bluuebunny/crossref_metadata_2025 huggingface dataset:
Plant DNA isolation: a method to efficiently remove polyphenolics, polysaccharides, and RNA
Authors: Jobes David V. , Hurley David L. , Thien Leonard B.
Published: April 2006

Jobes, D. V., Hurley, D. L. & Thien, L. B.: Plant DNA isolation: a method to efficiently remove polyphenolics, polysaccharides, and RNA. – Taxon 44: 379‐386. 1995. – ISSN 0040‐0262.

The isolation of DNA from plants has been described by numerous authors, each contributing a different method to overcome the problems that arise when extracting DNA. There are at least three main contaminants associated with plant DNA that can cause considerable difficulties when conducting restriction enzyme analyses and PCR (polymerase chain reaction) experiments: polyphenolic compounds, polysaccharides, and RNA. The procedure described below alleviates the time and expense of CTAB (cetyltrimethylammonium bromide) and caesium chloride methods by utilizing PVP (polyvinylpyrrolidone) to bind the polyphenolic compounds, a high molar concentration of sodium chloride to inhibit co‐precipitation of the polysaccharides and DNA, and an improved method for removing RNA by selective precipitation with lithium chloride. Isolated DNA was easily digested with restriction enzymes and amplified by the PCR from widely different plant species.
Notes on the tribes Eremothamneae, Gundelieae, and Moquinieae, with comparisons of their pollen
Authors: Robinson Harold
Published: April 2006

Robinson, H.: Notes on the tribes Eremothamneae, Gundelieae, and Moquinieae, with comparisons of their pollen. – Taxon 43: 33‐44. 1994. – ISSN 0040‐0262.

The new tribe Moquinieae is established, and scanning electron micrographs of pollen are presented of Hoplophyllum of the Eremothamneae, Gundelia of the Gundelieae, and Pseudostifftia of the Moquinieae.
Subfamily names in an 1832 preprint of an article on botany for the seventh edition of the Encyclopaedia britannica
Authors: Reveal James L.
Published: April 2006

Reveal, J. L.: Subfamily names in an 1832 preprint of an article on botany for the seventh edition of the Encyclopaedia britannica. – Taxon 44: 589‐596. 1995. – ISSN 0040‐0262.

An article on botany, written by George A. W. Arnott and ultimately published in the seventh edition of the Encyclopaedia britannica in 1842, first appeared as a preprint a decade earlier, being effectively published on 9 Mar 1832. Arnott validly published numerous subfamily names, many of which are presently attributed to later authors.
A re‐examination of Sanango racemosum. 3. Chemotaxonomy
Authors: Jensen Søren Rosendal
Published: April 2006

Jensen, S. R.: A re‐examination of Sanango racemosum. 3. Chemotaxonomy. – Taxon 43: 619‐623. 1994. – ISSN 0040‐0262.

A chemical investigation of Sanango racemosum for the systematically useful iridoids and verbascosides has been performed. No iridoids could be detected, but verbascosides were shown to be present by high performance liquid chromatography and by nuclear magnetic resonance spectroscopy of the crude aqueous extract. Reversed phase chromatography provided two pure verbascosides, calceolarioside C and conandroside, as well as a new caffeic acid derivative which has been named sanangoside. The presence of verbascosides in Sanango, combined with the lack of iridoid glycosides, suggests affinity with the family Gesneriaceae. A closer chemical relationship with the Loganiaceae (Gentianales) is improbable.
Reinstatement of the genus Macledium Cass. (Asteraceae, Mutisieae): morphological and phylogenetic arguments
Authors: Ortiz Santiago
Published: April 2006

Ortiz, S.: Reinstatement of the genus Macledium Cass. (Asteraceae, Mutisieae): morphological and phylogenetic arguments. ‐ Taxon 50: 733–744. 2001. ‐ISSN 0040‐0262.

Studies of the genus Dicoma Cass. (Asteraceae, tribe Mutisieae) indicate that this taxon as currently defined is paraphyletic, and in fact comprises three groups showing marked morphological and anatomical differences. One of these groups is differentiated from Dicoma s.str. by a large number of characters relating to morphology and anatomy of phyllaries, corolla, anthers, style, cypsela, and testa. It is proposed that these species should be considered as a separate genus, for which the name Macledium Cass. has nomenclatural priority. A brief nomenclatural synopsis is presented, including synonyms and nomenclatural types for each taxon in this genus of 20 species.
Typification ofCaulerpa cupressoides(Vahl) C. Agardh andC. taxifolia(Vahl) C. Agardh(Chlorophyta, Caulerpaceae)
Authors: Nielsen Ruth , Price Ian R.
Published: April 2006

Nielsen, R. & Price, I. R.: Typification ofCaulerpa cupressoides(Vahl) C. Agardh andC. taxifolia(Vahl) C. Agardh(Chlorophyta, Caulerpaceae). ‐ Taxon 50: 827–836. 2001.‐ISSN 0040‐0262.

No specimen of either of two Vahl (1802) taxa,Fucus cupressoidesandF. taxifolia, that could represent the holotypes of these names was indicated unambiguously in the protologues. Almost 200 years later, due largely to the lack of critical labelling of original herbarium specimens, it has not been possible to distinguish conclusively any original material of the two taxa. As a result of detailed consideration of numerous specimens in many herbaria, appropriate material for neotypification has been identified: both specimens are at Copenhagen (C), Type No. A‐826 (C 31688) forC. cupressoidesand Type No. A‐1086 (C 27833) for C.taxifolia.
Notes on some species of Chloris (Poaceae) described for the Philippines by P. Durand
Authors: Veldkamp J. F.
Published: April 2006

Veldkamp, J. F.: Notes on some species of Chloris (Poaceae) described for the Philippines by P. Durand. ‐ Taxon 50: 845–852. 2001. ‐ ISSN 0040‐0262.

P. Durand (1808) described three species of Chloris Sw. (Poaceae) for the Philippines. In fact they are American: C. hispida P. Durand is Bouteloua hirsuta Lag., C. peregrina P. Durand is C. rufescens Lag., and C. procumbens P. Durand is Bouteloua prostrata Lag. The likely modern identities of the other six Chloris species treated in the work are noted.
Nomenclatural notes on Notocactus and on Alwin Berger's “Kakteen”
Authors: Doweld Alexander , Greuter Werner
Published: April 2006

Doweld, A. & Greuter, W.: Nomenclatural notes on Notocactus and on Alwin Berger's “Kakteen”. ‐ Taxon 50: 879–885. 2000. ‐ ISSN 0040‐0262.

Notocactus, a name first published by Frič in 1928, was clearly, if implicitly, based on Schumann's Echinocactus subg. Notocactus. The first type designation for the generic name and its subgeneric basionym was by Backeberg in 1938. It conforms to current usage and to the provisions of the Code and must stand. A later designation, based on the assumption that Frič had described a new genus, has no standing; it would have made Notocactus a homotypic earlier synonym of Eriocactus Backeb. (nom. cons. prop. against Eriocephalus Backeb.). More than 70 new combinations and at least three generic names published by Berger in 1929 under a narrow generic concept, differing from the wide concept he adopted in the main body of his book, are to be considered as alternative names accepted and validly published by him in the index to his book. They include 13 new combinations under Notocactus.
A note on the taxonomy of the Macaronesian Euphorbia obtusifolia complex (Euphorbiaceae)
Authors: Molero Julià , Rovira Anna Ma
Published: April 2006

Molero, J. & Rovira, A. M.: A note on the taxonomy of the Macaronesian Euphorbia obtusifolia complex (Euphorbiaceae). – Taxon 47: 321‐332. 1998. – ISSN 0040‐0262.

In a taxonomic synopsis of the Euphorbia obtusifolia complex, new data are presented on typification and synonymy. Keys, illustrations and a distribution map help clarify this complex and correct certain errors and historical inaccuracies regarding the identity and distribution of E. obtusifolia and E. regis‐jubae. A new variety, E. obtusifolia var. wildpretii, is described.
Typification of 10 specific names in Veronica L. (Scrophulariaceae, Veroniceae)
Authors: Martínez‐Ortega María Montserrat , Rico Enrique
Published: April 2006

Martínez‐Ortega, M. M. & Rico, E.: Typification of 10 specific names in Veronica L. (Scrophulariaceae, Veroniceae). – Taxon 50: 543–549. 2001. – ISSN 0040‐0262.

Types for the names V. aragonensis Stroh, V. micrantha Hoffmanns. & Link, V. nummularia Gouan, V. orbiculata A. Kern., V. orsinitana Ten., V. ponae Gouan, V. rosea Desf., V. saturejoides Vis., V. tenuifolia Asso and V. teucrioides Boiss. & Heldr. are here designated.
Wood and stem anatomy ofSarcobatus (Caryophyllales):systematic and ecological implications
Authors: Carlquist Sherwin
Published: April 2006

Carlquist, S.: Wood and stem anatomy ofSarcobatus (Caryophyllales):systematic and ecological implications. – Taxon 49: 27‐34. 2000. – ISSN 0040‐0262.

Quantitative and qualitative data are given forSarcobatus vermiculatus(Hook.) Torr, stem anatomy in order to provide information relevant to Behnke's segregation ofSarcobatusfromChenopodiaceaeand his idea thatSarcobataceaebelong in suborderPhytolaccineaerather than suborderChenopodiineae. Sarcobatushas highly xeromorphic wood such as in xericChenopodiaceae(presence of vasicentric tracheids, narrow vessels, short vessel elements, numerous vessels per group, helical sculpturing of vessel walls), but thesefeaturescould have evolved independently in both suborders. Nonbordered perforation plates, present inSarcobatus, are widespread inCaryophyllaless.str. and may prove to be a defining feature for the recently expandedCaryophyllalestogether with the neighbouring orderSantalales.A single‐layered lateral meristem occurs in genera ofChenopodiinaewith successive cambia, but also in genera ofPhytolaccineae.Likewise, raylessness occurs in both suborders. Stem and wood anatomy does not provide decisive evidence for placement ofSarcobatusinPhytolaccineae, but it does not provide any evidence against that treatment.
The Prometheus Taxonomic Model: a practical approach to representing multiple classifications
Authors: Pullan Martin R. , Watson Mark F. , Kennedy Jessie B. , Raguenaud Cédric , Hyam Roger
Published: April 2006

Pullan, M. R., Watson, M. F., Kennedy, J. B., Raguenaud, C. & Hyam, R.: The Prometheus Taxonomic Model: a practical approach to representing multiple classifications. – Taxon 49: 55‐75. 2000. – ISSN 0040‐0262.

A model for representing taxonomic data in a flexible and dynamic system capable of handling and comparing multiple simultaneous classifications is presented. The Prometheus Taxonomic Model takes as its basis the idea that a taxon can be circumscribed by the specimens or taxa of lower rank which are said to belong to it. In this model alternative taxon concepts are therefore represented in terms of differing circumscriptions. This provides a more objective way of expressing taxonomic concepts than purely descriptive circumscriptions, and is more explicit than merely providing pointers to where circumscriptions have been published. Using specimens as the fundamental elements of taxon circumscription also allows for the automatic naming of taxa based upon the distribution and priority of types within each circumscription, and by application of the International Code of Botanical Nomenclature. This approach effectively separates the process of naming taxa (nomenclature) from that of classification, and therefore enables the system to store multiple classifications. The derivation of the model, how it compares with other models, and the implications for the construction of global data sets and taxonomic working practice are discussed.
Pontechium: a new genus distinct from Echium and Lobostemon (Boraginaceae)
Authors: Hilger Hartmut H. , Böhle Uta‐Regina
Published: April 2006

Hilger, H. H. & Böhle, U.‐R.: Pontechium: a new genus distinct from Echium and Lobostemon (Boraginaceae). – Taxon 49: 737–746. 2000. – ISSN 0040‐0262.

The phylogenetic relationships of Echium, Lobostemon, and Echiostachys (Boraginaceae‐Lithospermeae) were inferred from DNA sequence variation. The presence of a bicapitate rather than a bifid stigma and plastid trnL(UAA), intron, trnL(UAA)‐trnF(UAA) spacer and nuclear (ITS1) DNA sequence analyses confirm an isolated position for Echium maculatum L. and recommend exclusion from the genus Echium (Boraginaceae) as a new genus: Pontechium.
Taxonomy of Cardamine amara (Cruciferae) in the Iberian Peninsula
Authors: Lihová Judita , Marhold Karol , Neuffer Barbara
Published: April 2006

Lihová, J., Marhold, K. & Neuffer, B.: Taxonomy of Cardamine amara (Cruciferae) in the Iberian Peninsula. – Taxon 49: 747–763. 2000. – ISSN 0040‐0262.

Cardamine amara is represented in the Iberian Peninsula by two subspecies: the diploid (2n = 16) subsp. pyrenaea, occurring in the Eastern Pyrenees, and the tetraploid (2n = 32) subsp. olotensis, concentrated at the lower altitudes in Catalonia, N and NE of Barcelona. Morphometric analysis of populations of these taxa and four other subspecies of C. amara, which occur in other parts of Europe, supported their subspecific distinctness. RAPD (Random Amplified Polymorphic DNA) analysis of all six European subspecies of C. amara provided more evidence supporting this taxonomic treatment. Lectotypes were designated for the following names: C. amara var. parviflora Cadevall, C. amara subsp. pyrenaea Sennen, C. amara subsp. siifolia Sennen, and C. amporitana Sennen & Pau.
Viola barceloi Nyman, V. barceloi L. Chodat and V. suavis var. barceloi O. Bolós & Vigo: too many eponyms or too many taxa?
Authors: Mus Maurici , Sáez Llorenç , Rosselló Josep A.
Published: April 2006

Mus, M., Sáez, L. & Rosselló, J. A.: Viola barceloi Nyman, V. barceloi L. Chodat and V. suavis var. barceloi O. Bolós & Vigo: too many eponyms or too many taxa? – Taxon 49: 785–788. 2000. – ISSN 0040‐0262.

The type specimens of three names of taxa of Viola described from Mallorca (Balearic Islands) bearing the epithet barceloi have been studied. The lectotype of Viola barceloi Nyman and the holotype of V. suavis M. Bieb. var. barceloi O. Bolós & Vigo cannot be distinguished from V. alba Besser s.l. A neotype is chosen for V. barceloi L. Chodat (= V. × balearica Rosselló et al.), which is believed to be the natural hybrid between V. jaubertiana Marès & Vigineix and V. alba.
The structure of the paracladial zone in Poaceae
Authors: Vegetti Abelardo C. , Weberling Focko
Published: April 2006

Vegetti, A. C. & Weberling, F.: The structure of the paracladial zone in Poaceae. – Taxon 45: 453‐460. 1996. – ISSN 0040‐0262.

Terms are proposed to designate different subzones and regions within the paracladial zone of the inflorescence, in the Poaceae. In some taxa the inflorescence is composed of short paracladia only. In others the main axis bears short paracladia in the distal region and long paracladia in the proximal region, so that two subzones can be distinguished. In general the inflorescences of grasses lack bracts other than those belonging to the spikelets. In the Andropogoneae, however, some inflorescences have long paracladia that lack bracts and prophylls but others have long paracladia with well developed bracts and prophylls. The former are designated as “long paracladia without trophotagma”, and the latter as “long paracladia with trophotagma”.
The valid publication of Acidosasa (Gramineae, Bambusoideae)
Authors: Li De‐Zhu
Published: April 2006

Li, D.‐Z.: The valid publication of Acidosasa (Gramineae, Bambusoideae). – Taxon 46: 105‐107. 1997. – ISSN 0040‐0262.

The name Acidosasa was proposed by Chu & Chao in 1979 for a new monospecific genus, with A. chinensis as type, but neither name was validly published because two “type” specimens were cited for A. chinensis. In 1991, the same authors designated a lectotype for A. chinensis. Meanwhile, Keng in 1982 had fulfilled the requirements for valid publication by designating a single specimen as the type, which is the same as the later “lectotype”. Thanks to Keng's early validation the nomenclatural repercussions of the original fault are minimal, with but a single species having to change its currently accepted name.
Sarcobataceae – a new family of Caryophyllales
Authors: Behnke H.‐Dietmar
Published: April 2006

Behnke, H.‐D.: Sarcobataceae – a new family of Caryophyllales. – Taxon 46: 495‐507. 1997. – ISSN 0040‐0262.

A review of the discovery and early descriptions of Sarcobatus as well as of its taxonomic history is presented. Studies of the form and size of sieve‐element plastids in the order Caryophyllales reveal significant differences between Sarcobatus (so far in Chenopodiaceae) and the majority of the Chenopodiaceae/Amaranthaceae clade (i.e., suborder Chenopodiineae). The presence of P3cf‐form sieve‐element plastids and concomitant absence of chenopod‐specific P3f‐form plastids reinforce other evidence, in particular from chloroplast DNA sequencing, to make appear Sarcobatus quite distinct from the Chenopodiineae clade and suggest that its proper place is in the vicinity of the Phytolaccaceae and Nyctaginaceae. Therefore, Sarcobatus is segregated as a new family, Sarcobataceae.
Reproductive anatomy and relationships of Setchellanthus caeruleus (Setchellanthaceae)
Authors: Tobe Hiroshi , Carlquist Sherwin , Iltis Hugh H.
Published: April 2006

Tobe, H., Carlquist, S. & litis, H. H.: Reproductive anatomy and relationships of Setchellanthus caeruleus (Setchellanthaceae). – Taxon 48: 277‐283. 1999. – ISSN 0040‐0262.

Floral, seed, and fruit anatomy of the unispecific Mexican genus Setchellanthus are described. The genus has floral features that are characteristic of some traditionally defined Capparales or close allies of an expanded order Capparales, viz., a (5‐)6(‐7)‐merous flower with a 3‐merous gynoecium and an androecium comprising (5‐)6(‐7) fascicles of stamens that develop centrifugally; a short androgynophore and well‐developed gynophore; a 3‐loculed gynoecium with a 3‐lobed style and 3 conduplicate valves that separate from the vascular placental column at maturity much as do the valves of Cleome or Brassicaceae. Setchellanthus, however, has straight seeds with a spatulate embryo and a non‐fibrous exotegmen; it lacks the reniform seeds with fibrous exotegmen characteristic of the core Capparales. Vascular bundles in the fruit wall are amphivasal and show an extensive secondary growth that produces tracheids like those of the secondary xylem of stems; bordered pits are present in the wall of the inner epidermis cells. The floral and seed anatomy as well as the distinctive fruit anatomy support a position of Setchellanthus that is near‐basal to the core Capparales.
A tribal classification of the Periplocoideae (Apocynaceae)
Authors: Venter H. J. T. , Verhoeven R. L.
Published: April 2006

Venter, H. J. T. & Verhoeven, R. L.: A tribal classification of the Periplocoideae (Apocynaceae). – Taxon 46: 705‐720. 1997. – ISSN 0040‐0262.

The diagnostic features used to delimit genera are enumerated and critically analysed. Floral characteristics are important: shape and depth of the corolla tube, and positions of outer corona, stamens, and gynostegium. Coronal structure is valuable but can be misleading. Vegetative features are sometimes consistent within genera and may serve as a complement to floral characteristics. The Periplocoideae are, for the first time, subdivided: three tribes are recognized, two of them newly described and named, and the individual genera and generic synonyms are mentioned for each. Some nomenclatural new combinations, required as a consequence of newly proposed synonyms, are validated in the genera Camptocarpus (4), Cryptolepis (4), Decalepis (2), and Pentopetia (2).
Latin, the Renaissance lingua franca, and English, the 20th century language of science: their role in biotaxonomy
Authors: McNeill J.
Published: April 2006

McNeill, J.: Latin, the Renaissance lingua franca, and English, the 20th century language of science: their role in biotaxonomy. – Taxon 46: 751‐757. 1997. – ISSN 0040‐0262.

In response to the plea by Filgueiras that Latin diagnoses remain mandatory for the establishment of names of new taxa, and to his protest against the use of English as an alternative to Latin, foreseen in the Draft BioCode, the role of these two languages in biotaxonomic descriptions is discussed. It is pointed out that the origin of the existing requirement for Latin diagnoses of new taxa under the botanical Code is based not on Latin being a neutral language, or a simple language, but on the fact that it was the language of scholarship in the 18th century, at the point of origin of modern biological nomenclature. Likewise the suggestion that a BioCode should permit English diagnoses is not a matter of linguistic chauvinism but a simple reflection of the reality that English is the dominant language of science as we enter the 21st century.
A list of suprageneric names in Ranunculaceae (Magnoliophyta)
Authors: Keener Carl S. , Reveal James L. , Dutton Bryan E. , Ziman Svetlana
Published: April 2006

Keener, C. S., Reveal, J. L., Dutton, B. E. & Ziman, S.: A list of suprageneric names in Ranunculaceae (Magnoliophyta). – Taxon 48: 497‐506. 1999. – ISSN 0040‐0262.

A list of suprageneric names associated with the Ranunculaceae is given, including the validly published names of 5 orders, 15 families, 18 subfamilies, 23 tribes, and 21 subtribes, as well as 23 unranked names with Latin diagnoses and 74 invalidly published “names”. For the latter, some of which are in current use, the reason of their non‐valid status is given by means of a reference to the pertinent article in the Code.
On the circumscription of the Blennospermatinae (Asteraceae, Senecioneae) based on ndhF sequence data
Authors: Swenson Ulf , Bremer Kåre
Published: April 2006

Swenson, U. & Bremer, K.: On the circumscription of the Blennospermatinae (Asteraceae, Senecioneae) based on ndhF sequence data. – Taxon 48: 7‐14. 1999. – ISSN 0040‐0262.

The subtribe Blennospermatinae is usually defined to comprise four genera (Abrotanella, Blennosperma, Crocidium, and Ischnea). The placement of Abrotanella in the Blennospermatinae has been disputed, and the monogeneric subtribe Abrotanellinae was recently erected. A cladistic analysis of ndhF sequence data provides strong support for grouping Blennosperma with the Senecioneae, while Abrotanella is only weakly associated with the Senecioneae and does not form a monophyletic group with Blennosperma. Crocidium and Ischnea (not sequenced) are morphologically close to Blennosperma. Hence, the Blennospermatinae are best circumscribed to include only Blennosperma, Crocidium, and Ischnea, but not Abrotanella. The tribal position of Abrotanella remains uncertain.
TaxLink, a program for computer‐assisted documentation of different circumscriptions of biological taxa
Authors: Gradstein S. Rob , Sauer Michael , Braun Walter , Koperski Monika , Ludwig Gerhard
Published: April 2006

Gradstein, S. R., Sauer, M., Braun, W., Koperski, M. & Ludwig, G.: TaxLink, a program for computer‐assisted documentation of different circumscriptions of biological taxa. – Taxon 50:1075–1084. 2001. ISSN 0040–0262.

Taxonomic interpretations of species or other taxa may vary considerably among authors. A database program called TaxLink has been developed, which allows for a detailed visualisation of comparisons between different taxonomic concepts. The basic entities of TaxLink are “taxonyms” (= potential taxa; Berendsohn, 1995). TaxLink may store taxonyms with their references, synonyms, relationships between taxonyms, and nomenclatural status of names. Information can be vizualised on screen, printed, and retrieved as textdocument in Microsoft Word format.
A survey of the theory of characteristic functions
Authors: Lukacs Eugene
Published: April 2006

The paper gives a survey of the theory of univariate characteristic functions. These functions were originally introduced as tools in the study of limit theorems but it was later realized that they had an independent mathematical interest. Those parts of the theory which can be found in textbooks are treated only briefly; the main emphasis is placed on more recent developments and areas where active research is still in progress.
A hamiltonian approach to optimal stochastic resource allocation
Authors: Nash P. , Gittins J. C.
Published: April 2006

The problem of scheduling items for service with random service times is formulated as an optimal control problem. Pontryagin's maximum principle is used to determine the optimal schedule in certain cases.
A mixed autoregressive-moving average exponential sequence and point process (EARMA 1,1)
Authors: Jacobs P. A. , Lewis P. A. W.
Published: April 2006

A stationary sequence of random variables with exponential marginal distributions and the correlation structure of an ARMA (1, 1) process is defined. The process is formed as a random linear combination of i.i.d. exponential random variables and is very simple to generate on a computer. Moments and joint distributions for the sequence are obtained, as well as limiting properties of sums of the random variables and of the point process whose intervals have the EARMA (1, 1) structure.
The covariance function of the virtual waiting-time process in an M/G/1 queue
Authors: Ott Teunis J.
Published: April 2006

Let R(t) be the covariance function of the stationary virtual waiting-time process of a stable M/G/1 queue. It is proven that if R(t) exists, i.e., if the service-times have a finite third moment, then R(t) is positive and convex on [0, ∞), with an absolutely continuous derivative R’ and a bounded, non-negative second derivative R″. Also, and R″ cannot be chosen monotone. Contrary to a finding by Beneš [1] it is proven that if and only if the service-times have a finite fourth moment.
The intrinsic random functions and their applications
Authors: Matheron G.
Published: April 2006

The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments. They constitute a much wider class than the stationary RF, and are used in practical applications for representing non-stationary phenomena. The most important topics are: existence of a generalized covariance (GC) for which statistical inference is possible from a unique realization; theory of the best linear intrinsic estimator (BLIE) used for contouring and estimating problems; the turning bands method for simulating IRF; and the models with polynomial GC, for which statistical inference may be performed by automatic procedures.
Optimal decision procedures for finite Markov chains. Part II: Communicating systems
Authors: Bather John
Published: April 2006

A Markov process in discrete time with a finite state space is controlled by choosing the transition probabilities from a given convex family of distributions depending on the present state. The immediate cost is prescribed for each choice and it is required to minimise the average expected cost over an infinite future. The paper considers a special case of this general problem and provides the foundation for a general solution. The main result is that an optimal policy exists if each state of the system can be reached with positive probability from any other state by choosing a suitable policy.
Optimal decision procedures for finite Markov chains. Part III: General convex systems
Authors: Bather John
Published: April 2006

This paper is concerned with the general problem of finding an optimal transition matrix for a finite Markov chain, where the probabilities for each transition must be chosen from a given convex family of distributions. The immediate cost is determined by this choice, but it is required to minimise the average expected cost in the long run. The problem is investigated by classifying the states according to the accessibility relations between them. If an optimal policy exists, it can be found by considering the convex subsystems associated with the states at different levels in the classification scheme.
Drift in haploid models
Authors: Cannings C.
Published: April 2006

The classical models for genetic drift of Wright (1931) and Moran (1958) have been generalized by Karlin and McGregor (1965), and Chia and Watterson (1969), this last treatment including the other three. The basic technique for the generalized models was to consider the change of certain expectations of the underlying random variables, the generalization being in terms of the conditional branching process.
The chance of survival of an advantageous mutant in an age-structured population
Authors: Charlesworth Brian , Williamson John A.
Published: April 2006

The evaluation of the chance of survival of an advantageous mutant gene in an age-structured population is of interest since, as pointed out by Charlesworth (1973), the usual evolutionary arguments concerning the long-term relative effectiveness of natural selection on genes acting at different ages (Cole (1954), Hamilton (1966)) should be translated into statements about the survival probabilities of genes with age-specific effects. We shall be concerned with this quantity for the case of a mutant introduced into a large population with discrete age-classes (Leslie (1945)). Let unity be the index of the birth age-class, b that of the age of first reproduction, and d that of the age of last reproduction. Let px be the probability of survival of individuals from age x to x + 1, and let lx be the probability of surviving from conception to age x (lx = πy=1x-1px). Let mx be half the expected number of offspring at age x (demographic differences between the sexes are assumed to be absent; the environment is assumed constant). Since a new mutant gene is carried largely in heterozygotes for a long time after its first appearance, the problem reduces to that of finding the chance of survival of the line descended from a single individual of age-class 1, with the parameters of the heterozygote for the mutant gene. Let the probability generating function for the distribution of heterozygous offspring by a heterozygote aged x be hx(z). If offspring distributions at different ages are independent, the p.g.f. for the total offspring produced at ages b to x by an individual aged x (x ≧ b) is given as
The asymptotic behaviour of birth and death and some related processes
Authors: Barbour Andrew D.
Published: April 2006

The paper examines those continuous time Markov processesZ(·) on the positive integers which have the ‘skip free upwards’ property, with regard to their asymptotic behaviour in the event ofZ(t) tending to infinity. The behaviour is characterised in terms of the convergence or divergence of an appropriate function ofZ(t), and the description is improved by central limit and iterated logarithm theorems. The conditions of the theorems are expressed entirely in terms of the matrixQof instantaneous transition rates forZ(·). The method is applied, by way of example, to the super-critical linear birth and death process.
Asymptotic properties of super-critical branching processes II: Crump-Mode and Jirina processes
Authors: Bingham N. H. , Doney R. A.
Published: April 2006

We obtain results connecting the distribution of the random variablesYandWin the supercritical generalized branching processes introduced by Crump and Mode. For example, if β > 1,EYβandEWβconverge or diverge together and regular variation of the tail of one ofY, Wwith non-integer exponent β > 1 is equivalent to regular variation of the other. We also prove analogous results for the continuous-time continuous state-space branching processes introduced by Jirina.
Queue length for the Ek/G/1 queue by finite waiting room
Authors: Truslove A. L.
Published: April 2006

For the Ek/G/1 queue with finite waiting room the phase technique is used to analyse the Markov chain imbedded in the queueing process at successive instants at which customers complete service, and the distribution of queue length is obtained. The limit as the size of the waiting room becomes infinite is found.
Markov processes associated with critical Galton-Watson processes with application to extinction probabilities
Authors: Sze Michael
Published: April 2006

As an alternative to the embedding technique of T. E. Harris, S. Karlin and J. McGregor, we show that given a critical Galton–Watson process satisfying some mild assumptions, we can always construct a continuous-time Markov branching process having the same asymptotic behaviour as the given process. Thus, via the associated continuous process, additional information about the original process is obtained. We apply this technique to the study of extinction probabilities of a critical Galton–Watson process, and provide estimates for the extinction probabilities by regularly varying functions.
The asymptotic behavior of a divergent linear birth and death process
Authors: Siegel Martha J.
Published: April 2006

We consider a birth and death process withQ-matrix of ratesqm,m+ 1=mβ, qm,m− 1=mδ, qm,m= –m(β+δ) andqm,n= 0 otherwise. We assume that 0 <δ<βandβ–δ= 1. The asymptotic behavior of first-arrival time at statengiven that the process is at statemat time zero is expressed in terms of polynomials and it is shown that ifm<nandmis large that the first-arrival time is close to logn/mwith high probability.
On random processes that are almost strict sense stationary
Authors: Tj⊘stheim Dag
Published: April 2006

An extension of the class of strict sense stationary processes is studied. The extended class represents the strict sense analogy of an extension of wide sense stationary processes considered in an earlier paper [9]. The relations between the various types of processes defined are investigated in the general and in the Gaussian case, and some examples are given. It is shown that associated with a process belonging to the extended class there is a strict sense stationary process. The associated strict sense stationary process is unique iff the original process is ergodic.
Spectral generating operators for non-stationary processes
Authors: Tj⊘stheim D.
Published: April 2006

A new method for obtaining spectral-like representations for a large class of non-stationary random processes is formulated. For a wide sense stationary processX(t) in continuous-time the spectral representation is generated by a self-adjoint operatorHsuch thatX(t)=eiHtX(0). Extending certain recently established operator identities for wide sense stationary processes, it is shown that similar operators exist for classes of non-stationary processes. The representation generated by such an operator has the formand it shares some of the properties of the wide sense stationary spectral representation: it is dual in a precisely defined sense to the time domain representation ofX(t). There exists a classLof linear transformations ofX(t) such that forG∈Lfor some functiongdetermined byG.
On the many server queue with exponential service times
Authors: De Smit J. H. A.
Published: April 2006

The general theory for the many server queue due to Pollaczek (1961) and generalized by the author (de Smit (1973)) is applied to the system with exponential service times. In this way many explicit results are obtained for the distributions of characteristic quantities, such as the actual waiting time, the virtual waiting time, the queue length, the number of busy servers, the busy period and the busy cycle. Most of these results are new, even for the special case of Poisson arrivals.
Regenerative processes in the theory of queues, with applications to the alternating-priority queue
Authors: Stidham Shaler
Published: April 2006

Using some well-known and some recently proved asymptotic properties of regenerative processes, we present a new proof in a general regenerative setting of the equivalence of the limiting distributions of a stochastic process at an arbitrary point in time and at the time of an event from an associated Poisson process. From the same asymptotic properties, several conservation equations are derived that hold for a wide class of GI/G/1 priority queues. Finally, focussing our attention on the alternating-priority queue with Poisson arrivals, we use both types of result to give a new, simple derivation of the expected steady-state delay in the queue in each class.
The structure of extremal processes
Authors: Resnick Sidney I. , Rubinovitch Michael
Published: April 2006

An extremal-F process {Y (t); t ≧ 0} is defined as the continuous time analogue of sample sequences of maxima of i.i.d. r.v.'s distributed like F in the same way that processes with stationary independent increments (s.i.i.) are the continuous time analogue of sample sums of i.i.d. r.v.'s with an infinitely divisible distribution. Extremal-F processes are stochastically continuous Markov jump processes which traverse the interval of concentration of F. Most extremal processes of interest are broad sense equivalent to the largest positive jump of a suitable s.i.i. process and this together with known results from the theory of record values enables one to conclude that the number of jumps of Y (t) in (t1, t2] follows a Poisson distribution with parameter log t2/t1. The time transformation t→ et gives a new jump process whose jumps occur according to a homogeneous Poisson process of rate 1. This fact leads to information about the jump times and the inter-jump times. When F is an extreme value distribution the Y-process has special properties. The most important is that if F(x) = exp {—e–x} then Y(t) has an additive structure. This structure plus non parametric techniques permit a variety of conclusions about the limiting behaviour of Y(t) and its jump times.
Computational and estimation procedures in multidimensional right-shift processes and some applications
Authors: Kryscio Richard J. , Severo Norman C.
Published: April 2006

A right-shift process is a Markov process with multidimensional finite state space on which the infinitesimal transition movement is a shifting of one unit from one coordinate to some other to its right. A multidimensional right-shift process consists ofv≧ 1 concurrent and dependent right-shift processes. In this paper applications of multidimensional right-shift processes to some well-known examples from epidemic theory, queueing theory and the Beetle probblem due to Lucien LeCam are discussed. A transformation which orders the Kolmogorov forward equations into a triangular array is provided and some computational procedures for solving the resulting system of equations are presented. One of these procedures is concerned with the problem of evaluating a given transition probability function rather than obtaining the solution to the complete system of forward equations. This particular procedure is applied to the problem of estimating the parameters of a multidimensional right-shift process which is observed at only a finite number of fixed timepoints.
The covariance structure of queues and related processes – a survey of recent work
Authors: Reynolds John F.
Published: April 2006

This paper surveys recent results on the covariance structure of processes generated by queues and related stochastic processes. The generated processes include the numberX(t) of customers at timet, the waiting timeWnof thenth customer and the inter-departure intervalDn, i.e., the interval between departures of thenth and (n+1)th customers. The importance of these results is discussed, particularly in the field of estimation.
Stochastic compartmental models as approximations to more general stochastic systems with the general stochastic epidemic as an example
Authors: Faddy M. J.
Published: April 2006

A general time-dependent stochastic compartmental model is considered, where particles may move between a set of m compartments or out of the system, and new particles may be introduced into the compartments by immigration. A simple argument not relying on generating function techniques is given for the solution of such a system. It is then demonstrated that this class of compartmental models can be used as approximations to more complex stochastic systems by replacing dependence on certain stochastic variables by dependence on corresponding deterministic variables, with some recent examples being discussed. A compartmental approximation to the general stochastic epidemic is then constructed which appears on the basis of some simulations to compare favourably with the true process, particularly after the infection has got established in the population.
Combinatorial and analytic methods in the theory of queues
Authors: Takács Lajos
Published: April 2006

This paper is a survey of the solutions of various first-passage time problems in the theory of queues.
Random packing of an interval
Authors: Mannion David
Published: April 2006

At each stage of the packing of a closed intervalK, a random number of random open intervals (the packing objects) are placed in that part ofKwhich is as yet unoccupied. No overlapping between the packing objects is allowed. The packing prescription is such that the packing process terminates after at most a finite number of stages. Attention is focused on the final configuration,K=K–+G, whereGis a random open subset ofK, and is that part ofKwhich is eventually occupied by packing objects, whileK–, a random closed subset ofK, is that part ofKwhich remains unoccupied.
The virtual waiting time of theGI/G/1 queue in heavy traffic
Authors: Kyprianou E.
Published: April 2006

Investigations in the theory of heavy traffic were initiated by Kingman ([5], [6] and [7]) in an effort to obtain approximations for stable queues. He considered the Markov chains {Wni} of a sequence {Qi} of stableGI/G/1 queues, whereWniis the waiting time of thenth customer in theith queueing system, and by making use of Spitzer's identity obtained limit theorems as firstn→ ∞ and then ρi↑ 1 asi→ ∞. Here &rHiis the traffic intensity of theith queueing system. After Kingman the theory of heavy traffic was developed by a number of Russians mainly. Prohorov [10] considered the double sequence of waiting times {Wni} and obtained limit theorems in the three cases whenn1/2(ρi-1) approaches (i) - ∞, (ii) -δ and (iii) 0 asn→ ∞ andi→ ∞ simultaneously. The case (i) includes the result of Kingman. Viskov [12] also studied the double sequence {Wni} and obtained limits in the two cases whenn1/2(ρi− 1) approaches + δ and + ∞ asn→ ∞ andi→ ∞ simultaneously.
Channels without synchronization
Authors: Ahlswede R. , Wolfowitz J.
Published: April 2006

Let X = {1, …, a} and Y = {1, …, a} be the input and output alphabets, respectively. In the (unsynchronized) channels studied in this paper, when an element of X is sent over the channel, the receiver receives either nothing or a sequence of k letters, each a member of Y, where k, determined by chance, can be 1, or 2, or … or L, a given integer. The channel is called unsynchronized because the sequence received (for each letter sent) is not separated from the previous sequence or the following sequence, so that the receiver does not know which letters received correspond to which letter transmitted.

In Sections 1 and 2 we give the necessary definitions and auxiliary results. In Section 3 we extend the results of Dobrushin [2] by proving a strong converse to the coding theorem1 and making it possible to compute the capacity to within any desired accuracy.

In Section 4 we study the same channel with feedback, prove a coding theorem and strong converse, and give an algorithm for computing the capacity.

In Section 5 we study the unsynchronized channel where the transmission of each word is governed by an arbitrary element of a set of channel probability functions. Again we obtain the capacity of the channel, prove a coding theorem and strong converse, and give an algorithm for computing the capacity.

In Section 6 we apply results of Shannon [4] and supplement Dobrushin's results on continuous transmission with a fidelity criterion.
Functionals of an infinite particle system with independent motions, creation, and annihilation
Authors: Jacobs P. A.
Published: April 2006

Particles enter a state space at random times. Each particle travels in the space independent of the other particles until its death. Functionals of the particle system are studied with strong laws and central limit theorems being obtained.
Continuous-time gambling problems
Authors: Heath David C. , Sudderth William D.
Published: April 2006

An abstract gambler's problem is formulated in a continuous-time setting and analogues are proved for some of the discrete-time results of Dubins and Savage in their book How to Gamble if You Must. Applications are made to problems of controlling a Brownian motion process.
Genetic drift with polygamy and arbitrary offspring distribution
Authors: Cannings C.
Published: April 2006

Wright (1931) introduced a simple model for a bisexual, diploid population of fixed size and with non-overlapping generations. WithN1males andN2females, the rate of drift wasλ0= 1 – (N/8N1N2) whereN=N1+N2.
The Hardy-Weinberg law with overlapping generations
Authors: Charlesworth Brian
Published: April 2006

The Hardy-Weinberg law is generally regarded as one of the most important results of population genetics. It was originally proved for the case of populations with distinct generations (Hardy (1908), Weinberg (1908)); a general proof for populations with overlapping generations has apparently not been given before. The case of a single autosomal locus with an arbitrary number of alleles is considered here. Births and deaths are assumed to occur in continuous time. The weak ergodicity property of the birth rate and age structure of such a population, first derived by Norton (1928), is used to establish the fact that allele frequencies tend to constant limits in the absence of mutation, migration, selection and genetic drift.
On a functional central limit theorem for Markov population processes
Authors: Barbour Andrew D.
Published: April 2006

Let {XN(t)} be a sequence of continuous time Markov population processes on ann-dimensional integer lattice, such thatXNhas initial stateNx(0) and has a finite number of possible transitionsJfrom any stateX: let the transitionX→X + Jhave rateNgJ(N–1X), and letgJ(x) andx(0) be fixed asNvaries. The rate of convergence of √N(N–1XN(t) —ζ(t)) to a Gaussian diffusion is investigated, whereζ(t) is the deterministic approximation toN–1XN(t), and a method of deriving higher order asymptotic expansions for its distribution is justified. The methods are applied to two birth and death processes, and to the closed stochastic epidemic.
Estimation and control in Markov chains
Authors: Mandl P.
Published: April 2006

We consider a finite controlled Markov chain, the description of which depends on an unknown parameter a, and investigate the following control policy. To each a an optimal stationary control is associated. a is estimated recurrently from the trajectory by the minimum contrast method, and the optimal stationary control corresponding to the estimate is used. We present asymptotic properties of the estimate and of the criterion function. They follow from the law of large numbers and from the central limit theorem for controlled Markov chains derived with the aid of martingales.
Periodicity in Markov renewal theory
Authors: Çinlar Erhan
Published: April 2006

In an irreducible Markov renewal process either all states are periodic or none are. In the former case they all have the same period. Periodicity and the period can be determined by direct inspection from the semi-Markov kernel defining the process. The periodicity considerably increases the complexity of the limits in Markov renewal theory especially for transient initial states. Two Markov renewal limit theorems will be given with particular attention to the roles of periodicity and transient states. The results are applied to semi-Markov and semi-regenerative processes.
Renewal theory in two dimensions: Basic results
Authors: Hunter Jeffrey J.
Published: April 2006

In this paper a unified theory for studying renewal processes in two dimensions is developed. Bivariate generating functions and bivariate Laplace transforms are the basic tools used in generalizing the standard theory of univariate renewal processes. An example involving a bivariate exponential distribution is presented. This is used to illustrate the general theory and explicit expressions for the two-dimensional renewal density, the two-dimensional renewal function, the correlation between the marginal univariate renewal counting processes, and other related quantities are derived.