Optimized Cell Planning for Network Slicing in Heterogeneous Wireless Communication Networks

We propose a cell planning scheme to maximize the resource efficiency of a wireless communication network while considering quality-of-service requirements imposed by different mobile services. In dense and heterogeneous cellular 5G networks, the available time-frequency resources are orthogonally partitioned among different slices, which are serviced by the cells. The proposed scheme achieves a joint optimization of the resource distribution between network slices, the allocation of cells to operate on different slices, and the allocation of users to cells. Since the original problem formulation is computationally intractable, we propose a convex inner approximation. Simulations show that the proposed approach optimizes the resource efficiency and enables a service-centric network design paradigm.Comment: This article has been accepted for publication in a future issue of the IEEE Communications Letters, https://ieeexplore.ieee.org/document/8368293, (c) 2018 IEE

Stretching an heteropolymer

We study the influence of some quenched disorder in the sequence of monomers on the entropic elasticity of long polymeric chains. Starting from the Kratky-Porod model, we show numerically that some randomness in the favoured angles between successive segments induces a change in the elongation versus force characteristics, and this change can be well described by a simple renormalisation of the elastic constant. The effective coupling constant is computed by an analytic study of the low force regime.Comment: Latex, 7 pages, 3 postscript figur

Uniqueness of Lagrangian Self-Expanders

We show that zero-Maslov class Lagrangian self-expanders in C^n which are asymptotic to a pair of planes intersecting transversely are locally unique if n>2 and unique if n=2.Comment: 32 page

The thermodynamics of general anesthesia

It is known that the action of general anesthetics is proportional to their partition coefficient in lipid membranes (Meyer-Overton rule). This solubility is, however, directly related to the depression of the temperature of the melting transition found close to body temperature in biomembranes. We propose a thermodynamic extension of the Meyer-Overton rule which is based on free energy changes in the system and thus automatically incorporates the effects of melting point depression. This model provides a quantitative explanation of the pressure reversal of anesthesia. Further, it explains why inflammation and the addition of divalent cations reduce the effectiveness of anesthesia.Comment: 7 pages, 2 figure

Midwinter suppression of baroclinic storm activity on Mars: observations and models

Baroclinic instability and intense traveling wave activity on Mars is well known to occur in “storm zones” (Hollingsworth et al. 1996) close to the edge of the advancing or retreating polar ice cap. Such activity usually sets in during Martian fall and continues until the onset of the summer season when large-scale instability mostly ceases as the atmosphere is no longer baroclinically unstable. The stormy season is typically characterized by large-scale, zonally-propagating waves with zonal wavenumbers m = 1-3, the lower wavenumber modes typically penetrating to considerable altitude though may also be surface-intensified. As we show below, however, some observations suggest that this eddy activity does not persist uniformly throughout the autumn, winter and spring seasons, but appears to die down quite consistently within 10 sols or so either side of the winter solstice. This midwinter ‘solsticial pause’ appears to be a sufficiently consistent feature of each winter season in both hemispheres to be regarded as a significant feature of Martian climatology, and could affect a variety of aspects of Martian meteorology including global heat and momentum transport, occurrence of dust storms etc. A somewhat similar phenomenon has also been documented for the Earth (e.g. Nakamura 1992; Penny et al. 2010), especially in relation to seasonal variations in the north Pacific storm tracks. The cause of this phenomenon is still not well established, though suggested mechanisms include the effects of enhanced barotropic shear (the so-called ‘barotropic governor’ (James & Gray 1986) and interactions with topography over central Asia. In this presentation we examine evidence for this phenomenon in the assimilated record of Martian climate from the Thermal Emission Spectrometer on board the Mars Global Surveyor mission (MGSTES), in conjunction with the UK version of the LMD-Oxford-OU-IAA Mars GCM (Forget et al. 1999; Montabone et al. 2006; Lewis et al. 2007). This is further corroborated in other evidence from seasonal variations in the incidence of local and regional dust storms that owe their origin to circumpolar baroclinic storms. We also discuss the extent to which this ‘solsticial pause’ phenomenon is reproduced in stand-alone atmospheric models and present results of some simulations to test a number of hypotheses for its dynamical origin on Mars

A new geometric invariant on initial data for Einstein equations

For a given asymptotically flat initial data set for Einstein equations a new geometric invariant is constructed. This invariant measure the departure of the data set from the stationary regime, it vanishes if and only if the data is stationary. In vacuum, it can be interpreted as a measure of the total amount of radiation contained in the data.Comment: 5 pages. Important corrections regarding the generalization to the non-time symmetric cas

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Structural, mechanical and thermodynamic properties of a coarse-grained DNA model

We explore in detail the structural, mechanical and thermodynamic properties of a coarse-grained model of DNA similar to that introduced in Thomas E. Ouldridge, Ard A. Louis, Jonathan P.K. Doye, Phys. Rev. Lett. 104 178101 (2010). Effective interactions are used to represent chain connectivity, excluded volume, base stacking and hydrogen bonding, naturally reproducing a range of DNA behaviour. We quantify the relation to experiment of the thermodynamics of single-stranded stacking, duplex hybridization and hairpin formation, as well as structural properties such as the persistence length of single strands and duplexes, and the torsional and stretching stiffness of double helices. We also explore the model's representation of more complex motifs involving dangling ends, bulged bases and internal loops, and the effect of stacking and fraying on the thermodynamics of the duplex formation transition.Comment: 25 pages, 16 figure

Perturbative Solutions of the Extended Constraint Equations in General Relativity

The extended constraint equations arise as a special case of the conformal constraint equations that are satisfied by an initial data hypersurface $Z$ in an asymptotically simple spacetime satisfying the vacuum conformal Einstein equations developed by H. Friedrich. The extended constraint equations consist of a quasi-linear system of partial differential equations for the induced metric, the second fundamental form and two other tensorial quantities defined on $Z$, and are equivalent to the usual constraint equations that $Z$ satisfies as a spacelike hypersurface in a spacetime satisfying Einstein's vacuum equation. This article develops a method for finding perturbative, asymptotically flat solutions of the extended constraint equations in a neighbourhood of the flat solution on Euclidean space. This method is fundamentally different from the `classical' method of Lichnerowicz and York that is used to solve the usual constraint equations.Comment: This third and final version has been accepted for publication in Communications in Mathematical Physic