Poisson-like Distributions Research Articles

Bed-thickness frequency distributions and recurrence intervals of sediment-gravity-flow deposits intercalated in lacustrine varved diatomite: examples from the middle Pleistocene Hiruzenbara Formation, southwest Japan

ABSTRACTBed-thickness frequency distributions of sediment-gravity-flow deposits, especially turbidites, are one of the major interests of sedimentology. Lognormal, power-law, exponential, and truncated normal distributions have all been proposed for their frequency distributions. Although these frequency distributions have been obtained from many field observations and estimated from statistical models, problems associated with the complexity of sedimentary processes have remained. In this study, bed-thickness frequency distributions and the recurrence intervals of sediment-gravity-flow deposits intercalated in the Pleistocene lacustrine varved diatomite in southwest Japan were analyzed. The results reveal that the bed thicknesses of sediment-gravity-flow deposits induced by different mechanisms show different types of frequency distribution. For example, flood-induced sediment-gravity-flow deposits show power-law-like distributions, whereas such deposits caused by lake-slope-failure show lognormal distributions. The suggestion is that flood-induced types are deposited from floods having a power-law scale. However, the bed thicknesses of the deposits induced by lake-slope-failure do not purely reflect the event scale, because the lateral variation of their thicknesses reflects the depositional processes. The recurrence intervals of both types of event show Poisson-like distributions except for lake-slope-failure deposits at the slope-base section. Despite observed ranges, the distributions of lake-slope-failure deposits at the slope-base section have a high amount of zero value and the recurrence interval show exponentially decreasing. These results suggest that both events were generated randomly, despite different origins. In addition, the incompleteness of the records was also suggested from sediment bypass of a lake-slope-failure event at the slope-base section.

Facile synthesis of amphiphilic AB3 and A3B miktoarm PeptoMiktoStars

Amphiphilic miktoarm star copolymers have a unique internal structure and many attractive properties with respect to solution self-assembly, such as a high density of internal and peripheral functionalities, low CMC values, and high loading efficiency. However, compared to their linear analogs, the complex architecture demands asymmetric polymer arms emanating from a single core, which poses a significant synthetic challenge. Herein, we demonstrate an approach for the synthesis of polypept(o)ide-based AB3- and A3B-type miktoarm PeptoStars consisting of polypeptidic poly(γ-benzyl-l-glutamate (pGlu(OBn)) as the hydrophobic A arm and polypeptoidic polysarcosine (pSar) as the hydrophilic B arm. These structures, which are completely derived from endogenous amino acids, were realized by the core-first method using a tetrafunctional initiator and the corresponding N-carboxyanhydrides (NCAs) via a controlled, living nucleophilic ring-opening polymerization (ROP). The asymmetric architecture was achieved through an orthogonal protecting group strategy with multiple protection/deprotection steps. Characterization via 1H NMR-, 1H DOSY-spectroscopy, and size-exclusion chromatography (SEC) indicate the presence of well-formed miktoarm PeptoStars with low dispersities (Đ = 1.09–1.14), the precise control over the degree of polymerization and Poisson-like molecular weight distributions. Schwiertz et al. report on the synthesis of miktoarm star polymers based on polypept(o)ides by nucleophilic ring opening polymerization of N-carboxyanhydrides. The reported procedures allow for precise control over chain length, number of arms and end group functionality.

Synthesis and Characterization of Stimuli-Responsive Star-Like Polypept(o)ides: Introducing Biodegradable PeptoStars.

Star-like polymers are one of the smallest systems in the class of core crosslinked polymeric nanoparticles. This article reports on a versatile, straightforward synthesis of three-arm star-like polypept(o)ide (polysarcosine-block-polylysine) polymers, which are designed to be either stable or degradable at elevated levels of glutathione. Polypept(o)ides are a recently introduced class of polymers combining the stealth-like properties of the polypeptoid polysarcosine with the functionality of polypeptides, thus enabling the synthesis of materials completely based on endogenous amino acids. The star-like homo and block copolymers are synthesized by living nucleophilic ring opening polymerization of the corresponding N-carboxyanhydrides (NCAs) yielding polymeric stars with precise control over the degree of polymerization (Xn = 25, 50, 100), Poisson-like molecular weight distributions, and low dispersities (Đ = 1.06-1.15). Star-like polypept(o)ides display a hydrodynamic radius of 5 nm (μ2 < 0.05) as determined by dynamic light scattering (DLS). While star-like polysarcosines and polypept(o)ides based on disulfide containing initiators are stable in solution, degradation occurs at 100 × 10-3 m glutathione concentration. The disulfide cleavage yields the respective polymeric arms, which possess Poisson-like molecular weight distributions and low dispersities (Đ = 1.05-1.12). Initial cellular uptake and toxicity studies reveal that PeptoStars are well tolerated by HeLa, HEK 293, and DC 2.4 cells.

Product-Form Poisson-Like Distributions and Complex Balanced Reaction Systems

Stochastic reaction networks are dynamical models of biochemical reaction systems and form a particular class of continuous-time Markov chains on $\mathbb{N}^n$. Here we provide a fundamental characterisation that connects structural properties of a network to its dynamical features. Specifically, we define the notion of `stochastically complex balanced systems' in terms of the network's stationary distribution and provide a characterisation of stochastically complex balanced systems, parallel to that established in the 70-80ies for deterministic reaction networks. Additionally, we establish that a network is stochastically complex balanced if and only if an associated deterministic network is complex balanced (in the deterministic sense), thereby proving a strong link between the theory of stochastic and deterministic networks. Further, we prove a stochastic version of the `deficiency zero theorem' and show that any (not only complex balanced) deficiency zero reaction network has a product-form Poisson-like stationary distribution on all irreducible components. Finally, we provide sufficient conditions for when a product-form Poisson-like distribution on a single (or all) component(s) implies the network is complex balanced, and explore the possibility to characterise complex balanced systems in terms of product-form Poisson-like stationary distributions.

Polypept(o)ides: Hybrid Systems Based on Polypeptides and Polypeptoids

Polypept(o)ides combine the multifunctionality and intrinsic stimuli-responsiveness of synthetic polypeptides with the "stealth"-like properties of the polypeptoid polysarcosine (poly(N-methyl glycine)). This class of block copolymers can be synthesized by sequential ring opening polymerization of α-amino acid N-carboxy-anhydrides (NCAs) and correspondingly of the N-substituted glycine N-carboxyanhydride (NNCA). The resulting block copolymers are characterized by Poisson-like molecular weight distributions, full end group integrity, and dispersities below 1.2. While polysarcosine may be able to tackle the currently arising issues regarding the gold standard PEG, including storage diseases in vivo and immune responses, the polypeptidic block provides the functionalities for a specific task. Additionally, polypeptides are able to form secondary structure motives, e.g., α-helix or β-sheets, which can be used to direct self-assembly in solution. In this feature article, we review the relatively new field of polypept(o)ides with respect to synthesis, characterization, and first data on the application of block copolypept(o)ides in nanomedicine. The summarized data already indicates the great potential of polypept(o)ides.

Splitting of a turbulent puff in pipe flow

The transition to turbulence of the flow in a pipe of constant radius is numerically studied over a range of Reynolds numbers where turbulence begins to expand by puff splitting. We first focus on the case where splitting occurs as discrete events. Around this value only long-lived pseudo-equilibrium puffs can be observed in practice, as typical splitting times become very long. When is further increased, the flow enters a more continuous puff splitting regime where turbulence spreads faster. Puff splitting presents itself as a two-step stochastic process. A splitting puff first emits a chaotic pseudopod made of azimuthally localized streaky structures at the downstream (leading) laminar–turbulent interface. This structure can later expand azimuthally as it detaches from the parent puff. Detachment results from a collapse of turbulence over the whole cross-section of the pipe. Once the process is achieved a new puff is born ahead. Large-deviation consequences of elementary stochastic processes at the scale of the streak are invoked to explain the statistical nature of splitting and the Poisson-like distributions of splitting times reported by Avila et al (2011 Science 333 192–6).

Predictive modeling of non‐viral gene transfer

In non-viral gene delivery, the variance of transgenic expression stems from the low number of plasmids successfully transferred. Here, we experimentally determine Lipofectamine- and PEI-mediated exogenous gene expression distributions from single cell time-lapse analysis. Broad Poisson-like distributions of steady state expression are observed for both transfection agents, when used with synchronized cell lines. At the same time, co-transfection analysis with YFP- and CFP-coding plasmids shows that multiple plasmids are simultaneously expressed, suggesting that plasmids are delivered in correlated units (complexes). We present a mathematical model of transfection, where a stochastic, two-step process is assumed, with the first being the low-probability entry step of complexes into the nucleus, followed by the subsequent release and activation of a small number of plasmids from a delivered complex. This conceptually simple model consistently predicts the observed fraction of transfected cells, the cotransfection ratio and the expression level distribution. It yields the number of efficient plasmids per complex and elucidates the origin of the associated noise, consequently providing a platform for evaluating and improving non-viral vectors.

Statistics and geometry of cosmic voids

We introduce new statistical methods for the study of cosmic voids,focusing on the statistics of largest size voids. We distinguish threedifferent types of distributions of voids, namely, Poisson-like,lognormal-like and Pareto-like distributions. The last two distributions areconnected with two types of fractal geometry of the matterdistribution. Scaling voids with Pareto distribution appear in fractaldistributions with box-counting dimension smaller than three (its maximumvalue), whereas the lognormal void distribution corresponds to multifractalswith box-counting dimension equal to three. Moreover, voids of the formertype persist in the continuum limit, namely, as the number density ofobservable objects grows, giving rise to lacunar fractals, whereas voids ofthe latter type disappear in the continuum limit, giving rise to non-lacunar(multi)fractals. We propose both lacunar and non-lacunar multifractal modelsof the cosmic web structure of the Universe. A non-lacunar multifractal modelis supported by current galaxy surveys as well as cosmological N-bodysimulations. This model suggests, in particular, that small dark matter halosand, arguably, faint galaxies are present in cosmic voids.

Does a fitness factor contribute to the association between intelligence and health outcomes? Evidence from medical abnormality counts among 3654 US Veterans

We suggest that an over-arching ‘fitness factor’ (an index of general genetic quality that predicts survival and reproductive success) partially explains the observed associations between health outcomes and intelligence. As a proof of concept, we tested this idea in a sample of 3654 US Vietnam veterans aged 31–49 who completed five cognitive tests (from which we extracted a g factor), a detailed medical examination, and self-reports concerning lifestyle health risks (such as smoking and drinking). As indices of physical health, we aggregated ‘abnormality counts’ of physician-assessed neurological, morphological, and physiological abnormalities in eight categories: cranial nerves, motor nerves, peripheral sensory nerves, reflexes, head, body, skin condition, and urine tests. Since each abnormality was rare, the abnormality counts showed highly skewed, Poisson-like distributions. The correlation matrix amongst these eight abnormality counts formed only a weak positive manifold and thus yielded only a weak common factor. However, Poisson regressions showed that intelligence was a significant positive predictor of six of the eight abnormality counts, even controlling for diverse lifestyle covariates (age, obesity, combat and toxin exposure owing to service in Vietnam, and use of tobacco, alcohol, marijuana, and hard drugs). These results give preliminary support for the notion of a superordinate fitness factor above intelligence and physical health, which could be further investigated with direct genetic assessments of mutation load across individuals.

Development of micro-scale frequency distributions of plankton for inclusion in foraging models of larval fish, results from a Video Plankton Recorder

A self-contained, analog Video Plankton Recorder (VPR) mounted on a 1-m 2 MOCNESS sampling system was used to obtain data on micro-scale (<10 m) distributions of zooplankton as prey for larval cod and haddock during May 1997 and May 1999 on Georges Bank. The negative binomial frequency distribution was selected to best describe the more abundant plankton categories in 10-second bins for 10-m depth intervals. Most of the strata had asymmetrical frequency distributions with low means and low k values indicating a clumped distribution. Water-column stratification was especially important in structuring micro-scale high-density layers of phytoplankton and copepods. The most symmetrical Poisson-like distributions with high means and high k values occurred in the upper 30 m above the base of the thermocline.

Statistical properties of quasiparticle spectra in deformed nuclei

The statistical properties of quasiparticle spectra in deformed heavy nuclei are studied. It has been found that at the ground state and at minima of the potential, Poisson-like spacing distributions are observed both in the quasiparticle spectra and in the single-particle ones. However, at the saddle point configuration in an even system, the original Wigner-like single-particle spacing distribution changes to a mixture of Wigner- and Poisson-like quasiparticle distributions, whereas for an odd system the pairing hardly changes the Wigner-like distribution. Therefore, from this study we have observed the tendency of the pairing effect to act to make the system more stable. [S0556-2813(99)05701-5].

Composition analysis of detergents of the polyoxyethylene type: comparison of thin-layer chromatography, reversed-phase chromatography and matrix-assisted laser desorption/ionization mass spectrometry

Matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS) can be used to determine the distribution of single polymer species of non-ionic detergents of the polyoxyethylene type (Triton X-100 and 114, Tween 20 and Brij 35). Thin-layer chromatographic (TLC) and reversed-phase chromatographic (RPC) methods are presented which may separate single polymer species as verified by MALDI-MS. Comparison of chromatographic and MALDI-MS data show Poisson-like distributions for Triton X-100 without marked differences between different methods. Distribution parameters obtained with Triton X-100 charges from different suppliers are very similar. The RPC method used can be scaled up for preparation of pure detergent species.

Psychophysiological Basis for Errors in Identification of Degraded Geometric Forms under Conditions of High Information Uncertainty

Identification of ambiguous geometric forms by human subjects with brief experience or pre-knowledge of the stimulus may call upon Bayesian specialised mechanisms. Subjects were presented with a 2-alternative forced choice between a pair of incomplete geometric figures in conditions with common and varying components. Stimuli of 1, 3, 5, and 6 pixel acuity grades were displayed in iterative order in randomised blocks at 100, 200, 260, and 360 ms exposure times, rotated or upright, under local or global viewing. Analysis of probability of correct identification against stimulus intensity, acuity demand, and stimulus duration revealed: (i) sigmoid or dipper-shaped nonmonotonic psychometric functions; (ii) Poisson-like skewed binomial distributions of errors; and (iii) category-based dependence on the stimulus and its ambiguity. This is attributable to the high uncertainty constraints imposed on tasks sharing and also varying in their stimulus parameters and dimensions. Nonlinearities shown reflect category-based strategies and attention allocation, interactions as a drive for performance stability manifested in equalisation across sub-categories and invariances of errors, with acuity demand accounted for perhaps by mechanisms of differential attention allocation. Two sources of error are apparent: (i) possibly ‘bottleneck of attention’-related and individually varying ‘blink of attention’, with small falls distributed across stimulus intensities, and (ii) ‘lapse of attention’ with large falls on easier tasks, and rightward-skewed deviations from normal Poisson-like binomial distributions ( p&lt;0.001), the high correlation to performance effort suggesting an active process of pay-off.

Development of activity patterns in auditory nerve fibres of pigeons

Little is known about inner ear development in pigeons. This paper addresses the question of maturation in activity patterns of pigeon auditory nerve fibres. Pigeons that were 1, 2 and 4 weeks and 1, 2, 3 and 4 years old were investigated. Adult-like activity patterns are found 4 weeks post-hatching. Spontaneous activities of fibres in immature animals (about 40 spikes/s) are half that found in adults. Spontaneous discharge rate does not increase with decreasing characteristic frequency (CF) of the fibre if the animals are immature. Rate thresholds are less sensitive in immature animals. Differences between the age groups are generally significant if the CFs of the fibres are below 1.3 kHz. Sharpness of tuning is already adult-like in 1-week-old animals. Inter-spike time interval histograms (ISTH) of auditory fibres recorded in animals of all age groups often show Poisson-like distributions. Preferred intervals are found in 10% of the ISTHs of fibres in immature animals but in 30% of adults. Cross-correlations between heart beats of the animal and spontaneous activities show good correlation for about 70% of the fibres in immature animals. With the growth of the animals, the number of fibres showing correlation of spontaneous activities and heart beats decreases to about 40%. The basilar papilla of a 1-week-old animal is smaller than in an adult animal (by 10% in length and by 10% in width), judged by scanning electron microscopy (SEM). Changes of activity patterns in this study are likely to be a result of maturation of the middle ear. In addition to the latter, development of the inner ear is conceivable.

Somatic intrachromosomal homologous recombination events in populations of plant siblings

Intrachromosomal homologous recombination in whole tobacco plants was analyzed using beta-glucuronidase as non-selectable marker. We found that recombination frequencies were additive for transgenes in allelic positions and could be enhanced by treatment of plants with DNA-damaging agents. We compared the patterns of distribution of recombination events of different transgenic lines of tobacco and Arabidopsis with the respective Poisson distributions. Some lines showed Poisson-like distributions, indicating that recombination at the transgene locus was occurring in a random fashion in the plant population. In other cases, however, the distributions deviated significantly from Poisson distributions indicating that for specific transgene loci and/or configurations recombination events are not randomly distributed in the population. This was due to overrepresentation of plants with especially many as well as especially few recombination events. Analysis of one tobacco line indicated furthermore that the distribution of recombination events could be influenced by treating the seedlings with external factors. Our results suggest that different plant individuals, or parts of them, might exhibit different transient 'states' of recombination competence. A possible model relating 'recombination silencing' and transcription silencing to heterochromatization of the transgene locus is discussed.

Statistical description of coagulation in finite spatially inhomogenous systems (Part 2)

An analysis of statistical properties of spatially heterogeneous systems has been carried out for constant coagulation nucleus and droplet diffusion coefficient. A universal connection is found for particle size distribution function and particle mean number. It is shown that all possible statistics controlling the particle number in a system can be subdivided into narrow, Poisson-like and broad distributions. In this case initial subdivision of a statistics into a class of narrow distributions remains with time, as for broad statistics—it goes to the class of a narrow one with time. It is shown that the existence of spatial microfluctuations leads to an increase of spectrum large-droplet fraction. This effect is a fluctuation source of large droplets playing a considerable role in understanding the precipitation formation process.

Electrodepositions in thin-gap geometry

We report sensitive gap dependence of morphology in aggregates obtained from electrochemical deposition of zinc in two-dimensional geometry in low concentration and low applied potential limits. The gap effect is similar to the results of noise-reduced or anisotropic diffusion-limited-aggregation simulations. The branching length and angle of the aggregates obtained from digitized images are found to follow Poisson-like and Gaussian distributions, respectively. A diffusion-limited-aggregation branching model captures the experimental results and provides new insights to electrodeposition processes.

Mesoscopic rings driven by time-dependent magnetic flux: Level correlations and localization in energy space.

A mesoscopic ring threaded by a magnetic flux that varies linearly in time (\ensuremath{\varphi}=\ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}t) is considered. A tight-binding model of the problem is formulated, and the transitions among the adiabatic energy levels induced by the time dependence of the Hamiltonian are analyzed. When \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{} is not small, the problem cannot be expressed in terms of a set of decouple two-level Zener problems. It is found that the system is localized in the basis of the adiabatic energy levels. The localization ``length'' in the energy space is shown to be finite even for arbitrarily large \ensuremath{\varphi}\ifmmode \dot{}\else \.{}\fi{}, in contradistinction to previous analyses of free-electron models. The dynamics of the model is governed by a linear equation with time-periodic coefficients; consequently, it is characterized by appropriate Floquet exponents. The latter have a statistical structure that bears similarities to spectra obtained in the context of ``quantum-chaos'' problems. In particular, one obtains Poisson-like or Wigner-like level-spacing distributions depending on the degree of energy localization.

Remarks on the thermodynamical model of strong interactions

The thermodynamical model of strong interactions is described with the emphasis on aspects neglected in previous papers and on its relation to other recent developments and proposals in high-energy physics. Kinematical aspects: “limiting fragmentation”. The pure thermodynamical part: how to incorporate strong interactions in phase space; passing from phase space to thermodynamics (canonical ensemble); attempt to incorporate the whole of strong interactions (bootstrap, duality); the consequence (exponential hadron-mass spectrum, universal highest temperature T o ≈ 160 MeV, Planck-type momentum spectra, limited transverse momenta, Poisson-like multiplicity distributions). A glance at Feynman's ideas: exclusive experiments (for examples A + B → A′ + B′ at forward and large angles); inclusive experiments (one-particle distributions; equivalence of “limiting fragmentation” with Feynman's predictions and with energy independence of the velocity weight functions of the thermodynamical model; are partons fireballs? an approximate scaling law for differential production cross sections). Main results of the thermodynamical model: transverse momenta in very high-energy collisions; can the transverse-momentum distribution be derived from the uncertainty relation applied to the interaction volume? Complications arising from applying the model to a variety of experimental situations. Detailed examples: differential cross sections, invariant-mass distributions, multiplicities, transverse momentum as a function of mass and longitudinal momentum, log tan 1 2 Θ ∗− distribution . Philosophy: the case for bootstrap and non-existence of “truly elementary” material building blocks. Symmetries, not material particles are fundamental.

The Average Volume of Leukemic Leukocytes

Abstract 1. The technic used to determine the average volume per cell of leukocytes from patients with leukemia has been described. 2. The distribution of the average volumes of leukocytes from 15 patients with granulocytic leukemia, based on 52 determinations, has a median value of 450 cu. µ and a mean of 460 cu. µ. 2. The 95 per cent range for this distribution is 340 to 570 cu. µ. 3. Sufficient data are not presently available to determine the Shape of the distribution for the volume of monocytes, but the average value for the leukocytes from 8 patients with monocytic leukemia is 470 cu. µ and the range is 360 to 580 cu. µ. 4. The average volumes of leukocytes from 27 patients with lymphocytic leukemia, based on 74 determinations, have a Poisson-like distribution with a median value of 230 cu. µ and a mean of 250 cu. µ. Ninety-five per cent of the values in this distribution fall in the range of 130 to 410 cu. µ. 5. Although leukocyte volumes from both granulocytic and lymphocytic leukemias follow Poisson-like distributions, the central values of these distributions are significantly different. However, there is an overlap of the distributions with approximately a 15 per cent chance that average lymphocytic volumes will fall into the range of the small granulocytic volumes. 6. For many purposes it may be assumed that two billion cells of the granulocytic or monocytic series or four billion cells of the lymphocytic series equal 1 ml.