Graphs of Transportation Polytopes

This paper discusses properties of the graphs of 2-way and 3-way transportation polytopes, in particular, their possible numbers of vertices and their diameters. Our main results include a quadratic bound on the diameter of axial 3-way transportation polytopes and a catalogue of non-degenerate transportation polytopes of small sizes. The catalogue disproves five conjectures about these polyhedra stated in the monograph by Yemelichev et al. (1984). It also allowed us to discover some new results. For example, we prove that the number of vertices of an $m\times n$ transportation polytope is a multiple of the greatest common divisor of $m$ and $n$.Comment: 29 pages, 7 figures. Final version. Improvements to the exposition of several lemmas and the upper bound in Theorem 1.1 is improved by a factor of tw

Similarity classes of 3x3 matrices over a local principal ideal ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr

LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q=0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.Comment: changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 p

Nonlinear Matroid Optimization and Experimental Design

We study the problem of optimizing nonlinear objective functions over matroids presented by oracles or explicitly. Such functions can be interpreted as the balancing of multi-criteria optimization. We provide a combinatorial polynomial time algorithm for arbitrary oracle-presented matroids, that makes repeated use of matroid intersection, and an algebraic algorithm for vectorial matroids. Our work is partly motivated by applications to minimum-aberration model-fitting in experimental design in statistics, which we discuss and demonstrate in detail

A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs

In this paper we generalize N-fold integer programs and two-stage integer programs with N scenarios to N-fold 4-block decomposable integer programs. We show that for fixed blocks but variable N, these integer programs are polynomial-time solvable for any linear objective. Moreover, we present a polynomial-time computable optimality certificate for the case of fixed blocks, variable N and any convex separable objective function. We conclude with two sample applications, stochastic integer programs with second-order dominance constraints and stochastic integer multi-commodity flows, which (for fixed blocks) can be solved in polynomial time in the number of scenarios and commodities and in the binary encoding length of the input data. In the proof of our main theorem we combine several non-trivial constructions from the theory of Graver bases. We are confident that our approach paves the way for further extensions

Modification of LSF-YSZ Composite Cathodes by Atomic Layer Deposition

composite, Solid-Oxide-Fuel-Cell (SOFC) electrodes of La0.8Sr0.2FeO3 (LSF) and yttria-stabilized zirconia (YSZ) were prepared by infiltration methods and then modified by Atomic Layer Deposition (ALD) of ZrO2, La2O3, Fe2O3, or La2O3-Fe2O3 codeposited films of different thicknesses to determine the effect of surface composition on cathode performance. Film growth rates for ALD performed using vacuum procedures at 573 K for Fe2O3 and 523 K for ZrO2 and La2O3 were determined to be 0.024 nm ZrO2/cycle, 0.019 nm La2O3/cycle, and 0.018 nm Fe2O3/cycle. For ZrO2 and Fe2O3, impedance spectra on symmetric cells at 873 K indicated that polarization resistances increased with coverage in a manner suggesting simple blocking of O2 adsorption sites. With La2O3, the polarization resistance decreased with small numbers of ALD cycles before again increasing at higher coverages. When La2O3 and Fe2O3 were co-deposited, the polarization resistances remained low at high film coverages, implying that O2 adsorption sites were formed on the co-deposited films. The implications fo these results for future SOFC electrode development are discussed

Learning intrinsic excitability in medium spiny neurons

We present an unsupervised, local activation-dependent learning rule for intrinsic plasticity (IP) which affects the composition of ion channel conductances for single neurons in a use-dependent way. We use a single-compartment conductance-based model for medium spiny striatal neurons in order to show the effects of parametrization of individual ion channels on the neuronal activation function. We show that parameter changes within the physiological ranges are sufficient to create an ensemble of neurons with significantly different activation functions. We emphasize that the effects of intrinsic neuronal variability on spiking behavior require a distributed mode of synaptic input and can be eliminated by strongly correlated input. We show how variability and adaptivity in ion channel conductances can be utilized to store patterns without an additional contribution by synaptic plasticity (SP). The adaptation of the spike response may result in either "positive" or "negative" pattern learning. However, read-out of stored information depends on a distributed pattern of synaptic activity to let intrinsic variability determine spike response. We briefly discuss the implications of this conditional memory on learning and addiction.Comment: 20 pages, 8 figure

A polynomial oracle-time algorithm for convex integer minimization

In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex $N$-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex $N$-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

Peripheral interface controller-based maximum power point tracking algorithm for photovoltaic DC to DC boost controller

A method of developing a maximum power point tracking (MPPT) algorithm for photovoltaic (PV) utilizing a peripheral interface controller (PIC) is presented in this paper. The efficiency and adequacy of a PV depend on the temperature and the exposed position to the sun. Thus, there is an optimum point at which the operating power is at maximum. The goal is to operate the PV module at this point (MPP). It can be accomplished by using the MPPT algorithm designed with a DC-DC boost converter. The boost converter, MPPT circuit, PIC18F4550 microcontroller and PV panel are the main components used in this design. The current and voltage produced by the solar panel are observed continuously by a closed-loop control system. The microcontroller-based control system adjusts the duty cycle of the converter to extract the maximum power. With a DC input voltage of 15 V, the boost converter is capable of generating an output voltage of an approximately 60 Vdc at a maximum power of 213.42 W with minimum voltage ripple as compared to 84 W without the MPPT. It proved the effectiveness of the developed algorithm