Comment on “The Free Will Theorem”

In a recent paper Conway and Kochen, Found. Phys. 36, 2006, claim to have established that theories of the Ghirardi-Rimini-Weber (RW) type, i.e., of spontaneous wave function collapse, cannot be made relativistic. On the other hand, relativistic GRW-type theories have already been presented, in my recent paper, J. Stat. Phys. 125, 2006, and by Dowker and Henson, J. Stat. Phys. 115, 2004. Here, I elucidate why these are not excluded by the arguments of Conway and Kochen.      

Gravitational Collapse of Self-Similar Perfect Fluid in 2 + 1 Gravity

Perfect fluid with kinematic self-similarity is studied in 2+1 dimensional spacetimes with circular symmetry, and various exact solutions to the Einstein field equations are given. These include all the solutions of dust and stiff perfect fluid with self-similarity of the first kind, and all the solutions of perfect fluid with a linear equation of state and self-similarity of the zeroth and second kinds. It is found that some of these solutions represent gravitational collapse, and the final state of the collapse can be either a black hole or a null singularity. It is also shown that one solution can have two different kinds of kinematic self-similarity.     

Consequence for Wavefunction Collapse Model of the Sudbury Neutrino Observatory Experiment

It is shown that data on the dissociation rate of deuterium obtained in an experiment at the Sudbury Neutrino Observatory provides evidence that the Continuous Spontaneous Localization wavefunction collapse model should have mass–proportional coupling to be viable.     

Incremental unknowns preconditioning for solving the Helmholtz equation

An efficient preconditioner is developed for solving the Helmholtz problem in both high and low frequency (wavenumber) regimes. The preconditioner is based on hierarchical unknowns on nested grids, known as incremental unknowns (IU). The motivation for the IU preconditioner is provided by an eigenvalue analysis of a simplified Helmholtz problem. The performance of our preconditioner is tested on the iterative solution of two‐dimensional electromagnetic scattering problems. When compared with other well‐known methods, our technique is shown to often provide a better numerical efficacy and, most importantly, to be more robust. Moreover, for the best performance, the number of IU levels used in the preconditioner should be designed for the coarsest grid to have roughly two points per linear wavelength. This result is consistent with the conventional sampling criteria for wave phenomena in contrast with existing IU applications for solving the Laplace/Poisson problem, where the coarsest grid comprises just one interior point. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Collapse transition and asymptotic scaling behavior of lattice animals: Low-temperature expansion

A low-temperature expansion for the free energy density of lattice animals is derived. Analysis of the series yields a collapse transition temperature ofT _c - 0.54, in close agreement with previous estimates. It is demonstrated that _p,k, the number ofp-particle,p-bond animals, obeys the asymptotic scaling law log _p,k pg(k/p) + o(p). The low-temperature series and numerical data are used to estimate the scaling function.     

A finite volume cell‐centered Lagrangian hydrodynamics approach for solids in general unstructured grids

A finite volume cell‐centered Lagrangian hydrodynamics approach, formulated in Cartesian frame, is presented for solving elasto‐plastic response of solids in general unstructured grids. Because solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum, and energy conservation laws. The total stress is split into deviatoric shear stress and dilatational components. The dilatational response of the material is modeled using the Mie‐Grüneisen equation of state. A predicted trial elastic deviatoric stress state is evolved assuming a pure elastic deformation in accordance with the hypo‐elastic stress‐strain relation. The evolution equations are advanced in time by constructing vertex velocity and corner traction force vectors using multi‐dimensional Riemann solutions erected at mesh vertices. Conservation of momentum and total energy along with the increase in entropy principle are invoked for computing these quantities at the vertices. Final state of deviatoric stress is effected via radial return algorithm based on the J‐2 von Mises yield condition. The scheme presented in this work is second‐order accurate both in space and time. The suitability of the scheme is evinced by solving one‐ and two‐dimensional benchmark problems both in structured grids and in unstructured grids with polygonal cells. Copyright © 2013 John Wiley & Sons, Ltd.     

The use of relative residues in fitting experimental data: an example from fluid mechanics

A curve fitting model is presented which minimizes the sum of squares of relative residues and expressions for the fit coefficients and their respective errors are derived. The new model is compared to the normal least squares model, using as an example the Reynolds number-drag coefficient data for a sphere. The results show that the best fit was obtained with the new model, indicating it may provide a useful tool for data analysis.     

Effect of intramolecular crosslinker properties on the mechanochemical fragmentation of covalently folded polymers

The mechanochemical stability of polymers in solution is enhanced if the chains are covalently folded. Under shear forces, the additional bonds absorb mechanical energy and inhibit unfolding, and as a result, slow down fragmentation. However, not all crosslinkers are equal in terms of their properties (length, strength, etc.). In order to understand the role of these added bonds in the polymers' stability under mechanical stress, a thorough study compares the rate of mechanochemistry on single-chain polymer nanoparticles which have been folded with crosslinkers with different lengths, strengths, positioning, and valencies. The usage of bonds with different mechanical strengths in the crosslinkers was found to be the most powerful way to change the mechanochemical fragmentation rate. In addition, positioning and valency also play significant role in the mechanical stabilization mechanism. © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 © 2020 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2020 , 58, 692–703     

Non-singular Brans–Dicke collapse in deformed phase space

We study the collapse process of a homogeneous perfect fluid (in FLRW background) with a barotropic equation of state in Brans–Dicke (BD) theory in the presence of phase space deformation effects. Such a deformation is introduced as a particular type of non-commutativity between phase space coordinates. For the commutative case, it has been shown in the literature (Scheel, 1995), that the dust collapse in BD theory leads to the formation of a spacetime singularity which is covered by an event horizon. In comparison to general relativity (GR), the authors concluded that the final state of black holes in BD theory is identical to the GR case but differs from GR during the dynamical evolution of the collapse process. However, the presence of non-commutative effects influences the dynamics of the collapse scenario and consequently a non-singular evolution is developed in the sense that a bounce emerges at a minimum radius, after which an expanding phase begins. Such a behavior is observed for positive values of the BD coupling parameter. For large positive values of the BD coupling parameter, when non-commutative effects are present, the dynamics of collapse process differs from the GR case. Finally, we show that for negative values of the BD coupling parameter, the singularity is replaced by an oscillatory bounce occurring at a finite time, with the frequency of oscillation and amplitude being damped at late times.     

Protein Secondary Structure Prediction with Partially Recurrent Neural Networks

Abstract

Partially recurrent neural networks with different topologies are applied for secondary structure prediction of proteins. The state of some activations in the network is available after a pattern presentation via feedback connections as additional input during the processing of the next pattern in a sequence. A reference data set containing 91 proteins in the training set and 15 non-homologous proteins in the test set is used for training and testing a network with a modified, hierarchical Elman architecture. The network predicts the secondary structures α-helix, β-sheet, and “coil” for each amino acid. The percentage of correctly classified amino acids is 67.83% on the training set and 63.98% on the test set. The best performance of a three-layer feedforward network is 62.7% on the same test set. A cascaded network, where the outputs of the recurrent network are processed by a second net with 13 × 3 inputs, four hidden and three output units has a predictive performance of 64.49%. The best corresponding feedforward net has a performance of 64.3%.