How to gamble if you're in a hurry

The beautiful theory of statistical gambling, started by Dubins and Savage (for subfair games) and continued by Kelly and Breiman (for superfair games), has mostly been studied under the unrealistic assumption that we live in a continuous world, that money is indefinitely divisible and that our life is indefinitely long. Here, we study these fascinating problems from a purely discrete, finitistic and computational viewpoint, using both symbol-crunching and number-crunching (and simulation just for checking purposes).     

Novel methodology for 3D reconstruction of carotid arteries and plaque characterization based upon magnetic resonance imaging carotid angiography data

In this study, we present a novel methodology that allows reliable segmentation of the magnetic resonance images (MRIs) for accurate fully automated three-dimensional (3D) reconstruction of the carotid arteries and semiautomated characterization of plaque type. Our approach uses active contours to detect the luminal borders in the time-of-flight images and the outer vessel wall borders in the T(1)-weighted images. The methodology incorporates the connecting components theory for the automated identification of the bifurcation region and a knowledge-based algorithm for the accurate characterization of the plaque components. The proposed segmentation method was validated in randomly selected MRI frames analyzed offline by two expert observers. The interobserver variability of the method for the lumen and outer vessel wall was -1.60%±6.70% and 0.56%±6.28%, respectively, while the Williams Index for all metrics was close to unity. The methodology implemented to identify the composition of the plaque was also validated in 591 images acquired from 24 patients. The obtained Cohen's k was 0.68 (0.60-0.76) for lipid plaques, while the time needed to process an MRI sequence for 3D reconstruction was only 30 s. The obtained results indicate that the proposed methodology allows reliable and automated detection of the luminal and vessel wall borders and fast and accurate characterization of plaque type in carotid MRI sequences. These features render the currently presented methodology a useful tool in the clinical and research arena.     

A mononuclear complex and a cubane cluster from the initial use of 2-(hydroxymethyl)pyridine in nickel(II) carboxylate chemistry

The reactions of 2-(hydromethyl)pyridine, hmpH, with Ni(O₂CMe)₂·4H₂O in H₂O, in the absence of counterions, have been investigated. The synthetic study has led to the two new complexes [Ni(O₂CMe)₂(hmpH)₂] (1) and [Ni₄(O₂CMe)₄(hmp)₄(H₂O)₂] (2). Complex 1 can also be transformed into 2 by reacting with an excess of NaOH in H₂O. The structures of 1 and 2·2.25H₂O·0.5(1,4-dioxane) have been solved by single-crystal, X-ray crystallography. The octahedral Ni^II center in centrosymmetric 1 is coordinated by two 1.10 (Harris notation) MeCO₂⁻ groups and two N,O-chelating (1.11) hpmH ligands. The tetranuclear cluster molecule of 2·2.25H₂O·0.5(1,4-dioxane) possesses a distorted cubane {Ni₄(μ₃-OR′)₄}⁴⁺ core [R′ = (2-pyridyl)CH₂–] with the Ni^II ions and the oxygen atoms from the 3.31 hmp⁻ ligands occupying alternate vertices of the cube. Two 2.11 MeCO₂⁻ groups cap two opposite faces of the cube, while two 1.10 MeCO₂⁻ ions and two aqua ligands complete the octahedral coordination sphere of the metal centers. Characteristic IR bands for the two complexes are discussed in terms of the nature of bonding and the structures of the two complexes. The variable-temperature magnetic properties of 2 have been modeled with two J values, and reveal antiferromagnetic exchange interactions between the four Ni^II ions to give a diamagnetic ground state.     

Selective Activation of the C−H Bond in Methane by Single Platinum Atomic Anions

Mass spectrometric analysis of the anionic products of interaction between platinum atomic anions, Pt^?, and methane, CH₄ and CD₄, in a collision cell shows the preferred generation of [PtCH₄]^? and [PtCD₄]^? complexes and a low tendency toward dehydrogenation. [PtCH₄]^? is shown to be H?Pt?CH₃^? by a synergy between anion photoelectron spectroscopy and quantum chemical calculations, implying the rupture of a single C?H bond. The calculated reaction pathway accounts for the observed selective activation of methane by Pt^?. This study presents the first example of methane activation by a single atomic anion.     

Isogeometric analysis for the dynamic problem of curved structures including warping effects

Curved beam structures have been used in many civil, mechanical, aircraft, and aerospace constructions. The analysis is mainly based on solid and plate models due to the fact that traditional curved beam elements do not include nonuniform warping effects, especially in the dynamic analysis. In this article, independent warping parameters have been taken into account and the initial curvature effect is considered. Curved beam’s behavior becomes more complex, even for dead loading, due to the coupling between axial force, bending moments, and torque that curvature produces. In addition to these, the Isogeometric tools (b-splines or NURBS), either integrated in the Finite Element Method or in a Boundary Element–based Method called Analog Equation Method, have been employed in this contribution for the dynamic analysis of horizontally curved beams of open or closed (box-shaped) cross sections. Free vibration characteristics and responses of the stress resultants and displacements to moving loading have been studied.     

Steady shear banding in complex fluids

Shear banding (SB) is manifested by the abrupt “demixing” of the flow into regions of high and low shear rate. In this paper, we first relate analytically the rheological parameters of the fluid with the range of shear rates and stresses of SB occurrence. For this, we accept that the origin of shear banding is constitutive, and adopt a non-linear viscoelastic expression able to accommodate the double-valuedness of the stress with flow intensity, under certain conditions. We then implement the model for the case of pressure driven flow through a cylindrical pipe; we derive approximate expressions for the velocity profile in the two-banded regions (core and outer annular), the overall throughput in the presence or absence of “spurt”, and the radial location limits of the shear rate discontinuity.     

An efficient spectral method for ordinary differential equations with rational function coefficients

We present some relations that allow the efficient approximate inversion of linear differential operators with rational function coefficients. We employ expansions in terms of a large class of orthogonal polynomial families, including all the classical orthogonal polynomials. These families obey a simple 3-term recurrence relation for differentiation, which implies that on an appropriately restricted domain the differentiation operator has a unique banded inverse. The inverse is an integration operator for the family, and it is simply the tridiagonal coefficient matrix for the recurrence. Since in these families convolution operators (i.e., matrix representations of multiplication by a function) are banded for polynomials, we are able to obtain a banded representation for linear differential operators with rational coefficients. This leads to a method of solution of initial or boundary value problems that, besides having an operation count that scales linearly with the order of truncation , is computationally well conditioned. Among the applications considered is the use of rational maps for the resolution of sharp interior layers.

     

Synthesis, structural characterization, and computational studies of novel diiodine adducts with the heterocyclic thioamides N-methylbenzothiazole-2-thione and benzimidazole-2-thione: implications with the mechanism of action of antithyroid drugs

Reaction of N-methylbenzothiazole-2-thione (C8H7NS2 or NMBZT) with diiodine produced the charge-transfer (ct) complex [(NMBZT).I2] (1). NMBZT reacts with diiodine in the presence of FeCl3 in a molar ratio of 3:6:1 and forms the ionic complex [[(NMBZT)2I+].[FeCl4]-] (2) together with [[(NMBZT)2I+].[I7]-] (2a) iodonium salt. The reaction of benzimidazole-2-thione (C7H6N2S or MBZIM) with diiodine on the other hand results in the formation of the ct [[(MBZIM)2I]+[I3]-].[(MBZIM).I2] (3) compound. The compounds have been characterized by elemental analyses, DTA-TG, FT-Raman, FT-IR, UV-vis, and 1H NMR spectroscopies, and X-ray crystal structure determinations. Compound 1, C8H7I2NS2, is orthorhombic with a space group Pna2(1) and a = 12.5147(13) angstroms, b = 22.536(3) angstroms, c = 4.2994(5) angstroms, and Z = 4. Compound 2, C16H14Cl4FeIN2S4, is monoclinic, space group C2/c, a = 35.781(2) angstroms, b = 7.4761(5) angstroms, c = 18.4677(12) angstroms, beta = 107.219(1) degrees, and Z = 8. Compound 3, C21H18I6N6S3, monoclinic, space group P2(1)/n, a = 14.0652(11) angstroms, b = 22.536(3) angstroms, c = 4.2994(5) angstroms, beta = 99.635(7) degrees, and Z = 4, consists of two component moieties cocrystallized, one neutral which contains the benzimidazole-2-thione (MBIZM) ligand bonded with an iodine atom through sulfur, forming a compound with a "spoke" structure [(MBZIM)I2] 3a, while the other is the ionic complex [[(MBZII)2I+].[I3]-] (3b). The X-ray crystal structure of 1 shows a bond between the thione-sulfur atom and one of the iodine atoms in an essentially planar arrangement. In the cation of 2, an iodine is coordinated by two thione-sulfur atoms in a linear arrangement but the molecule is not planar. For the first time in the solid state a spoke-ionic mixed complex has been characterized in 3. One component of the structure is a molecular diiodine adduct, i.e., [(MBZIM)I2] (3a), with a linear coordination geometry in a decidedly planar arrangement, and the other component is an ionic adduct [[(MBZIM)2I]+.[I3]-] (3b) with the cation having an arrangement similar to that found for 1. Theoretical calculations using density functional (DFT) and ab initio Hartree-Fock theory have been carried out for 1 and 3a,b. The results are consistent with the experimental data. Conclusions on the behavior of a thioamide, when used as an antithyroid drug, have also been made.     

Lower bounds for the zeros of analytic functions

Summary In the present work the problem of finding lower bounds for the zeros of an analytic function is reduced by a Hilbert space technique to the well-known problem of finding upper bounds for the zeros of a polynomial. Several lower bounds for all the zeros of analytic functions are thus found, which are always better than the well-known Carmichael-Mason inequality. Several numerical examples are also given and a comparison of our bounds with well-known bounds in literature and/or the exact solution is made.