
based on the probability of winning a game where two players are given inputs
with different function values and are asked to output such that (zero-communication setting).
We give upper and lower bounds for private coin, public coin, shared
entanglement and non-signaling strategies, and give some separations. We show
that complexity in the public coin model is upper bounded by Randomized query
and Certificate complexity. On the other hand, it is lower bounded by
fractional and randomized certificate complexity, making it a good candidate to
prove strong lower bounds on randomized query complexity. Complexity in the
private coin model is bounded from below by zero-error randomized query
complexity.
The quantum measure highlights an interesting and surprising difference
between classical and quantum query models. Whereas the public coin certificate
game complexity is bounded from above by randomized query complexity, the
quantum certificate game complexity can be quadratically larger than quantum
query complexity. We use non-signaling, a notion from quantum information, to
give a lower bound of on the quantum certificate game complexity of the
function, whose quantum query complexity is , then go on
to show that this ``non-signaling bottleneck'' applies to all functions with
high sensitivity, block sensitivity or fractional block sensitivity.
We consider the single-bit version of certificate games (inputs of the two
players have Hamming distance ). We prove that the single-bit version of
certificate game complexity with shared randomness is equal to sensitivity up
to constant factors, giving a new characterization of sensitivity. The
single-bit version with private randomness is equal to , where
is the spectral sensitivity.Comment: 43 pages, 1 figure, ITCS202
Application of a Fractional Order Integral Resonant Control to increase the achievable bandwidth of a nanopositioner
The congress program will essentially include papers selected on the highest standard by the IPC, according to the IFAC guidelines www.ifac-control.org/publications/Publications-requirements-1.4.pdf, and published in open access in partnership with Elsevier in the IFAC-PapersOnline series, hosted on the ScienceDirect platform www.sciencedirect.com/science/journal/24058963. Survey papers overviewing a research topic are also most welcome. Contributed papers will have usual 6 pages length limitation. 12 pages limitation will apply to survey papers.Publisher PD
Quadratically Tight Relations for Randomized Query Complexity
Let be a Boolean function. The certificate
complexity is a complexity measure that is quadratically tight for the
zero-error randomized query complexity : . In this paper we study a new complexity measure that we call
expectational certificate complexity , which is also a quadratically
tight bound on : . We prove that and show that there is a quadratic separation between
the two, thus gives a tighter upper bound for . The measure is
also related to the fractional certificate complexity as follows:
. This also connects to an open question by
Aaronson whether is a quadratically tight bound for , as
is in fact a relaxation of .
In the second part of the work, we upper bound the distributed query
complexity for product distributions by the square of
the query corruption bound () which improves upon a
result of Harsha, Jain and Radhakrishnan [2015]. A similar statement for
communication complexity is open.Comment: 14 page
Blocks adjustment -- reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation
The length of minimal and maximal blocks equally distant on log-log scale
versus fluctuation function considerably influences bias and variance of DFA.
Through a number of extensive Monte Carlo simulations and different fractional
Brownian motion/fractional Gaussian noise generators, we found the pair of
minimal and maximal blocks that minimizes the sum of mean-squared error of
estimated Hurst exponents for the series of length N=2^p, p=7,...,15.
Sensitivity of DFA to sort-range correlations was examined using ARFIMA(p,d,q)
generator. Due to the bias of the estimator for anti-persistent processes, we
narrowed down the range of Hurst exponent to 1/2<=H< 1.Comment: 20 pages, 14 figures, accepted for publication in Physica A: August
9, 200
Beyond the Waterbed Effect: Development of Fractional Order CRONE Control with Non-Linear Reset
In this paper a novel reset control synthesis method is proposed: CRONE reset
control, combining a robust fractional CRONE controller with non-linear reset
control to overcome waterbed effect. In CRONE control, robustness is achieved
by creation of constant phase behaviour around bandwidth with the use of
fractional operators, also allowing more freedom in shaping the open-loop
frequency response. However, being a linear controller it suffers from the
inevitable trade-off between robustness and performance as a result of the
waterbed effect. Here reset control is introduced in the CRONE design to
overcome the fundamental limitations. In the new controller design, reset phase
advantage is approximated using describing function analysis and used to
achieve better open-loop shape. Sufficient quadratic stability conditions are
shown for the designed CRONE reset controllers and the control design is
validated on a Lorentz-actuated nanometre precision stage. It is shown that for
similar phase margin, better performance in terms of reference-tracking and
noise attenuation can be achieved.Comment: American Control Conference 201
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