Consequences of weak Allee effect on prey in the May–Holling–Tanner predator–prey model

In this work, a modified Holling–Tanner predator–prey model is analyzed, considering important aspects describing the interaction such as the predator growth function is of a logistic type; a weak Allee effect acting in the prey growth function, and the functional response is of hyperbolic type. Making a change of variables and time rescaling, we obtain a polynomial differential equations system topologically equivalent to the original one in which the non‐hyperbolic equilibrium point (0,0) is an attractor for all parameter values. An important consequence of this property is the existence of a separatrix curve dividing the behavior of trajectories in the phase plane, and the system exhibits the bistability phenomenon, because the trajectories can have different ω ? limit sets; as example, the origin (0,0) or a stable limit cycle surrounding an unstable positive equilibrium point. We show that, under certain parameter conditions, a positive equilibrium may undergo saddle‐node, Hopf, and Bogdanov–Takens bifurcations; the existence of a homoclinic curve on the phase plane is also proved, which breaks in an unstable limit cycle. Some simulations to reinforce our results are also shown. Copyright © 2015 John Wiley & Sons, Ltd.     

Additive hazards regression with random effects for clustered failure times

Additive hazards model with random effects is proposed for modelling the correlated failure time data when focus is on comparing the failure times within clusters and on estimating the correlation between failure times from the same cluster, as well as the marginal regression parameters. Our model features that, when marginalized over the random effect variable, it still enjoys the structure of the additive hazards model. We develop the estimating equations for inferring the regression parameters. The proposed estimators are shown to be consistent and asymptotically normal under appropriate regularity conditions. Furthermore, the estimator of the baseline hazards function is proposed and its asymptotic properties are also established. We propose a class of diagnostic methods to assess the overall fitting adequacy of the additive hazards model with random effects. We conduct simulation studies to evaluate the finite sample behaviors of the proposed estimators in various scenarios. Analysis of the Diabetic Retinopathy Study is provided as an illustration for the proposed method.     

Homoclinic bifurcation for a general state-dependent Kolmogorov type predator–prey model with harvesting

In this paper, a general Kolmogorov type predator–prey model is considered. Together with a constant-yield predator harvesting, the state dependent feedback control strategies which take into account the impulsive harvesting on predators as well as the impulsive stocking on the prey are incorporated in the process of population interactions. We firstly study the existence of an order-1 homoclinic cycle for the system. It is shown that an order-1 positive periodic solution bifurcates from the order-1 homoclinic cycle through a homoclinic bifurcation as the impulsive predator harvesting rate crosses some critical value. The uniqueness and stability of the order-1 positive periodic solution are derived by applying the geometry theory of differential equations and the method of successor function. Finally, some numerical examples are provided to illustrate the main results. These results indicate that careful management of resources and harvesting policies is required in the applied conservation and renewable resource contexts.     

Human Y‐chromosome SNP characterization by multiplex amplified product‐length polymorphism analysis

We designed an allele‐specific amplification protocol to optimize Y‐chromosome SNP typing, which is an unavoidable step for defining the phylogenetic status of paternal lineages. It allows the simultaneous highly specific definition of up to six mutations in a single reaction by amplification fragment length polymorphism (AFLP) without the need of specialized equipment, at a considerably lower cost than that based on single‐base primer extension (SNaPshot?) technology or PCR‐RFLP systems, requiring as little as 0.5 ng DNA and compatible with the small fragments characteristic of low‐quality DNA. By designation of two primers recognizing the derived and ancestral state for each SNP, which can be differentiated by size by the addition of a noncomplementary nucleotide tail, we could define major Y clades E, F, K, R, Q, and subhaplogroups R1, R1a, R1b, R1b1b, R1b1c, J1, J2, G1, G2, I1, Q1a3, and Q1a3a1 through amplification fragments that ranged between 60 and 158bp.     

Adaptive lambda square dynamics simulation: An efficient conformational sampling method for biomolecules

A novel, efficient sampling method for biomolecules is proposed. The partial multicanonical molecular dynamics (McMD) was recently developed as a method that improved generalized ensemble (GE) methods to focus sampling only on a part of a system (GEPS); however, it was not tested well. We found that partial McMD did not work well for polylysine decapeptide and gave significantly worse sampling efficiency than a conventional GE. Herein, we elucidate the fundamental reason for this and propose a novel GEPS, adaptive lambda square dynamics (ALSD), which can resolve the problem faced when using partial McMD. We demonstrate that ALSD greatly increases the sampling efficiency over a conventional GE. We believe that ALSD is an effective method and is applicable to the conformational sampling of larger and more complicated biomolecule systems. © 2013 Wiley Periodicals, Inc.     

Software package SIMPRE—Revisited

This article elucidates the pitfalls identified in the software package SIMPRE recently developed by Baldoví et al. (J. Comput. Chem. 2013, 34, 1961) for modeling the spectroscopic and magnetic properties of single ion magnets as well as single‐molecule magnets. Analysis of the methodology used therein reveals that the crystal field parameters (CFPs), expressed nominally in the Stevens formalism, exhibit features characteristic for the CFPs expressed in the Wybourne notation. The resemblance of the two types of CFPs introduces a serious confusion that may lead to wrong comparisons of the CFPs taken from various sources. To clarify this confusion, the properties of the CFPs ( , ) associated with the Stevens operators ( X = S , J , or L ), which belong to the class of the tesseral‐tensor operators, are contrasted with those of the CFPs B_kq associated with the Wybourne operators , which belong to the class of the spherical‐tensor operators. Importantly, the confused properties of Stevens and Wybourne operators may bear on reliability of SIMPRE calculations. To consider this question independent calculations are carried out using the complete approach and compared with those of the restricted approach utilized earlier. It appears that the numerical results of the package SIMPRE are formally acceptable, however, the meaning of the CFPs must be properly reformulated. Several other conceptual problems arising from misinterpretations of the crucial notions and the CFP notations identified therein are also discussed and clarified. © 2014 Wiley Periodicals, Inc.     

Exploiting space‐group symmetry in fragment‐based molecular crystal calculations

Recent developments in fragment‐based methods make it increasingly feasible to use high‐level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space‐group symmetry in fragment‐based methods which often provides computational speed‐ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described. © 2014 Wiley Periodicals, Inc.     

Conductor‐like screening model for relaxed excited states: Implementation in the semiempirical method MSINDO

Two approaches to treat solvent polarization and reorientation effects for excited states of molecules and surfaces have been implemented in the recently developed MSINDO‐sCIS method (Gadaczek, Krause, Hintze, Bredow, J. Chem. Theory Comput. 2011, 7, 3675). They allow for an efficient calculation of analytical energy gradients and hence open the opportunity to investigate fluorescence effects or photochemical reactions in solution for large molecules that are difficult to treat with high‐level methods. Both approaches are based on the conductor‐like screening model (COSMO) (Klamt and Schüürmann, J. Chem. Soc., Perkin Trans. 1993, 2, 799) in combination with the configuration interaction singles (CIS) method (Foresman, Head‐Gordon, Pople, and Frisch, J. Phys. Chem. 1992, 96, 135). The paper gives a brief outline of the theoretical background. As a first application, solvent shifts of three well‐studied, environment‐sensitive fluorescent dyes (Kucherak, Didier, Mély, and Klymchenko, J. Phys. Chem. Lett. 2010, 1, 616) have been calculated and compared with experimental results and standard time‐dependent density functional theory. A statistical evaluation of MSINDO‐COSMO‐sCIS is provided for a set of 39 molecules suggested recently by Jacquemin et al. (Jacquemin, Planchat, Adamo, and Mennucci, J. Chem. Theory Comput. 2012, 8, 2359). Calculated vertical and adiabatic excitation energies and fluorescence energies are compared to experimental data. © 2014 Wiley Periodicals, Inc.     

The cyclic cluster model at hartree–fock level

We present the implementation of the cyclic cluster model (CCM) formalism at the Hartree–Fock (HF) level. In contrast to other periodic models, the CCM is a Γ‐point approach. Integration is carried out in real space within a finite interaction area determined by the size and the shape of the cluster that corresponds to a supercell of the solid, surface, or polymer. Particular care has to be taken for the proper treatment of three‐ and four‐center integrals that involve basis functions located at the boundaries of the Wigner–Seitz supercell, which defines the interaction region. The similarity between the CCM formalism and molecular approaches allows in principle the application of sophisticated post HF methods to solid‐state problems with only moderate modification of the molecular code. We show for selected model systems, that with our approach, the electronic structure and energetics obtained by the conventional supercell model is fully reproduced. © 2014 Wiley Periodicals, Inc.