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

Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

Size, shape, and flexibility of RNA structures

Determination of sizes and flexibilities of RNA molecules is important in understanding the nature of packing in folded structures and in elucidating interactions between RNA and DNA or proteins. Using the coordinates of the structures of RNA in the Protein Data Bank we find that the size of the folded RNA structures, measured using the radius of gyration, $R_G$, follows the Flory scaling law, namely, $R_G =5.5 N^{1/3}$ \AA where N is the number of nucleotides. The shape of RNA molecules is characterized by the asphericity $\Delta$ and the shape $S$ parameters that are computed using the eigenvalues of the moment of inertia tensor. From the distribution of $\Delta$, we find that a large fraction of folded RNA structures are aspherical and the distribution of $S$ values shows that RNA molecules are prolate ($S>0$). The flexibility of folded structures is characterized by the persistence length $l_p$. By fitting the distance distribution function $P(r)$ to the worm-like chain model we extracted the persistence length $l_p$. We find that $l_p\approx 1.5 N^{0.33}$ \AA. The dependence of $l_p$ on $N$ implies the average length of helices should increases as the size of RNA grows. We also analyze packing in the structures of ribosomes (30S, 50S, and 70S) in terms of $R_G$, $\Delta$, $S$, and $l_p$. The 70S and the 50S subunits are more spherical compared to most RNA molecules. The globularity in 50S is due to the presence of an unusually large number (compared to 30S subunit) of small helices that are stitched together by bulges and loops. Comparison of the shapes of the intact 70S ribosome and the constituent particles suggests that folding of the individual molecules might occur prior to assembly.Comment: 28 pages, 8 figures, J. Chem. Phys. in pres

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

Statistical mechanics of base stacking and pairing in DNA melting

We propose a statistical mechanics model for DNA melting in which base stacking and pairing are explicitly introduced as distinct degrees of freedom. Unlike previous approaches, this model describes thermal denaturation of DNA secondary structure in the whole experimentally accessible temperature range. Base pairing is described through a zipper model, base stacking through an Ising model. We present experimental data on the unstacking transition, obtained exploiting the observation that at moderately low pH this transition is moved down to experimentally accessible temperatures. These measurements confirm that the Ising model approach is indeed a good description of base stacking. On the other hand, comparison with the experiments points to the limitations of the simple zipper model description of base pairing.Comment: 13 pages with figure

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

Terminal deoxynucleotidyl transferase is found in prothymocytes

Terminal deoxynucleotidyl transferase is an enzyme which has the unique property of polymerizing polydeoxynucleotides onto a primer in the absence of a template (1,2). This enzyme is found both in the thymus and the bone marrow of birds, rodents, and humans (3-7). Whether the marrow cells that contain terminal transferase are related to thymocytes, or are on a separate pathway of differentiation, is not yet known (7,8). To determine the lineage of the murine bone marrow cells that have terminal transferase, we have investigated whether these cells have the antigen Thy-1 induced on the cells by treatment with thymopoietin (9). Thymopoietin is known to induce a set of characteristic T-cell markers including the Thy-1 alloantigen on the surface of a subpopulation of bone marrow cells committed to T-cell differentiation (prothymocytes) (10). Destruction of Thy- 1-positive cells after exposure to thymopoietin allows elimination of a substantial fraction of those bone marrow cells that can repopulate an irradiated thymus (11). We find that such an elimination after induction with the thymic polypeptide removes a substantial amount of terminal transferase from the bone marrow cell population, suggesting that at least one-half of the marrow cells bearing this enzyme are related to those found in the thymus