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Abschieds-Rede des Bruder Lindner aus der g. u. v. [Loge] Amalia im O. z. Weimar d. 3. Mai 1814
No full textABSCHIEDS-REDE DES BRUDER LINDNER AUS DER G. U. V. [LOGE] AMALIA IM O. Z. WEIMAR D. 3. MAI 1814
Abschieds-Rede des Bruder Lindner aus der g. u. v. [Loge] Amalia im O. z. Weimar d. 3. Mai 1814 ([1])
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Pursuit problem with a stochastic prey that sees its chasers
No full textA recent stochastic pursuit model describes a pack of chasers (hounds) that actively move toward a target (hare) that undergoes pure Brownian diffusion (Bernardi and Lindner 2022 Phys. Rev. Lett. 128 040601). Here, this model is extended by introducing a deterministic ‘escape term’, which depends on the hounds’ positions. In other words, the hare can ‘see’ the approaching hounds and run away from them, in addition to the ‘blind’ random diffusion. In the case of a single chaser, the mean capture time (CT) can still be computed analytically. At weak noise, the qualitative behavior of the system depends on whether the hare’s maximum running drift speed is above or below a critical value (the pursuers’ speed), but not on the target’s viewing range, whereas the capture statistics at strong noise is similar to those of the original model without escape term. When multiple hounds are present, the behavior of the system is surprisingly similar to the original model with purely diffusing target, because the escape terms tend to compensate each other if the prey is encircled. At weak noise levels and ‘supracritical’ maximum escape speed, the hare can slip through the chaser pack and lead to a very strong increase of the mean CT with respect to the blind case. This large difference is due to rare events, which are enhanced when the symmetry in the initial conditions is disrupted by some randomness. Comparing the median of the CT probability density (which reflects the typical CT) with the mean CT makes clear the contribution of rare events with exceptionally long CTs
Toll-like Rezeptor-vermittelte Regulation der Leukotrien-Biosynthese in menschlichen Monozyten
No full textLeukotrienes (LTs) are pro-inflammatory lipid mediators that belong to the group of eicosanoids, which are oxygenated metabolites of one common precursor, the aracidonic acid (AA). This polyunsaturated fatty acid is esterified at the sn-2 position of cellular membrane phospholipids and can be released by cytosolic phospholipase A2 alpha (cPLA2alpha) enzymatic deacylation. AA can be converted into LTs by the catalytic reaction of 5-lipoxygenase (5-LO). Enzymatic activation of cPLA2alpha as well as of 5-LO is regulated by similar determinants. In response to cellular stimuli that elevate the intracellular Ca2+ level and/or activate MAP kinase pathways, cPLA2alpha and 5-LO comigrate from a soluble cell compartment (mainly the cytosol) to the nuclear membrane, where AA is released und converted into LTs. LTs play a significant role in promoting inflammatory reactions and immune processes. They have been shown to be released from leukocytes in response to bacterial and viral infections and substantially contribute to an effective immune reaction for host defense. Innate immune pathogen recognition is mediated to a substantial part by the Toll-like receptor (TLR) family. So far, 10 human TLR subtypes have been identified, all of which detect distinct highly conserved microbial structures and trigger the induction of signaling pathways that lead to the expression of numerous immune and inflammatory genes. TLR signaling culminates in the activation NF-kappaB and/or MAP kinases, which as well are known to be involved in the regulation of cellular LT biosynthesis. In this regard, it seemed conceivable that the release of LTs might be regulated by TLR activation. Present studies were undertaken in order to verify and characterize a possible influence of TLR activation on the LT biosynthesis, and furthermore to identify the involved signaling pathways and underlying mechanisms. First experiments revealed that pre-incubation of differentiated Mono Mac 6 (MM6) cells with a TLR4 ligand, a TLR5 ligand, as well as with different TLR2 ligands led to an about 2-fold enhancement of Ca2+ ionophore induced LT biosynthesis. Ligands of other TLR subtypes did not show any influence. These observations could also be confirmed in primary human monocytes stimulated with ionophore or fMLP. With focus on TLR2 ligands, further studies were carried out to characterize the observed enhancement of LT biosynthesis in MM6 cells. It was demonstrated that the extent of LT formation was dependent on the ligand concentration used, but was also dependent on the duration of pre-incubation. Ligand pre-incubation of 15 minutes was optimal to maximally enhance LT formation and further prolongation of pre-incubation decreased LT formation again. Moreover, simultaneous addition of TLR2 ligands with ionophore did also not enhance LT formation. These results indicated that TLR2 ligands seemed to prime human monocytes for an enhanced response upon ionophore stimulation, but did not act as costimuli, which per se were not capable of directly stimulating the biosynthesis of LTs. To analyze the underlying mechanism, the impact of TLR2 ligands on the two key enzymes of the LT biosynthesis pathway, cPLA2alpha and 5-LO, was investigated. In this regard, 5-LO could not been shown to be positively regulated by TLR ligand priming. Neither a direct stimulation, nor an enhancement of 5-LO activity by TLR ligands was detectable in MM6 cells. Similarly, TLR2 ligands did also not enhance ionophore induced 5-LO translocation to the nuclear membrane. However, it was shown that TLR2 ligands enhanced ionophore induced release of AA in MM6 cells, which occurred with a similar time course as LT formation, displaying a maximum at 10 minutes of pre-incubation. A direct stimulation of AA release, however, could not been detected. Inhibitor studies revealed cPLA2alpha to be essential for AA release in TLR2 ligand primed, ionophore stimulated MM6 cells, but also sPLA2 was found to be involved. However, the priming effect of TLR2 ligands was mediated exclusively by cPLA2alpha. Western Blot analyses revealed that p38 MAP kinase, as well as ERK1/2, are activated in MM6 cells in response to TLR2 ligands, and also Ser-505 phosphorylation of cPLA2alpha was detected, which is known to be mediated by MAP kinases and to increase cPLA2alpha activity in vitro. Maximal cPLA2alpha phosphorylation occurred after 5-10 minutes of TLR2 ligand incubation, slightly preceding maximal AA release at 10 minutes and maximal LT formation at 15 minutes of priming. The combined use of a specific p38 MAPK inhibitor with an inhibitor of the ERK1/2 signaling pathway resulted in a complete prevention of cPLA2alpha phosphorylation and TLR2 ligand mediated enhancement of AA release. Thus, both MAPK pathways seem to play a role for TLR2 ligand mediated priming effects on the release of AA. An impact of other kinases such as Mnk-1 and CamKII, which can also regulate cPLA2alpha by phosphorylation, was excluded. Finally, an anti-hTLR2 antibody significantly reduced enhanced AA release, confirming the priming effects to be dependent on TLR2 activation. In summary, it was concluded that the increase of LT biosynthesis by TLR2 ligand priming is considerably due to an enhanced cellular AA supply, which arises from a MAPK mediated phosphorylation and up-regulation of cPLA2alpha. TLR dependent enhancement of LT biosynthesis represents an interesting link between activation of innate immune receptors and the rapid formation of pro-inflammatory lipid mediators. On the one hand, this support the role of LTs in host defence and infectious diseases, but may also be relevant in pathophysiological processes, which involve TLRs as well as LTs, as it has been shown for the pathogenesis of atherosclerosis or allergic diseases.Leukotriene (LTs) sind Entzündungsmediatoren aus der Gruppe der Eikosanoide, welche sich von der Arachidonsäure (AA) als ihre gemeinsame Vorstufe ableiten. Diese mehrfach ungesättigte Fettsäure ist in der Zelle in Membranphospholipiden verestert, und kann enzymatisch durch die zytosolische PLA2alpha (cPLA2alpha) freigesetzt werden. Weiterhin wird die AA durch die 5-Lipoxygenase (5-LO) zu LTs umgesetzt. 5-LO und cPLA2alpha sind sehr ähnlich reguliert. Zelluläre Stimuli, die zu einer Erhöhung der intrazellulären Ca2+-Konzentration und/oder Aktivierung von Mitogen-aktivierten Proteinkinasen (MAPKs) führen, lösen eine Aktivierung, und die konzertierte Translokation beider Enzyme aus dem Zytosol zur Kernmembran aus, wo die Freisetzung der AA und die LT-Biosynthese erfolgt. LTs spielen eine wichtige Rolle in Entzündungsreaktionen und Immunprozessen. Sie werden von Leukozyten bei bakteriellen und viralen Infektionen gebildet, und tragen zur Aktivierung entsprechender Immunabwehrmechanismen bei. Toll-like Rezeptoren (TLRs) sind Rezeptoren des angeborenen Immunsystems, die eine Schlüsselrolle für die Detektion von Pathogenen im Organismus spielen. Sie erkennen hoch konservierte pathogen-assoziierte molekulare Strukturen und aktivieren Signaltransduktionswege, die zur Expression entzündungsrelevanter Proteine und somit zur Entwicklung einer Immunantwort führen. Die TLR-Aktivierung führt im Allgemeinen zur Aktivierung des Transkriptionsfaktors NF-kappaB, und zur Aktivierung von MAP-Kinasen, deren Rolle in der Regulation der LT-Biosynthese bereits erwähnt wurde. Vor diesem Hintergrund schien es denkbar, dass im Zuge einer TLR-Aktivierung auch eine Regulation der LT-Bildung erfolgen könnte. Ziel dieser Arbeit war es, diesen Zusammenhang zu verifizieren, den Einfluss von TLR-Liganden auf die Biosynthese von LTs zu charakterisieren und die zugrundeliegenden Mechanismen aufzuklären. Erste Versuche zeigten, dass die Vorbehandlung differenzierter Mono Mac 6 (MM6)-Zellen mit einem TLR4-, einem TLR5- und mit verschiedenen TLR2-Liganden zu einer Verdopplung der LT-Biosynthese führte, die durch Ca2+-Ionophor stimuliert worden war. Die Liganden anderer TLR-Subtypen zeigten dagegen keine Wirkung. Der verstärkende Effekt der TLR2-Liganden konnte in primären humanen Monozyten ebenfalls bestätigt werden. In Folgeexperimenten zur Charakterisierung des beobachteten Effektes in MM6-Zellen war die verstärkende Wirkung der TLR2-Liganden abhängig von der eingesetzten Konzentration und der Vorinkubationszeit. Eine 15-minütige Vorbehandlung mit den Liganden erwies sich als optimal, während eine Verlängerung der Inkubationsdauer zum Verschwinden des Effektes führte. Wurden die TLR2-Liganden zusammen mit Ionophor inkubiert, war ebenfalls keine Verstärkung der LT-Bildung messbar. Diese Beobachtungen führten zu der Annahme, dass die TLR2-Liganden zwar als Priming-Agenzien in der Lage sind, die Stimulation der LT-Bildung zu verstärken, selbst jedoch nicht direkt aktivieren können. Zur Aufdeckung des zugrundeliegenden Mechanismus wurde der Einfluss der TLR2-Liganden auf die cPLA2alpha und auf die 5-LO untersucht. Für die 5-LO ließ sich keine positive Regulation durch Priming von MM6-Zellen mit TLR2-Liganden nachweisen: es konnte keine Stimulation, und keine Verstärkung der Ionophor-induzierten 5-LO-Aktivität detektiert werden. Weiterhin bewirkten die TLR2-Liganden keine Verstärkung der 5-LO-Translokation zur nukleären Membran. Dagegen konnte gezeigt werden, dass TLR2-Liganden in MM6-Zellen die Ionophor-induzierte AA-Freisetzung verstärken. Hierbei war, wie für die LT-Bildung, eine Zeitabhängigkeit des Effektes mit einer optimalen Vorinkubationszeit der Liganden von etwa 10 Minuten feststellbar. Eine direkte Stimulation der AA-Freisetzung durch die TLR2-Liganden erfolgte nicht. In Inhibitor-Studien stellte sich heraus, dass sowohl die cPLA2alpha als auch sPLA2 an der AA-Freisetzung in geprimten MM6-Zellen beteiligt sind. Der Verstärkungseffekt der Liganden war jedoch allein durch die cPLA2alpha vermittelt. Weiterhin konnte in MM6-Zellen nach Inkubation mit TLR2-Liganden sowohl die Aktivierung der p38 und der p42/44 MAP-Kinase (ERK1/2), als auch die Phosphorylierung der cPLA2alpha an Ser-505 nachgewiesen werden, welche durch MAP-Kinasen erfolgt, und in vitro zur Aktivitätssteigerung der cPLA2alpha führt. Nach etwa 5-minütiger Behandlung riefen die Liganden maximale Phosphorylierung hervor, die somit einer maximalen AA-Freisetzung bei 10-minütigem Priming und einer maximalen LT-Bildung bei 15-minütigen Priming vorauszugehen schien. Die Kombination von Inhibitoren des p38 und des p42/44 MAP-Kinase Signalweges führte zur vollständigen Aufhebung sowohl der beobachteten cPLA2alpha-Phosphorylierung, als auch der Verstärkung der AA-Freisetzung. Beide MAP-Kinasewege scheinen somit eine Rolle für diesen Verstärkungseffekt der TLR2-Liganden zu spielen. Der Einfluss weiterer für die Regulation der cPLA2alpha relevanter Kinasen (Mnk-1 und CamKII) konnte ausgeschlossen werden. Abschließend wurde gezeigt, dass die beobachtete Steigerung der AA-Freisetzung durch Aktivierung des TLR2 vermittelt wird. Die TLR2-vermittelte Verstärkung der LT-Biosynthese in MM6-Zellen ist somit hauptsächlich auf eine vermehrte AA-Freisetzung zurückzuführen, die wiederum aus der cPLA2alpha-Phosphorylierung durch MAP-Kinasen und der dadurch verstärkten cPLA2alpha-Aktivierung resultiert. Die TLR-abhängige Verstärkung der LT-Bildung stellt einen interessanten Zusammenhang zwischen der Aktivierung von Rezeptoren des angeborenen Immunsystems und der kurzfristigen Freisetzung von Entzündungsmediatoren dar, der die Bedeutung der LTs für die Immunabwehr einmal mehr unterstreicht
Receiver operating characteristic curves for a simple stochastic process that carries a static signal
No full textThe detection of a weak signal in the presence of noise is an important problem that is often studied in terms of the receiver operating characteristic (ROC) curve, in which the probability of correct detection is plotted against the probability for a false positive. This kind of analysis is typically applied to the situation in which signal and noise are stochastic variables; the detection problem emerges, however, also often in a context in which both signal and noise are stochastic processes and the (correct or false) detection is said to take place when the process crosses a threshold in a given time window. Here we consider the problem for a combination of a static signal which has to be detected against a dynamic noise process, the well-known Ornstein-Uhlenbeck process. We give exact (but difficult to evaluate) quadrature expressions for the detection rates for false positives and correct detections, investigate systematically a simple sampling approximation suggested earlier, compare to an approximation by Stratonovich for the limit of high threshold, and briefly explore the case of multiplicative signal; all theoretical results are compared to extensive numerical simulations of the corresponding Langevin equation. Our results demonstrate that the sampling approximation provides a reasonable description of the ROC curve for this system, and it clarifies limit cases for the ROC curve
[Cove Springs Public School Students]
No full textCopy negative of the Cove Springs School class of 1926. First row, kneeling: an unidentified student, Delvin Foster, Clarence Douglas, Oscar Holcomb, Bertrum Hood, Jessie Durrett, Leo Creel, Grady Durrett, Norvell Creel, Royal Teal, W. T. Foster, Knowles Jones, Oscar Payne, Robert "Tud" Mullins, Billy Jackson, Bruce McLendon, Guy Teasdale, and Robert Lee Isaacks. Second row: Aline Douglas, Emma Frances Mullins, Nellie Moseley, Wynona Broadway, Lucille Creel, Billie Fisher, Helen McLendon, Ila Mae Mullins, Inez Greer, Merle Reagan, Joyce Bridges, Burnese Jones, Ruby Holcomb, Carrie McAnally, Ivory Dunn, Margaret Lindner, Elsie Hood, Thelma Moseley, Aline McNew, Lillie McLendon, Marguerite Jones, Jimmie McNew, Louise Payne, Virdie Douglas, and Delores Jones. Third row: teacher Lizzie Thompson, Cleo Holcomb, Elva Greer, Dewey Hood, Alvarine Durrett, Fred Collie, Elizabeth Lindner, Floyd Isaacks, Claudine Teasdale, teacher Lula Bridges, Henry Lindner, Catherine Payne, J. D. Isaacks, Louise Collie, J. C. Bridges, Glen Teal, Hazel Hood, Jim Isaacks, Principal Horace Clifton, and Ora Holcomb
A frequency-resolved mutual information rate and its application to neural systems
No full textThe encoding and processing of time-dependent signals into sequences of action potentials of sensory neurons is still a challenging theoretical problem. Although, with some effort, it is possible to quantify the flow of information in the model-free framework of Shannon’s information theory, this yields just a single number, the mutual information rate. This rate does not indicate which aspects of the stimulus are encoded. Several studies have identified mechanisms at the cellular and network level leading to low- or high-pass filtering of information, i.e., the selective coding of slow or fast stimulus components. However, these findings rely on an approximation, specifically, on the qualitative behavior of the coherence function, an approximate frequency-resolved measure of information flow, whose quality is generally unknown. Here, we develop an assumption-free method to measure a frequency-resolved information rate about a time-dependent Gaussian stimulus. We demonstrate its application for three paradigmatic descriptions of neural firing: an inhomogeneous Poisson process that carries a signal in its instantaneous firing rate; an integrator neuron (stochastic integrate-and-fire model) driven by a time-dependent stimulus; and the synchronous spikes fired by two commonly driven integrator neurons. In agreement with previous coherence-based estimates, we find that Poisson and integrate-and-fire neurons are broadband and low-pass filters of information, respectively. The band-pass information filtering observed in the coherence of synchronous spikes is confirmed by our frequency-resolved information measure in some but not all parameter configurations. Our results also explicitly show how the response-response coherence can fail as an upper bound on the information rate
Detecting single-cell stimulation in a large network of integrate-and-fire neurons
No full textSeveral experiments have shown that the stimulation of a single neuron in the cortex can influence the local network activity and even the behavior of an animal. From the theoretical point of view, it is not clear how stimulating a single cell in a cortical network can evoke a statistically significant change in the activity of a large population. Our previous study considered a random network of integrate-and-fire neurons and proposed a way of detecting the stimulation of a single neuron in the activity of a local network: a threshold detector biased toward a specific subset of neurons. Here, we revisit this model and extend it by introducing a second network acting as a readout. In the simplest scenario, the readout consists of a collection of integrate-and-fire neurons with no recurrent connections. In this case, the ability to detect the stimulus does not improve. However, a readout network with both feed-forward and local recurrent inhibition permits detection with a very small bias, if compared to the readout scheme introduced previously. The crucial role of inhibition is to reduce global input cross correlations, the main factor limiting detectability. Finally, we show that this result is robust if recurrent excitatory connections are included or if a different kind of readout bias (in the synaptic amplitudes instead of connection probability) is used
Optimal Detection of a Localized Perturbation in Random Networks of Integrate-and-Fire Neurons
No full textExperimental and theoretical studies suggest that cortical networks are chaotic and coding relies on averages over large populations. However, there is evidence that rats can respond to the short stimulation of a single cortical cell, a theoretically unexplained fact. We study effects of single-cell stimulation on a large recurrent network of integrate-and-fire neurons and propose a simple way to detect the perturbation. Detection rates obtained from simulations and analytical estimates are similar to experimental response rates if the readout is slightly biased towards specific neurons. Near-optimal detection is attained for a broad range of intermediate values of the mean coupling between neurons
Sport and exercise participation: motivation and barriers
No full textpublished_or_final_versionEditor's note Lindner, K.J. Lindner, K.J. Speak, M.A. Speak, M.A. iiiConference contributors vIntroduction to the conference Wells, Howard J. Wells, Howard J. viParticipation in sport and physical activity Seefeldt, Vern D. Seefeldt, Vern D. 1Participation in sport by students entering the University of Hong Kong: results of a survey undertaken in September 1993 Speak, Mike Speak, Mike Lindner, Koenraad Lindner, Koenraad Li, Daniel Li, Daniel 3Sports activities and the use of sports facilities in Hong Kong Sivan, Atara Sivan, Atara Robertson, Robert W. Robertson, Robert W. 19Factor impacting upon youth sport participation Shuttleworth, John Shuttleworth, John 25Factors affecting withdrawal reasons in youth sport Lindner, Koernaad Lindner, Koernaad Butcher, Janice Butcher, Janice Johns, David Johns, David 43Motivation and the belief system Chan, Chin-ming, Roy Chan, Chin-ming, Roy 55Analyzing thought patterns in relation to sport performance and motivation McGill, J.O. Lewis McGill, J.O. Lewis 61The social-cognitive approach to motivation: practical implications for coaches and physical educators (abstract) Leahey, Trisha Leahey, Trisha 7
On quasi-infinitely divisible distributions
No full textIn this thesis, we investigate the class of quasi-infinitely divisible distributions.
By definition, a distribution is quasi-infinitely divisible if its characteristic function can be written as the quotient of the characteristic functions of two infinitely divisible distributions.
Hence, quasi-infinitely divisible distributions generalize the class of infinitely divisible distributions, which corresponds to the class of L\'evy processes in a natural way.
Several distributional properties of infinitely divisible distributions can be characterized in terms of their characteristic triplet.
In case of quasi-infinitely divisible distributions, this is more difficult, as was observed by Lindner, Pan and Sato (2018).
There, Lindner et al. studied quasi-infinitely divisible distributions on the real line \bR systematically.
In Chapter 2 we focus on multivariate quasi-infinitely divisible distributions and collect various results on those.
We derive some examples and study distributional properties of quasi-infinitely divisible distributions on \bR^d for d \in \bN.
In particular, we study their absolute continuity, weak convergence, support properties and the existence of certain moments for those distributions.
Moreover, we study some topological properties of the class of quasi-infinitely divisible distributions on \bR^d.
The class of quasi-infinitely divisible distributions on \bR is dense in the class of all distributions on \bR with respect to weak convergence.
That this is no longer true in higher dimensions is shown in Chapter 3, where for we give an example of a probability distribution on \bR^d, which cannot be approximated arbitrarily well by quasi-infinitely divisible distributions.
In particular, it is shown that its characteristic function cannot be approximated arbitrarily well by a zero-free continuous function with respect to compact uniform convergence, and hence especially not by the characteristic function of a quasi-infinitely divisible distribution, since those are zero-free.
In Chapter 4 we consider distributions on \bR of the form with , a discrete distribution and an absolutely continuous distribution .
We show that such a distribution is quasi-infinitely divisible if and only if its characteristic function is bounded away from zero.
Moreover, we characterise the existence of certain moments for such a distribution.
In 1983, Marcus gave for arbitrary an example of a distribution with all of its one-dimensional projections being -stable, but such that the distribution itself is not infinitely divisible, thus, in particular not stable.
In Chapter 5 we show that this distribution is quasi-infinitely divisible.
Furthermore, we show that a quasi-infinitely divisible distribution with finite drift, and with all of its one-dimensional projections being stable, is necessarily stable itself.In dieser Arbeit untersuchen wir die Klasse der quasi-unendlich teilbaren Verteilungen.
Per Definition ist eine Verteilung quasi-unendlich teilbar, falls ihre charakteristische Funktion als Quotient der charakteristischen Funktionen zweier unendlich teilbarer Verteilungen geschrieben werden kann.
Quasi-unendlich teilbare Verteilungen verallgemeinern also die Klasse der unendlich teilbaren Verteilungen, welche auf natürliche Weise der Klasse der L\'evy-Prozesse entspricht.
Einige Verteilungseigenschaften unendlich teilbarer Verteilungen können anhand ihres charakteristischen Triplets charakterisiert werden.
Bei quasi-unendlich teilbaren Verteilungen ist dies schwieriger, wie von Lindner, Pan und Sato (2018) gezeigt wurde.
Dort haben Lindner et al. quasi-unendlich teilbare Verteilungen auf der reellen Geraden \bR systematisch untersucht.
In Kapitel 2 konzentrieren wir uns auf multivariate quasi-unendlich teilbare Verteilungen und sammeln verschiedene Aussagen über diese.
Wir leiten Beispiele her und untersuchen Verteilungseigenschaften quasi-unendlich teilbarer Verteilungen auf \bR^d für d \in \bN.
Im Speziellen untersuchen wir ihre Absolutstetigkeit, schwache Konvergenz, Trägereigenschaften und die Existenz bestimmter Momente für diese Verteilungen.
Außerdem untersuchen wir einige topologische Eigenschaften der Klasse der quasi-unendlich teilbaren Verteilungen auf \bR^d.
Die Klasse der quasi-unendlich teilbaren Verteilungen auf \bR liegt dicht in der Klasse aller Verteilungen auf \bR bezüglich schwacher Konvergenz.
Dass dies in höheren Dimensionen nicht mehr gilt, zeigen wir in Kapitel 3, wo wir für ein Beispiel für eine Verteilung auf \bR^d angeben, die sich nicht beliebig gut durch quasi-unendlich teilbare Verteilungen approximieren lässt.
Im Speziellen wird gezeigt, dass ihre charakteristische Funktion nicht beliebig gut durch eine nullstellenfreie, stetige Funktion bezüglich kompakt gleichmäßiger Konvergenz approximiert werden kann, und damit insbesondere nicht durch die charakteristische Funktion einer quasi-unendlich teilbaren Verteilung, da diese nullstellenfrei sind.
In Kapitel 4 betrachten wir Verteilungen auf \bR von der Form mit , einer diskreten Verteilung und einer absolut stetigen Verteilung .
Wir zeigen, dass eine solche Verteilung genau dann quasi unendlich teilbar ist, wenn ihre charakteristische Funktion von Null weg beschränkt ist.
Außerdem charakterisieren wir die Existenz bestimmter Momente für eine solche Verteilung.
1983 gab Marcus für beliebiges ein Beispiel einer Verteilung, deren eindimensionalen Projektionen alle -stabil sind, aber so, dass die Verteilung selbst nicht unendlich teilbar ist, also insbesondere nicht stabil.
In Kapitel 5 zeigen wir, dass diese Verteilung quasi unendlich teilbar ist.
Darüber hinaus zeigen wir, dass eine quasi-unendlich teilbare Verteilung mit endlichem Drift, dessen eindimensionale Projektionen alle stabil sind, notwendigerweise selbst stabil ist
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