Comment on "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains"

Dukelsky, Mart\'in-Delgado, Nishino and Sierra (Europhys. Lett., 43, 457 (1998) - hereafter referred to as DMNS) investigated the matrix product method (MPM), comparing it with the infinite-size density matrix renormalization group (DMRG). For equivalent basis size, the MPM produces an improved variational energy over that produced by DMRG and, unlike DMRG, produces a translationally-invariant wavefunction. The DMRG results presented were significantly worse than the MPM, caused by a shallow bound state appearing at the join of the two DMRG blocks. They also suggested that the DMRG results can be improved by using an alternate superblock construction $[B] \bullet [B]$ for the last few steps of the calculation. In this comment, we show that the DMRG results presented by DMNS are in error and the artificial bound state produced by the standard superblock configuration is very small even for $m=2$ states kept. In addition, we calculate explicitly the energy and wavefunction for the $[B] \bullet [B]$ superblock structure and verify that the energy coincides with that of the MPM, as conjectured by S. Ostlund and S. Rommer (Phys. Rev. Lett., 75, 3537 (1995)).Comment: 2 pages, 1 eps figure included. eps.cls include

Galaxy rotations from quantised inertia and visible matter only

It is shown here that a model for inertial mass, called quantised inertia, or MiHsC (Modified inertia by a Hubble-scale Casimir effect) predicts the rotational acceleration of the 153 good quality galaxies in the SPARC dataset (2016 AJ 152 157), with a large range of scales and mass, from just their visible baryonic matter, the speed of light and the co-moving diameter of the observable universe. No dark matter is needed. The performance of quantised inertia is comparable to that of MoND, yet it needs no adjustable parameter. As a further critical test, quantised inertia uniquely predicts a specific increase in the galaxy rotation anomaly at higher redshifts. This test is now becoming possible and new data shows that galaxy rotational accelerations do increase with redshift in the predicted manner, at least up to Z=2.2.Comment: 9 pages, 2 figures. Published in Astrophys Space Sc

Testing quantised inertia on galactic scales

Galaxies and galaxy clusters have rotational velocities apparently too fast to allow them to be gravitationally bound by their visible matter. This has been attributed to the presence of invisible (dark) matter, but so far this has not been directly detected. Here, it is shown that a new model that modifies inertial mass by assuming it is caused by Unruh radiation, which is subject to a Hubble-scale (Theta) Casimir effect predicts the rotational velocity (v) to be: v^4=2GMc^2/Theta (the Tully-Fisher relation) where G is the gravitational constant, M is the baryonic mass and c is the speed of light. The model predicts the outer rotational velocity of dwarf and disk galaxies, and galaxy clusters, within error bars, without dark matter or adjustable parameters, and makes a prediction that local accelerations should remain above 2c^2/Theta at a galaxy's edge.Comment: 7 pages, 1 figure. Accepted for publication in Astrophysics and Space Science on 27/7/201

The Non-Abelian Density Matrix Renormalization Group Algorithm

We describe here the extension of the density matrix renormalization group algorithm to the case where Hamiltonian has a non-Abelian global symmetry group. The block states transform as irreducible representations of the non-Abelian group. Since the representations are multi-dimensional, a single block state in the new representation corresponds to multiple states of the original density matrix renormalization group basis. We demonstrate the usefulness of the construction via the one-dimensional Hubbard model as the symmetry group is enlarged from $U(1) \times U(1)$, up to $SU(2) \times SU(2)$.Comment: Revised version discusses the Hubbard model with SO(4) symmetr

Inertia from an asymmetric Casimir effect

The property of inertia has never been fully explained. A model for inertia (MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is due to Unruh radiation and 2) this radiation is subject to a Hubble-scale Casimir effect. This model has no adjustable parameters and predicts the cosmic acceleration, and galaxy rotation without dark matter, suggesting that Unruh radiation indeed causes inertia, but the exact mechanism by which it does this has not been specified. The mechanism suggested here is that when an object accelerates, for example to the right, a dynamical (Rindler) event horizon forms to its left, reducing the Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces an imbalance in the radiation pressure on the object, and a net force that always opposes acceleration, like inertia. A formula for inertia is derived, and an experimental test is suggested.Comment: 7 pages, 1 figure. Accepted by EPL (Europhysics Letters) on the 11th February, 201

Continuum emission associated with 6.7-GHz methanol masers

We have used the Australia Telescope Compact Array (ATCA) to search for continuum emission toward three strong 6.7-GHz methanol maser sources. For two of the sources, G339.88-1.26 and NGC 6334F (G351.42+0.64), we detect continuum emission closely associated with the methanol masers. A further three clusters of masers showed no radio continuum emission above our sensitivity limit of 1-5 mJy. We find the position of the 6.7-GHz methanol masers in G339.88-1.26 to be consistent with the hypothesis that the masers lie in the circumstellar disc surrounding a massive star. We also argue that one of the clusters of methanol masers in NGC 6334F provides indirect observational support for the circumstellar disc hypothesis.Comment: 8 pages including 2 figures, using LaTeX formatted with mn.sty, accepted for publication in MNRA

Phase Diagram of the 1D Kondo Lattice Model

We determine the boundary of the fully polarized ferromagnetic ground state in the one dimensional Kondo lattice model at partial conduction electron band filling by using a newly developed infinite size DMRG method which conserves the total spin quantum number. The obtained paramagnetic to ferromagnetic phase boundary is below $J \approx 3.5$ for the whole range of band filling. By this we solve the controversy in the phase diagram over the extent of the ferromagnetic region close to half filling.Comment: 6 pages, 4 EPS figures. Presented at MOS9

Applying matrix product operators to model systems with long-range interactions

An algorithm is presented which computes a translationally invariant matrix product state approximation of the ground state of an infinite 1D system; it does this by embedding sites into an approximation of the infinite ``environment'' of the chain, allowing the sites to relax, and then merging them with the environment in order to refine the approximation. By making use of matrix product operators, our approach is able to directly model any long-range interaction that can be systematically approximated by a series of decaying exponentials. We apply our techniques to compute the ground state of the Haldane-Shastry model and present results.Comment: 7 pages, 3 figures; manuscript has been expanded and restructured in order to improve presentation of the algorith

Policy needs and options for a common approach towards modelling and simulation of human physiology and diseases with a focus on the virtual physiological human.

Life is the result of an intricate systemic interaction between many processes occurring at radically different spatial and temporal scales. Every day, worldwide biomedical research and clinical practice produce a huge amount of information on such processes. However, this information being highly fragmented, its integration is largely left to the human actors who find this task increasingly and ever more demanding in a context where the information available continues to increase exponentially. Investments in the Virtual Physiological Human (VPH) research are largely motivated by the need for integration in healthcare. As all health information becomes digital, the complexity of health care will continue to evolve, translating into an ever increasing pressure which will result from a growing demand in parallel to limited budgets. Hence, the best way to achieve the dream of personalised, preventive, and participative medicine at sustainable costs will be through the integration of all available data, information and knowledge