Packing Radius Research Articles

Spectrometry and Reservoir Characteristics of Rudeis Formation in Belayim Marine Oil Field, Gulf of Suez, Egypt

Spectrometry and Reservoir Characteristics of Rudeis Formation in Belayim Marine Oil Field, Gulf of Suez, Egypt

A stopping radius for the sphere decoder and its application to MSDD of DPSK

In this letter we use a lower bound on the packing radius of discrete sets as a stopping radius in the sphere decoder (SD). This enables us to terminate the SD search process as early as possible while preserving the optimality of the final decoder output. As an example we investigate the application of this SD with early termination in multiple-symbol differential detection (MSDD) of differential phase-shift keying (DPSK) transmitted over time-varying fading channels, and provide numerical evidence that the proposed stopping radius achieves a notable complexity reduction.

Molecular Pair Analysis: CH⋅⋅⋅F Interactions in the Crystal Structure of Fluorobenzene? And Related Matters

The crystal structure of fluorobenzene is compared with isomorphous crystal structures of molecules of roughly similar shape. The lowest-energy fluorobenzene dimers are identified by theoretical calculations. Molecular pair analysis of the crystal structure of fluorobenzene and of an isomorphous virtual low-energy polymorph of benzene suggests that the important intermolecular interactions in the two structures are closely similar. In particular, the intermolecular C-H...F interactions in the fluorobenzene crystal have approximately the same structure-directing ability and influence on the intermolecular energy as the corresponding C-H...H interactions in benzene. Molecular pair analysis of the isomorphous crystal structures of benzonitrile, alloxan, and cyclopentene-1,2,3-trione indicates that essentially the same crystal structure can be adopted with quite different patterns of pair energies and atom-atom interactions. The question as to whether the packing radius of organic fluorine is larger or smaller than that of hydrogen, is addressed, but not answered.

The Conformationally Dynamic C Helix of the RIα Subunit of Protein Kinase A Mediates Isoform-specific Domain Reorganization upon C Subunit Binding

Different isoforms of the full-length protein kinase A (PKA) regulatory subunit homodimer (R2) and the catalytic (C) subunit-bound holoenzyme (R2C2) have very different global structures despite similar molecular weights and domain organization within their primary sequences. To date, it has been the linker sequence between the R subunit dimerization/docking domain and cAMP-binding domain A that has been implicated in modulating domain interactions to give rise to these differences in global structure. The small angle solution scattering data presented here for three different isoforms of PKA heterodimer (deltaR-C) complexes reveal a role for another conformationally dynamic sequence in modulating inter-subunit and domain interactions, the C helix that connects the cAMP-binding domains A and B of the R subunit. The deltaR-C heterodimer complexes studied here were each formed with a monomeric N-terminal deletion mutant of the R subunit (deltaR) that contains the inhibitor sequence and both cAMP-binding domains. The scattering data show that type IIalpha and type IIbeta deltaR-C heterodimers are relatively compact and globular, with the C subunit contacting the inhibitor sequence and both cAMP-binding domains. In contrast, the type Ialpha heterodimer is significantly more extended, with the C subunit interacting with the inhibitor sequence and cAMP-binding domain A, whereas domain B extends out such that its surface is almost completely solvent exposed. These data implicate the C helix of RIalpha in modulating isoform-specific interdomain communication in the PKA holoenzyme, adding another layer of structural complexity to our understanding of signaling dynamics in this multisubunit, multidomain protein kinase.

The mapping properties of filling radius and packing radius and their applications

Let f : V → W be a map between closed, oriented Riemannian n-manifolds. It is shown that FillRad ( W ) ⩽ dil ( f ) ⋅ FillRad ( V ) , if | deg ( f ) | = 1 . By this mapping property, we obtain an estimate from below for the filling radius of a closed, oriented, nonpositively curved manifold, or a manifold with sectional curvature bounded above by a positive constant. In addition, a similar mapping property of packing radius and a corollary are also obtained.

Protein Reorientation and Bound Water Molecules Measured by 1H Magnetic Spin-Lattice Relaxation

The water-proton spin-lattice relaxation rate constant, 1 /T 1, was measured as a function of magnetic field strength for several dilute protein solutions. By separating the intermolecular contributions from the intramolecular contributions to the water-proton spin-lattice relaxation, the number of water molecules that bind to the protein for a time long compared with the rotational correlation time may be measured. We find a good correlation between the number of long-lived water molecules and the predictions based on available free volume in the proteins studied. The rotational correlation times of these proteins are larger than predicted by the Stokes-Einstein-Debye (SED) model for a sphere reorienting in a viscous liquid. The discrepancy between experiment and theory is usually attributed to hydration effects increasing the effective radius of the particle. However, the average lifetime of water molecules at the protein interface is far too short to justify such a picture. We suggest that surface roughness may be responsible for the retardation of rotational mobility and find that the SED model provides a reasonable representation of experiment if the radius assumed for the reorienting particle is the arithmetic mean of the crystallographic packing radius and the radius deduced from the effective surface area of the protein.

From circle packing to covering on a sphere with antipodal constraints

The problem treated here is: how must N antipodal pairs of equal circles (spherical caps) of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible? Conjectured solutions of this problem for N = 4,5,7 are given where r varies from the maximum antipodal packing radius to the minimum antipodal covering radius. These cases exhibit sequences of symmetry– and edge–number transitions in the contact polyhedra, which, in general, differ from those of the unconstrained problem where centrosymmetry is not enforced. New minimum antipodal covering arrangements are conjectured for 4, 5 and 7 pairs: they are a hexagonal bipyramid, a D 2h deltahedron and the cube+octahedron compound, respectively.

On the packing radius and the covering radius of equal-weight codes

The paper is devoted to a study of the packing radius and the covering radius of a well-known equal-weight code. Under some conditions tight estimates or exact values of these parameters are obtained.

On the covering radius of Z/sub 4/-codes and their lattices

In this correspondence, we investigate the covering radius of codes over Z/sub 4/ for the Lee and Euclidean distances in relation with those of binary nonlinear codes and lattices obtained by the Gray map and Construction A/sub 4/, respectively. We give several upper and lower bounds on covering radii, including Z/sub 4/-analogs of the sphere-covering bound, the packing radius bound, the Delsarte bound, and the redundancy bound. We show that any Euclidean-optimal Type II code of length 24 has covering radius 8 with respect to the Euclidean distance. We determine the covering radius of the Klemm codes with respect to the Lee distance. We derive lower bounds on the covering radii of the Niemeier lattices.

Transition from spherical circle packing to covering: geometrical analogues of chemical isomerization

How must n equal circles (spherical caps) of given angular radius r be arranged on the surface of a sphere so that the area covered by the circles will be as large as possible? In this paper, conjectured solutions of this problem for n = 5, 7, 8, 9, 10, 11 are given when r varies from the maximum packing radius to the minimum covering radius. The relation of the results of this problem to the extremal configurations of n mutually repulsive equal point charges on the surface of a sphere is discussed. Variation of the solution polyhedra with r gives an abstract model of chemical isomerization processes, for example for n = 5 where the packing → covering transition models the Berry pseudo-rotation of a trigonal bipyramid.

Generalized minimum-distance decoding of Euclidean-space codes and lattices

It is shown that multistage generalized minimum-distance (GMD) decoding of Euclidean-space codes and lattices can provide an excellent tradeoff between performance and complexity. We introduce a reliability metric for Gaussian channels that is easily computed from an inner product, and prove that a multistage GMD decoder using this metric is a bounded-distance decoder up to the true packing radius. The effective error coefficient of multistage GMD decoding is determined. Two simple modifications in the GMD decoding algorithm that drastically reduce this error coefficient are proposed. It is shown that with these modifications GMD decoding achieves the error coefficient of maximum-likelihood decoding for block codes and for generalized construction A lattices. Multistage GMD decoding of the lattices D/sub 4/, E/sub 8/, K/sub 12/, BW/sub 16/, and /spl Lambda//sub 24/ is investigated in detail. For K/sub 12/BW/sub 16/, and /spl Lambda//sub 24/, the GMD decoders have considerably lower complexity than the best known maximum-likelihood or bounded-distance decoding algorithms, and appear to be the most practically attractive decoders available. For high-dimensional codes and lattices (/spl ges/64 dimensions) maximum-likelihood decoding becomes infeasible, while GMD decoding algorithms remain quite practical. As an example, we devise a multistage GMD decoder for a 128-dimensional sphere packing with a nominal coding gain of 8.98 dB that attains an effective error coefficient of 1365760. This decoder requires only about 400 real operations, in addition to algebraic errors-and-erasures decoding of certain BCH and Hamming codes. It therefore appears to be practically feasible to implement algebraic multistage GMD decoders for high-dimensional sphere packings, and thus achieve high effective coding gains.

Hard and Soft Packing Radius Theorems

Singular spaces are playing an increasingly important role in Riemannian geometry. In particular this is true of the so-called Alexandrov spaces; i.e., finite-(Hausdorff) dimensional, complete, inner metric spaces with a lower curvature bound in the local triangle comparison sense. Interest in Alexandrov spaces is largely explained by the fact that the natural process of taking Gromov-Hausdorff limits is closed in Alexandrov geometry but not in Riemannian geometry. This simple observation has become a powerful tool in Riemannian geometry (see, for example, [FY], [GP2], or [GPW] and [Pe]). In this paper, we use a new means to obtain results in Riemannian geometry by studying Alexandrov spaces. The operation of forming spherical suspensions of positively curved spaces, an operation which is also closed in Alexandrov geometry but not in Riemannian geometry, will be applied to prove a differentiable sphere theorem which is unlike all previous solutions to the following basic problem.