Fragmentation of Random Trees

We study fragmentation of a random recursive tree into a forest by repeated removal of nodes. The initial tree consists of N nodes and it is generated by sequential addition of nodes with each new node attaching to a randomly-selected existing node. As nodes are removed from the tree, one at a time, the tree dissolves into an ensemble of separate trees, namely, a forest. We study statistical properties of trees and nodes in this heterogeneous forest, and find that the fraction of remaining nodes m characterizes the system in the limit N --> infty. We obtain analytically the size density phi_s of trees of size s. The size density has power-law tail phi_s ~ s^(-alpha) with exponent alpha=1+1/m. Therefore, the tail becomes steeper as further nodes are removed, and the fragmentation process is unusual in that exponent alpha increases continuously with time. We also extend our analysis to the case where nodes are added as well as removed, and obtain the asymptotic size density for growing trees.Comment: 9 pages, 5 figure

Extensions of Effective Medium Theory of Transport in Disordered Systems

Effective medium theory of transport in disordered systems, whose basis is the replacement of spatial disorder by temporal memory, is extended in several practical directions. Restricting attention to a 1-dimensional system with bond disorder for specificity, a transformation procedure is developed to deduce, from given distribution functions characterizing the system disorder, explicit expressions for the memory functions. It is shown how to use the memory functions in the Lapace domain forms in which they first appear, and in the time domain forms which are obtained via numerical inversion algorithms, to address time evolution of the system beyond the asymptotic domain of large times normally treated. An analytic but approximate procedure is provided to obtain the memories, in addition to the inversion algorithm. Good agreement of effective medium theory predictions with numerically computed exact results is found for all time ranges for the distributions used except near the percolation limit as expected. The use of ensemble averages is studied for normal as well as correlation observables. The effect of size on effective mediumtheory is explored and it is shown that, even in the asymptotic limit, finite size corrections develop to the well known harmonic mean prescription for finding the effective rate. A percolation threshold is shown to arise even in 1-d for finite (but not infinite) systems at a concentration of broken bonds related to the system size. Spatially long range transfer rates are shown to emerge naturally as a consequence of the replacement of spatial disorder by temporal memories, in spite of the fact that the original rates possess nearest neighbor character. Pausing time distributions in continuous time random walks corresponding to the effective medium memories are calculated.Comment: 15 pages, 11 figure

Effects of disorder in location and size of fence barriers on molecular motion in cell membranes

The effect of disorder in the energetic heights and in the physical locations of fence barriers encountered by transmembrane molecules such as proteins and lipids in their motion in cell membranes is studied theoretically. The investigation takes as its starting point a recent analysis of a periodic system with constant distances between barriers and constant values of barrier heights, and employs effective medium theory to treat the disorder. The calculations make possible, in principle, the extraction of confinement parameters such as mean compartment sizes and mean intercompartmental transition rates from experimentally reported published observations. The analysis should be helpful both as an unusual application of effective medium theory and as an investigation of observed molecular movements in cell membranes.Comment: 9 pages, 5 figure

Serangan Perenosclerospora Spp pada Tanaman Jagung di Desa Rumahtiga, Kecamatan Teluk Ambon Baguala Kota Ambon

Peronosclerospora spp. is one of the fungal pathogen that causes downy mildew on corn, and can cause yield losses up to 100%. Field research has been done to determine the development of Perenosclerospora spp. attack and contributing factors on corn at corn plantation in Rumahtiga village. The experiment was conducted by using survey method at local farmer's plantation where they cultivated corn in Taeno Hamlet, Talaga Pange, Air Ali, and Wailela areas. The results showed that downy mildew development in corn reached 8.92% which is belong to low diseases intensity. Cultivation techniques including the use of hybrid varieties C1, appropriate fertilization, crop rotation and weed control, as well as good sanitation were key factors of low scale infestation of Peronosclerospora spp

Molecular motion in cell membranes: analytic study of fence-hindered random walks

A theoretical calculation is presented to describe the confined motion of transmembrane molecules in cell membranes. The study is analytic, based on Master equations for the probability of the molecules moving as random walkers, and leads to explicit usable solutions including expressions for the molecular mean square displacement and effective diffusion constants. One outcome is a detailed understanding of the dependence of the time variation of the mean square displacement on the initial placement of the molecule within the confined region. How to use the calculations is illustrated by extracting (confinement) compartment sizes from experimentally reported published observations from single particle tracking experiments on the diffusion of gold-tagged G-protein coupled mu-opioid receptors in the normal rat kidney cell membrane, and by further comparing the analytical results to observations on the diffusion of phospholipids, also in normal rat kidney cells.Comment: 10 pages, 5 figure

The nonlinear time-dependent response of isotactic polypropylene

Tensile creep tests, tensile relaxation tests and a tensile test with a constant rate of strain are performed on injection-molded isotactic polypropylene at room temperature in the vicinity of the yield point. A constitutive model is derived for the time-dependent behavior of semi-crystalline polymers. A polymer is treated as an equivalent network of chains bridged by permanent junctions. The network is modelled as an ensemble of passive meso-regions (with affine nodes) and active meso-domains (where junctions slip with respect to their positions in the bulk medium with various rates). The distribution of activation energies for sliding in active meso-regions is described by a random energy model. Adjustable parameters in the stress--strain relations are found by fitting experimental data. It is demonstrated that the concentration of active meso-domains monotonically grows with strain, whereas the average potential energy for sliding of junctions and the standard deviation of activation energies suffer substantial drops at the yield point. With reference to the concept of dual population of crystalline lamellae, these changes in material parameters are attributed to transition from breakage of subsidiary (thin) lamellae in the sub-yield region to fragmentation of primary (thick) lamellae in the post-yield region of deformation.Comment: 29 pages, 12 figure

Quantifying single nucleotide variant detection sensitivity in exome sequencing

BACKGROUND: The targeted capture and sequencing of genomic regions has rapidly demonstrated its utility in genetic studies. Inherent in this technology is considerable heterogeneity of target coverage and this is expected to systematically impact our sensitivity to detect genuine polymorphisms. To fully interpret the polymorphisms identified in a genetic study it is often essential to both detect polymorphisms and to understand where and with what probability real polymorphisms may have been missed. RESULTS: Using down-sampling of 30 deeply sequenced exomes and a set of gold-standard single nucleotide variant (SNV) genotype calls for each sample, we developed an empirical model relating the read depth at a polymorphic site to the probability of calling the correct genotype at that site. We find that measured sensitivity in SNV detection is substantially worse than that predicted from the naive expectation of sampling from a binomial. This calibrated model allows us to produce single nucleotide resolution SNV sensitivity estimates which can be merged to give summary sensitivity measures for any arbitrary partition of the target sequences (nucleotide, exon, gene, pathway, exome). These metrics are directly comparable between platforms and can be combined between samples to give “power estimates” for an entire study. We estimate a local read depth of 13X is required to detect the alleles and genotype of a heterozygous SNV 95% of the time, but only 3X for a homozygous SNV. At a mean on-target read depth of 20X, commonly used for rare disease exome sequencing studies, we predict 5–15% of heterozygous and 1–4% of homozygous SNVs in the targeted regions will be missed. CONCLUSIONS: Non-reference alleles in the heterozygote state have a high chance of being missed when commonly applied read coverage thresholds are used despite the widely held assumption that there is good polymorphism detection at these coverage levels. Such alleles are likely to be of functional importance in population based studies of rare diseases, somatic mutations in cancer and explaining the “missing heritability” of quantitative traits

Variabilitas Suhu Dan Salinitas Di Laut Halmahera

Suhu dan salinitas memiliki peranan penting dalam mencerminkan kondisi massa air dan secara langsung berpengaruh terhadap kondisi biologi dan kimia perairan. Tujuan penelitian ini adalah menganalisis dinamika angin di perairan Laut Halmahera dan mendiskripsikan kondisi suhu dan salinitas permukaan laut (SPL) di Laut Halmahera. Data yang digunakan yaitu data penginderaan jauh Marine Copernicus untuk data Suhu dan salinitas sedangkan data angin dari ECMWF. Pengolahan data menggunakan software ODV untuk mengolah data SPL dan salinitas dari tahun 2016-2020, selanjutnya data angin diolah menggunakan software surfer 16. Laut Halmahera memiliki suhu permukaan laut berkisar antara 26.20 - 31.6°C dimana kondisi maksimum terjadi bulan Mei dan November. Sedangkan salinitas berkisar antara 29.38 - 34.9 psu, dimana kondisi maksimum pada bulan Desember sampai Maret. Dinamika angin di Laut Halmahera mempengaruhi pola sebaran suhu permukaan laut dan salinitas yang ada pada perairan tersebut, dimana kecepatan angin berkisar antara 6.5 - 2.5 m/s

Efek Pemberian Metabolit Sekunder Trichoderma harzianum Dan Fungisida Propineb Terhadap Penyakit Bercak Neocordana Dan Pertumbuhan Pisang Abaka (Musa textilis) Di Persemaian

Pemanfaatan agens hayati dalam budidaya tanaman merupakan pendekatan ramah lingkungan yang berpotensi digunakan dalam pengendalian penyakit tanaman, termasuk pada tanaman pisang Abaka. Penelitian ini bertujuan untuk mengevaluasi efektivitas metode aplikasi dan interval pemberian metabolit sekunder Trichoderma harzianum dalam menekan perkembangan penyakit bercak Neocordana serta pengaruhnya terhadap pertumbuhan bibit pisang Abaka di persemaian. Perlakuan yang diuji meliputi variasi metode aplikasi dan interval waktu pemberian metabolit sekunder T. harzianum, dengan rancangan percobaan menggunakan Rancangan Acak Kelompok (RAK) yang terdiri atas tiga ulangan. Hasil penelitian menunjukkan bahwa aplikasi metabolit sekunder T. harzianum dengan metode penyemprotan setiap empat hari mampu menurunkan intensitas penyakit sebesar 56,18% dibandingkan dengan kontrol, dan 18,67% dibandingkan dengan perlakuan fungisida propineb. Selain itu, perlakuan ini juga berdampak positif terhadap pertumbuhan tanaman, yang ditunjukkan oleh peningkatan tinggi tanaman sebesar 31,86% dibandingkan dengan kontrol dan 3,37% dibandingkan dengan fungisida propineb, serta peningkatan diameter batang sebesar 39,41% dibandingkan dengan kontrol dan 1,37% dibandingkan dengan perlakuan fungisida