118,453 research outputs found
Magnetic fields in the early universe in the string approach to MHD
There is a reformulation of magnetohydrodynamics in which the fundamental
dynamical quantities are the positions and velocities of the lines of magnetic
flux in the plasma, which turn out to obey equations of motion very much like
ideal strings. We use this approach to study the evolution of a primordial
magnetic field generated during the radiation-dominated era in the early
Universe. Causality dictates that the field lines form a tangled random
network, and the string-like equations of motion, plus the assumption of
perfect reconnection, inevitably lead to a self-similar solution for the
magnetic field power spectrum. We present the predicted form of the power
spectrum, and discuss insights gained from the string approximation, in
particular the implications for the existence or not of an inverse cascade.Comment: 12 pages, 2 figure
Patterns hidden from simple algorithms
Is the number 9021960864034418159813 random? Educated opinions might
vary from “No! No single string can be random,” to the more contemptuous
”Come on! Those are just the 714th to 733rd digits of π.” Yet, to my limited
mind, the string did appear random. Is there a way to use some formal
mathematics to justify my naïveté? The modern theory of pseudorandomness indeed manages to explain such phenomena, where strings appear random to simple minds. The key, this theory argues, is that randomness is really in the “eyes of the beholder,” or rather in the computing power of the tester of randomness. More things appear random to simpler, or resource limited, algorithms than to complex, powerful, algorithms
Quantum Arthur-Merlin Games
This paper studies quantum Arthur-Merlin games, which are Arthur-Merlin games
in which Arthur and Merlin can perform quantum computations and Merlin can send
Arthur quantum information. As in the classical case, messages from Arthur to
Merlin are restricted to be strings of uniformly generated random bits. It is
proved that for one-message quantum Arthur-Merlin games, which correspond to
the complexity class QMA, completeness and soundness errors can be reduced
exponentially without increasing the length of Merlin's message. Previous
constructions for reducing error required a polynomial increase in the length
of Merlin's message. Applications of this fact include a proof that logarithmic
length quantum certificates yield no increase in power over BQP and a simple
proof that QMA is contained in PP. Other facts that are proved include the
equivalence of three (or more) message quantum Arthur-Merlin games with
ordinary quantum interactive proof systems and some basic properties concerning
two-message quantum Arthur-Merlin games.Comment: 22 page
COBE vs Cosmic Strings: An Analytical Model
We construct a simple analytical model to study the effects of cosmic strings
on the microwave background radiation. Our model is based on counting random
multiple impulses inflicted on photon trajectories by the string network
between the time of recombination and today. We construct the temperature
auto-correlation function and use it to obtain the effective power spectrum
index n, the rms-quadrupole-normalized amplitude and the rms
temperature variation smoothed on small angular scales. For the values of the
scaling solution parameters obtained in Refs.\cite{bb90},\cite{as90} we obtain
, and . Demanding consistency of these results with the COBE data
leads to (where is the string mass per
unit length), in good agreement with direct normalizations of from
observations.Comment: 12 pages, 5 figures (available upon request), use late
Security of discrete log cryptosystems in the random oracle and the generic model
We introduce novel security proofs that use combinatorial counting arguments rather than reductions to the discrete logarithm or to the Diffie-Hellman problem. Our security results are sharp and clean with no polynomial reduction times involved. We consider a combination of the random oracle model and the generic model. This corresponds to assuming an ideal hash function H given by an oracle and an ideal group of prime order q, where the binary encoding of the group elements is useless for cryptographic attacks In this model, we first show that Schnorr signatures are secure against the one-more signature forgery : A generic adversary performing t generic steps including l sequential interactions with the signer cannot produce l+1 signatures with a better probability than (t 2)/q. We also characterize the different power of sequential and of parallel attacks. Secondly, we prove signed ElGamal encryption is secure against the adaptive chosen ciphertext attack, in which an attacker can arbitrarily use a decryption oracle except for the challenge ciphertext. Moreover, signed ElGamal encryption is secure against the one-more decryption attack: A generic adversary performing t generic steps including l interactions with the decryption oracle cannot distinguish the plaintexts of l + 1 ciphertexts from random strings with a probability exceeding (t 2)/q
Identifying Half-Twists Using Randomized Algorithm Methods
Since the braid group was discovered by E. Artin, the question of its
conjugacy problem has been solved by Garside and Birman, Ko and Lee. However,
the solutions given thus far are difficult to compute with a computer, since
the number of operations needed is extremely large. Meanwhile, random
algorithms used to solve difficult problems such as primality of a number were
developed, and the random practical methods have become an important tool. We
give a random algorithm, along with a conjecture of how to improve its
convergence speed, in order to identify elements in the braid group, which are
conjugated to its generators for a given power. These elements of the braid
group, the half-twists, are important in themselves, as they are the key
players in some geometrical and algebraical methods, the building blocks of
quasipositive braids and they construct endless sets of generators for the
group.Comment: 18 pages, 4 Postscript figures; Last proof read corrections before
printing - Paper accepted for publicatio
Optimal coding and the origins of Zipfian laws
The problem of compression in standard information theory consists of
assigning codes as short as possible to numbers. Here we consider the problem
of optimal coding -- under an arbitrary coding scheme -- and show that it
predicts Zipf's law of abbreviation, namely a tendency in natural languages for
more frequent words to be shorter. We apply this result to investigate optimal
coding also under so-called non-singular coding, a scheme where unique
segmentation is not warranted but codes stand for a distinct number. Optimal
non-singular coding predicts that the length of a word should grow
approximately as the logarithm of its frequency rank, which is again consistent
with Zipf's law of abbreviation. Optimal non-singular coding in combination
with the maximum entropy principle also predicts Zipf's rank-frequency
distribution. Furthermore, our findings on optimal non-singular coding
challenge common beliefs about random typing. It turns out that random typing
is in fact an optimal coding process, in stark contrast with the common
assumption that it is detached from cost cutting considerations. Finally, we
discuss the implications of optimal coding for the construction of a compact
theory of Zipfian laws and other linguistic laws.Comment: in press in the Journal of Quantitative Linguistics; definition of
concordant pair corrected, proofs polished, references update
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