Planting plan for grounds of Clifford M. Leonard, Lake Forest, Illinois

Ink , green, brown, blue pencil on tracing paper; plan of grounds, with plantings, pool, gardens, footpaths; unsigned. 85 x 105 cm. No scale. [from photographic copy by Lance Burgharrdt]

High-Rate, Multisymbol-Decodable STBCs From Clifford Algebras

It is well known that space-time block codes (STBCs) obtained from orthogonal designs (ODs) are single-symbol decodable (SSD) and from quasi-orthogonal designs (QODs) are double-symbol decodable (DSD). However, there are SSD codes that are not obtainable from ODs and DSD codes that are not obtainable from QODs. In this paper, a method of constructing g-symbol decodable (g-SD) STBCs using representations of Clifford algebras are presented which when specialized to g = 1, 2 gives SSD and DSD codes, respectively. For the number of transmit antennas 2(a) the rate (in complex symbols per channel use) of the g-SD codes presented in this paper is a+1-g/2(a-9). The maximum rate of the DSD STBCs from QODs reported in the literature is a/2(a-1) which is smaller than the rate a-1/2(a-2) of the DSD codes of this paper, for 2(a) transmit antennas. In particular, the reported DSD codes for 8 and 16 transmit antennas offer rates 1 and 3/4, respectively, whereas the known STBCs from QODs offer only 3/4 and 1/2, respectively. The construction of this paper is applicable for any number of transmit antennas. The diversity sum and diversity product of the new DSD codes are studied. It is shown that the diversity sum is larger than that of all known QODs and hence the new codes perform better than the comparable QODs at low signal-to-noise ratios (SNRs) for identical spectral efficiency. Simulation results for DSD codes at variousspectral efficiencies are provided.

Paavo Ravila ja Leonard Bloomfield kielitieteen oppihistoriassa : Vertaileva tutkimus tutkijankuvasta ja tieteenfilosofiasta

Tämä tutkielma käsittelee Paavo Ravilan (1902–1974) ja Leonard Bloomfieldin (1887–1949) tieteenfilosofisia näkemyksiä ja heistä muodostunutta tutkijankuvaa. Työn näkökulma on oppihistoriallinen, ja sen tavoitteena on selvittää Ravilan ja Bloomfieldin teoreettisten näkemysten yhtäläisyyksiä. Työn pääasiallinen lähdekirjallisuus sisältää sekä kotimaista että kansainvälistä kielitieteen historiankirjoitusta. Aineistona on Ravilan ja Bloomfieldin teoreettisen tason kirjoitukset kielitieteestä ja tieteenfilosofiasta; näin ollen heidän kielitieteelliset tutkimuksensa jäävät työn ulkopuolelle. Työtä varten on käytetty myös arkistolähteitä sekä ulkomailta että Suomesta. Ravilan kansainvälisyyttä käsiteltäessä arvokasta aineistoa ovat varsinkin yhdysvaltalaisten yliopistojen arkistoista löytynyt kirjeenvaihto ja muu arkistomateriaali. Luvussa 2 esitellään yleistä kielitieteen historiaa 1800-luvulta 1960-luvulle. Luvussa 3 käsitellään Ravilan ja Bloomfieldin elämää ja uraa ja analysoidaan heistä muodostunutta tutkijankuvaa. Luvussa 4 käsitellään niitä tieteenfilosofisia kysymyksiä, joissa Ravilan ja Bloomfieldin ajatusten samankaltaisuus parhaiten tulee esille: empirismiä, positivismia, merkitystä, formalismia sekä synkronian ja diakronian suhdetta. Ravila ja Bloomfield painottivat empiristisen asennoitumisen tärkeyttä kielitieteessä erityisesti suhteessa aineistoon ja siitä tehtäviin päätelmiin. Lisäksi molemmat olivat positivisteja ja vastustivat siksi sellaisia selityksiä, joita ei voi perustella aineistosta käsin suorien havaintojen avulla. Myös molemmilla toistuva tieteellisyyden vaatimus on johdettavissa positivistisesta asennoitumisesta. Kielitieteen oppihistoriassa Ravilan ja Bloomfieldin tutkijankuva on erilainen varsinkin suhteessa merkityksentutkimukseen, mutta heidän kannanottojensa yksityiskohtaisempi tarkastelu osoittaa, että heidän näkemyksistään voidaan löytää yllättäviä samankaltaisuuksia. Myös synkronian ja diakronian suhdetta tutkittaessa voidaan havaita yhtymäkohtia: synkronistina pidetty Bloomfield ja diakronistina pidetty Ravila pitivät molemmat parhaana lähestymistapana kieleen synkronian ja diakronian yhdistävää tutkimusotetta. Vertailemalla Ravilan ja Bloomfieldin tieteenfilosofisia näkemyksiä voidaan havaita, että heidän käsityksensä kielitieteestä on monilta osin yhteneväinen. Lisäksi vertailu avaa mielenkiintoisia näkökulmia Ravilan suhteeseen suomalaiseen kielitieteeseen. Esimerkiksi positivismin mukainen metafysiikkavastaisuus erottaa hänet ajan eurooppalaisesta kielitieteestä ja toisaalta yhdistää häntä yhdysvaltalaiseen kielitieteeseen.

STBC's from representation of extended Clifford Algebras

A set of sufficient conditions to construct lambda-real symbol Maximum Likelihood (ML) decodable STBCs have recently been provided by Karmakar et al. STBCs satisfying these sufficient conditions were named as Clifford Unitary Weight (CUW) codes. In this paper, the maximal rate (as measured in complex symbols per channel use) of CUW codes for lambda = 2(a), a is an element of N is obtained using tools from representation theory. Two algebraic constructions of codes achieving this maximal rate are also provided. One of the constructions is obtained using linear representation of finite groups whereas the other construction is based on the concept of right module algebra over non-commutative rings. To the knowledge of the authors, this is the first paper in which matrices over non-commutative rings is used to construct STBCs. An algebraic explanation is provided for the 'ABBA' construction first proposed by Tirkkonen et al and the tensor product construction proposed by Karmakar et al. Furthermore, it is established that the 4 transmit antenna STBC originally proposed by Tirkkonen et al based on the ABBA construction is actually a single complex symbol ML decodable code if the design variables are permuted and signal sets of appropriate dimensions are chosen.

Minimum-Decoding-Complexity, maximum-rate Space-Time Block Codes from Clifford algebras

It is well known that Alamouti code and, in general, Space-Time Block Codes (STBCs) from complex orthogonal designs (CODs) are single-symbol decodable/symbolby-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes are obtainable from designs that are not CODs. Recently, two such classes of SSD codes have been studied: (i) Coordinate Interleaved Orthogonal Designs (CIODs) and (ii) Minimum-Decoding-Complexity (MDC) STBCs from Quasi-ODs (QODs). In this paper, we obtain SSD codes with unitary weight matrices (but not CON) from matrix representations of Clifford algebras. Moreover, we derive an upper bound on the rate of SSD codes with unitary weight matrices and show that our codes meet this bound. Also, we present conditions on the signal sets which ensure full-diversity and give expressions for the coding gain.

High-rate, Double-Symbol-Decodable STBCs from Clifford Algebras

For the number of transmit antennas N = 2(a) the maximum rate (in complex symbols per channel use) of all the Quasi-Orthogonal Designs (QODs) reported in the literature is a/2(a)-1. In this paper, we report double-symbol-decodable Space-Time Block Codes with rate a-1/2(a)-2 for N = 2(a) transmit antennas. In particular, our code for 8 and 16 transmit antennas offer rates 1 and 3/4 respectively, the known QODs offer only 3/4 and 1/2 respectively. Our construction is based on the representations of Clifford algebras and applicable for any number of transmit antennas. We study the diversity sum and diversity product of our codes. We show that our diversity sum is larger than that of all known QODs and hence our codes perform better than the comparable QODs at low SNRs for identical spectral efficiency. We provide simulation results for various spectral efficiencies.

Multigroup-Decodable STBCs from Clifford Algebras

A Space-Time Block Code (STBC) in K symbols (variables) is called g-group decodable STBC if its maximum-likelihood decoding metric can be written as a sum of g terms such that each term is a function of a subset of the K variables and each variable appears in only one term. In this paper we provide a general structure of the weight matrices of multi-group decodable codes using Clifford algebras. Without assuming that the number of variables in each group to be the same, a method of explicitly constructing the weight matrices of full-diversity, delay-optimal g-group decodable codes is presented for arbitrary number of antennas. For the special case of Nt=2a we construct two subclass of codes: (i) A class of 2a-group decodable codes with rate a2(a−1), which is, equivalently, a class of Single-Symbol Decodable codes, (ii) A class of (2a−2)-group decodable with rate (a−1)2(a−2), i.e., a class of Double-Symbol Decodable codes. Simulation results show that the DSD codes of this paper perform better than previously known Quasi-Orthogonal Designs.

Pensamento científico, integridade de caráter e coletividade: uma leitura sobre a ética da crença de William Kingdon Clifford

Nesta tese abordamos alguns aspectos das inter-relações entre conhecimento, ética e valores dentro da atividade científica segundo as ideias do matemático-filósofo vitoriano William Clifford. O nosso tema geral coloca em jogo o envolvimento da produção, da avaliação e da transmissão de conhecimento científico com os comportamentos, as responsabilidades e os traços de caráter do investigador. Nosso objetivo é oferecer uma introdução ao pensamento e a algumas produções intelectuais de Clifford, um autor pouco familiar ao público filosófico brasileiro, bem como uma descrição comentada de seu escrito mais famoso, intitulado A Ética da Crença. Mediante esse objetivo, extraímos suas concepções a respeito das características e consequências éticas do empreendimento científico. As questões que orientam a tese são as seguintes: de que maneira a produção de conhecimento estaria condicionada à personalidade e ao comportamento ético de quem se lança àquela prática? Em que medida essa prática promove o cultivo de características pessoais socialmente desejáveis e favoráveis? Quais as conseqüências para a sociedade dessa inter-relação entre o caráter do investigador e os valores epistêmicos que estes colocam em ação e, sem os quais parece não ser possível a obtenção de conhecimento confiável?