Interference fracturing: Nonuniform distributions of perforation clusters that promote simultaneous growth of multiple hydraulic fractures

One of the important hurdles in horizontal-well stimulation is the generation of hydraulic fractures (HFs) from all perforation clusters within a given stage, despite the challenges posed by stress shadowing and reservoir variability. In this paper, we use a newly developed, fully coupled, parallel-planar 3D HF model to investigate the potential to minimize the negative impact of stress shadowing and thereby to promote more-uniform fracture growth across an array of HFs by adjusting the location of the perforation clusters. In this model, the HFs are assumed to evolve in an array of parallel planes with full 3D stress coupling while the constant fluid influx into the wellbore is dynamically partitioned to each fracture so that the wellbore pressure is the same throughout the array. The model confirms the phenomenon of inner-fracture suppression because of stress shadowing when the perforation clusters are uniformly distributed. Indeed, the localization of the fracture growth to the outer fractures is so dominant that the total fractured area generated by uniform arrays is largely independent of the number of perforation clusters. However, numerical experiments indicate that certain nonuniform cluster spacings promote a profound improvement in the even development of fracture growth. Identifying this effect relies on this new model's ability to capture the full hydrodynamical coupling between the simultaneously evolving HFs in their transition from radial to Perkins-Kern-Nordgren (PKN)-like geometries (Perkins and Kern 1961; Nordgren 1972)

A Simple Method for Combining Genetic Mapping Data from Multiple Crosses and Experimental Designs

Over the past decade many linkage studies have defined chromosomal intervals containing polymorphisms that modulate a variety of traits. Many phenotypes are now associated with enough mapping data that meta-analysis could help refine locations of known QTLs and detect many novel QTLs.We describe a simple approach to combining QTL mapping results for multiple studies and demonstrate its utility using two hippocampus weight loci. Using data taken from two populations, a recombinant inbred strain set and an advanced intercross population we demonstrate considerable improvements in significance and resolution for both loci. 1-LOD support intervals were improved 51% for Hipp1a and 37% for Hipp9a. We first generate locus-wise permuted P-values for association with the phenotype from multiple maps, which can be done using a permutation method appropriate to each population. These results are then assigned to defined physical positions by interpolation between markers with known physical and genetic positions. We then use Fisher's combination test to combine position-by-position probabilities among experiments. Finally, we calculate genome-wide combined P-values by generating locus-specific P-values for each permuted map for each experiment. These permuted maps are then sampled with replacement and combined. The distribution of best locus-specific P-values for each combined map is the null distribution of genome-wide adjusted P-values.Our approach is applicable to a wide variety of segregating and non-segregating mapping populations, facilitates rapid refinement of physical QTL position, is complementary to other QTL fine mapping methods, and provides an appropriate genome-wide criterion of significance for combined mapping results

Using Evolutionary Algorithms for Fitting High-Dimensional Models to Neuronal Data

In the study of neurosciences, and of complex biological systems in general, there is frequently a need to fit mathematical models with large numbers of parameters to highly complex datasets. Here we consider algorithms of two different classes, gradient following (GF) methods and evolutionary algorithms (EA) and examine their performance in fitting a 9-parameter model of a filter-based visual neuron to real data recorded from a sample of 107 neurons in macaque primary visual cortex (V1). Although the GF method converged very rapidly on a solution, it was highly susceptible to the effects of local minima in the error surface and produced relatively poor fits unless the initial estimates of the parameters were already very good. Conversely, although the EA required many more iterations of evaluating the model neuron’s response to a series of stimuli, it ultimately found better solutions in nearly all cases and its performance was independent of the starting parameters of the model. Thus, although the fitting process was lengthy in terms of processing time, the relative lack of human intervention in the evolutionary algorithm, and its ability ultimately to generate model fits that could be trusted as being close to optimal, made it far superior in this particular application than the gradient following methods. This is likely to be the case in many further complex systems, as are often found in neuroscience

Metabolic rate limits the effect of sperm competition on mammalian spermatogenesis.

Sperm competition leads to increased sperm production in many taxa. This response may result from increases in testes size, changes in testicular architecture or changes in the kinetics of spermatogenesis, but the impact of each one of these processes on sperm production has not been studied in an integrated manner. Furthermore, such response may be limited in species with low mass-specific metabolic rate (MSMR), i.e., large-bodied species, because they cannot process energy and resources efficiently enough both at the organismic and cellular levels. Here we compare 99 mammalian species and show that higher levels of sperm competition correlated with a) higher proportions of seminiferous tubules, b) shorter seminiferous epithelium cycle lengths (SECL) which reduce the time required to produce sperm, and c) higher efficiencies of Sertoli cells (involved in sperm maturation). These responses to sperm competition, in turn, result in higher daily sperm production, more sperm stored in the epididymides, and more sperm in the ejaculate. However, the two processes that require processing resources at faster rates (SECL and efficiency of Sertoli cells) only respond to sperm competition in species with high MSMR. Thus, increases in sperm production with intense sperm competition occur via a complex network of mechanisms, but some are constrained by MSMR

High order structure preserving explicit methods for solving linear-quadratic optimal control problems

[EN] We consider the numerical integration of linear-quadratic optimal control problems. This problem requires the solution of a boundary value problem: a non-autonomous matrix Riccati differential equation (RDE) with final conditions coupled with the state vector equation with initial conditions. The RDE has positive definite matrix solution and to numerically preserve this qualitative property we propose first to integrate this equation backward in time with a sufficiently accurate scheme. Then, this problem turns into an initial value problem, and we analyse splitting and Magnus integrators for the forward time integration which preserve the positive definite matrix solutions for the RDE. Duplicating the time as two new coordinates and using appropriate splitting methods, high order methods preserving the desired property can be obtained. The schemes make sequential computations and do not require the storrage of intermediate results, so the storage requirements are minimal. The proposed methods are also adapted for solving linear-quadratic N-player differential games. The performance of the splitting methods can be considerably improved if the system is a perturbation of an exactly solvable problem and the system is properly split. Some numerical examples illustrate the performance of the proposed methods.The author wishes to thank the University of California San Diego for its hospitality where part of this work was done. He also acknowledges the support of the Ministerio de Ciencia e Innovacion (Spain) under the coordinated project MTM2010-18246-C03. The author also acknowledges the suggestions by the referees to improve the presentation of this work.Blanes Zamora, S. (2015). High order structure preserving explicit methods for solving linear-quadratic optimal control problems. Numerical Algorithms. 69:271-290. https://doi.org/10.1007/s11075-014-9894-0S27129069Abou-Kandil, H., Freiling, G., Ionescy, V., Jank, G.: Matrix Riccati equations in control and systems theory. Basel, Burkhäuser Verlag (2003)Al-Mohy, A.H., Higham, N.J.: Computing the Action of the Matrix Exponential, with an Application to Exponential Integrators. SIAM. J. Sci. Comp. 33, 488–511 (2011)Anderson, B.D.O., Moore, J.B.: Optimal control: linear quadratic methods. Dover, New York (1990)Ascher, U.M., Mattheij, R.M., Russell, R.D.: Numerical solutions of boundary value problems for ordinary differential equations. Prentice-Hall, Englewood Cliffs (1988)Bader, P., Blanes, S., Ponsoda, E.: Structure preserving integrators for solving linear quadratic optimal control problems with applications to describe the flight of a quadrotor. J. Comput. Appl. Math. 262, 223–233 (2014)Basar, T., Olsder, G.J.: Dynamic non cooperative game theory, 2nd Ed, SIAM, Philadelphhia (1999)Blanes, S., Casas, F.: On the necessity of negative coefficients for operator splitting schemes of order higher than two. Appl. Num. Math. 54, 23–37 (2005)Blanes, S., Casas, F., Farrés, A., Laskar, J., Makazaga, J., Murua, A.: New families of symplectic splitting methods for numerical integration in dynamical astronomy. Appl. Numer. Math. 68, 58–72 (2013)Blanes, S., Casas, F., Oteo, J.A., Ros, J.: The Magnus expansion and some of its applications. Phys. Rep. 470, 151–238 (2009)Blanes, S., Casas, F., Ros, J.: High order optimized geometric integrators for linear differential equations. BIT 42, 262–284 (2002)Blanes, S., Diele, F., Marangi, C., Ragni, S.: Splitting and composition methods for explicit time dependence in separable dynamical systems. J. Comput. Appl. Math. 235, 646–659 (2010)Blanes, S., Moan, P.C.: Practical symplectic partitioned Runge-Kutta and Runge-Kutta-Nystrm methods. J. Comput. Appl. Math. 142, 313–330 (2002)Blanes, S., Ponsoda, E.: Magnus integrators for solving linear-quadratic differential games. J. Comput. Appl. Math. 236, 3394–3408 (2012)Brif, C., Chakrabarti, R., Rabitz, H.: Control of quantum phenomena: past, present and future. New J. Phys. 12, 075008(68pp) (2010)Cruz, J.B., Chen, C.I.: Series Nash solution of two person non zero sum linear quadratic games. J. Optim. Theory Appl. 7, 240–257 (1971)Dieci, L., Eirola, T.: Positive definitness in the numerical solution of Riccati differential quations. Numer. Math. 67, 303–313 (1994)Engwerda, J.: LQ dynamic optimization and differential games. Wiley (2005)Hairer, E., Lubich, C., Wanner, G.: Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations (2nd edition). Springer Series in Computational Mathematics, 31. Springer-Verlag (2006)Hochbruck, M., Ostermann, A.: Exponential integrators. Acta Numerica 19, 209–286 (2010)Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, New York (1985)Iserles, A., Munthe-Kaas, H.Z., Nørsett, S.P., Zanna, A.: Lie group methods. Acta Numerica 9, 215–365 (2000)Iserles, A., Nørsett, S.P.: On the solution of linear differential equations in Lie groups. Phil. Trans. R. Soc. Lond. A 357, 983–1019 (1999)Jódar, L., Ponsoda, E.: Non-autonomous Riccati-type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds. IMA. J. Num. Anal. 15, 61–74 (1995)Jódar, L., Ponsoda, E., Company, R.: Solutions of coupled Riccati equations arising in differential games. Control. Cybern. 24, 117–128 (1995)Kaitala, V, Pohjola, M. In: Carraro, Filar (eds.) : Sustainable international agreement on greenhouse warming. A game theory study. Control and Game Theoretic Models of the Environment, pp 67–87. Birkhauser, Boston (1995)Keller, H.B.: Numerical solution of two point boundary value problems. In: CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 24. SIAM, Philadelphia (1976)McLachlan, R.I.: Composition methods in the presence of small parameters. BIT 35, 258–268 (1995)McLachlan, R.I., Quispel, R.: Splitting Methods. Acta Numer. 11, 341–434 (2002)Moler, C.B., Van Loan, C.F.: Nineteen Dubious Ways to Compute the Exponential of a Matrix, twenty-five years later. SIAM Rev. 45, 3–49 (2003)Na, T.Y.: Computational methods in engineering boundary value problems. In: Mathematics in Science and Engineering, Vol. 145. Accademic Press, New York (1979)Palao, J.P., Kosloff, R.: Quantum computing by an optimal control algorithm for unitry transformations. Phys. Rev. Lett. 28 (2002)Peirce, A.P., Dahleh, M.A., Rabitz, H.: Optimal control of quantum-mechanical systems: existence, numerical approximation, and applications. Phys. Rev. A 37, 4950–4967 (1988)Reid, W.T.: Riccati Differential Equations. Academic, New York (1972)Sanz-Serna, J.M., Calvo, M.P.: Numerical Hamiltonian Problems. Chapman & Hall, London (1994)Sidje, R.B.: Expokit: a software package for computing matrix exponentials. ACM Trans. Math. Software 24, 130–156 (1998)Speyer, J.L., Jacobson, D.H.: Primer on optimal control theory. SIAM, Philadelphia (2010)Starr, A.W., Ho, Y.C.: Non-zero sum differential games. J. Optim. Theory and Appl 3, 179–197 (1969)Zhu, W., Rabitz, H.: A rapid monotonically convergent iteration algorithm for quantum optimal control ever the expectation value of a positive definite operator. J. Chem. Phys. 109, 385–391 (1998

Developing adaptive control:Age-related differences in task choices and awareness of proactive and reactive control demands

Developmental changes in executive function are often explained in terms of core cognitive processes and associated neural substrates. For example, younger children tend to engage control reactively in the moment as needed, whereas older children increasingly engage control proactively, in anticipation of needing it. Such developments may reflect increasing capacities for active maintenance dependent upon dorsolateral prefrontal cortex. However, younger children will engage proactive control when reactive control is made more difficult, suggesting that developmental changes may also reflect decisions about whether to engage control, and how. We tested awareness of temporal control demands and associated task choices in 5-year-olds and 10-year-olds and adults using a demand selection task. Participants chose between one task that enabled proactive control and another task that enabled reactive control. Adults reported awareness of these different control demands and preferentially played the proactive task option. Ten-year-olds reported awareness of control demands but selected task options at chance. Five-year-olds showed neither awareness nor task preference, but a subsample who exhibited awareness of control demands preferentially played the reactive task option, mirroring their typical control mode. Thus, developmental improvements in executive function may in part reflect better awareness of cognitive demands and adaptive behavior, which may in turn reflect changes in dorsal anterior cingulate in signaling task demands to lateral prefrontal cortex

Estimating Impact Forces of Tail Club Strikes by Ankylosaurid Dinosaurs

BACKGROUND: It has been assumed that the unusual tail club of ankylosaurid dinosaurs was used actively as a weapon, but the biological feasibility of this behaviour has not been examined in detail. Ankylosaurid tail clubs are composed of interlocking vertebrae, which form the handle, and large terminal osteoderms, which form the knob. METHODOLOGY/PRINCIPAL FINDINGS: Computed tomographic (CT) scans of several ankylosaurid tail clubs referred to Dyoplosaurus and Euoplocephalus, combined with measurements of free caudal vertebrae, provide information used to estimate the impact force of tail clubs of various sizes. Ankylosaurid tails are modeled as a series of segments for which mass, muscle cross-sectional area, torque, and angular acceleration are calculated. Free caudal vertebrae segments had limited vertical flexibility, but the tail could have swung through approximately 100 degrees laterally. Muscle scars on the pelvis record the presence of a large M. longissimus caudae, and ossified tendons alongside the handle represent M. spinalis. CT scans showed that knob osteoderms were predominantly cancellous, which would have lowered the rotational inertia of the tail club and made it easier to wield as a weapon. CONCLUSIONS/SIGNIFICANCE: Large knobs could generate sufficient force to break bone during impacts, but average and small knobs could not. Tail swinging behaviour is feasible in ankylosaurids, but it remains unknown whether the tail was used for interspecific defense, intraspecific combat, or both

Blood Parasites in Owls with Conservation Implications for the Spotted Owl (Strix occidentalis)

The three subspecies of Spotted Owl (Northern, Strix occidentalis caurina; California, S. o. occidentalis; and Mexican, S. o. lucida) are all threatened by habitat loss and range expansion of the Barred Owl (S. varia). An unaddressed threat is whether Barred Owls could be a source of novel strains of disease such as avian malaria (Plasmodium spp.) or other blood parasites potentially harmful for Spotted Owls. Although Barred Owls commonly harbor Plasmodium infections, these parasites have not been documented in the Spotted Owl. We screened 111 Spotted Owls, 44 Barred Owls, and 387 owls of nine other species for haemosporidian parasites (Leucocytozoon, Plasmodium, and Haemoproteus spp.). California Spotted Owls had the greatest number of simultaneous multi-species infections (44%). Additionally, sequencing results revealed that the Northern and California Spotted Owl subspecies together had the highest number of Leucocytozoon parasite lineages (n = 17) and unique lineages (n = 12). This high level of sequence diversity is significant because only one Leucocytozoon species (L. danilewskyi) has been accepted as valid among all owls, suggesting that L. danilewskyi is a cryptic species. Furthermore, a Plasmodium parasite was documented in a Northern Spotted Owl for the first time. West Coast Barred Owls had a lower prevalence of infection (15%) when compared to sympatric Spotted Owls (S. o. caurina 52%, S. o. occidentalis 79%) and Barred Owls from the historic range (61%). Consequently, Barred Owls on the West Coast may have a competitive advantage over the potentially immune compromised Spotted Owls

Characterization of MHC-I in the blue tit (Cyanistes caeruleus) reveals low levels of genetic diversity and trans-population evolution across European populations

The major histcompatibility complex (MHC) is a vital component of the adaptive immune system in all vertebrates. This study is the first to characterize MHC class I (MHC-I) in blue tits (Cyanistes caeruleus), and we use MHC-I exon 3 sequence data from individuals originating from three locations across Europe: Spain, the Netherlands to Sweden. Our phylogeny of the 17 blue tit MHC-I alleles contains one allele cluster with low nucleotide diversity compared to the remaining more diverse alleles. We found a significant evidence for balancing selection in the peptide-binding region in the diverse allele group only. No separation according to geographic location was found in the phylogeny of alleles. Although the number of MHC-I loci of the blue tit is comparable to that of other passerine species, the nucleotide diversity of MHC-I appears to be much lower than that of other passerine species, including the closely related great tit (Parus major) and the severely inbred Seychelles warbler (Acrocephalus sechellensis). We believe that this initial MHC-I characterization in blue tits provides an important step towards understanding the mechanisms shaping MHC-I diversity in natural populations