Elias Bound for General Distances and Stable Sets in Edge-Weighted Graphs

This paper presents an extension of the Elias bound on the minimum distance of codes for discrete alphabets with general, possibly infinite-valued, distances. The bound is obtained by combining a previous extension of the Elias bound, introduced by Blahut, with an extension of a bound previously introduced by the author which builds upon ideas of Gallager, Lov\'asz and Marton. The result can in fact be interpreted as a unification of the Elias bound and of Lov\'asz's bound on graph (or zero-error) capacity, both being recovered as particular cases of the one presented here. Previous extensions of the Elias bound by Berlekamp, Blahut and Piret are shown to be included as particular cases of our bound. Applications to the reliability function are then discussed.Comment: Accepted, IEEE Transaction on Information Theor

Successive Cancellation Decoding of Single Parity-Check Product Codes

We introduce successive cancellation (SC) decoding of product codes (PCs) with single parity-check (SPC) component codes. Recursive formulas are derived, which resemble the SC decoding algorithm of polar codes. We analyze the error probability of SPC-PCs over the binary erasure channel under SC decoding. A bridge with the analysis of PCs introduced by Elias in 1954 is also established. Furthermore, bounds on the block error probability under SC decoding are provided, and compared to the bounds under the original decoding algorithm proposed by Elias. It is shown that SC decoding of SPC-PCs achieves a lower block error probability than Elias' decoding

Immanuel Kant's Idea of Time vs. Norbert Elias’ Critique on his Conception

Abstract: In his Critique of Pure Reason, Kant describes time as the formal condition on which all phenomena are based upon. He considers it as a one-dimensional subject, that is not an empirical perception, which is given a priori and nothing else but the form of an inner sense. Elias contradicts this, as he differentiates between a social time and a physical time. He demands an understanding for the relation between time in ’society' and in ’nature'. Elias states that languages (he specifically mentions German) often don't have a word that would be equivalent to the English term “timing". For Elias ’time' is part of the fifth dimension, the dimension of symbols, of experience, of awareness. Only this makes it possible to find out and know what time really is in a social context, a specific synthesis of occurrences, that has to be learned in higher developed societies that are based on the division of labour. Elias mentions ’time', but he states that it's only a synchronisation of positions in the seriatim of events

A Carriage Ride from Home

Elias Sheads Jr. worked in his father\u27s shop. They made wagons and coaches, some of the bedrock laborers in Gettysburg\u27s society. In 1860, when census taker Aaron Sheely walked the streets of the borough counting heads and recording in vivid detail what Gettysburg looked like, Elias lived with his mother and father. [excerpt

Language, Culture and Symbolic Forms

As Ernst Cassierer introduced in his “Philosophie der symbolischen Formen” in 1923, he specifically mentioned “language” as well as a way of symbolic forms. In 1991, the self declared “researcher on human sciences”, Norbert Elias, published his work called “The Symbol Theory” where he mainly writes about language as an application of symbolic forms and symbols. Elias does not make any reference to Cassirer at all, but states that languages are a part of a civilization process and part of cultur

Ice Cores from the St. Elias Mountains, Yukon, Canada: Their Significance for Climate, Atmospheric Composition and Volcanism in the North Pacific Region

A major achievement in research supported by the Kluane Lake Research Station was the recovery, in 2001 –02, of a suite of cores from the icefields of the central St. Elias Mountains, Yukon, by teams of researchers from Canada, the United States, and Japan. This project led to the development of parallel, long (103 – 104 year) ice-core records of climate and atmospheric change over an altitudinal range of more than 2 km, from the Eclipse Icefield (3017 m) to the ice-covered plateau of Mt. Logan (5340 m). These efforts built on earlier work recovering single ice cores in this region. Comparison of these records has allowed for variations in climate and atmospheric composition to be linked with changes in the vertical structure and dynamics of the North Pacific atmosphere, providing a unique perspective on these changes over the Holocene. Owing to their privileged location, cores from the St. Elias Icefields also contain a remarkably detailed record of aerosols from various sources around or across the North Pacific. In this paper we review major scientific findings from the study of St. Elias Mountain ice cores, focusing on five main themes: (1) The record of stable water isotopes (δ18O, δD), which has unique characteristics that differ from those of Greenland, other Arctic ice cores, and even among sites in the St. Elias; (2) the snow accumulation history; (3) the record of pollen, biomass burning aerosol, and desert dust deposition; (4) the record of long-range air pollutant deposition (sulphate and lead); and (5) the record of paleo-volcanism. Our discussion draws on studies published since 2000, but based on older ice cores from the St. Elias Mountains obtained in 1980 and 1996

Infrared Observations of Hot Gas and Cold Ice toward the Low Mass Protostar Elias 29

We have obtained the full 1-200 um spectrum of the low luminosity (36 Lsun) Class I protostar Elias 29 in the Rho Ophiuchi molecular cloud. It provides a unique opportunity to study the origin and evolution of interstellar ice and the interrelationship of interstellar ice and hot core gases around low mass protostars. We see abundant hot CO and H2O gas, as well as the absorption bands of CO, CO2, H2O and ``6.85 um'' ices. We compare the abundances and physical conditions of the gas and ices toward Elias 29 with the conditions around several well studied luminous, high mass protostars. The high gas temperature and gas/solid ratios resemble those of relatively evolved high mass objects (e.g. GL 2591). However, none of the ice band profiles shows evidence for significant thermal processing, and in this respect Elias 29 resembles the least evolved luminous protostars, such as NGC 7538 : IRS9. Thus we conclude that the heating of the envelope of the low mass object Elias 29 is qualitatively different from that of high mass protostars. This is possibly related to a different density gradient of the envelope or shielding of the ices in a circumstellar disk. This result is important for our understanding of the evolution of interstellar ices, and their relation to cometary ices.Comment: 18 pages and 14 figures, accepted for publication in A&