Kostant Partitions Functions and Flow Polytopes

This paper discusses volumes and Ehrhart polynomials in the context of flow polytopes. The general approach that studies these functions via rational functions with poles on arrangement of hyperplanes and the total residue of such functions allows us, via a unified approach, to reobtain many interesting calculations existing in the literature. In particular we generalize Lidskii formula relating the Ehrhart polynomial to the volume function.     

How Does Diet Influence Our Lives? Evaluating the Relationship between Isotopic Signatures and Mortality Patterns in Italian Roman Imperial and Medieval Periods

The present research investigates the relationship between dietary habits and mortality patterns in the Roman Imperial and Medieval periods. The reconstructions of population dynamics and subsistence strategies provide a fascinating source of information for understanding our history. This is particularly true given that the changes in social, economic, political, and religious aspects related to the transition from the Roman period to the Middle Ages have been widely discussed. We analyzed the isotopic and mortality patterns of 616 individuals from 18 archeological sites (the Medieval Latium sites of Colonna, Santa Severa, Allumiere, Cencelle, and 14 Medieval and Imperial funerary contexts from Rome) to compile a survivorship analysis. A semi-parametric approach was applied, suggesting variations in mortality patterns between sexes in the Roman period. Nitrogen isotopic signatures influenced mortality in both periods, showing a quadratic and a linear effect for Roman Imperial and Medieval populations, respectively. No influence of carbon isotopic signatures has been detected for Roman Imperial populations. Conversely, increased mortality risk for rising carbon isotopic values was observed in Medieval samples.     

The quantum analog of a symmetric pair: a construction in type

Let be the ideal in the enveloping algebra of generated by the maximal compact subalgebra of . In this paper we construct an analog of in the quantized enveloping algebra corresponding to a type diagram at generic . We find generators for and explicit bases for .

     

Buoyancy-induced deformations in a compressible elastic solid

Given a rectangular slab of a purely elastic material (neo-Hookean) with different temperatures imposed on the lateral surfaces, it is shown, within the context of a linearized theory, that the resulting deformation field is, under suitable boundary conditions, virtually identical to its fluid-mechanical counterpart given by a rectangular trench filled with a Newtonian liquid. A second, more general analogy between problems involving buoyancy induced deformations and the classical theory of thin plates is also presented.     

Finite-length models of carbon nanotubes based on Clar sextet theory

Finite-length models of metallic and semiconducting carbon nanotubes (CNTs) based on Clar sextet theory of aromatic systems are proposed. For metallic CNTs, the electronic properties of finite-length models converge monotonically to the values expected for quasi-monodimensional metallic systems. For semiconducting CNTs, the use of finite-length models as proposed in this work leads to a fast convergence of the electronic properties to the values expected for the corresponding infinite-length nanotube.     

Performance of density functional models to reproduce observed (13)C(alpha) chemical shifts of proteins in solution

The purpose of this work is to test several density functional models (namely, OPBE, O3LYP, OPW91, BPW91, OB98, BPBE, B971, OLYP, PBE1PBE, and B3LYP) to determine their accuracy and speed for computing (13)C(alpha) chemical shifts in proteins. The test is applied to 10 NMR-derived conformations of the 76-residue alpha/beta protein ubiquitin (protein data bank id 1D3Z). With each functional, the (13)C(alpha) shielding was computed for 760 amino acid residues by using a combination of approaches that includes, but is not limited to, treating each amino acid X in the sequence as a terminally blocked tripeptide with the sequence Ac-GXG-NMe in the conformation of the regularized experimental protein structure. As computation of the (13)C(alpha) chemical shifts, not their shielding, is the main goal of this work, a computation of the (13)C(alpha) shielding of the reference, namely, tetramethylsilane, is investigated here and an effective and a computed tetramethylsilane shielding value for each of the functionals is provided. Despite observed small differences among all functionals tested, the results indicate that four of them, namely, OPBE, OPW91, OB98, and OLYP, provide the most accurate functionals with which to reproduce observed (13)C(alpha) chemical shifts of proteins in solution, and are among the faster ones. This study also provides evidence for the applicability of these functionals to proteins of any size or class, and for the validation of our previous results and conclusions, obtained from calculations with the slower B3LYP functional.     

Computation of the Highest Coefficients of Weighted Ehrhart Quasi-polynomials of Rational Polyhedra

This article concerns the computational problem of counting the lattice points inside convex polytopes, when each point must be counted with a weight associated to it. We describe an efficient algorithm for computing the highest degree coefficients of the weighted Ehrhart quasi-polynomial for a rational simple polytope in varying dimension, when the weights of the lattice points are given by a polynomial function h. Our technique is based on a refinement of an algorithm of A.?Barvinok in the unweighted case (i.e., h≡1). In contrast to Barvinok’s method, our method is local, obtains an approximation on the level of generating functions, handles the general weighted case, and provides the coefficients in closed form as step polynomials of the dilation. To demonstrate the practicality of our approach, we report on computational experiments which show that even our simple implementation can compete with state-of-the-art software.     

Peptide models XXIX. cis–trans Isomerism of peptide bonds: ab initio study on small peptide model compound; the 3D-Ramachandran map of formylglycinamide

Thermodynamic separations for cis and trans-amides and formylglycinamide range from 0.00 to 4.77 kcal/mol as computed at various levels of theory. The barriers for trans→cis-isomerization, for the same set of compounds, computed at various levels of theory, were found between 15.69 and 22.67 kcal/mol. The cis- and trans-Ramachandran maps of formylglycinamide are compared and the topology of the ab initio 3D-Ramachandran map is presented for the first time.