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This article elaborates an n-order multinomial lattice approach to value derivative instruments on asset prices characterized by a lognormal distribution. Nonlinear optimization is employed, specified moments are matched, and n-order multinomial trees are developed. The proposed methodology represents an alternative specification to models of jump processes of order greater than three developed by other researchers. The main contribution of this work is pedagogical. Its strength is in its straightforward explanation of the underlying tree building procedure for which numerical efficiency is a motivation for actual implementation.

This article elaborates an n-order multinomial lattice approach to value derivative instruments on asset prices characterized by a lognormal distribution. Nonlinear optimization is employed, specified moments are matched, and n-order multinomial trees are developed. The proposed methodology represents an alternative specification tomodels of jump processes of order greater than three developed by other researchers. The main contribution of this work is pedagogical. Its strength is in its straightforward explanation of the underlying tree building procedure for which numerical efficiency is a motivation for actual implementation.

Measurement, cognition and understanding can be regarded as gluing parts by using of the notion of wholeness, and forgetting a limit called de-measurement leads to dissolution. Although measurement and de-measurement is convertible if the wholeness is expressed as a limit, they give rise to negotiation between parts and whole in a real world since wholeness has vagueness. We introduce a particular limit that has vagueness, call it open limit, and show that an open limit plays an essential role in making intrinsic development, by illustrating physarum mold pattern formation.

Non-perturbative physics on the light cone is investigated in a Hamiltonian lattice framework. We use near light cone coordinates and perform a limiting procedure onto the light cone. Such a formulation is natural in order to describe high energy scattering. It contains an additional parameter η which represents the distance to the light cone and is varying the energy. The QCD vacuum is planned to be generated by a quantum diffusion Monte Carlo algorithm. In order to minimize the algorithmic variance, a guidance wave functional close to the exact ground state is required. We present a solution for the ground state corresponding to the dominant part of the Hamiltonian in the light cone limit.

The bocage landscape has evolved very radically during the last fifty years with the agricultural developement. The shapes of the hedgerow lattice have many consequences for example, in hydrological or ecological functions of this landscape. So we attempt to characterize the network structure by means of fractal geometry. The box-counting method permits to get significantly different results to analyse this structure with fractal parameters (dimension, upper and lower cuts off). Combining them with other parameters, we plan to model the functionning of this landscape.

This article introduces the basic segmentation problems in Chinese handwriting and also several prior work to solve these problems. A new segmentation method is proposed, which is applicable to both on-line and off-line systems for free-format handwritten Chinese character sentences. This method performs basic segmentation and fine segmentation based on the varying spacing thresholds and the minimum variance criteria. The five most probable ways of segmentation are derived from this stage and all the possible segments are extracted and recognized. A lattice is created from all the segments and searched using a viterbi based algorithm to find the most likely character sequence. The algorithm presented in this paper provides large flexibility and robustness to handle free-format continuous Chinese handwriting and is a promising solution for a natural and fast Chinese pen input system. The character accuracy is 85.0% for on-line and 77.4% for the off-line test data.

The properties of magnetic white dwarfs are computed for an equation of state which describes white dwarf matter in terms of a regular crystal lattice of atomic nuclei at zero temperature, immersed in a totally magnetized electron gas. The minimum critical densities at which electron capture reactions and possibly pycnonuclear fusion reactions occur inside of rotating white dwarfs are studied for different magnetic fields and stellar rotation rates. Moreover we calculate the mass-radius relationships of magnetic white dwarfs for magnetic fields ranging from zero up to 10¹³ Gauss and rotational stellar frequencies between zero and the Kepler frequency, which sets an absolute limit on rapid rotation. Our results show that the presence of strong magnetic fields in white dwarfs decreases the value of the critical density for the onset of electron capture and of pycnonuclear reactions. We also find that rotating magnetized white dwarfs may be up to one hundred times less dense than ordinary white dwarfs, depending on their rate of rotation.

We report on the storage and manipulation of hundreds of mesoscopic ensembles of ultracold ⁸⁷Rb atoms in a vast two-dimensional array of magnetic microtraps, defined lithographically in a permanently magnetized film. The atom numbers typically range from tens to hundreds of atoms per site. The traps are optically resolved using absorption imaging and individually addressed using a focused probe laser. We shift the entire array, without heating, along the surface by rotating an external bias field. We evaporatively cool the atoms to the critical temperature for quantum degeneracy. At the lowest temperatures, density dependent loss allows small and well defined numbers of atoms to be prepared in each microtrap. This microtrap array is a promising novel platform for quantum information processing, where hyperfine ground states act as qubit states, and Rydberg excitation may orchestrate interaction between neighbouring sites.

We present selected new results on chiral symmetry breaking in nearly conformal gauge theories with fermions in the fundamental representation of the SU(3) color gauge group. We found chiral symmetry breaking (χ^SB) for all flavors between N_f = 4 and N_f = 12 with most of the results discussed here for N_f = 4, 8, 12 as we approach the conformal window. To identify χ^SB we apply several methods which include, within the framework of chiral perturbation theory, the analysis of the Goldstone spectrum in the p-regime and the spectrum of the fermion Dirac operator with eigenvalue distributions of random matrix theory in the ε-regime. Chiral condensate enhancement is observed with increasing N_f when the electroweak symmetry breaking scale F is held fixed in technicolor language. Important finite-volume consistency checks from the theoretical understanding of the SU(N_f) rotator spectrum of the δ-regime are discussed. We also consider these gauge theories at N_f = 16 inside the conformal window. Our work on the running coupling is presented separately.

New strongly-interacting gauge theories are possible Beyond Standard Model candidates. It is essential to determine if a given non-abelian gauge theory is QCD-like or conformal. One way is to calculate the running of the renormalized gauge coupling. We describe a method to do this using Wilson loop ratios measured in lattice simulations. We demonstrate this in SU(3) pure gauge theory and show initial results for dynamical fermions in the fundamental representation.

We study transverse momentum dependent parton distribution functions (TMDs) with non-local operators in lattice QCD, using MILC/LHPC lattices. Results obtained with a simplified operator geometry show visible dipole deformations of spin-dependent quark momentum densities. We discuss the basic concepts of the method, including renormalization of the gauge link, and an extension to a more elaborate operator geometry that would allow us to analyze process-dependent TMDs such as the Sivers-function.

Though the electrostatic, ionic, van der Waals, Lennard-Jones, hydrogen bonding, and other forces play an important role in the energy function minimized at a protein's native state, it is widely believed that the hydrophobic force is the dominant term in protein folding. Here we attempt to quantify the extent to which the hydrophobic force determines the positions of the backbone α-carbon atoms in PDB data, by applying Monte-carlo and genetic algorithms to determine the predicted conformation with minimum energy, where only the hydrophobic force is considered (i.e. Dill's HP-model, and refinements using Woese's polar requirement). This is done by computing the root mean square deviation between the normalized distance matrix D = (d_i,j) (d_i,j is normalized Euclidean distance between residues r_i and r_j) for PDB data with that obtained from the output of our algorithms. Our program was run on the database of ancient conserved regions drawn from GenBank 101 generously supplied by W. Gilbert's lab ^{1, 2}, as well as medium-sized proteins (E. Coli RecA, 2reb, Erythrocruorin, 1eca, and Actinidin 2act). The root mean square deviation (RMSD) between distance matrices derived from the PDB data and from our program output is quite small, and by comparison with RMSD between PDB data and random coils, allows a quantification of the hydrophobic force contribution. A preliminary version of this paper appeared at GCB'99 (http://bibiserv.techfak.uni-bielefeld.de/gcb99/).

We study the possibility that the scalar mesons exist as tetraquark states. The energy shift of two pions as a function of spatial lattice size makes a distinction between bound states and scattering states. We perform a calculation of two pion scattering amplitudes, using quenched N_f = 2 Wilson fermion and plaquette/Iwasaki gauge actions. We obtain the indication that the tetraquark states in the case of the I = 0, 2 channels are no bound states. And we find that the bound energy depends strongly on m_π rather than m_π/m_ρ.

In this paper we apply a method to extend n-dimensional lattice-valued fuzzy negations by preserving the largest possible number of properties of these negations which are invariants under homomorphisms. Further, we also prove some related results and properties.