27 research outputs found
Killing-Yano tensors and some applications
The role of Killing and Killing-Yano tensors for studying the geodesic motion
of the particle and the superparticle in a curved background is reviewed.
Additionally the Papadopoulos list [74] for Killing-Yano tensors in G
structures is reproduced by studying the torsion types these structures admit.
The Papadopoulos list deals with groups G appearing in the Berger
classification, and we enlarge the list by considering additional G structures
which are not of the Berger type. Possible applications of these results in the
study of supersymmetric particle actions and in the AdS/CFT correspondence are
outlined.Comment: 36 pages, no figure
Patterns in rational base number systems
Number systems with a rational number as base have gained interest
in recent years. In particular, relations to Mahler's 3/2-problem as well as
the Josephus problem have been established. In the present paper we show that
the patterns of digits in the representations of positive integers in such a
number system are uniformly distributed. We study the sum-of-digits function of
number systems with rational base and use representations w.r.t. this
base to construct normal numbers in base in the spirit of Champernowne. The
main challenge in our proofs comes from the fact that the language of the
representations of integers in these number systems is not context-free. The
intricacy of this language makes it impossible to prove our results along
classical lines. In particular, we use self-affine tiles that are defined in
certain subrings of the ad\'ele ring and Fourier
analysis in . With help of these tools we are able to
reformulate our results as estimation problems for character sums
Power-law distributions and Levy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements
A generic model of stochastic autocatalytic dynamics with many degrees of
freedom is studied using computer simulations. The time
evolution of the 's combines a random multiplicative dynamics at the individual level with a global coupling through a
constraint which does not allow the 's to fall below a lower cutoff given
by , where is their momentary average and is a
constant. The dynamic variables are found to exhibit a power-law
distribution of the form . The exponent
is quite insensitive to the distribution of the random factor
, but it is non-universal, and increases monotonically as a function
of . The "thermodynamic" limit, N goes to infty and the limit of decoupled
free multiplicative random walks c goes to 0, do not commute:
for any finite while (which is the common range
in empirical systems) for any positive . The time evolution of exhibits intermittent fluctuations parametrized by a (truncated)
L\'evy-stable distribution with the same index . This
non-trivial relation between the distribution of the 's at a given time
and the temporal fluctuations of their average is examined and its relevance to
empirical systems is discussed.Comment: 7 pages, 4 figure
Polylog space compression is incomparable with Lempel-Ziv and pushdown compression
This paper considers online compression algorithms that use
at most polylogarithmic space (plogon). These algorithms correspond
to compressors in the data stream model. We study the performance
attained by these algorithms and show they are incomparable with both
pushdown compressors and the Lempel-Ziv compression algorithm
Modeling and signal processing for flash memory
This thesis examines the effects of noise and interference on the performance of NAND flash memory. Chapter 3 studies the probabilistic input/output relation between the data stored and the read threshold voltage of a cell and generalizes it to a group of cells. It is then concluded that adjacent cells are correlated due to common aggressors. This motivates the study of adequate signal processing techniques to optimize the reliability performance. Chapter 4 proposes two techniques that can reduce the error rate in light of the result of the previous chapter. The first is based on dividing a group of cells into sub-groups and detecting each sub-group independently. The second approximates the flash system model by a hidden Markov model, then uses the sum-product algorithm to detect the inputs. The soft outputs of the proposed detectors are passed on to the ECC soft decoder. It is shown that the second approach provides significant improvements. Then, it is shown that quantization negatively affects the performance of the sum-product algorithm more in comparison with the first approach. To partially mitigate this effect, an iterative detection/decoding strategy is proposed and shown to improve the performance. Chapter 5 proposes a novel data representation scheme that provides a trade-off between reliability and the amount of data stored per cell, and partially mitigates the effects of device degradation. The scheme divides the stored data into two streams stored in the indices and levels of the non-erased cells, respectively, allowing the first to be detected without any knowledge about the channel. The simulation results show an improvement in the error rate while partially mitigating the need to track the channel parameters and the read references as the device degrade.</p
Dimensions of Copeland-Erdös Sequences
The base-k Copeland-Erdös sequence given by an infinite set A of positive integers is the infinite sequence CEk(A) formed by concatenating the base-k representations of the elements of A in numerical order. This paper concerns the following four quantities. ⹠The finite-state dimension dimFS(CEk(A)), a finite-state version of classical Hausdorff dimension introduced in 2001. ⹠The finite-state strong dimension DimFS(CEk(A)), a finite-state version of classical packing dimension introduced in 2004. This is a dual of dimFS(CEk(A)) satisfying DimFS(CEk(A)) ℠dimFS(CEk(A)). ⹠The zeta-dimension Dimζ(A), a kind of discrete fractal dimension discovered many times over the past few decades. ⹠The lower zeta-dimension dimζ(A), a dual of Dimζ(A) satisfying dimζ(A) †Dimζ(A). We prove the following. 1. dimFS(CEk(A)) ℠dimζ(A). This extends the 1946 proof by Copeland and Erdös that the sequence CEk(PRIMES) is Borel normal. 2. DimFS(CEk(A)) ℠Dimζ(A). 3. These bounds are tight in the strong sense that these four quantities can have (simultaneously) any four values in [0, 1] satisfying the four above-mentioned inequalities
Normal Numbers and Pseudorandom Generators
For an integer b â„ 2 a real number α is b -normal if, for all m > 0, every m-long string of digits in the base-b expansion of α appears, in the limit, with frequency b<sup>-m</sup>. Although almost all reals in [0, 1] are b-normal for every b, it has been rather difficult to exhibit explicit examples. No results whatsoever are known, one way or the other, for the class of ânaturalâ mathematical constants, such as Ï,e,2â and log2. In this paper, we summarize some previous normality results for a certain class of explicit reals and then show that a specific member of this class, while provably 2-normal, is provably not 6-normal. We then show that a practical and reasonably effective pseudorandom number generator can be defined based on the binary digits of this constant and conclude by sketching out some directions for further research
Champernownes Number, Strong Normality, and the X Chromosome
Champernowneâs number is the best-known example of a normal number, but its digits are far from random. The sequence of nucleotides in the human X-chromosome appears non-random in a similar way. We give a new test of pseudorandomness, strong normality, based on the law of the iterated logarithm. Almost all numbers are strongly normal, and we show that a strongly normal number must necessarily be normal. However, Champernowneâs number fails to be strongly normal