Optimal shapes of compact strings

Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest packing fraction; only recently has it been proved that the answer for infinite systems is a face-centred-cubic lattice. This simply stated problem has had a profound impact in many areas, ranging from the crystallization and melting of atomic systems, to optimal packing of objects and subdivision of space. Here we study an analogous problem--that of determining the optimal shapes of closely packed compact strings. This problem is a mathematical idealization of situations commonly encountered in biology, chemistry and physics, involving the optimal structure of folded polymeric chains. We find that, in cases where boundary effects are not dominant, helices with a particular pitch-radius ratio are selected. Interestingly, the same geometry is observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure

A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

Towards Uniform Online Spherical Tessellations

The problem of uniformly placing N points onto a sphere finds applications in many areas. An online version of this problem was recently studied with respect to the gap ratio as a measure of uniformity. The proposed online algorithm of Chen et al. was upper-bounded by 5.99 and then improved to 3.69, which is achieved by considering a circumscribed dodecahedron followed by a recursive decomposition of each face. We analyse a simple tessellation technique based on the regular icosahedron, which decreases the upper-bound for the online version of this problem to around 2.84. Moreover, we show that the lower bound for the gap ratio of placing up to three points is 1+5√2≈1.618 . The uniform distribution of points on a sphere also corresponds to uniform distribution of unit quaternions which represent rotations in 3D space and has numerous applications in many areas

Interaction of Imidazole Containing Hydroxamic Acids with Fe(III): Hydroxamate Versus Imidazole Coordination of the Ligands

Solution equilibrium studies on Fe(III) complexes formed with imidazole-4-carbohydroxamic acid (Im-4-Cha), N-Me-imidazole-4-carbohydroxamic acid (N-Me-Im-4-Cha), imidazole-4-acetohydroxamic acid (Im-4-Aha), and histidinehydroxamic acid (Hisha) have been performed by using pH-potentiometry, UV-visible spectrophotometry, EPR, ESI-MS, and H1-NMR methods. All of the obtained results demonstrate that the imidazole moiety is able to play an important role very often in the interaction with Fe(III), even if this metal ion prefers the hydroxamate chelates very much. If the imidazole moiety is in α-position to the hydroxamic one (Im-4-Cha and N-Me-Im-4-Cha) its coordination to the metal ion is indicated unambiguously by our results. Interestingly, parallel formation of (Nimidazole, Ohydroxamate), and (Ohydroxamate, Ohydroxamate) type chelates seems probable with N-Me-Im-4-Cha. The imidazole is in β-position to the hydroxamic moiety in Im-4-Aha and an intermolecular noncovalent (mainly H-bonding) interaction seems to organize the intermediate-protonated molecules in this system. Following the formation of mono- and bishydroxamato mononuclear complexes, only EPR silent species exists in the Fe(III)-Hisha system above pH 4, what suggests the rather significant “assembler activity” of the imidazole (perhaps together with the ammonium moiety)

Women's colposcopy experience and preferences: a mixed methods study

<p>Abstract</p> <p>Background</p> <p>The colposcopy service is a key component in the UK Cervical Screening Programme. Over 120,000 women are referred to the service annually, however up to 25% of women fail to attend their appointment. Little is known about patients' preferences for colposcopic investigation and treatment. This study aims to investigate women's experience of colposcopy, to identify patients' preferences for aspects of appointments within the colposcopy service, and to make suggestions for service improvement.</p> <p>Methods/Design</p> <p>This study has been designed as a two stage, mixed method project. Stage one will involve in-depth interviews with new colposcopy patients to ascertain their experience of colposcopy services. This qualitative stage will generate factors thought to be important by service users in their experience. Stage two will utilise a choice based quantitative technique to identify women's preferences and determine the representativeness of factors generated through the interviews.</p> <p>The initial stage of in-depth interviews will be conducted with patients who are newly referred to colposcopy clinics to investigate the experience that they have of the referral process and appointment attendance. The outcome of these interviews will be analysed qualitatively using Framework analysis. Factors found to be important in women's experience will be extracted and used to construct a choice based questionnaire.</p> <p>The discrete choice experiment (questionnaire) will apply a best-worst technique through scenario-based questions to find women's relative preferences for different aspects of the service. It will be offered to women attending follow-up appointments at two colposcopy clinics in the West Midlands. Women will complete the questionnaire whilst they wait for their appointment, or, if they prefer, will take it home to complete in private. Women who do not attend their appointment will be posted the research information and questionnaire. The questionnaire analysis will use a weighted least squares regression technique for each best/worst pair. The accept/reject 'would you attend this appointment' question will be analysed using a random effects logit model.</p> <p>Discussion</p> <p>Colposcopy is a common procedure and one that is associated with raised anxiety among women experiencing the service. Little is known about women's experience of the service or their preferences for service delivery. The outcomes of the study will comprise a description of women's experience of colposcopy and establishing their preferences for how aspects of the service should be provided. Women's preferences will be fed back to service providers to enable improvements to the service to be made.</p

A handbook of integer sequences

A Handbook of Integer Sequence

A new operation on sequences: The boustrophedon transform

A generalization of the Seidel-Entringer-Arnold method for calculating the alternating permutation numbers (or secant-tangent numbers) leads to a new operation on sequences, the boustrophedon transform. © 1996 Academic Press, Inc. * Present address: Math. and Computer Science Department, Dartmouth College, Hanover, New Hampshire

A Note on Projecting the Cubic Lattice

It is shown that, given any (n-1)-dimensional lattice I >, there is a vector vaa'currency sign (n) such that the orthogonal projection of a'currency sign (n) onto v (aSyen) is, up to a similarity, arbitrarily close to I >. The problem arises in attempting to find the largest cylinder anchored at two points of a'currency sign (n) and containing no other points of a'currency sign (n) .46347247