Journal articles: 'Branching rate'

1

Klenke, Achim, and Leonid Mytnik. "Infinite rate mutually catalytic branching." Annals of Probability 38, no. 4 (July 2010): 1690–716. http://dx.doi.org/10.1214/09-aop520.

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2

Döring, Leif, Achim Klenke, and Leonid Mytnik. "Finite system scheme for mutually catalytic branching with infinite branching rate." Annals of Applied Probability 27, no. 5 (October 2017): 3113–52. http://dx.doi.org/10.1214/17-aap1277.

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3

Liu, Jiaqi, and Jason Schweinsberg. "Particle configurations for branching Brownian motion with an inhomogeneous branching rate." Latin American Journal of Probability and Mathematical Statistics 20, no. 1 (2023): 731. http://dx.doi.org/10.30757/alea.v20-28.

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4

Shiozawa, Yuichi. "Spread Rate of Branching Brownian Motions." Acta Applicandae Mathematicae 155, no. 1 (November 30, 2017): 113–50. http://dx.doi.org/10.1007/s10440-017-0148-8.

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5

Hu, Xi, Yun-Zhi Yan, Zhong-Tuan Zheng, Hong-Yan Li, and Hong-Yan Zhao. "Extinction Moment for a Branching Tree Evolution with Birth Rate and Death Rate Both Depending on Age." Mathematical Problems in Engineering 2021 (February 10, 2021): 1–13. http://dx.doi.org/10.1155/2021/6643349.

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In this paper, a branching tree evolution is established, in which the birth rate and the death rate are both dependent on node’s age. The extinction probability and the t-pre-extinction (extinct before time t ) probability are studied, by which the distribution of the extinction moment can be given. The analytical formula and the approximation algorithm for the distribution of extinction moment are given; furthermore, the analytical formula and the approximation algorithm of extinction probability are given, and a necessary and sufficient condition of extinction with probability 1 is given. It is the first time to study the distribution of extinction time for the branching process with birth rate and the death rate both depending on node’s age, and the results will do great help in the theory of branching process. It is expected to be applied in the fields of biology, genetics, medicine, epidemiology, demography, nuclear physics, actuarial mathematics, algorithm, and data structures, etc.

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6

Shiozawa, Yuichi. "Extinction of branching symmetric α-stable processes." Journal of Applied Probability 43, no. 4 (December 2006): 1077–90. http://dx.doi.org/10.1239/jap/1165505209.

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We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.

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Shiozawa, Yuichi. "Extinction of branching symmetric α-stable processes." Journal of Applied Probability 43, no. 04 (December 2006): 1077–90. http://dx.doi.org/10.1017/s0021900200002448.

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We give a criterion for extinction or local extinction of branching symmetric α-stable processes in terms of the principal eigenvalue for time-changed processes of symmetric α-stable processes. Here the branching rate and the branching mechanism are spatially dependent. In particular, the branching rate is allowed to be singular with respect to the Lebesgue measure. We apply this criterion to some branching processes.

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8

Bansaye, Vincent, Juan Carlos Pardo, and Charline Smadi. "Extinction rate of continuous state branching processes in critical Lévy environments." ESAIM: Probability and Statistics 25 (2021): 346–75. http://dx.doi.org/10.1051/ps/2021014.

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We study the speed of extinction of continuous state branching processes in a Lévy environment, where the associated Lévy process oscillates. Assuming that the Lévy process satisfies Spitzer’s condition, we extend recent results where the associated branching mechanism is stable. The study relies on the path analysis of the branching process together with its Lévy environment, when the latter is conditioned to have a non-negative running infimum. For that purpose, we combine the approach developed in Afanasyev et al. [2], for the discrete setting and i.i.d. environments, with fluctuation theory of Lévy processes and a result on exponential functionals of Lévy processes due to Patie and Savov [28].

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9

Mallein, Bastien. "Branching random walk with selection at critical rate." Bernoulli 23, no. 3 (August 2017): 1784–821. http://dx.doi.org/10.3150/15-bej796.

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10

Reni Sagayaraj, M., S. Anand Gnana Selvam, and R. Reynald Susainathan. "A Study of Markov Branching Process with Varying Growth Rate." Asian Journal of Science and Applied Technology 4, no. 1 (May 5, 2015): 17–20. http://dx.doi.org/10.51983/ajsat-2015.4.1.909.

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Branching processes in random environments occurs when the values of the reproduction probabilities and instantaneous reproduction rates are themselves sample paths of stochastic processes. These processes occur very naturally as models to describe the growth mechanism of biological systems. In this paper, we consider a Markov branching process with varying growth rates controlled by a random environment described by an alternating renewal process; we will derive expression for the mean number of the size of the population.

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11

Spies, J. M., T. Warkentin, and S. Shirtliffe. "Basal branching in field pea cultivars and yield-density relationships." Canadian Journal of Plant Science 90, no. 5 (September 1, 2010): 679–90. http://dx.doi.org/10.4141/cjps09195.

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The current recommended plant density in field pea (Pisum sativum L.) in western Canada is 88 plants m–2. This rate may exceed the optimum for yield in cultivars with more basal branching than typical. The objective of this research was to determine how the seed yield of pea cultivars differing in basal branching ability responds to changes in plant density. Ten pea cultivars were sown at target plant populations of 10, 30, 90, 120, and 150 plant m–2 for 3 yr at Rosthern and Saskatoon, Saskatchewan. At very low plant densities there was greater than a twofold difference in branching potential between cultivars (range 0.85 to 1.99 branches plant–1). Increasing field pea plant density reduced branching by 0.097 branches for each additional plant. The response of yield to plant density differed, as the forage cultivars 40-10 and CDC Sonata reached their potential yield at lower densities, while Courier required higher densities to reach the same proportion of yield. Field pea cultivars with greater basal branching achieved their maximum yield at lower plant densities compared with cultivars with low basal branching. The optimum economic plant density for the pea cultivars ranged from 59 to 84 plants m–2, which is below the current recommended plant density. However, with the exception of the forage cultivars and the low-branching cultivar Courier, the optimum seeding rate was within 8% of 88 seeds m–2. It is recommended that pea growers avoid low-branching pea cultivars and seed at a rate of 88 viable seeds m–2.Key words: Basal branching, seeding rate, plant density, light interception, leafed pea, semi-leafless pea, forage pea

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12

Golubtsov, G. B., and R. S. Chalov. "COMPARATIVE HYDRO-MORPHOLOGICAL ANALYSIS OF THE ISLANDS OF DIFFERENTLY BRANCHED UPPER OB AND MIDDLE LENA RIVER CHANNELS." Bulletin of Udmurt University. Series Biology. Earth Sciences 30, no. 2 (July 30, 2020): 164–74. http://dx.doi.org/10.35634/2412-9518-2020-30-2-164-174.

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This article is devoted to the formation conditions and morphometric features of the river islands. Also it considers the rate of branching of the Upper Ob and Middle Lena river channels. They are the largest rivers, but the Middle Lena River is bigger than the Upper Ob River by 6.15 times of total runoff and 2.5 times of width. However, both of them have unstable or weakly stable channels, characterized by parallel-sleeve, alternating, one-sided and single branchings, formed by numerous islands. Their comparison makes it possible to establish the dependence of the conditions of islands formation, their parameters (length - L , width - B , shape - L / B ), types and number on the indicators of stability, total runoff, branching types and location in the channel (active or peripheral part). These correlations based on hydro-morphological analysis show that the shape of islands L / B and the branching rate of the channel - n / x depend on the degree of stability. It is a common feature of all branching types and stages of island evolution (elementary, small, large islands and island massifs). Uniform dependencies of island parameters on river bed stability for both rivers, despite their large-scale distortions, were obtained by taking into account the connection of channel width ( b ) with its runoff ( Q ) by introducing a correction factor of 2.5 for the river size. Also the formation conditions of elongated islands ( L / B > 5), were determined. Their shape does not correspond to the optimal ratio L / B = 3...4. The revealed patterns give an opportunity to clarify the previously proposed classification of the islands.

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13

Watters, Michael K., and Anthony J. F. Griffiths. "Tests of a Cellular Model for Constant Branch Distribution in the Filamentous Fungus Neurospora crassa." Applied and Environmental Microbiology 67, no. 4 (April 1, 2001): 1788–92. http://dx.doi.org/10.1128/aem.67.4.1788-1792.2001.

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ABSTRACT The growth of mycelial fungi is characterized by the highly polarized extension of hyphal tips and the formation of subapical branches, which themselves extend as new tips. In Neurospora crassa, tip growth and branching are crucial elements for this saprophyte in the colonization and utilization of organic substrates. Much research has focused on the mechanism of tip extension, but a cellular model that fully explains the known phenomenology of branching by N. crassa has not been proposed. We described and tested a model in which the formation of a lateral branch in N. crassa was determined by the accumulation of tip-growth vesicles caused by the excess of the rate of supply over the rate of deposition at the apex. If both rates are proportional to metabolic rate, then the model explains the known lack of dependence of branch interval on growth rate. We tested the model by manipulating the tip extension rate, first by shifting temperature in both the wild type and hyperbranching (colonial) mutants and also by observing the behavior of both tipless colonies and colonyless tips. We found that temperature shifts in either direction result in temporary changes in branching. We found that colonyless tips also pass through a temporary transition phase of branching. The tipless colonies produced a cluster of new tips near the point of damage. We also found that branching in colonial mutants is dependent on growth rate. The results of these tests are consistent with a model of branching in which branch initiation is controlled by the dynamics of tip growth while being independent of the actual rate of this growth.

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14

Neuhauser, Claudia, and Aidan Sudbury. "The biased annihilating branching process." Advances in Applied Probability 25, no. 1 (March 1993): 24–38. http://dx.doi.org/10.2307/1427494.

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In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution vλ /(λ +1), the product measure with density λ/(1 +λ). It is shown that vλ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is vλ /(λ +1) provided the initial measure converges.

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Neuhauser, Claudia, and Aidan Sudbury. "The biased annihilating branching process." Advances in Applied Probability 25, no. 01 (March 1993): 24–38. http://dx.doi.org/10.1017/s0001867800025155.

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In the biased annihilating branching process, particles place offspring on empty neighboring sites at rate A and destroy neighbors at rate 1. It is conjectured that for any λ ≥ 0 the population will spread to ∞, and this is shown in one dimension for The process on a finite graph when starting with a non-empty configuration has limiting distribution v λ /(λ +1), the product measure with density λ/(1 +λ). It is shown that v λ /(λ +1) and δ Ø are the only stationary distributions on Moreover, if and the initial configuration is non-empty, then the limiting measure is v λ /(λ +1) provided the initial measure converges.

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16

Schmitz, Y., J. Luccarelli, M. Kim, M. Wang, and D. Sulzer. "Glutamate Controls Growth Rate and Branching of Dopaminergic Axons." Journal of Neuroscience 29, no. 38 (September 23, 2009): 11973–81. http://dx.doi.org/10.1523/jneurosci.2927-09.2009.

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17

Oehlschlaeger, Matthew A., David F. Davidson, and Ronald K. Hanson. "Thermal decomposition of toluene: Overall rate and branching ratio." Proceedings of the Combustion Institute 31, no. 1 (January 2007): 211–19. http://dx.doi.org/10.1016/j.proci.2006.07.002.

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18

FU, YunBin, YunZhi YAN, Xi HU, HanXing WANG, GuiLin LU, and Na YU. "Birth-death branching tree with age-dependent birth-rate." SCIENTIA SINICA Mathematica 43, no. 4 (April 1, 2013): 383–98. http://dx.doi.org/10.1360/012012-477.

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19

Kashikar, Akanksha S. "Estimation of growth rate in second order branching process." Journal of Statistical Planning and Inference 191 (December 2017): 1–12. http://dx.doi.org/10.1016/j.jspi.2017.06.003.

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20

Huang, Ying, and Arthur F. Veinott. "Markov Branching Decision Chains with Interest-Rate-Dependent Rewards." Probability in the Engineering and Informational Sciences 9, no. 1 (January 1995): 99–121. http://dx.doi.org/10.1017/s0269964800003715.

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Finite-state-and-action Markov branching decision chains are studied with bounded endogenous expected population sizes and interest-rate-dependent one-period rewards that are analytic in the interest rate at zero. The existence of a stationary strong-maximum-present-value policy is established. Miller and Veinott's [1969] strong policy-improvement method is generalized to find in finite time a stationary n-present-value optimal policy and, when the one-period rewards are rational in the interest rate, a stationary strong-maximum-present-value policy. This extends previous studies of Blackwell [1962], Miller and Veinott [1969], Veinott [1974], and Rothblum [1974, 1975], in which the one-period rewards are independent of the interest rate, and Denardo [1971] in which semi-Markov decision chains with small interest rates are studied. The problem of finding a stationary n-present-value optimal policy is also formulated as a staircase linear program in which the objective function and right-hand sides, but not the constraint matrix, depend on the interest rate, and solutions for all small enough positive interest rates are sought. The optimal solutions of the primal and dual are polynomials in the reciprocal of the interest rate. A constructive rule is given for finding a stationary n-present-value optimal policy from an optimal solution of the asymptotic linear program. This generalizes the linear programming approaches for finding maximum-reward-rate and maximum-present-value policies for Markov decision chains studied by Manne [1960], d'Epenoux [1960, 1963], Balinski [1961], Derman [1962], Denardo and Fox [1968], Denardo [1970], Derman and Veinott [1972], Veinott [1973], and Hordijk and Kallenberg [1979, 1984].

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21

Girija, K. K., and Antony Joseph. "Role of shape and quadrupole deformation of parents in the cluster emission of rare earth nuclei." International Journal of Modern Physics E 23, no. 01 (January 2014): 1450002. http://dx.doi.org/10.1142/s0218301314500025.

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The nuclear structure effects on α decay and cluster emission are investigated in the case of even–even rare earth nuclei150–160Dy ,150–160Er ,150–160Yb ,158,162,166–176Hf ,160,164–178W and162,166,170–180Os . The role of shape and deformation of parent nuclei in the decay rate is studied by taking the Coulomb and proximity potentials as the interacting barrier for the post scission configuration. The quadrupole deformation of parent nuclei causes a slight change in the half-life of α emissions, but it affects the rate of heavy cluster emissions significantly. Prolate deformation of parents enhances cluster emission, while an oblate deformation slows down the decay. Shape and deformation of parent nuclei causes change in the branching ratio also. A prolate deformation increases the branching ratio, whereas an oblate deformation reduces it. Highest branching ratio is predicted at N ~ 90.

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22

Xie, Y. J., Xiao Zhi Hu, and X. H. Wang. "A Theoretical Note on Mode I Crack Kinking and Branching." Advanced Materials Research 118-120 (June 2010): 314–18. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.314.

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An energy-based fracture mode has been derived for the mode I crack kinking and branching. The classic -integral has been further explored by a new partial integral path and the analytical solution of the energy release rate for crack kinking and branching from a mode-I crack tip has been established. The crack kinking/branching angle has also been analytically derived. It shows that the Griffith’s theorem and conservation law can be applied to both model I crack extension and model I crack kinking and branching. The branching mechanism for quasi-static mode-I crack has been theoretically investigated. The branching toughness and the K-based criterion for crack branching have been defined. The crack branching phenomena predicted by the present model are in well agreement with the experimental observations reported in the literatures.

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23

Minh, Nguyen Thai, Le Quang Thien, Nguyen Sinh Hien, and Nguyen Hoang Ha. "Using self -suture branching artificial vesssels in aortic arch surgery at Hanoi Heart Hospital." Tạp chí Phẫu thuật Tim mạch và Lồng ngực Việt Nam 35 (January 6, 2022): 158–64. http://dx.doi.org/10.47972/vjcts.v35i.696.

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Background: For aortic arch surgery, the improvement of anastomosis technique, and the improvement of using self-suture branching artificial vessels have shortened the time and reduced the cost of surgery. The study aimed to evaluate the improved results of using self-suture branched artificial vessels in aortic arch surgery. Methods: A retrospective descriptive study of the use of self-suture branching artificial vessels in aortic arch surgery at Hanoi Heart Hospital from October 2018 to May 2021. Results: There were 33 cases of aortic arch replacement using self-suture branching artificial vessels. The rate of postoperative bleeding was 6.06%. The rate of artificial vessel infection is 0%. Conclusion: Using self-suture branching artificial vessels in aortic arch surgery is a safe and effective technique.

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24

Khusanbaev, Ya, S. Sharipov, and V. Golomoziy. "Berry-Esseen bound for nearly critical branching processes with immigration." Bulletin of Taras Shevchenko National University of Kyiv. Series: Physics and Mathematics, no. 4 (2019): 42–49. http://dx.doi.org/10.17721/1812-5409.2019/4.5.

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25

Getan, A., S. Molchanov, and B. Vainberg. "Intermittency for branching walks with heavy tails." Stochastics and Dynamics 17, no. 06 (August 13, 2017): 1750044. http://dx.doi.org/10.1142/s0219493717500447.

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Branching random walks on multidimensional lattice with heavy tails and a constant branching rate are considered. It is shown that under these conditions (heavy tails and constant rate), the front propagates exponentially fast, but the particles inside of the front are distributed very non-uniformly. The particles exhibit intermittent behavior in a large part of the region behind the front (i.e. the particles are concentrated only in very sparse spots there). The zone of non-intermittency (were particles are distributed relatively uniformly) extends with a power rate. This rate is found.

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26

Huillet, Thierry E. "Nonconservative Diffusions on with Killing and Branching: Applications to Wright-Fisher Models with or without Selection." International Journal of Stochastic Analysis 2011 (July 18, 2011): 1–37. http://dx.doi.org/10.1155/2011/605068.

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We consider nonconservative diffusion processes on the unit interval, so with absorbing barriers. Using Doob-transformation techniques involving superharmonic functions, we modify the original process to form a new diffusion process presenting an additional killing rate part . We limit ourselves to situations for which is itself nonconservative with upper bounded killing rate. For this transformed process, we study various conditionings on events pertaining to both the killing and the absorption times. We introduce the idea of a reciprocal Doob transform: we start from the process , apply the reciprocal Doob transform ending up in a new process which is but now with an additional branching rate , which is also upper bounded. For this supercritical binary branching diffusion, there is a tradeoff between branching events giving birth to new particles and absorption at the boundaries, killing the particles. Under our assumptions, the branching diffusion process gets eventually globally extinct in finite time. We apply these ideas to diffusion processes arising in population genetics. In this setup, the process is a Wright-Fisher diffusion with selection. Using an exponential Doob transform, we end up with a killed neutral Wright-Fisher diffusion . We give a detailed study of the binary branching diffusion process obtained by using the corresponding reciprocal Doob transform.

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27

YU, WEI, LUYAO XU, SHUNJIA CHEN, and FENG YAO. "NUMERICAL STUDY ON FLOW BOILING IN A TREE-SHAPED MICROCHANNEL." Fractals 27, no. 07 (November 2019): 1950111. http://dx.doi.org/10.1142/s0218348x19501111.

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A two-dimensional model is developed to numerically study the water flow boiling through a tree-shaped microchannel by VOF method. In this work, the bubble dynamics and flow patterns along the channel are examined. Additionally, the pressure drop, heat transfer performance and the effects of mass flow rate and heat flux on the heat transfer coefficient are analyzed and discussed. The numerical results indicate that, there are three main bubble dynamic behaviors at the wall, namely coalesce-lift-off, coalesce-slide and coalesce-reattachment. At the bifurcation in high branching level, the slug bubbles may coalesce or breakup. The flow patterns of bubbly, bubbly-slug flows occur at low branching level and slug flow occurs at high branching level. The passage of bubbles causes the increasing of fluid temperature and local pressure. Additionally, the pressure drop decreases with the branching level. The flow pattern and channel confinement effect play a vital role in heat transfer performance. The nucleate boiling dominant heat transfer is observed at low branching level, the heat transfer performance is enhanced with increasing branching level from [Formula: see text] to 2. While, at high branching level, the heat transfer performance becomes weaker due to the suppression of nucleate boiling. Moreover, the heat transfer coefficient increases with the mass flow rate and heat flux.

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28

Lv, You, and Huaping Huang. "The Asymptotic Behavior for Generalized Jiřina Process." Axioms 12, no. 1 (December 23, 2022): 13. http://dx.doi.org/10.3390/axioms12010013.

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As the classic branching process, the Galton-Watson process has obtained intensive attentions in the past decades. However, this model has two idealized assumptions–discrete states and time-homogeneity. In the present paper, we consider a branching process with continuous states, and for any given n∈N, the branching law of every particle in generation n is determined by the population size of generation n. We consider the case that the process is extinct with Probability 1 since in this case the process will be substantially different from the size-dependent branching process with discrete states. We give the extinction rate in the sense of L2 and almost surely by the form of harmonic moments, that is to say, we show how fast {Zn−1} grows under a group of sufficient conditions. From the result of the present paper, we observe that the extinction rate will be determined by an asymptotic behavior of the mean of the branching law. The results obtained in this paper have the more superiority than the counterpart from the existing literature.

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Allen, Frances I. "Branched High Aspect Ratio Nanostructures Fabricated by Focused Helium Ion Beam Induced Deposition of an Insulator." Micromachines 12, no. 3 (February 25, 2021): 232. http://dx.doi.org/10.3390/mi12030232.

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Helium ion beam induced deposition using the gaseous precursor pentamethylcyclopentasiloxane is employed to fabricate high aspect ratio insulator nanostructures (nanopillars and nanocylinders) that exhibit charge induced branching. The branched nanostructures are analyzed by transmission electron microscopy. It is found that the side branches form above a certain threshold height and that by increasing the flow rate of the precursor, the vertical growth rate and branching phenomenon can be significantly enhanced, with fractalesque branching patterns observed. The direct-write ion beam nanofabrication technique described herein offers a fast single-step method for the growth of high aspect ratio branched nanostructures with site-selective placement on the nanometer scale.

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Brémaud, Pierre, and Laurent Massoulié. "Hawkes branching point processes without ancestors." Journal of Applied Probability 38, no. 1 (March 2001): 122–35. http://dx.doi.org/10.1239/jap/996986648.

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In this article, we prove the existence of critical Hawkes point processes with a finite average intensity, under a heavy-tail condition for the fertility rate which is related to a long-range dependence property. Criticality means that the fertility rate integrates to 1, and corresponds to the usual critical branching process, and, in the context of Hawkes point processes with a finite average intensity, it is equivalent to the absence of ancestors. We also prove an ergodic decomposition result for stationary critical Hawkes point processes as a mixture of critical Hawkes point processes, and we give conditions for weak convergence to stationarity of critical Hawkes point processes.

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Brémaud, Pierre, and Laurent Massoulié. "Hawkes branching point processes without ancestors." Journal of Applied Probability 38, no. 01 (March 2001): 122–35. http://dx.doi.org/10.1017/s0021900200018556.

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In this article, we prove the existence of critical Hawkes point processes with a finite average intensity, under a heavy-tail condition for the fertility rate which is related to a long-range dependence property. Criticality means that the fertility rate integrates to 1, and corresponds to the usual critical branching process, and, in the context of Hawkes point processes with a finite average intensity, it is equivalent to the absence of ancestors. We also prove an ergodic decomposition result for stationary critical Hawkes point processes as a mixture of critical Hawkes point processes, and we give conditions for weak convergence to stationarity of critical Hawkes point processes.

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32

Kiayias, Aggelos, Nikos Leonardos, Helger Lipmaa, Kateryna Pavlyk, and Qiang Tang. "Optimal Rate Private Information Retrieval from Homomorphic Encryption." Proceedings on Privacy Enhancing Technologies 2015, no. 2 (June 1, 2015): 222–43. http://dx.doi.org/10.1515/popets-2015-0016.

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Abstract We consider the problem of minimizing the communication in single-database private information retrieval protocols in the case where the length of the data to be transmitted is large. We present first rate-optimal protocols for 1-out-of-n computationallyprivate information retrieval (CPIR), oblivious transfer (OT), and strong conditional oblivious transfer (SCOT). These protocols are based on a new optimalrate leveled homomorphic encryption scheme for large-output polynomial-size branching programs, that might be of independent interest. The analysis of the new scheme is intricate: the optimal rate is achieved if a certain parameter s is set equal to the only positive root of a degree-(m + 1) polynomial, where m is the length of the branching program. We show, by using Galois theory, that even when m = 4, this polynomial cannot be solved in radicals. We employ the Newton-Puiseux algorithm to find a Puiseux series for s, and based on this, propose a Θ (logm)-time algorithm to find an integer approximation to s.

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Alekseev, A. A., K. N. Bol’shev, V. A. Ivanov, A. S. Syromyatnikova, A. M. Bol’shakov, and A. R. Ivanov. "Experimental Determination of the Rate of Crack Branching in Steel." Russian Metallurgy (Metally) 2020, no. 10 (October 2020): 1222–24. http://dx.doi.org/10.1134/s0036029520100031.

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HOPFNER, R., M. HOFFMANN, and E. LOCHERBACH. "Non-parametric Estimation of the Death Rate in Branching Diffusions." Scandinavian Journal of Statistics 29, no. 4 (December 2002): 665–92. http://dx.doi.org/10.1111/1467-9469.00312.

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35

Bédard-Tremblay, Laurie, Josue Melguizo-Gavilanes, and Luc Bauwens. "Detonation structure under chain-branching kinetics with small initiation rate." Proceedings of the Combustion Institute 32, no. 2 (2009): 2339–47. http://dx.doi.org/10.1016/j.proci.2008.05.049.

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36

Lei, Wenfeng, Dan Zhang, Renyi Zhang, Luisa T. Molina, and Mario J. Molina. "Rate constants and isomeric branching of the Cl–isoprene reaction." Chemical Physics Letters 357, no. 1-2 (May 2002): 45–50. http://dx.doi.org/10.1016/s0009-2614(02)00437-2.

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37

Klenke, Achim, and Mario Oeler. "A Trotter-type approach to infinite rate mutually catalytic branching." Annals of Probability 38, no. 2 (March 2010): 479–97. http://dx.doi.org/10.1214/09-aop488.

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38

Klippenstein, Stephen J., Lawrence B. Harding, Peter Glarborg, Yide Gao, Huanzhen Hu, and Paul Marshall. "Rate Constant and Branching Fraction for the NH2 + NO2 Reaction." Journal of Physical Chemistry A 117, no. 37 (September 9, 2013): 9011–22. http://dx.doi.org/10.1021/jp4068069.

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Cayco-Gajic, N. Alex, and Eric Shea-Brown. "Neutral Stability, Rate Propagation, and Critical Branching in Feedforward Networks." Neural Computation 25, no. 7 (July 2013): 1768–806. http://dx.doi.org/10.1162/neco_a_00461.

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Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing patterns. We seek the simplest setting in which these properties emerge, clarifying their origin and relationship in random, feedforward networks of McCullochs-Pitts neurons. Two key parameters are the thresholds at which neurons fire spikes and the overall level of feedforward connectivity. When neurons have low thresholds, we show that there is always a connectivity for which the properties in question all occur, that is, these networks preserve overall firing rates from layer to layer and produce broad distributions of activity in each layer. This fails to occur, however, when neurons have high thresholds. A key tool in explaining this difference is the eigenstructure of the resulting mean-field Markov chain, as this reveals which activity modes will be preserved from layer to layer. We extend our analysis from purely excitatory networks to more complex models that include inhibition and local noise, and find that both of these features extend the parameter ranges over which networks produce the properties of interest.

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Larsson, Sara, Tobias Rydén, Ulla Holst, Stina Oredsson, and Maria Johansson. "Estimating the Total Rate of DNA Replication Using Branching Processes." Bulletin of Mathematical Biology 70, no. 8 (September 26, 2008): 2177–94. http://dx.doi.org/10.1007/s11538-008-9339-9.

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Ishida, A. T., and M. H. Cheng. "Synchronous neurite branchings in single goldfish retinal ganglion cells." Visual Neuroscience 6, no. 5 (May 1991): 537–49. http://dx.doi.org/10.1017/s0952523800001371.

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AbstractWe have examined the time course of branch formation in neurites of retinal ganglion cells isolated from adult goldfish (Carassius auratus). These neurites elongate at approximately 13 μm/h, and usually branch by bifurcation of growth cones at their tips. The times elapsed between branchings in different neurites of single cells can be described by a Poisson distribution with a mean interval of approximately 2 h. As predicted by this distribution, a relatively large number of branchings occur simultaneously in different neurites of individual cells. Simultaneous branchings of neurites elongating at a common rate generate branch points that lay equidistant from their soma. Since similar branching patterns can be seen in dendrites of retinal ganglion and amacrine cells in situ, these results are consistent with the possibility that dendrites of individual neurons branch synchronously and grow at common rates during development.

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Жураев, Ш. Ю., and А. Ф. Алиев. "Estimates of the convergence rate in the limit theorems on transition phenomena for branching random processes." Вестник КРАУНЦ. Физико-математические науки, no. 3 (November 22, 2021): 15–28. http://dx.doi.org/10.26117/2079-6641-2021-36-3-15-28.

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В данной работе рассматриваются ветвящиеся случайные процессы с дискретным временем в двух предположениях: в начальный момент времени имеется одна частица или в начальный момент времени существует большое число частиц. В переходных явлениях для таких ветвящихся случайных процессов получены оценки скорости сходимости условных законов распределений к предельному распределению. We consider branching random processes with discrete time in two assumptions: at the initial moment of time there is one particle and there are large number of particles. In transition phenomena for such branching random processes, estimates of the convergence rate of conditional distributions are obtained.

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Meng, Xinzhu, Yang Yang, and Shengnan Zhao. "Adaptive Evolution of Virulence-Related Traits in a Susceptible-Infected Model with Treatment." Abstract and Applied Analysis 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/891401.

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Evolution problem is now a hot topic in the mathematical biology field. This paper investigates the adaptive evolution of pathogen virulence in a susceptible-infected (SI) model under drug treatment. We explore the evolution of a continuous trait, virulence of a pathogen, and consider virulence-dependent cure rate (recovery rate) that dramatically affects the outcome of evolution. With the methods of critical function analysis and adaptive dynamics, we identify the evolutionary conditions for continuously stable strategies, evolutionary repellers, and evolutionary branching points. First, the results show that a high-intensity strength drug treatment can result in evolutionary branching and the evolution of pathogen strains will tend towards a higher virulence with the increase of the strength of the treatment. Second, we use the critical function analysis to investigate the evolution of virulence-related traits and show that evolutionary outcomes strongly depend on the shape of the trade-off between virulence and transmission. Third, after evolutionary branching, the two infective species will evolve to an evolutionarily stable dimorphism at which they can continue to coexist, and no further branching is possible, which is independent of the cure rate function.

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Brummer, Alexander B., Panagiotis Lymperopoulos, Jocelyn Shen, Elif Tekin, Lisa P. Bentley, Vanessa Buzzard, Andrew Gray, Imma Oliveras, Brian J. Enquist, and Van M. Savage. "Branching principles of animal and plant networks identified by combining extensive data, machine learning and modelling." Journal of The Royal Society Interface 18, no. 174 (January 2021): 20200624. http://dx.doi.org/10.1098/rsif.2020.0624.

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Branching in vascular networks and in overall organismic form is one of the most common and ancient features of multicellular plants, fungi and animals. By combining machine-learning techniques with new theory that relates vascular form to metabolic function, we enable novel classification of diverse branching networks—mouse lung, human head and torso, angiosperm and gymnosperm plants. We find that ratios of limb radii—which dictate essential biologic functions related to resource transport and supply—are best at distinguishing branching networks. We also show how variation in vascular and branching geometry persists despite observing a convergent relationship across organisms for how metabolic rate depends on body mass.

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Fleischer, Robert. "Probing new physics with $B^0_s\to\mu^+\mu^-$: Status and perspectives." International Journal of Modern Physics A 29, no. 21 (August 20, 2014): 1444004. http://dx.doi.org/10.1142/s0217751x14440047.

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The rare decay [Formula: see text] plays a key role for the testing of the Standard Model. It is pointed out that the sizable decay width difference ΔΓsof the Bs-meson system affects this channel in a subtle way. As a consequence, its calculated Standard Model branching ratio has to be upscaled by about 10%. Moreover, the sizable ΔΓsmakes a new observable through the effective [Formula: see text] lifetime accessible, which probes New Physics in a way complementary to the branching ratio and adds an exciting new topic to the agenda for the high-luminosity upgrade of the LHC. Further probes of New Physics are offered by a CP-violating rate asymmetry. Correlations between these observables and the [Formula: see text] branching ratio are illustrated for specific models of New Physics.

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van Tuyl, Minke, Jason Liu, Jinxia Wang, Maciek Kuliszewski, Dick Tibboel, and Martin Post. "Role of oxygen and vascular development in epithelial branching morphogenesis of the developing mouse lung." American Journal of Physiology-Lung Cellular and Molecular Physiology 288, no. 1 (January 2005): L167—L178. http://dx.doi.org/10.1152/ajplung.00185.2004.

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Recent investigations have suggested an active role for endothelial cells in organ development, including the lung. Herein, we investigated some of the molecular mechanisms underlying normal pulmonary vascular development and their influence on epithelial branching morphogenesis. Because the lung in utero develops in a relative hypoxic environment, we first investigated the influence of low oxygen on epithelial and vascular branching morphogenesis. Two transgenic mouse models, the C101-LacZ (epithelial-LacZ marker) and the Tie2-LacZ (endothelial-LacZ marker), were used. At embryonic day 11.5, primitive lung buds were dissected and cultured at either 20 or 3% oxygen. At 24-h intervals, epithelial and endothelial LacZ gene expression was visualized by X-galactosidase staining. The rate of branching of both tissue elements was increased in explants cultured at 3% oxygen compared with 20% oxygen. Low oxygen increased expression of VEGF, but not that of the VEGF receptor (Flk-1). Expression of two crucial epithelial branching factors, fibroblast growth factor-10 and bone morphogenetic protein-4, were not affected by low oxygen. Epithelial differentiation was maintained at low oxygen as shown by surfactant protein C in situ hybridization. To explore epithelial-vascular interactions, we inhibited vascular development with antisense oligonucleotides targeted against either hypoxia inducible factor-1α or VEGF. Epithelial branching morphogenesis in vitro was dramatically abrogated when pulmonary vascular development was inhibited. Collectively, the in vitro data show that a low-oxygen environment enhances branching of both distal lung epithelium and vascular tissue and that pulmonary vascular development appears to be rate limiting for epithelial branching morphogenesis.

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Singh, Sumit Randhir, Prakhar Goyal, Deepika C. Parameswarappa, Abhilash Goud, and Jay Chhablani. "Angiographic features of polypoidal choroidal vasculopathy using indocyanine green angiography and optical coherence tomography angiography: A comparative study." European Journal of Ophthalmology 30, no. 5 (May 22, 2019): 1076–81. http://dx.doi.org/10.1177/1120672119850075.

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Background: To compare the vascular lesion size using optical coherence tomography angiography and indocyanine green angiography in eyes with polypoidal choroidal vasculopathy. Methods: Treatment-naïve cases (46 eyes of 44 patients) with polypoidal choroidal vasculopathy were retrospectively analyzed. The comparison of mean area of branching vascular network and polyp detection rate was done between indocyanine green angiography and optical coherence tomography angiography and correlated with various optical coherence tomography features. Results: The mean age of the study patients was 62.33 ± 10.74 years. The mean branching vascular network size was 7.47 ± 5.74 and 7.51 ± 5.69 mm² in indocyanine green angiography and optical coherence tomography angiography, respectively, with an excellent correlation (r = 0.997). Optical coherence tomography angiography overestimated (mean ± SD: 0.28 ± 0.19 mm²) and underestimated branching vascular network area (0.36 ± 0.33 mm²) in 23 eyes each as compared to indocyanine green angiography. However, the difference in branching vascular network size was not statistically significant (p = 0.53). Indocyanine green angiography and optical coherence tomography angiography could identify polyps in 43 of 46 (93.48%) and 32 of 46 (69.57%) patients, respectively. Conclusion: Branching vascular network size measurements with indocyanine green angiography and optical coherence tomography angiography were comparable and showed significant correlation, albeit the polyp identification rate was lower with optical coherence tomography angiography. Optical coherence tomography angiography may serve as a useful substitute to indocyanine green angiography in measurements of branching vascular network for photodynamic therapy and follow-up of polypoidal choroidal vasculopathy eyes.

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Skrdla, Peter J. "Use of Coupled Rate Equations To Describe Nucleation-and-Branching Rate-Limited Solid-State Processes." Journal of Physical Chemistry A 108, no. 32 (August 2004): 6709–12. http://dx.doi.org/10.1021/jp0487758.

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Hamzehlou, Shaghayegh, M. Ali Aboudzadeh, and Yuri Reyes. "On the Recovery of PLP-Molar Mass Distribution at High Laser Frequencies: A Simulation Study." Processes 7, no. 8 (August 2, 2019): 501. http://dx.doi.org/10.3390/pr7080501.

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Due to the inherent difficulties in determination of the degree of branching for polymers produced in pulsed laser polymerization (PLP) experiments, the behavior of the degree of branching and backbiting reaction in high laser frequency and relatively high reaction temperatures have not been well-established. Herein, through a simulation study, the validity of different explanations on the recovery of PLP-molar mass distribution at high laser frequencies is discussed. It is shown that the reduction of the backbiting reaction rate at high laser frequency, and consequent decrease in the degree of branching, is not a necessary condition for recovering the PLP-molar mass distribution. The findings of this work provide simulation support to a previous explanation about the possibility of using high laser frequency for reliable determination of the propagation rate coefficient for acrylic monomers.

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Greub, C., H. Simma, and D. Wyler. "Branching ratio and direct CP-violating rate asymmetry of the rare decays and B → ϱγ." Nuclear Physics B 434, no. 1-2 (January 1995): 39–55. http://dx.doi.org/10.1016/0550-3213(94)00463-o.

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Journal articles on the topic 'Branching rate'

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