5. Krypto-Tag - Workshop über Kryptographie

Dieser Tagungsband enthält die gesammelten Zusammenfassungen der acht eingereichten Vorträge des 5. Krypto-Tags. Der Kryptotag ist eine zentrale Aktivität der Fachgruppe "Angewandte Kryptologie" der Gesellschaft für Informatik e.V. Er ist eine wissenschaftliche Veranstaltung im Bereich der Kryptologie und von der organisatorischen Arbeit der Fachgruppe getrennt.

Cereal/legume rotation effects on rhizosphere bacterial community structure in West African soils

The increased use of cereal/legume crop rotation has been advocated as a strategy to increase cereal yields of subsistence farmers in West Africa, and is believed to promote changes in the rhizosphere that enhance early plant growth. In this study we investigated the microbial diversity of the rhizoplane from seedlings grown in two soils previously planted to cereal or legume from experimental plots in Gaya, Niger, and Kaboli, Togo. Soils from these legume rotation and continuous cereal plots were placed into containers and sown in a growth chamber with maize (Zea mays L.), millet (Pennisetum glaucum L.), sorghum (Sorghum bicolor L. Moench.), cowpea (Vigna unguiculata L.) or groundnut (Arachis hypogaea L.). At 7 and 14 days after sowing, 16S rDNA profiles of the eubacterial and ammoniaoxidizing communities from the rhizoplane and bulk soil were generated using denaturing gradient gel electrophoresis (DGGE). Community profiles were subjected to peak fitting analyses to quantify the DNA band position and intensities, after which these data were compared using correspondence and principal components analysis. The data showed that cropping system had a highly significant effect on community structure (p <0.005), irrespective of plant species or sampling time. Continuous cereal-soil grown plants had highly similar rhizoplane communities across crop species and sites, whereas communities from the rotation soil showed greater variability and clustered with respect to plant species. Analyses of the ammonia-oxidizing communities provided no evidence of any effects of plant species or management history on ammonia oxidizers in soil from Kaboli, but there were large shifts with respect to this group of bacteria in soils from Gaya. The results of these analyses show that crop rotation can cause significant shifts in rhizosphere bacterial communities.

Heterochromatin und epigenetische Kontrolle der Centromere in Dictyostelium discoideum

Heterochromatin Protein 1 (HP1) is an evolutionarily conserved protein required for formation of a higher-order chromatin structures and epigenetic gene silencing. The objective of the present work was to functionally characterise HP1-like proteins in Dictyostelium discoideum, and to investigate their function in heterochromatin formation and transcriptional gene silencing. The Dictyostelium genome encodes three HP1-like proteins (hcpA, hcpB, hcpC), from which only two, hcpA and hcpB, but not hcpC were found to be expressed during vegetative growth and under developmental conditions. Therefore, hcpC, albeit no obvious pseudogene, was excluded from this study. Both HcpA and HcpB show the characteristic conserved domain structure of HP1 proteins, consisting of an N-terminal chromo domain and a C-terminal chromo shadow domain, which are separated by a hinge. Both proteins show all biochemical activities characteristic for HP1 proteins, such as homo- and heterodimerisation in vitro and in vivo, and DNA binding activtity. HcpA furthermore seems to bind to K9-methylated histone H3 in vitro. The proteins thus appear to be structurally and functionally conserved in Dictyostelium. The proteins display largely identical subnuclear distribution in several minor foci and concentration in one major cluster at the nuclear periphery. The localisation of this cluster adjacent to the nucleus-associated centrosome and its mitotic behaviour strongly suggest that it represents centromeric heterochromatin. Furthermore, it is characterised by histone H3 lysine-9 dimethylation (H3K9me2), which is another hallmark of Dictyostelium heterochromatin. Therefore, one important aspect of the work was to characterise the so-far largely unknown structural organisation of centromeric heterochromatin. The Dictyostelium homologue of inner centromere protein INCENP (DdINCENP), co-localized with both HcpA and H3K9me2 during metaphase, providing further evidence that H3K9me2 and HcpA/B localisation represent centromeric heterochromatin. Chromatin immunoprecipitation (ChIP) showed that two types of high-copy number retrotransposons (DIRS-1 and skipper), which form large irregular arrays at the chromosome ends, which are thought to contain the Dictyostelium centromeres, are characterised by H3K9me2. Neither overexpression of full-length HcpA or HcpB, nor deletion of single Hcp isoforms resulted in changes in retrotransposon transcript levels. However, overexpression of a C-terminally truncated HcpA protein, assumed to display a dominant negative effect, lead to an increase in skipper retrotransposon transcript levels. Furthermore, overexpression of this protein lead to severe growth defects in axenic suspension culture and reduced cell viability. In order to elucidate the proteins functions in centromeric heterochromatin formation, gene knock-outs for both hcpA and hcpB were generated. Both genes could be successfully targeted and disrupted by homologous recombination. Surprisingly, the degree of functional redundancy of the two isoforms was, although not unexpected, very high. Both single knock-out mutants did not show any obvious phenotypes under standard laboratory conditions and only deletion of hcpA resulted in subtle growth phenotypes when grown at low temperature. All attempts to generate a double null mutant failed. However, both endogenous genes could be disrupted in cells in which a rescue construct that ectopically expressed one of the isoforms either with N-terminal 6xHis- or GFP-tag had been introduced. The data imply that the presence of at least one Hcp isoform is essential in Dictyostelium. The lethality of the hcpA/hcpB double mutant thus greatly hampered functional analysis of the two genes. However, the experiment provided genetic evidence that the GFP-HcpA fusion protein, because of its ability to compensate the loss of the endogenous HcpA protein, was a functional protein. The proteins displayed quantitative differences in dimerisation behaviour, which are conferred by the slightly different hinge and chromo shadow domains at the C-termini. Dimerisation preferences in increasing order were HcpA-HcpA << HcpA-HcpB << HcpB-HcpB. Overexpression of GFP-HcpA or a chimeric protein containing the HcpA C-terminus (GFP-HcpBNAC), but not overexpression of GFP-HcpB or GFP-HcpANBC, lead to increased frequencies of anaphase bridges in late mitotic cells, which are thought to be caused by telomere-telomere fusions. Chromatin targeting of the two proteins is achieved by at least two distinct mechanisms. The N-terminal chromo domain and hinge of the proteins are required for targeting to centromeric heterochromatin, while the C-terminal portion encoding the CSD is required for targeting to several other chromatin regions at the nuclear periphery that are characterised by H3K9me2. Targeting to centromeric heterochromatin likely involves direct binding to DNA. The Dictyostelium genome encodes for all subunits of the origin recognition complex (ORC), which is a possible upstream component of HP1 targeting to chromatin. Overexpression of GFP-tagged OrcB, the Dictyostelium Orc2 homologue, showed a distinct nuclear localisation that partially overlapped with the HcpA distribution. Furthermore, GFP-OrcB localized to the centrosome during the entire cell cycle, indicating an involvement in centrosome function. DnmA is the sole DNA methyltransferase in Dictyostelium required for all DNA(cytosine-)methylation. To test for its in vivo activity, two different cell lines were established that ectopically expressed DnmA-myc or DnmA-GFP. It was assumed that overexpression of these proteins might cause an increase in the 5-methyl-cytosine(5-mC)-levels in the genomic DNA due to genomic hypermethylation. Although DnmA-GFP showed preferential localisation in the nucleus, no changes in the 5-mC-levels in the genomic DNA could be detected by capillary electrophoresis.

Analysis of the electronic structure, hyperfine structure, and volume isotope shifts in the low lying states of BA I and BA II

Relativistic multi-configuration Dirac Fock (MCDF) wavefunctions coupled to good angular momentum J have been calculated for low lying states of Ba I and Ba II. These wavefunctions are compared with semiempirical ones derived from experimental atomic energy levels. It is found that significantly better agreement is obtained when close configurations are included in the MCDF wavefunctions. Calculations of the electronic part of the field isotope shift lead to very good agreement with electronic factors derived from experimental data. Furthermore, the slopes of the lines in a King plot analysis of many of the optical lines are predicted accurately by these calculations. However, the MCDF wavefunctions seem not to be of sufficient accuracy to give agreement with the experimental magnetic dipole and electric quadrupole hyperfine structure constants.

Electronic structure and properties of the group 4, 5 and 6 highest chlorides including elements 104, 105, and 106

Results of the Dirac-Slater discrete variational calculations for the group 4, 5, and 6 highest chlorides including elements 104, 105, and 106 have shown that the groups are not identical with respect to trends in the electronic structure and bonding. The charge density distribution data show that notwithstanding the basic increase in covalency within the groups this increase diminishes in going from group 4 to group 6. As a result, E106Cl_6 will be less stable toward thermal decomposition than WCl_6, which is confirmed by an estimated low E106-Cl bond energy. \delta H_form equal to -90.3 ± 6 kcal/rnol is obtained for E106Cl_6 in the gas phase, which is indicative of a very low stability of this compound. The stability of the maximum oxidation state is shown to decrease in the direction E104(+4) > E105(+5) > E106(+6).

Numerical aspects in the data model of conceptual information systems

While most data analysis and decision support tools use numerical aspects of the data, Conceptual Information Systems focus on their conceptual structure. This paper discusses how both approaches can be combined.

Network properties of folksonomies

Social resource sharing systems like YouTube and del.icio.us have acquired a large number of users within the last few years. They provide rich resources for data analysis, information retrieval, and knowledge discovery applications. A first step towards this end is to gain better insights into content and structure of these systems. In this paper, we will analyse the main network characteristics of two of the systems. We consider their underlying data structures – socalled folksonomies – as tri-partite hypergraphs, and adapt classical network measures like characteristic path length and clustering coefficient to them. Subsequently, we introduce a network of tag co-occurrence and investigate some of its statistical properties, focusing on correlations in node connectivity and pointing out features that reflect emergent semantics within the folksonomy. We show that simple statistical indicators unambiguously spot non-social behavior such as spam.

Network properties of folksonomies

Social resource sharing systems like YouTube and del.icio.us have acquired a large number of users within the last few years. They provide rich resources for data analysis, information retrieval, and knowledge discovery applications. A first step towards this end is to gain better insights into content and structure of these systems. In this paper, we will analyse the main network characteristics of two of these systems. We consider their underlying data structures – so-called folksonomies – as tri-partite hypergraphs, and adapt classical network measures like characteristic path length and clustering coefficient to them. Subsequently, we introduce a network of tag cooccurrence and investigate some of its statistical properties, focusing on correlations in node connectivity and pointing out features that reflect emergent semantics within the folksonomy. We show that simple statistical indicators unambiguously spot non-social behavior such as spam.

Development of hybrid UV VCSEL with organic active material and dielectric DBR mirrors for medical, sensoric and data storage applications

Lasers play an important role for medical, sensoric and data storage devices. This thesis is focused on design, technology development, fabrication and characterization of hybrid ultraviolet Vertical-Cavity Surface-Emitting Lasers (UV VCSEL) with organic laser-active material and inorganic distributed Bragg reflectors (DBR). Multilayer structures with different layer thicknesses, refractive indices and absorption coefficients of the inorganic materials were studied using theoretical model calculations. During the simulations the structure parameters such as materials and thicknesses have been varied. This procedure was repeated several times during the design optimization process including also the feedback from technology and characterization. Two types of VCSEL devices were investigated. The first is an index coupled structure consisting of bottom and top DBR dielectric mirrors. In the space in between them is the cavity, which includes active region and defines the spectral gain profile. In this configuration the maximum electrical field is concentrated in the cavity and can destroy the chemical structure of the active material. The second type of laser is a so called complex coupled VCSEL. In this structure the active material is placed not only in the cavity but also in parts of the DBR structure. The simulations show that such a distribution of the active material reduces the required pumping power for reaching lasing threshold. High efficiency is achieved by substituting the dielectric material with high refractive index for the periods closer to the cavity. The inorganic materials for the DBR mirrors have been deposited by Plasma- Enhanced Chemical Vapor Deposition (PECVD) and Dual Ion Beam Sputtering (DIBS) machines. Extended optimizations of the technological processes have been performed. All the processes are carried out in a clean room Class 1 and Class 10000. The optical properties and the thicknesses of the layers are measured in-situ by spectroscopic ellipsometry and spectroscopic reflectometry. The surface roughness is analyzed by atomic force microscopy (AFM) and images of the devices are taken with scanning electron microscope (SEM). The silicon dioxide (SiO2) and silicon nitride (Si3N4) layers deposited by the PECVD machine show defects of the material structure and have higher absorption in the ultra violet range compared to ion beam deposition (IBD). This results in low reflectivity of the DBR mirrors and also reduces the optical properties of the VCSEL devices. However PECVD has the advantage that the stress in the layers can be tuned and compensated, in contrast to IBD at the moment. A sputtering machine Ionsys 1000 produced by Roth&Rau company, is used for the deposition of silicon dioxide (SiO2), silicon nitride (Si3N4), aluminum oxide (Al2O3) and zirconium dioxide (ZrO2). The chamber is equipped with main (sputter) and assisted ion sources. The dielectric materials were optimized by introducing additional oxygen and nitrogen into the chamber. DBR mirrors with different material combinations were deposited. The measured optical properties of the fabricated multilayer structures show an excellent agreement with the results of theoretical model calculations. The layers deposited by puttering show high compressive stress. As an active region a novel organic material with spiro-linked molecules is used. Two different materials have been evaporated by utilizing a dye evaporation machine in the clean room of the department Makromolekulare Chemie und Molekulare Materialien (mmCmm). The Spiro-Octopus-1 organic material has a maximum emission at the wavelength λemission = 395 nm and the Spiro-Pphenal has a maximum emission at the wavelength λemission = 418 nm. Both of them have high refractive index and can be combined with low refractive index materials like silicon dioxide (SiO2). The sputtering method shows excellent optical quality of the deposited materials and high reflection of the multilayer structures. The bottom DBR mirrors for all VCSEL devices were deposited by the DIBS machine, whereas the top DBR mirror deposited either by PECVD or by combination of PECVD and DIBS. The fabricated VCSEL structures were optically pumped by nitrogen laser at wavelength λpumping = 337 nm. The emission was measured by spectrometer. A radiation of the VCSEL structure at wavelength 392 nm and 420 nm is observed.

3D Simultaneous Inversion for Seismic Structure and Local Hypocenters in Germany under Consideration of Seismic Anisotropy in the Upper Mantel

The main task of this work has been to investigate the effects of anisotropy onto the propagation of seismic waves along the Upper Mantle below Germany and adjacent areas. Refraction- and reflexion seismic experiments proved the existence of Upper Mantle anisotropy and its influence onto the propagation of Pn-waves. By the 3D tomographic investigations that have been done here for the crust and the upper mantle, considering the influence of anisotropy, a gap for the investigations in Europe has been closed. These investigations have been done with the SSH-Inversionprogram of Prof. Dr. M. Koch, which is able to compute simultaneously the seismic structure and hypocenters. For the investigation, a dataset has been available with recordings between the years 1975 to 2003 with a total of 60249 P- and 54212 S-phase records of 10028 seismic events. At the beginning, a precise analysis of the residuals (RES, the difference between calculated and observed arrivaltime) has been done which confirmed the existence of anisotropy for Pn-phases. The recognized sinusoidal distribution has been compensated by an extension of the SSH-program by an ellipse with a slow and rectangular fast axis with azimuth to correct the Pn-velocities. The azimuth of the fast axis has been fixed by the application of the simultaneous inversion at 25° - 27° with a variation of the velocities at +- 2.5 about an average value at 8 km/s. This new value differs from the old one at 35°, recognized in the initial residual analysis. This depends on the new computed hypocenters together with the structure. The application of the elliptical correction has resulted in a better fit of the vertical layered 1D-Model, compared to the results of preceding seismological experiments and 1D and 2D investigations. The optimal result of the 1D-inversion has been used as initial starting model for the 3D-inversions to compute the three dimensional picture of the seismic structure of the Crust and Upper Mantle. The simultaneous inversion has showed an optimization of the relocalization of the hypocenters and the reconstruction of the seismic structure in comparison to the geology and tectonic, as described by other investigations. The investigations for the seismic structure and the relocalization have been confirmed by several different tests. First, synthetic traveltime data are computed with an anisotropic variation and inverted with and without anisotropic correction. Further, tests with randomly disturbed hypocenters and traveltime data have been proceeded to verify the influence of the initial values onto the relocalization accuracy and onto the seismic structure and to test for a further improvement by the application of the anisotropic correction. Finally, the results of the work have been applied onto the Waldkirch earthquake in 2004 to compare the isotropic and the anisotropic relocalization with the initial optimal one to verify whether there is some improvement.

Identifying the component structure of job satisfaction by principal components analysis among extension officers in North West Province, South Africa

The component structure of a 34-item scale measuring different aspects of job satisfaction was investigated among extension officers in North West Province, South Africa. A simple random sampling technique was used to select 40 extension officers from which data were collected. A structured questionnaire consisting of 34 job satisfaction and 10 personal characteristic items was administered to the extension officers. Items on job satisfaction were measured at interval level and analyzedwith Principal ComponentAnalysis. Most of the respondents (82.5%) weremales, between 40 to 45 years, 85% were married and 87.5% had a diploma as their educational qualification. Furthermore, 54% of the households size between 4 to 6 persons, whereas 75% were Christians. The majority of the extension officers lived in their job area (82.5), while 80% covered at least 3 communities and 3 farmer groups. In terms of number of farmers covered, only 40% of the extension officers covered more than 500 farmers and 45% travelled more than 40 km to reach their farmers. From the job satisfaction items 9 components were extracted to show areas for job satisfaction among extension officers. These were in-service training, research policies, communicating recommended practices, financial support for self and family, quality of technical help, opportunity to advance education, management and control of operations, rewarding system and sanctions. The results have several implications for motivating extension officers for high job performance especially with large number of clients and small number of extension agents.

Characterization of the molecular clockwork in the cockroach Rhyparobia maderae

Der Wechsel von Tag und Nacht erzeugt einen regelmäßigen Rhythmus von verschiedenen Umweltreizen, allen voran Licht und Temperatur. Fast jedes bis zum heutigen Tage untersuchte Lebewesen besitzt einen endogenen Mechanismus zur Zeitwahrnehmung, und diese "innere Uhr" befähigt Lebewesen dazu, sich vorausschauend an rhythmische Umwelt-Änderungen anzupassen. Circadiane Rhythmen bestehen auch ohne jegliche äußere Reize und basieren auf einem molekularen Rückkopplungs-Mechanismus, der Rhythmen in Genexpression und Proteinkonzentration von etwa 24 Stunden erzeugt. Obwohl sich die grundsätzlichen Mechanismen und Komponenten dieses molekularen Uhrwerks in allen Insekten ähneln, zeigte sich jedoch immer mehr, dass es im Detail doch wesentliche Unterschiede zwischen verschiedenen Insektengruppen gibt. Während das molekulare Uhrwerk der Fruchtfliege Drosophila melanogaster inzwischen sehr gut untersucht ist, fehlen bei den meisten Insektengruppen immernoch eingehende Untersuchungen. Fast nichts ist über die molekulare Basis von circadianen Rhythmen bei der Schabe Rhyparobia maderae bekannt, obwohl diese Art bereits seit Langem als Modellorganismus in der Chronobiologie dient. Um mit der Forschung am molekularen, circadianen System von R. maderae zu beginnen, wurde die Struktur und das Expressionsprofil der core feedback loop Gene per, tim1 und cry2 analysiert. Mittels degenerierten Primern und RACE konnte das vollständige offene Leseraster (OLR) von rmPer und rmCry2, und ein Teil des rmTim1 OLR kloniert werden. Eine phylogenetische Analyse gruppierte rmPER und rmCRY2 gemeinsam mit den Orthologa hemimetaboler Insekten. Viele bei D. melanogaster funktionell charakterisierte Domänen sind bei diesen Proteinen konserviert, was auf eine ähnliche Funktion in der inneren Uhr von R. maderae hinweist. Mittels quantitativer PCR konnte gezeigt werden, dass die mRNA von rmPer, rmTim1 und rmCry2 in verschiedenen Lichtregimen in der gleichen Phasenlage Tageszeit-abhängig schwankt. Die Phasenlage stellte sich bei unterschiedlichen Photoperioden jeweils relativ zum Beginn der Skotophase ein, mit Maxima in der ersten Hälfte der Nacht. Auch im Dauerdunkel zeigen sich Rhythmen in der rmTim1 und rmCry2 Expression. Die Amplitude der rmPer Expressionsrhythmen war jedoch so gering, dass keine signifikanten Unterschiede zwischen den einzelnen Zeitgeberzeiten (ZT) festgestellt werden konnten. Mittels Laufrad-Assays wurde untersucht wie Kurz- und Langtag Lichtregime die Verhaltensrhythmen beeinflussen. Es konnten nur Unterschiede in der Periodenlänge unter freilaufenden Bedingungen festgestellt werden, wenn höhere Lichtintensitäten (1000lx) zur Synchronisation (entrainment) genutzt wurden. Die Periode des freilaufenden Rhythmus war bei Tieren aus dem Kurztag länger. Die photoperiodische Plastizität zeigte sich also auch auf Verhaltensebene, obwohl höhere Lichtintensitäten notwendig waren um einen Effekt zu beobachten. Basierend auf den Sequenzen der zuvor klonierten OLR wurden gegen rmPER, rmTIM1 und rmCRY2 gerichtete Antikörper hergestellt. Die Antikörper gegen rmPER und rmTIM1 erkannten in western blots sehr wahrscheinlich spezifisch das jeweilige Protein. Zeitreihen von Gehirngewebe-Homogenisaten zeigten keinen offensichtlichen circadianen Rhythmus in der Proteinkonzentration, wahrscheinlich auf Grund einer Oszillation mit niedriger Amplitude. In Immunhistochemischen Färbungen konnte nur mit dem gegen rmPER gerichteten Antikörper aus Kaninchen ein Signal beobachtet werden. Beinahe jede Zelle des Zentralnervensystems war rmPER-immunreaktiv im Zellkern. Es konnten keine Unterschiede zwischen den untersuchten ZTs festgestellt werden, ähnlich wie bei den western blot Zeitreihen. In dieser Studie konnten erstmals molekulare Daten der circadianen Uhr von R. maderae erfasst und dargestellt werden. Die Uhrgene per, tim1 und cry2 werden in dieser Schabenart exprimiert und ihre Domänenstruktur sowie das circadiane Expressionsmuster ähneln dem hypothetischen ursprünglichen Insektenuhrwerk, welches der circadianen Uhr von Vertebraten nahesteht. Das molekulare Uhrwerk von R. maderae kann sich an unterschiedliche Photoperioden anpassen, und diese Anpassungen manifestieren sich im Expressionsprofil der untersuchten Uhrgene ebenso wie im Verhalten.

A Statistical Image-Based Shape Model for Visual Hull Reconstruction and 3D Structure Inference

We present a statistical image-based shape + structure model for Bayesian visual hull reconstruction and 3D structure inference. The 3D shape of a class of objects is represented by sets of contours from silhouette views simultaneously observed from multiple calibrated cameras. Bayesian reconstructions of new shapes are then estimated using a prior density constructed with a mixture model and probabilistic principal components analysis. We show how the use of a class-specific prior in a visual hull reconstruction can reduce the effect of segmentation errors from the silhouette extraction process. The proposed method is applied to a data set of pedestrian images, and improvements in the approximate 3D models under various noise conditions are shown. We further augment the shape model to incorporate structural features of interest; unknown structural parameters for a novel set of contours are then inferred via the Bayesian reconstruction process. Model matching and parameter inference are done entirely in the image domain and require no explicit 3D construction. Our shape model enables accurate estimation of structure despite segmentation errors or missing views in the input silhouettes, and works even with only a single input view. Using a data set of thousands of pedestrian images generated from a synthetic model, we can accurately infer the 3D locations of 19 joints on the body based on observed silhouette contours from real images.

Statistical Models for Co-occurrence Data

Modeling and predicting co-occurrences of events is a fundamental problem of unsupervised learning. In this contribution we develop a statistical framework for analyzing co-occurrence data in a general setting where elementary observations are joint occurrences of pairs of abstract objects from two finite sets. The main challenge for statistical models in this context is to overcome the inherent data sparseness and to estimate the probabilities for pairs which were rarely observed or even unobserved in a given sample set. Moreover, it is often of considerable interest to extract grouping structure or to find a hierarchical data organization. A novel family of mixture models is proposed which explain the observed data by a finite number of shared aspects or clusters. This provides a common framework for statistical inference and structure discovery and also includes several recently proposed models as special cases. Adopting the maximum likelihood principle, EM algorithms are derived to fit the model parameters. We develop improved versions of EM which largely avoid overfitting problems and overcome the inherent locality of EM--based optimization. Among the broad variety of possible applications, e.g., in information retrieval, natural language processing, data mining, and computer vision, we have chosen document retrieval, the statistical analysis of noun/adjective co-occurrence and the unsupervised segmentation of textured images to test and evaluate the proposed algorithms.

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By an essential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur in many compositional situations, such as household budget patterns, time budgets, palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful in such situations. From consideration of such examples it seems sensible to build up a model in two stages, the first determining where the zeros will occur and the second how the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data