Testing for a Unit Root in Panels with Dynamic Factors

This paper studies testing for a unit root for large n and T panels in which the cross-sectional units are correlated. To model this cross-sectional correlation, we assume that the data is generated by an unknown number of unobservable common factors. We propose unit root tests in this environment and derive their (Gaussian) asymptotic distribution under the null hypothesis of a unit root and local alternatives. We show that these tests have significant asymptotic power when the model has no incidental trends. However, when there are incidental trends in the model and it is necessary to remove heterogeneous deterministic components, we show that these tests have no power against the same local alternatives. Through Monte Carlo simulations, we provide evidence on the finite sample properties of these new tests.

Beyond Panel Unit Root Tests: Using Multiple Testing to Determine the Non Stationarity Properties of Individual Series in a Panel

Most panel unit root tests are designed to test the joint null hypothesis of a unit root for each individual series in a panel. After a rejection, it will often be of interest to identify which series can be deemed to be stationary and which series can be deemed nonstationary. Researchers will sometimes carry out this classification on the basis of n individual (univariate) unit root tests based on some ad hoc significance level. In this paper, we demonstrate how to use the false discovery rate (FDR) in evaluating I(1)=I(0) classifications based on individual unit root tests when the size of the cross section (n) and time series (T) dimensions are large. We report results from a simulation experiment and illustrate the methods on two data sets.

The association between caries and periodontal diseases

Objectifs: Le but de cette étude clinique était de comparer un groupe d’adultes ayant un parodonte sain avec un groupe d’adultes atteints de parodontite chronique en terme de risque carieux et mesures cliniques et microbiologiques de la carie. Méthodes: Quatre-vingt-seize individus ont été divisés en deux groupes en fonction de leur état de santé parodontal et ont été appariés pour l'âge, le sexe et l'origine ethnique. Trente-huit sujets étaient atteints de parodontite chronique définie comme ayant au moins quatre dents avec ≥ 1 site avec une profondeur de sondage ≥ 4 mm et une perte d'attache clinique ≥ 2 mm, et 58 sujets présentaient un parodonte sain. Par la suite, les groupes ont été subdivisés en deux groupes en fonction de leur statut carieux : les participants ayant au moins une lésion carieuse non traitée sur une surface dentaire et ceux n’ayant pas de lésion carieuse non traitée. Les données ont été recueillies par le biais d’un questionnaire, un examen clinique et des échantillons de plaque supra- et sous-gingivale. L’évaluation de la charge buccale de Streptococcus mutans et de six agents pathogènes parodontaux a été réalisée par la technique d'amplification de la réaction en chaine de la polymérase (PCR). Les données ont été analysées à l'aide d’analyses statistiques descriptives et bivariées. Résultats: Les individus atteints de parodontite chronique étaient 3,5 fois plus susceptibles d'avoir des caries que les individus en bonne santé (OR 3,5 ; IC: 1,5 - 8,3 ; P = 0,006). Les sujets à la fois atteints de parodontite chronique et de caries dentaires ont eu un niveau d’éducation significativement plus faible que les sujets ayant un parodonte sain et sans caries dentaires (OR 6,0 ; IC: 1,7 à 21,7 ; P = 0,04). La proportion de sujets ayant une charge buccale élevée de Porphyromonas gingivalis (P. g.) et Treponema denticola (T. d.) était significativement plus élevée chez les patients atteints de parodontite chronique et de carie que chez les patients sains présentant des caries (P. g.: OR 8,6 ; IC: 2,4 - 30,3 ; P = 0,004 et T. d.: OR 10,0 ; CI: 2,6 - 38.1 ; P = 0,003). Conclusions: Les résultats de cette étude suggèrent que, chez les sujets adultes atteints de la parodontite chronique, la fréquence des caries est plus élevée que chez les sujets ayant un parodonte sain. De plus, le faible niveau d'éducation influence négativement le statut parodontal des individus.

Spectroscopic Investigation of Tooth Caries and Demineralization

Dental caries persists to be the most predominant oral disease in spite of remarkable progress made during the past half- century to reduce its prevalence. Early diagnosis of carious lesions is an important factor in the prevention and management of dental caries. Conventional procedures for caries detection involve visual-tactile and radiographic examination, which is considered as “gold standard”. These techniques are subjective and are unable to detect the lesions until they are well advanced and involve about one-third of the thickness of enamel. Therefore, all these factors necessitate the need for the development of new techniques for early diagnosis of carious lesions. Researchers have been trying to develop various instruments based on optical spectroscopic techniques for detection of dental caries during the last two decades. These optical spectroscopic techniques facilitate noninvasive and real-time tissue characterization with reduced radiation exposure to patient, thereby improving the management of dental caries. Nonetheless, a costeffective optical system with adequate sensitivity and specificity for clinical use is still not realized and development of such a system is a challenging task.Two key techniques based on the optical properties of dental hard tissues are discussed in this current thesis, namely laser-induced fluorescence (LIF) and diffuse reflectance (DR) spectroscopy for detection of tooth caries and demineralization. The work described in this thesis is mainly of applied nature, focusing on the analysis of data from in vitro tooth samples and extending these results to diagnose dental caries in a clinical environment. The work mainly aims to improve and contribute to the contemporary research on fluorescence and diffuse reflectance for discriminating different stages of carious lesions. Towards this, a portable and compact laser-induced fluorescence and reflectance spectroscopic system (LIFRS) was developed for point monitoring of fluorescence and diffuse reflectance spectra from tooth samples. The LIFRS system uses either a 337 nm nitrogen laser or a 404 nm diode laser for the excitation of tooth autofluorescence and a white light source (tungsten halogen lamp) for measuring diffuse reflectance.Extensive in vitro studies were carried out on extracted tooth samples to test the applicability of LIFRS system for detecting dental caries, before being tested in a clinical environment. Both LIF and DR studies were performed for diagnosis of dental caries, but special emphasis was given for early detection and also to discriminate between different stages of carious lesions. Further the potential of LIFRS system in detecting demineralization and remineralization were also assessed.In the clinical trial on 105 patients, fluorescence reference standard (FRS) criteria was developed based on LIF spectral ratios (F500/F635 and F500/F680) to discriminate different stages of caries and for early detection of dental caries. The FRS ratio scatter plots developed showed better sensitivity and specificity as compared to clinical and radiographic examination, and the results were validated with the blindtests. Moreover, the LIF spectra were analyzed by curve-fitting using Gaussian spectral functions and the derived curve-fitted parameters such as peak position, Gaussian curve area, amplitude and width were found to be useful for distinguishing different stages of caries. In DR studies, a novel method was established based on DR ratios (R500/R700, R600/R700 and R650/R700) to detect dental caries with improved accuracy. Further the diagnostic accuracy of LIFRS system was evaluated in terms of sensitivity, specificity and area under the ROC curve. On the basis of these results, the LIFRS system was found useful as a valuable adjunct to the clinicians for detecting carious lesions.

Root effects on the turnover of grain legume residues in soil

Das Ziel dieser Arbeit war, die Einflüsse von Wurzeln und Rhizodeposition auf den Umsatz von Körnerleguminosenresiduen und damit verknüpfte mikrobielle Prozesse zu untersuchen. In einem integrierten Versuch wurden Ackerbohne (Vicia faba L.), Erbse (Pisum sativum L.) und Weiße Lupine (Lupinus albus L.) untersucht. Der Versuch bestand aus drei Teilen, zwei Gefäß-Experimenten und einem Inkubationsexperiment, in denen ausgehend von einem Gefäß-Experiment derselbe Boden und dasselbe Pflanzenmaterial verwendet wurden. In Experiment I wurde die Stickstoff-Rhizodeposition der Körnerleguminosenarten, definiert als wurzelbürtiger N nach dem Entfernen aller sichtbaren Wurzeln im Boden, gemessen und der Verbleib des Rhizodepositions-N in verschiednenen Bodenpools untersucht. Dazu wurden die Leguminosen in einem Gefäßversuch unter Verwendung einer in situ 15N-Docht-Methode mit einer 15N Harnstofflösung pulsmarkiert. In Experiment II wurde der Umsatz der N-Rhizodeposition der Körnerleguminosen und der Einfluss der Rhizodeposition auf den anschließenden C- und N-Umsatz der Körnerleguminosenresiduen in einem Inkubationsexperiment untersucht. In Experiment III wurde der N-Transfer aus den Körnerleguminosenresiduen einschließlich N-Rhizodeposition in die mikrobielle Biomasse und die Folgefrüchte Weizen (Triticum aestivum L.) und Raps (Brassica napus L.) in einem Gewächshaus-Gefäßversuch ermittelt. Die in situ 15N Docht-Markierungs-Methode wies hohe 15N Wiederfindungsraten von ungefähr 84 Prozent für alle drei Leguminosenarten auf und zeigte eine vergleichsweise homogene 15N Verteilung zwischen verschiedenen Pflanzenteilen zur Reife. Die Wurzeln zeigten deutliche Effekte auf die N-Dynamik nach dem Anbau von Körnerleguminosen. Die Effekte konnten auf die N-Rhizodeposition und deren anschließenden Umsatz, Einflüsse der Rhizodeposition von Körnerleguminosen auf den anschließenden Umsatz ihrer Residuen (Stängel, Blätter, erfassbare Wurzeln) und die Wirkungen nachfolgender Nichtleguminosen auf den Umsatzprozess der Residuen zurückgeführt werden: Die N-Rhizodeposition betrug zur Reife der Pflanzen bezogen auf die Gesamt-N- Aufnahme 13 Prozent bei Ackerbohne und Erbse und 16 Prozent bei Weißer Lupine. Bezogen auf den Residual N nach Ernte der Körner erhöhte sich der relative Anteil auf 35 - 44 Prozent. Die N-Rhizodeposition ist daher ein wesentlicher Pool für die N-Bilanz von Körnerleguminosen und trägt wesentlich zur Erklärung positiver Fruchtfolgeeffekte nach Körnerleguminosen bei. 7 - 21 Prozent des Rhizodepositions-N wurden als Feinwurzeln nach Nasssiebung (200 µm) wiedergefunden. Nur 14 - 18 Prozent des Rhizodepositions-N wurde in der mikrobiellen Biomasse und ein sehr kleiner Anteil von 3 - 7 Prozent in der mineralischen N Fraktion gefunden. 48 bis 72 Prozent der N-Rhizodeposition konnte in keinem der untersuchten Pools nachgewiesen werden. Dieser Teil dürfte als mikrobielle Residualmasse immobilisiert worden sein. Nach 168 Tagen Inkubation wurden 21 bis 27 Prozent des Rhizodepositions-N in den mineralisiert. Der mineralisierte N stammte im wesentlichen aus zwei Pools: Zwischen 30 Prozent und 55 Prozent wurde aus der mikrobiellen Residualmasse mineralisiert und eine kleinere Menge stammte aus der mikrobielle Biomasse. Der Einfluss der Rhizodeposition auf den Umsatz der Residuen war indifferent. Durch Rhizodeposition wurde die C Mineralisierung der Leguminosenresiduen nur in der Lupinenvariante erhöht, wobei der mikrobielle N und die Bildung von mikrobieller Residualmasse aus den Leguminosenresiduen in allen Varianten durch Rhizodepositionseinflüsse erhöht waren. Das Potential des residualen Körnerleguminosen-N für die N Ernährung von Folgefrüchten war gering. Nur 8 - 12 Prozent des residualen N wurden in den Folgenfrüchten Weizen und Raps wiedergefunden. Durch die Berücksichtigung des Rhizodepositions-N war der relative Anteil des Residual-N bezogen auf die Gesamt-N-Aufnahme der Folgefrucht hoch und betrug zwischen 18 und 46 Prozent. Dies lässt auf einen höheren N-Beitrag der Körnerleguminosen schließen als bisher angenommen wurde. Die residuale N-Aufnahme von Weizen von der Blüte bis zur Reife wurde durch den Residual-N gespeist, der zur Blüte in der mikrobiellen Biomasse immobilisiert worden war. Die gesamte Poolgröße, Residual-N in der mikrobiellen Biomasse und in Weizen, veränderte sich von der Blüte bis zur Reife nicht. Jedoch konnte ein Rest von 80 Prozent des Residual-N in keinem der untersuchten Pools nachgewiesen werden und dürfte als mikrobielle Residualmasse immobilisiert worden sein oder ist noch nicht abgebaut worden. Die zwei unterschiedlichen Folgefrüchte - Weizen und Raps - zeigten sehr ähnliche Muster bei der N-Aufnahme, der Residual-N Wiederfindung und bei mikrobiellen Parametern für die Residuen der drei Körnerleguminosenarten. Ein differenzierender Effekt auf den Umsatz der Residuen bzw. auf das Residual-N-Aneignungsvermögen der Folgefrüchte konnte nicht beobachtet werden.

Root-induced increases in soil pH and nutrient availability to field-grown cereals and legumes on acid sandy soils of Sudano-Sahelian West Africa

A field experiment with millet (Pennisetum glaucum L.), sorghum [Sorghum bicolor (L.) Moench], cowpea (Vigna unguiculata L.) and groundnut (Arachnis hypogeae L.) was conducted on severely P-deficient acid sandy soils of Niger, Mali and Burkina Faso to measure changes in pH and nutrient availability as affected by distance from the root surface and by mineral fertiliser application. Treatments included three rates of phosphorus (P) and four levels of nitrogen (N) application. Bulk, rhizosphere and rhizoplane soils were sampled at 35, 45 and 75 DAS in 1997 and at 55 and 65 DAS in 1998. Regardless of the cropping system and level of mineral fertiliser applied, soil pH consistently increased between 0.7 and two units from the bulk soil to the rhizoplane of millet. Similar pH gradients were observed in cowpea, but pH changes were much smaller in sorghum with a difference of only 0.3 units. Shifts in pH led to large increases in nutrient availability close to the roots. Compared with the bulk soil, available P in the rhizoplane was between 190 and 270% higher for P-Bray and between 360 and 600% higher for P-water. Exchangeable calcium (Ca) and magnesium (Mg) levels were also higher in the millet rhizoplane than in the bulk soil, whereas exchangeable aluminium (Al) levels decreased with increasing pH close to the root surface. The results suggest an important role of root-induced pH increases for crops to cope with acidity-induced nutrient deficiency and Al stress of soils in the Sudano-Sahelian zone of West Africa.

Evaluating partial root-zone irrigation and mulching in okra (Abelmoschus esculentus L.) under a sub-humid tropical climate

The field experiments were conducted to compare the alternate partial root-zone irrigation (APRI) with and without black plastic mulch (BPM) with full root-zone irrigation (FRI) in furrow-irrigated okra (Abelmoschus esculentus L. Moench) at Bhubaneswar, India. APRI means that one of the two neighbouring furrows was alternately irrigated during consecutive watering. FRI was the conventional method where every furrow was irrigated during each watering. The used irrigation levels were 25% available soil moisture depletion (ASMD), 50% ASMD, and 75% ASMD. The plant growth and yield parameters were observed to be significantly (p < 0.05) higher with frequent irrigation (at 25% ASMD) under all irrigation strategies. However, APRI + BPM produced the maximum plant growth and yield using 22% and 56% less water over APRI without BPM and FRI, respectively. The highest pod yield (10025 kg ha^-1) was produced under APRI at 25% ASMD + BPM, which was statistically at par with the pod yield under APRI at 50% ASMD + BPM. Irrigation water use efficiency (IWUE), which indicates the pod yield per unit quantity of irrigation water, was estimated to be highest (12.3 kg m^-3) under APRI at 50% ASMD + BPM, followed by APRI at 25% ASMD + BPM. Moreover, the treatment APRI at 50% ASMD + BPM was found economically superior to other treatments, generating more net return (US $ 952 ha^-1) with higher benefit–cost ratio (1.70).

Root parametrized differential equations

The present thesis is about the inverse problem in differential Galois Theory. Given a differential field, the inverse  problem asks which linear algebraic groups can be realized as differential Galois groups of Picard-Vessiot extensions of this field.   In this thesis we will concentrate on the realization of the classical groups as differential Galois groups. We introduce a method for a very general realization of these groups. This means that we present for the classical groups of Lie rank $l$ explicit linear differential equations where the coefficients are differential polynomials in $l$ differential indeterminates over an algebraically closed field of constants $C$, i.e. our differential ground field is purely differential transcendental over the constants.   For the groups of type $A_l$, $B_l$, $C_l$, $D_l$ and $G_2$ we managed to do these realizations at the same time in terms of Abhyankar's program 'Nice Equations for Nice Groups'. Here the choice of the defining matrix is important. We found out that an educated choice of $l$ negative roots for the parametrization together with the positive simple roots leads to a nice differential equation and at the same time defines a sufficiently general element of the Lie algebra. Unfortunately for the groups of type $F_4$ and $E_6$ the linear differential equations for such elements are of enormous length. Therefore we keep in the case of $F_4$ and $E_6$ the defining matrix differential equation which has also an easy and nice shape.   The basic idea for the realization is the application of an upper and lower bound criterion for the differential Galois group to our parameter equations and to show that both bounds coincide. An upper and lower bound criterion can be found in literature. Here we will only use the upper bound, since for the application of the lower bound criterion an important condition has to be satisfied. If the differential ground field is $C_1$, e.g., $C(z)$ with standard derivation, this condition is automatically satisfied. Since our differential ground field is purely differential transcendental over $C$, we have no information whether this condition holds or not.   The main part of this thesis is the development of an alternative lower bound criterion and its application. We introduce the specialization bound. It states that the differential Galois group of a specialization of the parameter equation is contained in the differential Galois group of the parameter equation. Thus for its application we need a differential equation over $C(z)$ with given differential Galois group. A modification of a result from Mitschi and Singer yields such an equation over $C(z)$ up to differential conjugation, i.e. up to transformation to the required shape. The transformation of their equation to a specialization of our parameter equation is done for each of the above groups in the respective transformation lemma.

Cassava root peel as a replacement for maize in diets for growing pigs: effects on energy and nutrient digestibility, performance and carcass characteristics

Two experiments were conducted to evaluate cassava root peel (CRP) as diet component for fattening pigs. In the first experiment, ten male pigs were used to investigate the nutrient digestibility and the nutritive value of CRP as replacement for maize in the diet at 0 %, 30 %, 40 %, 50 % and 60 %, while supplementing free amino acids (fAA). During two experimental periods, faeces were quantitatively collected and analysed for chemical composition. In the second experiment, 40 pigs received the same diets as in Experiment 1, and daily feed intake and weekly weight changes were recorded. Four pigs per diet were slaughtered at 70 kg body weight to evaluate carcass traits. Digestibility of dry and organic matter, crude protein, acid detergent fibre and gross energy were depressed (p<0.05) at 60 % CRP; digestible energy content (MJ kg^(−1) DM) was 15.4 at 0 % CRP and 12.7 at 60 % CRP. In the second experiment, CRP inclusion had only a small impact on feed intake, weight gain and feed conversion ratio (p>0.05) as well as on the length of the small intestine and the Longissimus dorsi muscle area. The missing correlation of daily weight gain and feed-to-gain ratio up to a CRP inclusion of 40 % indicates that negative effects of CRP on pig growth can be avoided by respecting upper feeding limits. Hence, a combined use of CRP and fAA can reduce feeding costs for small-scale pig farmers in countries where this crop-by product is available in large amounts.