The one-warehouse multi-retailer problem: reformulation, classification, and computational results

We consider the one-warehouse multi-retailer problem where a warehouse replenishes multiple retailers with deterministic dynamic demands over a horizon. The problem is to determine when and how much to order to the warehouse and retailers such that the total system-wide costs are minimized. We propose a new (combined transportation and shortest path based) integer programming reformulation for the problem in addition to the echelon stock and transportation based formulations in the literature. We analyze the strength of the LP relaxations of three formulations and show that the new formulation is stronger than others. We also show that the new and transportation based formulations are equivalent for the joint replenishment problem, where the warehouse is a crossdocking facility. We extend all formulations to the case with initial inventory at the warehouse and reveal the relation among their LP relaxations. We present our computational experiments with all formulations over a set of randomly generated test instances.     

Exploring the trade-off between generalization and empirical errors in a one-norm SVM

We propose a one-norm support vector machine (SVM) formulation as an alternative to the well-known formulation that uses parameter C in order to balance the two inherent objective functions of the problem. Our formulation is motivated by the ?-constraint approach that is used in bicriteria optimization and we propose expressing the objective of minimizing total empirical error as a constraint with a parametric right-hand-side. Using dual variables we show equivalence of this formulation to the one with the trade-off parameter. We propose an algorithm that enumerates the entire efficient frontier by systematically changing the right-hand-side parameter. We discuss the results of a detailed computational analysis that portrays the structure of the efficient frontier as well as the computational burden associated with finding it. Our results indicate that the computational effort for obtaining the efficient frontier grows linearly in problem size, and the benefit in terms of classifier performance is almost always substantial when compared to a single run of the corresponding SVM. In addition, both the run time and accuracy compare favorably to other methods that search part or all of the regularization path of SVM.     

Exact diffraction calculation from fields specified over arbitrary curved surfaces

Calculation of the scalar diffraction field over the entire space from a given field over a surface is an important problem in computer generated holography. A straightforward approach to compute the diffraction field from field samples given on a surface is to superpose the emanated fields from each such sample. In this approach, possible mutual interactions between the fields at these samples are omitted and the calculated field may be significantly in error. In the proposed diffraction calculation algorithm, mutual interactions are taken into consideration, and thus the exact diffraction field can be calculated. The algorithm is based on posing the problem as the inverse of a problem whose formulation is straightforward. The problem is then solved by a signal decomposition approach. The computational cost of the proposed method is high, but it yields the exact scalar diffraction field over the entire space from the data on a surface.     

Magnetic field orientation dependence of flux pinning in (Gd,Y)Ba2Cu3O7−x coated conductor with tilted lattice and nanostructures

The dependence of the critical current density (J_c) on the orientation of an applied magnetic field was studied for a prototype (Gd,Y)Ba₂Cu₃O_7?x (GdYBCO) coated conductor fabricated by MOCVD on an IBAD-MgO template. Additional rare-earth cations (Y and Gd) and Zr were incorporated into the superconducting film to form (Y,Gd)₂O₃ and BaZrO₃ nanoparticles extended nearly parallel to the a–b planes and to the c-axis, respectively, to enhance the flux pinning. In-field measurement of J_c was carried out with electrical current flowing either along or perpendicular to the longitudinal axis of the tape, while a maximum Lorentz force configuration was always maintained. Details in the angular dependence of J_c were related to the unique structure of the film, specifically the tilt in the GdYBCO lattice and the tilts in the extended (Y,Gd)₂O₃ and BaZrO3 nanoparticles. XRD and TEM were used to study the structure of the coated conductor. The effect of the misalignment between the external field H and the internal field B on the angular dependence of J_c is discussed.     

Dielectrophoretic manipulation of particle mixtures employing asymmetric insulating posts

A novel scheme for particle separation with insulator‐based dielectrophoresis (iDEP) was developed. This technique offers the capability for an inverted order in particle elution, where larger particles leave the system before smaller particles. Asymmetrically shaped insulating posts, coupled with direct current (DC) biased low‐frequency alternating current (AC) electric potentials, were used to successfully separate a mixture of 500 nm and 1 μm polystyrene particles (size difference of 0.5 μm in diameter). In this separation, the 1 μm particles were eluted first, demonstrating the discriminatory potential of this methodology. To extend this technique to biological samples, a mixture containing Saccharomyces cerevisiae cells (6.3 μm) and 2 μm polystyrene particles was also separated, with the cells being eluted first. The asymmetric posts featured a shorter sharp half and a longer blunt half; this produced an asymmetry in the forces exerted on the particles. The negative DC offset produced a net displacement of the smaller particles toward the upstream direction, while the post asymmetry produced a net displacement of the larger particles toward the downstream direction. This new iDEP approach provides a setup where larger particles are quickly concentrated at the outlet of the post array and can be released first when in a mixture with smaller particles. This new scheme offers an extra set of parameters (alternating current amplitude, DC offset, post asymmetry, and shape) that can be manipulated to obtain a desired separation. This asymmetric post iDEP technique has potential for separations where it is important to quickly elute and enrich larger and more fragile cells in biological samples.     

Fuzzy logic based device to implement a single CAD model for a laser diode based on characteristic quantities

In this study, a single modelling approach based on fuzzy logic (FL) device is designed for a quantum-well (QW) laser diode to obtain the characteristic quantities and their dependences on wavelength and injection currents. The fuzzy rules are compiled using the input variables which are namely the wavelength and the injection currents, while the output parameters are the modal gain difference, the effective refractive index difference and alpha (α) parameter (linewidth enhancement factor). The suggested approach provides fast and reliable predictions which can prevent the engineers from rigorous experiments/calculations. The FL device provides the predictions of modal gain difference, effective refractive index difference and alpha parameter against the wavelength and the injection currents within the accuracy level of 90–99.9%.     

Improved acoustic signals discrimination using fractional Fourier transform based phase-space representations

In this communication we propose performing two-dimensional correlation operation between phase-space representations based on the fractional Fourier transform, instead of correlating the signals themselves. A numerical examples clearly indicates superior discrimination performance.     

Quantification of pH gradients and implications in insulator-based dielectrophoresis of biomolecules

Direct current (DC) insulator-based dielectrophoretic (iDEP) microdevices have the potential to replace traditional alternating current dielectrophoretic devices for many cellular and biomolecular separation applications. The use of large DC fields suggest that electrode reactions and ion transport mechanisms can become important and impact ion distributions in the nanoliters of fluid in iDEP microchannels. This work tracked natural pH gradient formation in a 100?μm wide, 1?cm-long microchannel under applicable iDEP protein manipulation conditions. Using fluorescence microscopy with the pH-sensitive dye FITC Isomer I and the pH-insensitive dye TRITC as a reference, pH was observed to drop drastically in the microchannels within 1?min in a 3000?V/cm electric field; pH drops were observed in the range of 6-10 min within a 100?V/cm electric field and varied based on the buffer conductivity. To address concerns of dye transport impacting intensity data, electrokinetic mobilities of FITC were carefully examined and found to be (i) toward the anode and (ii) 1 to 2 orders of magnitude smaller than H? transport which is responsible for pH drops from the anode toward the cathode. COMSOL simulations of ion transport showed qualitative agreement with experimental results. The results indicate that pH changes are severe enough and rapid enough to influence the net charge of a protein or cause aggregation during iDEP experiments. The results also elucidate reasonable time periods over which the phosphate buffering capacity can counter increases in H? and OH? for unperturbed iDEP manipulations.     

Fundamental structure of Fresnel diffraction: natural sampling grid and the fractional Fourier transform

Fresnel integrals corresponding to different distances can be interpreted as scaled fractional Fourier transformations observed on spherical reference surfaces. We show that by judiciously choosing sample points on these curved reference surfaces, it is possible to represent the diffracted signals in a nonredundant manner. The change in sample spacing with distance reflects the structure of Fresnel diffraction. This sampling grid also provides a simple and robust basis for accurate and efficient computation, which naturally handles the challenges of sampling chirplike kernels.     

Design and implementation of fuzzy logic based automatic gain controller for EDFAs

In this study, the design and implementation of a fuzzy logic (FL) based automatic gain controller card (AGC) is performed in order to control the pump laser current with respect to signal power and signal wavelength. The FL-AGC card consists of an amplifier, an analogue to digital converter (ADC), a digital to analogue converter (DAC), and a FL based software that is embedded to a microcontroller. With this configuration, gain flattening at the output of the erbium doped fibre amplifier (EDFA) along C band is achieved. In this way, ergonomically designed FL-AGC card can be easily matched with EDFAs and can be applicable to optical system applications.