67 research outputs found

    NeighborNet: improved algorithms and implementation

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    NeighborNet constructs phylogenetic networks to visualize distance data. It is a popular method used in a wide range of applications. While several studies have investigated its mathematical features, here we focus on computational aspects. The algorithm operates in three steps. We present a new simplified formulation of the first step, which aims at computing a circular ordering. We provide the first technical description of the second step, the estimation of split weights. We review the third step by constructing and drawing the network. Finally, we discuss how the networks might best be interpreted, review related approaches, and present some open questions

    On adaptive stochastic heavy ball momentum for solving linear systems

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    The stochastic heavy ball momentum (SHBM) method has gained considerable popularity as a scalable approach for solving large-scale optimization problems. However, one limitation of this method is its reliance on prior knowledge of certain problem parameters, such as singular values of a matrix. In this paper, we propose an adaptive variant of the SHBM method for solving stochastic problems that are reformulated from linear systems using user-defined distributions. Our adaptive SHBM (ASHBM) method utilizes iterative information to update the parameters, addressing an open problem in the literature regarding the adaptive learning of momentum parameters. We prove that our method converges linearly in expectation, with a better convergence rate compared to the basic method. Notably, we demonstrate that the deterministic version of our ASHBM algorithm can be reformulated as a variant of the conjugate gradient (CG) method, inheriting many of its appealing properties, such as finite-time convergence. Consequently, the ASHBM method can be further generalized to develop a brand-new framework of the stochastic CG (SCG) method for solving linear systems. Our theoretical results are supported by numerical experiments

    Advanced Mechanical Modeling of Nanomaterials and Nanostructures

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    This reprint presents a collection of contributions on the application of high-performing computational strategies and enhanced theoretical formulations to solve a wide variety of linear or nonlinear problems in a multiphysical sense, together with different experimental studies

    Computational and experimental studies of novel β-adrenoceptor ligands

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    With over 30% of available drugs targeting them, G protein-coupled receptors (GPCRs) are of significant pharmaceutical interest. Efforts to understand protein-ligand interactions among this group of proteins have been aided by the increase in available x-ray crystallography structures. β1-Adrenergic receptor (β1-AR) antagonists are used as treatment in patients with cardiovascular and airway conditions. However, current widely used medications are considerably prone to off-target side effects due to the lack of selectivity between the β1- and β2-AR subtypes. Therefore, a deeper understanding into the structural differences in characteristics is necessary to utilise them as a means of increasing ligand selectivity and therefore reducing the prevalence of off-target side effects. Here, two characteristics of the β1-AR are targeted as a means of increasing receptor selectivity. The first being receptor plasticity - recent research has shown that β-ARs contain a fissure between transmembrane helices 4 and 5 (TM4, TM5) (dubbed the ‘keyhole’) that differ slightly between β-AR subtypes that may accommodate for extended moieties or ligand entry and exit via the intramembrane space. The second characteristic being receptor dimerization. Receptor dimerization among GPCRs remains an active area of research, that so far has many pharmacological implications. Targeting receptor homodimerization has been proposed to be a method of improving receptor specificity within GPCRs. Research into β-AR dimers and findings from X-ray crystallography have shown that β1-AR homodimers may indeed align with a TM4/TM5 interface, aligning the ‘keyhole’. By combining and exploring both characteristics, we designed and computationally validated bivalent ligands capable of taking advantage of two unique β1-AR structural features as a means of improving ligand selectivity. Most current attempts at bivalent ligands in GPCRs explore using the extracellular space as a spacing route, leading to longer ligands, undesirably affecting molecular weight, lipophilicity, and viability. However, to validate our ligand design, we computationally demonstrate – by analyzing all-atom molecular dynamics (MD) simulations – that those ligands long enough to extend beyond the receptor via the keyhole can bind canonically and maintain key interactions that have previously been pharmacologically verified, as well as investigate structure activity relationships (SARs) of differing steric and electronic configurations of ligand components exposed to the intramembrane space. Bivalent ligand linkers were designed and computationally investigated within a GPCR dimer system to determine whether flexibility of the linker impacts the pharmacophores’ ability to maintain key canonical interactions. Long timescale coarse grained simulations of a membrane-bound β1-AR dimer showed the dimer interface to be stable, so shorter all-atom simulations could be used with confidence to aid bivalent ligand design. Bivalent ligands of the nature discussed in this work required at least one pharmacophore to enter/exit the receptor orthosteric binding site via the keyhole route. In house enhanced sampling computational methods were developed to study and validate the feasibility of this entry and exit route. Ligand exit pathways were generated by performing self-avoiding walk MD on protein-ligand complexes, then used to define starting and end points for weighted ensemble molecular dynamics (WEMD) to predict kinetic rate constants. These rate constants were then verified against pharmacologically derived β-AR kinetics data to validate the method, model, and ligand entry/exit pathway. The designed ligands would then lead to shorter and less hindering spacing between orthosteric sites

    Longitudinal Partitioning Waveform Relaxation Methods For The Analysis of Transmission Line Circuits

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    Three research projects are presented in this manuscript. Projects one and two describe two waveform relaxation algorithms (WR) with longitudinal partitioning for the time-domain analysis of transmission line circuits. Project three presents theoretical results about the convergence of WR for chains of general circuits. The first WR algorithm uses a assignment-partition procedure that relies on inserting external series combinations of positive and negative resistances into the circuit to control the speed of convergence of the algorithm. The convergence of the subsequent WR method is examined, and fast convergence is cast as a generic optimization problem in the frequency-domain. An automatic suboptimal numerical solution of the min-max problem is presented and a procedure to construct its objective function is suggested. Numerical examples illustrate the parallelizability and good scaling of the WR algorithm and point out to the limitation of resistive coupling. In the second WR algorithm, resistances from the previous insertion are replaced with dissipative impedances to address the slow convergence of standard resistive coupling of the first algorithm for low-loss highly reactive circuits. The pertinence and feasibility of impedance coupling are demonstrated and the properties of the subsequent WR method are studied. A new coupling strategy proposes judicious approximations of the optimal convergence conditions for faster speed of convergence. The proposed strategy avoids the difficult problem of optimisation and uses coarse macromodeling of the transmission line to construct approximations with delay under circuit form. Numerical examples confirm a superior speed of convergence which leads to further runtime saving. Finally, new results concerning the nilpotent WR algorithm are presented for chains of circuits when dissipative coupling is used. It is shown that optimal local convergence is necessary to achieve the optimal WR algorithm. However, the converse is not correct: the WR algorithm with optimal local convergences factors can be nilpotent yet not optimal or even be non-nilpotent at all. The second analysis concerns resistive coupling. It is demonstrated that WR always converges for chains circuits. More precisely, it is shown that WR will converge independently of the length of the chain when this late is made of identical symmetric circuits

    Multigrid for Chiral Lattice Fermions: Domain Wall

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    Critical slowing down for the Krylov Dirac solver presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. We propose a new multi-grid approach for chiral fermions, applicable to both the 5-d domain wall or 4-d Overlap operator. The central idea is to directly coarsen the 4-d Wilson kernel, giving an effective domain wall or overlap operator on each level. We provide here an explicit construction for the Shamir domain wall formulation with numerical tests for the 2-d Schwinger prototype, demonstrating near ideal multi-grid scaling. The framework is designed for a natural extension to 4-d lattice QCD chiral fermions, such as the M\"obius, Zolotarev or Borici domain wall discretizations or directly to a rational expansion of the 4-d Overlap operator. For the Shamir operator, the effective overlap operator is isolated by the use of a Pauli-Villars preconditioner in the spirit of the K\"ahler-Dirac spectral map used in a recent staggered MG algorithm [1].Comment: 39 pages, 13 figure
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