117,210 research outputs found
One-way communication complexity and non-adaptive decision trees
We study the relationship between various one-way communication complexity measures of a composed function with the analogous decision tree complexity of the outer function. We consider two gadgets: the AND function on 2 inputs, and the Inner Product on a constant number of inputs. More generally, we show the following when the gadget is Inner Product on 2b input bits for all b ≥ 2, denoted IP. If f is a total Boolean function that depends on all of its n input bits, then the bounded-error one-way quantum communication complexity of f ◦ IP equals Ω(n(b - 1)). If f is a partial Boolean function, then the deterministic one-way communication complexity of f ◦ IP is at least Ω(b · D→dt (f)), where D→dt (f) denotes non-adaptive decision tree complexity of f. To prove our quantum lower bound, we first show a lower bound on the VC-dimension of f ◦ IP. We then appeal to a result of Klauck [STOC’00], which immediately yields our quantum lower bound. Our deterministic lower bound relies on a combinatorial result independently proven by Ahlswede and Khachatrian [Adv. Appl. Math.’98], and Frankl and Tokushige [Comb.’99]. It is known due to a result of Montanaro and Osborne [arXiv’09] that the deterministic one-way communication complexity of f ◦ XOR equals the non-adaptive parity decision tree complexity of f. In contrast, we show the following when the inner gadget is the AND function on 2 input bits. There exists a function for which even the quantum non-adaptive AND decision tree complexity of f is exponentially large in the deterministic one-way communication complexity of f ◦ AND. However, for symmetric functions f, the non-adaptive AND decision tree complexity of f is at most quadratic in the (even two-way) communication complexity of f ◦ AND. In view of the first bullet, a lower bound on non-adaptive AND decision tree complexity of f does not lift to a lower bound on one-way communication complexity of f ◦ AND. The proof of the first bullet above uses the well-studied Odd-Max-Bit function. For the second bullet, we first observe a connection between the one-way communication complexity of f and the Möbius sparsity of f, and then give a lower bound on the Möbius sparsity of symmetric functions. An upper bound on the non-adaptive AND decision tree complexity of symmetric functions follows implicitly from prior work on combinatorial group testing; for the sake of completeness, we include a proof of this result. It is well known that the rank of the communication matrix of a function F is an upper bound on its deterministic one-way communication complexity. This bound is known to be tight for some F. However, in our final result we show that this is not the case when F = f ◦ AND. More precisely we show that for all f, the deterministic one-way communication complexity of F = f ◦ AND is at most (rank(MF))(1 - Ω(1)), where MF denotes the communication matrix of F
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Application of Advanced Early Warning Systems with Adaptive Protection
This project developed and field-tested two methods of Adaptive Protection systems utilizing synchrophasor data. One method detects conditions of system stress that can lead to unintended relay operation, and initiates a supervisory signal to modify relay response in real time to avoid false trips. The second method detects the possibility of false trips of impedance relays as stable system swings “encroach” on the relays’ impedance zones, and produces an early warning so that relay engineers can re-evaluate relay settings. In addition, real-time synchrophasor data produced by this project was used to develop advanced visualization techniques for display of synchrophasor data to utility operators and engineers
Sub-linear Upper Bounds on Fourier dimension of Boolean Functions in terms of Fourier sparsity
We prove that the Fourier dimension of any Boolean function with Fourier
sparsity is at most . Our proof method yields an
improved bound of assuming a conjecture of
Tsang~\etal~\cite{tsang}, that for every Boolean function of sparsity there
is an affine subspace of of co-dimension O(\poly\log s)
restricted to which the function is constant. This conjectured bound is tight
upto poly-logarithmic factors as the Fourier dimension and sparsity of the
address function are quadratically separated. We obtain these bounds by
observing that the Fourier dimension of a Boolean function is equivalent to its
non-adaptive parity decision tree complexity, and then bounding the latter
Optimal Error Rates for Interactive Coding II: Efficiency and List Decoding
We study coding schemes for error correction in interactive communications.
Such interactive coding schemes simulate any -round interactive protocol
using rounds over an adversarial channel that corrupts up to
transmissions. Important performance measures for a coding scheme are its
maximum tolerable error rate , communication complexity , and
computational complexity.
We give the first coding scheme for the standard setting which performs
optimally in all three measures: Our randomized non-adaptive coding scheme has
a near-linear computational complexity and tolerates any error rate with a linear communication complexity. This improves over
prior results which each performed well in two of these measures.
We also give results for other settings of interest, namely, the first
computationally and communication efficient schemes that tolerate adaptively, if only one party is required to
decode, and if list decoding is allowed. These are the
optimal tolerable error rates for the respective settings. These coding schemes
also have near linear computational and communication complexity.
These results are obtained via two techniques: We give a general black-box
reduction which reduces unique decoding, in various settings, to list decoding.
We also show how to boost the computational and communication efficiency of any
list decoder to become near linear.Comment: preliminary versio
Optimal Error Rates for Interactive Coding I: Adaptivity and Other Settings
We consider the task of interactive communication in the presence of
adversarial errors and present tight bounds on the tolerable error-rates in a
number of different settings.
Most significantly, we explore adaptive interactive communication where the
communicating parties decide who should speak next based on the history of the
interaction. Braverman and Rao [STOC'11] show that non-adaptively one can code
for any constant error rate below 1/4 but not more. They asked whether this
bound could be improved using adaptivity. We answer this open question in the
affirmative (with a slightly different collection of resources): Our adaptive
coding scheme tolerates any error rate below 2/7 and we show that tolerating a
higher error rate is impossible. We also show that in the setting of Franklin
et al. [CRYPTO'13], where parties share randomness not known to the adversary,
adaptivity increases the tolerable error rate from 1/2 to 2/3. For
list-decodable interactive communications, where each party outputs a constant
size list of possible outcomes, the tight tolerable error rate is 1/2.
Our negative results hold even if the communication and computation are
unbounded, whereas for our positive results communication and computation are
polynomially bounded. Most prior work considered coding schemes with linear
amount of communication, while allowing unbounded computations. We argue that
studying tolerable error rates in this relaxed context helps to identify a
setting's intrinsic optimal error rate. We set forward a strong working
hypothesis which stipulates that for any setting the maximum tolerable error
rate is independent of many computational and communication complexity
measures. We believe this hypothesis to be a powerful guideline for the design
of simple, natural, and efficient coding schemes and for understanding the
(im)possibilities of coding for interactive communications
Machine Learning in Wireless Sensor Networks: Algorithms, Strategies, and Applications
Wireless sensor networks monitor dynamic environments that change rapidly
over time. This dynamic behavior is either caused by external factors or
initiated by the system designers themselves. To adapt to such conditions,
sensor networks often adopt machine learning techniques to eliminate the need
for unnecessary redesign. Machine learning also inspires many practical
solutions that maximize resource utilization and prolong the lifespan of the
network. In this paper, we present an extensive literature review over the
period 2002-2013 of machine learning methods that were used to address common
issues in wireless sensor networks (WSNs). The advantages and disadvantages of
each proposed algorithm are evaluated against the corresponding problem. We
also provide a comparative guide to aid WSN designers in developing suitable
machine learning solutions for their specific application challenges.Comment: Accepted for publication in IEEE Communications Surveys and Tutorial
Adaptive Protocols for Interactive Communication
How much adversarial noise can protocols for interactive communication
tolerate? This question was examined by Braverman and Rao (IEEE Trans. Inf.
Theory, 2014) for the case of "robust" protocols, where each party sends
messages only in fixed and predetermined rounds. We consider a new class of
non-robust protocols for Interactive Communication, which we call adaptive
protocols. Such protocols adapt structurally to the noise induced by the
channel in the sense that both the order of speaking, and the length of the
protocol may vary depending on observed noise.
We define models that capture adaptive protocols and study upper and lower
bounds on the permissible noise rate in these models. When the length of the
protocol may adaptively change according to the noise, we demonstrate a
protocol that tolerates noise rates up to . When the order of speaking may
adaptively change as well, we demonstrate a protocol that tolerates noise rates
up to . Hence, adaptivity circumvents an impossibility result of on
the fraction of tolerable noise (Braverman and Rao, 2014).Comment: Content is similar to previous version yet with an improved
presentatio
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