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Concept: Fibonacci number


In a random number generation task, participants are asked to generate a random sequence of numbers, most typically the digits 1 to 9. Such number sequences are not mathematically random, and both extent and type of bias allow one to characterize the brain’s “internal random number generator”. We assume that certain patterns and their variations will frequently occur in humanly generated random number sequences. Thus, we introduce a pattern-based analysis of random number sequences. Twenty healthy subjects randomly generated two sequences of 300 numbers each. Sequences were analysed to identify the patterns of numbers predominantly used by the subjects and to calculate the frequency of a specific pattern and its variations within the number sequence. This pattern analysis is based on the Damerau-Levenshtein distance, which counts the number of edit operations that are needed to convert one string into another. We built a model that predicts not only the next item in a humanly generated random number sequence based on the item’s immediate history, but also the deployment of patterns in another sequence generated by the same subject. When a history of seven items was computed, the mean correct prediction rate rose up to 27% (with an individual maximum of 46%, chance performance of 11%). Furthermore, we assumed that when predicting one subject’s sequence, predictions based on statistical information from the same subject should yield a higher success rate than predictions based on statistical information from a different subject. When provided with two sequences from the same subject and one from a different subject, an algorithm identifies the foreign sequence in up to 88% of the cases. In conclusion, the pattern-based analysis using the Levenshtein-Damarau distance is both able to predict humanly generated random number sequences and to identify person-specific information within a humanly generated random number sequence.

Concepts: Scientific method, Mathematics, Prediction, Futurology, Randomness, Randomization, Fibonacci number, Hardware random number generator


Social information allows the rapid dissemination of novel information among individuals. However, an individual’s ability to use information is likely to be dependent on phenotypic constraints operating at three successive steps: acquisition, application, and exploitation. We tested this novel framework by quantifying the sequential process of social information use with experimental food patches in wild baboons (Papio ursinus). We identified phenotypic constraints at each step of the information use sequence: peripheral individuals in the proximity network were less likely to acquire and apply social information, while subordinate females were less likely to exploit it successfully. Social bonds and personality also played a limiting role along the sequence. As a result of these constraints, the average individual only acquired and exploited social information on.

Concepts: Person, Old World monkey, Baboon, Fibonacci number, Chacma Baboon


We study the properties of wavefunctions and the wavepacket dynamics in quasiperiodic tight-binding models in one, two, and three dimensions. The atoms in the one-dimensional quasiperiodic chains are coupled by weak and strong bonds aligned according to the Fibonacci sequence. The associated d-dimensional quasiperiodic tilings are constructed from the direct product of d such chains, which yields either the hypercubic tiling or the labyrinth tiling. This approach allows us to consider fairly large systems numerically. We show that the wavefunctions of the system are multifractal and that their properties can be related to the structure of the system in the regime of strong quasiperiodic modulation by a renormalization group (RG) approach. We also study the dynamics of wavepackets to get information about the electronic transport properties. In particular, we investigate the scaling behaviour of the return probability of the wavepacket with time. Applying again the RG approach we show that in the regime of strong quasiperiodic modulation the return probability is governed by the underlying quasiperiodic structure. Further, we also discuss lower bounds for the scaling exponent of the width of the wavepacket and propose a modified lower bound for the absolute continuous regime.

Concepts: Quantum mechanics, Fundamental physics concepts, Quantum field theory, Dimension, Set, String theory, Fibonacci number, Renormalization group


The availability of genomic sequences of many organisms has opened new challenges in many aspects particularly in terms of genome analysis. Sequence extraction is a vital step and many tools have been developed to solve this issue. These tools are available publically but have limitations with reference to the sequence extraction, length of the sequence to be extracted, organism specificity and lack of user friendly interface. We have developed a java based software package having three modules which can be used independently or sequentially. The tool efficiently extracts sequences from large datasets with few simple steps. It can efficiently extract multiple sequences of any desired length from a genome of any organism. The results are crosschecked by published data. AVAILABILITY: URL 1: URL 2:

Concepts: DNA, Gene, Genetics, Organism, Virus, Genome, Sequence, Fibonacci number


Gene annotations, such as those in GENCODE, are derived primarily from alignments of spliced cDNA sequences and protein sequences. The impact of RNA-seq data on annotation has been confined to major projects like ENCODE and Illumina Body Map 2.0.

Concepts: DNA, Protein, Gene expression, Transcription, Molecular biology, RNA, Splice, Fibonacci number


In humans, the monocyte pool comprises three subsets (classical, intermediate, and nonclassical) that circulate in dynamic equilibrium. The kinetics underlying their generation, differentiation, and disappearance are critical to understanding both steady-state homeostasis and inflammatory responses. Here, using human in vivo deuterium labeling, we demonstrate that classical monocytes emerge first from marrow, after a postmitotic interval of 1.6 d, and circulate for a day. Subsequent labeling of intermediate and nonclassical monocytes is consistent with a model of sequential transition. Intermediate and nonclassical monocytes have longer circulating lifespans (∼4 and ∼7 d, respectively). In a human experimental endotoxemia model, a transient but profound monocytopenia was observed; restoration of circulating monocytes was achieved by the early release of classical monocytes from bone marrow. The sequence of repopulation recapitulated the order of maturation in healthy homeostasis. This developmental relationship between monocyte subsets was verified by fate mapping grafted human classical monocytes into humanized mice, which were able to differentiate sequentially into intermediate and nonclassical cells.

Concepts: Inflammation, Monocyte, Bone marrow, Thermodynamics, Systems theory, Steady state, Fibonacci number, Dynamic equilibrium


In lipid biochemistry, a fundamental question is how the potential number of fatty acids increases with their chain length. Here, we show that it grows according to the famous Fibonacci numbers when cis/trans isomerism is neglected. Since the ratio of two consecutive Fibonacci numbers tends to the Golden section, 1.618, organisms can increase fatty acid variability approximately by that factor per carbon atom invested. Moreover, we show that, under consideration of cis/trans isomerism and/or of modification by hydroxy and/or oxo groups, diversity can be described by generalized Fibonacci numbers (e.g. Pell numbers). For the sake of easy comprehension, we deliberately build the proof on the recursive definitions of these number series. Our results should be of interest for mass spectrometry, combinatorial chemistry, synthetic biology, patent applications, use of fatty acids as biomarkers and the theory of evolution. The recursive definition of Fibonacci numbers paves the way to construct all structural formulas of fatty acids in an automated way.

Concepts: Carbon dioxide, Fatty acid, Fat, Fatty acid metabolism, Lipid, Biochemistry, Golden ratio, Fibonacci number


Complex structures and devices, both natural and manmade, are often constructed sequentially. From crystallization to embryogenesis, a nucleus or seed is formed and built upon. Sequential assembly allows for initiation, signaling, and logical programming, which are necessary for making enclosed, hierarchical structures. Although biology relies on such schemes, they have not been available in materials science. Here, we demonstrate programmed sequential self-assembly of DNA functionalized emulsions. The droplets are initially inert because the grafted DNA strands are pre-hybridized in pairs. Active strands on initiator droplets then displace one of the paired strands and thus release its complement, which in turn activates the next droplet in the sequence, akin to living polymerization. Our strategy provides time and logic control during the self-assembly process, and offers a new perspective on the synthesis of materials.Natural complex systems are often constructed by sequential assembly but this is not readily available for synthetic systems. Here, the authors program the sequential self-assembly of DNA functionalized emulsions by altering the DNA grafted strands.

Concepts: DNA, Series, Systems, Systems theory, Sequence, System, Real analysis, Fibonacci number


Single amplified genomes and genomes assembled from metagenomes have enabled the exploration of uncultured microorganisms at an unprecedented scale. However, both these types of products are plagued by contamination. Since these genomes are now being generated in a high-throughput manner and sequences from them are propagating into public databases to drive novel scientific discoveries, rigorous quality controls and decontamination protocols are urgently needed. Here, we present ProDeGe (Protocol for fully automated Decontamination of Genomes), the first computational protocol for fully automated decontamination of draft genomes. ProDeGe classifies sequences into two classes-clean and contaminant-using a combination of homology and feature-based methodologies. On average, 84% of sequence from the non-target organism is removed from the data set (specificity) and 84% of the sequence from the target organism is retained (sensitivity). The procedure operates successfully at a rate of ~0.30 CPU core hours per megabase of sequence and can be applied to any type of genome sequence.The ISME Journal advance online publication, 9 June 2015; doi:10.1038/ismej.2015.100.

Concepts: DNA, Bacteria, Sequence, Permutation, Topological space, Set, Fibonacci number, Exact sequence


The order and magnitude of pathologic processes in Alzheimer’s disease are not well understood, partly because the disease develops over many years. Autosomal dominant Alzheimer’s disease has a predictable age at onset and provides an opportunity to determine the sequence and magnitude of pathologic changes that culminate in symptomatic disease.

Concepts: Alzheimer's disease, Clinical trial, Death, Fibonacci number