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Concept: Probability distribution


Distributed robustness is thought to influence the buffering of random phenotypic variation through the scale-free topology of gene regulatory, metabolic, and protein-protein interaction networks. If this hypothesis is true, then the phenotypic response to the perturbation of particular nodes in such a network should be proportional to the number of links those nodes make with neighboring nodes. This suggests a probability distribution approximating an inverse power-law of random phenotypic variation. Zero phenotypic variation, however, is impossible, because random molecular and cellular processes are essential to normal development. Consequently, a more realistic distribution should have a y-intercept close to zero in the lower tail, a mode greater than zero, and a long (fat) upper tail. The double Pareto-lognormal (DPLN) distribution is an ideal candidate distribution. It consists of a mixture of a lognormal body and upper and lower power-law tails.

Concepts: Evolution, Fungus, Yeast, Saccharomyces cerevisiae, Saccharomyces pastorianus, Normal distribution, Probability distribution, Probability density function


We explore a spatially implicit patch-occupancy model of a population on a landscape with continuous-valued heterogeneous habitat quality, primarily considering the case where the habitat quality of a site affects the mortality rate but not the fecundity of individuals at that site. Two analytical approaches to the model are constructed, by summing over the sites in the landscape and by integrating over the range of habitat quality. We obtain results relating the equilibrium population density and all moments of the probability distribution of the habitat quality of occupied sites, and relating the probability distributions of total habitat quality and occupied habitat quality. Special cases are considered for landscapes where habitat quality has either a uniform or a linear probability density function. For these cases, we demonstrate habitat association, where the quality of occupied sites is higher than the overall mean quality of all sites; the discrepancy between the two is reduced at larger population densities. The variance of the quality of occupied sites may be greater or less than the overall variance of habitat quality, depending on the distribution of habitat quality across the landscape. Increasing the variance of habitat quality is also shown to increase the ability of a population to persist on a landscape.

Concepts: Population, Population density, Probability theory, Normal distribution, Probability distribution, Probability density function, Random variable, Cumulative distribution function


In single-molecule FRET experiments with pulsed lasers, not only the colors of the photons but also the fluorescence lifetimes can be monitored. Although these quantities appear to be random, they are modulated by conformational dynamics. In order to extract information about such dynamics, we develop the theory of the joint distribution of FRET efficiencies and fluorescence lifetimes determined from bins (or bursts) of photons. Our starting point is a rigorous formal expression for the distribution of the numbers of donor and acceptor photons and donor lifetimes in a bin that treats the influence of conformational dynamics on all timescales. This formula leads to an analytic result for a two-state system interconverting on a timescale slower than the interphoton time and to an efficient simulation algorithm for multistate dynamics. The shape of the joint distribution contains more information about conformational dynamics than the FRET efficiency histogram alone. In favorable cases, the connectivity of the underlying conformational states can be determined directly by simple inspection of the projection of the joint distribution on the efficiency-lifetime plane.

Concepts: Quantum mechanics, Light, Science, Probability distribution, Förster resonance energy transfer, Formal language, Albert Einstein, Formal grammar


In corrosion assessment, ultrasonic wall-thickness measurements are often presented in the form of a color map. However, this gives little quantitative information on the distribution of the thickness measurements. The collected data can be used to form an empirical cumulative distribution function (ECDF), which provides information on the fraction of the surface with less than a certain thickness. It has been speculated that the ECDF could be used to draw conclusions about larger areas, from inspection data of smaller sub-sections. A detailed understanding of the errors introduced by such an approach is required to be confident in its predictions. There are two major sources of error: the actual thickness variation due to the morphology of the surface and the interaction of the signal processing algorithm with the recorded ultrasonic signals. Parallel experimental and computational studies were performed using three surfaces, generated with Gaussian height distributions. The surfaces were machined onto mild steel plates and ultrasonic C-scans were performed, while the distributed point source method was used to perform equivalent simulations. ECDFs corresponding to each of these surfaces (for both the experimental and computational data) are presented and their variation with changing surface roughness and different timing algorithms is discussed.

Concepts: Scientific method, Algorithm, Distribution, Normal distribution, Probability distribution, Random variable, Cumulative distribution function, Empirical distribution function


The count of the nucleotides in a cloned, short genomic sequence has become an important criterion to annotate such a sequence as a miRNA molecule. While the majority of human mature miRNA sequences consist of 22 nucleotides, there exists discrepancy in the characteristic lengths of the miRNA sequences. There is also a lack of systematic studies on such length distribution and on the biological factors that are related to or may affect this length. In this paper, we intend to fill this gap by investigating the sequence structure of human miRNA molecules using statistics tools. We demonstrate that the traditional discrete probability distributions do not model the length distribution of the human mature miRNAs well, and we obtain the statistical distribution model with a decent fit. We observe that the four nucleotide bases in a miRNA sequence are not randomly distributed, implying that possible structural patterns such as dinucleotide (trinucleotide or higher order) may exist. Furthermore, we study the relationships of this length distribution to multiple important factors such as evolutionary conservation, tumorigenesis, the length of precursor loop structures, and the number of predicted targets. The association between the miRNA sequence length and the distributions of target site counts in corresponding predicted genes is also presented. This study results in several novel findings worthy of further investigation that include: (1) rapid evolution introduces variation to the miRNA sequence length distribution; (2) miRNAs with extreme sequence lengths are unlikely to be cancer-related; and (3) the miRNA sequence length is positively correlated to the precursor length and the number of predicted target genes.

Concepts: DNA, Gene, Genetics, Evolution, RNA, Nucleotide, Probability distribution, Discrete probability distribution


The glasswing butterfly (Greta oto) has, as its name suggests, transparent wings with remarkable low haze and reflectance over the whole visible spectral range even for large view angles of 80°. This omnidirectional anti-reflection behaviour is caused by small nanopillars covering the transparent regions of its wings. In difference to other anti-reflection coatings found in nature, these pillars are irregularly arranged and feature a random height and width distribution. Here we simulate the optical properties with the effective medium theory and transfer matrix method and show that the random height distribution of pillars significantly reduces the reflection not only for normal incidence but also for high view angles.

Concepts: Optics, English-language films, Simulated reality, Probability distribution, Probability density function, Greta oto, Greta, Danainae


Intuitively scientists accept that order can emerge from disorder and a significant amount of effort has been devoted over many years to demonstrate this. In metallic alloys and oxides, disorder at the atomic scale is the result of occupation at equivalent atomic positions by different atoms which leads to the material exhibiting a fully random or modulated scattering pattern. This arrangement has a substantial influence on the material’s properties, for example ionic conductivity. However it is generally accepted that oxides, such as defect fluorite as used for nuclear waste immobilization matrices and fuel cells, are the result of disorder at the atomic scale. To investigate how order at the atomic scale induces disorder at a larger scale length, we have applied different techniques to study the atomic composition of a homogeneous La 2 Zr 2 O 7 pyrochlore, a textbook example of such a structure. Here we demonstrate that a pyrochlore, which is considered to be defect fluorite, is the result of intricate disorder due to a random distribution of fully ordered nano-domains. Our investigation provides new insight into the order disorder transformations in complex materials with regards to domain formation, resulting in a concord of chemistry with crystallography illustrating that order can induce disorder.

Concepts: Crystal, Chemistry, Atom, Thermodynamics, Chemical element, Complexity, Ion, Probability distribution


Bayesian theories of neural coding propose that sensory uncertainty is represented by a probability distribution encoded in neural population activity, but direct neural evidence supporting this hypothesis is currently lacking. Using fMRI in combination with a generative model-based analysis, we found that probability distributions reflecting sensory uncertainty could reliably be estimated from human visual cortex and, moreover, that observers appeared to use knowledge of this uncertainty in their perceptual decisions.

Concepts: Scientific method, Psychology, Brain, Theory, Probability distribution, Random variable, Probability space, Probability and statistics


We propose a new express method of the correlation characterization of the particles suspended in the volume of optically transparent medium. It utilizes inline digital holography technique for obtaining two images of the adjacent layers from the investigated volume with subsequent matching of the cross-correlation function peak-to-basement ratio calculated for these images. After preliminary calibration via numerical simulation, the proposed method allows one to quickly distinguish parameters of the particle distribution and evaluate their concentration. The experimental verification was carried out for the two types of physical suspensions. Our method can be applied in environmental and biological research, which includes analyzing tools in flow cytometry devices, express characterization of particles and biological cells in air and water media, and various technical tasks, e.g. the study of scattering objects or rapid determination of cutting tool conditions in mechanisms.

Concepts: DNA, Particle physics, Cell biology, Flow cytometry, Monte Carlo method, Probability distribution


The mammalian neocortex has a repetitious, laminar structure and performs functions integral to higher cognitive processes, including sensory perception, memory, and coordinated motor output. What computations does this circuitry subserve that link these unique structural elements to their function? Potjans and Diesmann (2014) parameterized a four-layer, two cell type (i.e. excitatory and inhibitory) model of a cortical column with homogeneous populations and cell type dependent connection probabilities. We implement a version of their model using a displacement integro-partial differential equation (DiPDE) population density model. This approach, exact in the limit of large homogeneous populations, provides a fast numerical method to solve equations describing the full probability density distribution of neuronal membrane potentials. It lends itself to quickly analyzing the mean response properties of population-scale firing rate dynamics. We use this strategy to examine the input-output relationship of the Potjans and Diesmann cortical column model to understand its computational properties. When inputs are constrained to jointly and equally target excitatory and inhibitory neurons, we find a large linear regime where the effect of a multi-layer input signal can be reduced to a linear combination of component signals. One of these, a simple subtractive operation, can act as an error signal passed between hierarchical processing stages.

Concepts: Neuron, Mathematics, Maxwell's equations, Action potential, Cognition, Cerebral cortex, Probability theory, Probability distribution