A mixed integer program for partitioning graphs with supply and demand emphasizing sparse graphs

The focus of this paper is on finding optimal solutions for the problem of maximal partitioning of graphs with supply and demand (MPGSD) for arbitrary graphs. A mixed integer programming (MIP) model is developed for the problem of interest. We also present some specific constraints that can be used in the case of tree graphs. With the goal of lowering the computational cost for solving the underlying model, a preprocessing stage is included. It is used to produce additional constraints based on shortest paths in the graph. With the aim of exploring the effectiveness of the proposed MIP formulation we have performed computational experiments for general graphs and trees. The main objective of the tests is to observe the properties and sizes of supply/demand graphs that can be solved to optimality using the proposed approach in reasonable time. The conducted computational experiments have shown that the proposed method is especially suitable for sparse graphs.     

MCNP simulation of the dose distribution in liver cancer treatment for BNC therapy

The Boron Neutron Capture Therapy (BNCT) is based on selective uptake of boron in tumour tissue compared to the surrounding normal tissue. Infusion of compounds with boron is followed by irradiation with neutrons. Neutron capture on ¹⁰B, which gives rise to an alpha particle and recoiled ⁷Li ion, enables the therapeutic dose to be delivered to tumour tissue while healthy tissue can be spared. Here, therapeutic abilities of BNCT were studied for possible treatment of liver cancer using thermal and epithermal neutron beam. For neutron transport MCNP software was used and doses in organs of interest in ORNL phantom were evaluated. Phantom organs were filled with voxels in order to obtain depth-dose distributions in them. The result suggests that BNCT using an epithermal neutron beam could be applied for liver cancer treatment.     

Unimolecular and bimolecular transfer of N-substituents from pyridinium cations: Evidence for a clear mechanistic changeover

$\text{N}$-Substituents in 2, 4, 6-triphenylpyridiniums are transferred to piperidine, morpholine and pyridine by unimolecular and/or bimolecular processes in chlorobenzene solution. These processes are quite distinct and afford no evidence for a mechanism intermediate between S_N1 and S_N2.     

Gaussian-induced rotation in periodic photonic lattices

We numerically investigate time-dependent rotation of counterpropagating mutually incoherent self-trapped Gaussian beams in periodic optically induced fixed photonic lattices. We demonstrate the relation between such rotation and less confined discrete solitonic solutions.     

Assessment of image resolution improvement by phase-sensitive optical parametric amplification

Classical information theory can be used to quantify the resolution performance of optical imaging systems. When an optical parametric amplifier (OPA) operated as a phase-sensitive amplifier (PSA) in the transverse spatial domain is used for point source imaging, the angular resolution improvement can approach the de Broglie resolution (i.e. Heisenberg limit). In this paper, classical information theory is employed to quantify the signal-to-noise ratio (SNR) improvement for both an ideal and a realistic multimode PSA applied to the problem of sub-Rayleigh imaging. When only considering the noise originating from the detector, the SNR improvement is found to scale quadratically as a function of the PSA gain, in the limit of noise power comparable to signal power. Differences in performance of an ideal PSA and a realistic PSA are discussed.     

Reusable components in decision tree induction algorithms

We propose a generic decision tree framework that supports reusable components design. The proposed generic decision tree framework consists of several sub-problems which were recognized by analyzing well-known decision tree induction algorithms, namely ID3, C4.5, CART, CHAID, QUEST, GUIDE, CRUISE, and CTREE. We identified reusable components in these algorithms as well as in several of their partial improvements that can be used as solutions for sub-problems in the generic decision tree framework. The identified components can now be used outside the algorithm they originate from. Combining reusable components allows the replication of original algorithms, their modification but also the creation of new decision tree induction algorithms. Every original algorithm can outperform other algorithms under specific conditions but can also perform poorly when these conditions change. Reusable components allow exchanging of solutions from various algorithms and fast design of new algorithms. We offer a generic framework for component-based algorithms design that enhances understanding, testing and usability of decision tree algorithm parts.     

X-ray diffraction study of the composition and strain fields in buried SiGe islands

We report on studies of strain and composition of two-dimensionally ordered SiGe islands grown by molecular beam epitaxy using high resolution x-ray diffraction. To ensure a small size distribution of the islands, pit-patterned (001) Si wafers were used as substrates. The Si wafers were patterned by optical lithography and reactive ion etching. The pits for island growth are ordered in regular 2D arrays with periods ranging from 500 to 1000 nm along two orthogonal 〈110〉 directions. After the growth of a Si buffer layer, 5 to 9 monolayers of Ge are deposited, leading to the formation of islands with either dome- or barn shape, depending on the number of monolayers deposited. The Si capping of the islands is performed at low temperatures (300^○C) to avoid intermixing and thus strain relaxation. Information on the surface morphology obtained by atomic force microscopy (AFM) was used to set up models for three-dimensional Finite Element Method (FEM) simulations of the islands including the patterned Si substrate. In the model, special attention was given to the non uniform distribution of the Ge content within the islands. The FEM results served as an input for calculating the diffracted x-ray intensities using kinematical scattering theory. Reciprocal space maps around the vicinity of symmetric (004) and asymmetric (113) and (224) Bragg peaks were recorded in coplanar geometry. Simulating different germanium gradients leads to altered scattered intensity distribution and consequently information on this quantity is obtained for both dome- and barn-shaped islands as well as on the strain fields.     

Phase-sensitive multimodal optical parametric amplifier for beam angle amplification

The single-mode phase-sensitive parametric amplifier has been proposed as an approximation to an ideal quantum phase amplifier. We demonstrate numerically that a real, multimode parametric amplifier operated in the spatial domain, and realized by the use of three-wave mixing in nonlinear media, behaves similar to a single-mode quantum phase amplifier, but exhibits smaller phase gain. Constraints for operation in this regime are found to be consistent with small departures of phase from the ideal deamplification condition.     

Jet spaces in modern Hamiltonian biomechanics

In this paper we propose the time-dependent Hamiltonian form of human biomechanics, as a sequel to our previous work in time-dependent Lagrangian biomechanics [1]. This is the time-dependent generalization of an ‘ordinary’ autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. In our view, this time-dependent energetic approach is much more realistic than the autonomous one. Starting with the Covariant Force Law, we first develop autonomous Hamiltonian biomechanics. Then we extend it using a powerful geometrical machinery consisting of fibre bundles and jet manifolds associated to the biomechanical configuration manifold. We derive time-dependent, dissipative, Hamiltonian equations and the fitness evolution equation for the general time-dependent human biomechanical system.     

Efficient double-clad Yb3+-doped silica fibre laser pumped by an unfocused diode laser

A moderate output power Yb³⁺-doped double-clad fibre laser pumped by an unfocused diode laser is reported. This pumping configuration omits micro positioned lenses used in fibre coupled laser diodes, thus making the system significantly less complex and more robust. The maximum launch efficiency was ～80% and the maximum output power was >5 W with a measured FWHM of 18 pm.