Ronny Siegel - Academia.edu (original) (raw)

Papers by Ronny Siegel

Research paper thumbnail of The siegel modular variety of degree two and level four: A report

Research paper thumbnail of Improved bit-stuffing bounds on two-dimensional constraints

We derive lower bounds on the capacity of certain two-dimensional constraints by considering boun... more We derive lower bounds on the capacity of certain two-dimensional constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders.

Research paper thumbnail of Efficient coding for a two-dimensional runlength-limited constraint

Research paper thumbnail of Reviews of Books

International History Review, 2006

Research paper thumbnail of Peculiarities of rf SQUID response in finite magnetic fields

Physica C-superconductivity and Its Applications, 2000

Single-layer washer-type high-T YBa Cu O rf SQUIDs with grain-boundary Josephson junctions, as we... more Single-layer washer-type high-T YBa Cu O rf SQUIDs with grain-boundary Josephson junctions, as well as low-T c 2 3 7 yx c Nb rf SQUIDs with Nb-Al O -Nb tunnel junctions, have been investigated in finite magnetic fields. It was shown 2 3

Research paper thumbnail of On a Generalization of a Theorem of Erich Hecke

Proceedings of The National Academy of Sciences, 1982

E. Hecike initiated the application of representation theory to the study of cusp forms. He showe... more E. Hecike initiated the application of representation theory to the study of cusp forms. He showed that, for p a prime congruent to 3 mod 4, the difference ofmultiplicities ofcertain conjugate representations of SL4(F) on cusp forms of degree 1, level p, and weight 22 is given by the class number h(-p) of the field Q(Vj;). We apply the holomorphic Lefschetz theorem to actions on the Igusa compactification ofthe Siegel moduli space of degree 2 to compute the values of characters of the representations of SpN(FV) on certain spaces of cusp forms of degree 2 and level p at parabolic elements ofthis group. Our results imply that here too, the difference in multiplicities of conjugate representations of Sp4(F,) is a multiple of h(-p).

Research paper thumbnail of Goshawk diet during the nestling period in farmland and forest-dominated areas in southern Norway

HM Johansen: Department of Ecology and Natural Resource Management, The Nor-wegian University of ... more HM Johansen: Department of Ecology and Natural Resource Management, The Nor-wegian University of Life Sciences, PO Box 5003, NO-1432 Ås, Norway V. Selås: Department of Ecology and Natural Resource Management, The Norwegian University of Life Sciences, PO Box ...

Research paper thumbnail of High-order spectral-null codes-constructions and bounds

IEEE Transactions on Information Theory, 1994

denote the set of all words of length n over the alphabet { + 1, -11, having a kth order spectral... more denote the set of all words of length n over the alphabet { + 1, -11, having a kth order spectral-null at zero frequency. A subset of Y ' ( n , k ) is a spectral-null code of length n and order k. Upper and lower bounds on the cardinality of 9 ( n , k ) are derived. In particular we prove that ( k -1) log, ( n / k ) I nlog, l Y ( n , k)l I log, n ) for infinitely many values of n. On the other hand, we show that Y ( n , k ) is Furthermore, bounds on the minimum Hamming distance d of Y ( n , k ) are provided, showing that 2k 5 d I k ( k -1) + 2 for infinitely many n. We also investigate the minimum number of sign changes in a word x EY'(n, k ) and provide an equivalent definition of Y ( n , k ) in terms of the positions of these sign changes. An efficient algorithm for encoding arbitrary information sequences into a second-order spectral-null code of redundancy 3 log, n + O(log log n ) is presented. Furthermore, we prove that the first nonzero moment of any word in 9 ' ( n , k ) is divisible by k! and then show how to construct a word with a spectral null of order k whose first nonzero moment is any even multiple of k!. This leads to an encoding scheme for spectral-null codes of length n and any fixed order k, with rate approaching unity as n -W .

Research paper thumbnail of Single-Exclusion Number and the Stopping Redundancy of MDS Codes

We define the (n,t)-single-exclusion number, S(n,t) as the smallest number of t-subsets of an n-s... more We define the (n,t)-single-exclusion number, S(n,t) as the smallest number of t-subsets of an n-set, such that for each i-subset of the n-set, i=1,...,t+1, there exists a t-subset that contains all but one element of the i-subset. New upper bounds on the single-exclusion number are obtained via probabilistic methods, recurrent inequalities, as well as explicit constructions. The new bounds are used to better understand the stopping redundancy of MDS codes. In particular, it is shown that for [n,k=n-d+1,d] MDS codes, as n goes to infinity, the stopping redundancy is asymptotic to S(n,d-2), if d=o(\sqrt{n}), or if k=o(\sqrt{n}) and k goes to infinity, thus giving partial confirmation of the Schwartz-Vardy conjecture in the asymptotic sense.

Research paper thumbnail of The siegel modular variety of degree two and level four: A report

Research paper thumbnail of Improved bit-stuffing bounds on two-dimensional constraints

We derive lower bounds on the capacity of certain two-dimensional constraints by considering boun... more We derive lower bounds on the capacity of certain two-dimensional constraints by considering bounds on the entropy of measures induced by bit-stuffing encoders.

Research paper thumbnail of Efficient coding for a two-dimensional runlength-limited constraint

Research paper thumbnail of Reviews of Books

International History Review, 2006

Research paper thumbnail of Peculiarities of rf SQUID response in finite magnetic fields

Physica C-superconductivity and Its Applications, 2000

Single-layer washer-type high-T YBa Cu O rf SQUIDs with grain-boundary Josephson junctions, as we... more Single-layer washer-type high-T YBa Cu O rf SQUIDs with grain-boundary Josephson junctions, as well as low-T c 2 3 7 yx c Nb rf SQUIDs with Nb-Al O -Nb tunnel junctions, have been investigated in finite magnetic fields. It was shown 2 3

Research paper thumbnail of On a Generalization of a Theorem of Erich Hecke

Proceedings of The National Academy of Sciences, 1982

E. Hecike initiated the application of representation theory to the study of cusp forms. He showe... more E. Hecike initiated the application of representation theory to the study of cusp forms. He showed that, for p a prime congruent to 3 mod 4, the difference ofmultiplicities ofcertain conjugate representations of SL4(F) on cusp forms of degree 1, level p, and weight 22 is given by the class number h(-p) of the field Q(Vj;). We apply the holomorphic Lefschetz theorem to actions on the Igusa compactification ofthe Siegel moduli space of degree 2 to compute the values of characters of the representations of SpN(FV) on certain spaces of cusp forms of degree 2 and level p at parabolic elements ofthis group. Our results imply that here too, the difference in multiplicities of conjugate representations of Sp4(F,) is a multiple of h(-p).

Research paper thumbnail of Goshawk diet during the nestling period in farmland and forest-dominated areas in southern Norway

HM Johansen: Department of Ecology and Natural Resource Management, The Nor-wegian University of ... more HM Johansen: Department of Ecology and Natural Resource Management, The Nor-wegian University of Life Sciences, PO Box 5003, NO-1432 Ås, Norway V. Selås: Department of Ecology and Natural Resource Management, The Norwegian University of Life Sciences, PO Box ...

Research paper thumbnail of High-order spectral-null codes-constructions and bounds

IEEE Transactions on Information Theory, 1994

denote the set of all words of length n over the alphabet { + 1, -11, having a kth order spectral... more denote the set of all words of length n over the alphabet { + 1, -11, having a kth order spectral-null at zero frequency. A subset of Y ' ( n , k ) is a spectral-null code of length n and order k. Upper and lower bounds on the cardinality of 9 ( n , k ) are derived. In particular we prove that ( k -1) log, ( n / k ) I nlog, l Y ( n , k)l I log, n ) for infinitely many values of n. On the other hand, we show that Y ( n , k ) is Furthermore, bounds on the minimum Hamming distance d of Y ( n , k ) are provided, showing that 2k 5 d I k ( k -1) + 2 for infinitely many n. We also investigate the minimum number of sign changes in a word x EY'(n, k ) and provide an equivalent definition of Y ( n , k ) in terms of the positions of these sign changes. An efficient algorithm for encoding arbitrary information sequences into a second-order spectral-null code of redundancy 3 log, n + O(log log n ) is presented. Furthermore, we prove that the first nonzero moment of any word in 9 ' ( n , k ) is divisible by k! and then show how to construct a word with a spectral null of order k whose first nonzero moment is any even multiple of k!. This leads to an encoding scheme for spectral-null codes of length n and any fixed order k, with rate approaching unity as n -W .

Research paper thumbnail of Single-Exclusion Number and the Stopping Redundancy of MDS Codes

We define the (n,t)-single-exclusion number, S(n,t) as the smallest number of t-subsets of an n-s... more We define the (n,t)-single-exclusion number, S(n,t) as the smallest number of t-subsets of an n-set, such that for each i-subset of the n-set, i=1,...,t+1, there exists a t-subset that contains all but one element of the i-subset. New upper bounds on the single-exclusion number are obtained via probabilistic methods, recurrent inequalities, as well as explicit constructions. The new bounds are used to better understand the stopping redundancy of MDS codes. In particular, it is shown that for [n,k=n-d+1,d] MDS codes, as n goes to infinity, the stopping redundancy is asymptotic to S(n,d-2), if d=o(\sqrt{n}), or if k=o(\sqrt{n}) and k goes to infinity, thus giving partial confirmation of the Schwartz-Vardy conjecture in the asymptotic sense.