Efficient preprocessing for VLSI optimization problems

Advances in technology for the manufacturing of integrated circuits have resulted in extremely large, and time consuming, problems on how to lay out components for optimal circuit performance. These problems can be written as mixed integer programs which are easily relaxed to linear programs with a very high number of variables and constraints. The relaxed programs can often be solved by applying state-of-the-art linear programming software, however these solutions come at the expense of long solution time. In this paper we show that, by considering the structure inherent in VLSI problems, one can specialize classical preprocessing algorithms to take into account the standard form of the constraint matrix for VLSI problems, thereby achieving improved preprocessing results with relatively little effort. We provide analysis showing our preprocessing techniques are accurate and provide some numerical testing demonstrating the increased efficiency. The numerical tests also demonstrate that using our preprocessing in conjunction with internal preprocessing methods that come with many linear program solvers, can improve the overall performance of the linear program solver and its preprocessor.     

Fekete-like polynomials

In 2001, Borwein, Choi, and Yazdani looked at an extremal property of a class of polynomial with ±1 coefficients. Their key result was:

Theorem. (See Borwein, Choi, Yazdani, 2001.) Letf(z)=±z±z²±?±zN−1, and ζ a primitive Nth root of unity. If N is an odd positive integer then

     

Evaluating Mathematics Achievement of Middle School Students in a Looping Environment

Looping, a school structure where students remain with one group of teachers for two or more school years, is used by middle schools to meet the diverse needs of young adolescents. However, little research exists on how looping effects the academic performance of students. This study was designed to determine if looping influenced middle school students' mathematical academic achievement. Student scores on the Mississippi Curriculum Test (MCT) were compared between sixth and eighth grade years for 69 students who looped during the seventh and eighth grades with a group of 137 students who did not loop. Looping students achieved statistically significantly greater growth on the MCT than their nonlooping counterparts between sixth and eighth grades. Further, the data were disaggregated by gender, ethnicity, and socioeconomic status. Findings indicate that looping may academically reengage students during the middle school years. Advantages and disadvantages of looping at the middle grades are discussed.     

Quantitative Measurements of Individual Polycyclic Aromatic Hydrocarbons in a Mixture by Coherent Anti-Stokes Raman Spectrometry

Abstract

Coherent anti-Stokes Raman spectroscopy (CARS) was used to obtain Raman spectra of selected polycyclic aromatic hydrocarbons (PAHs) composed of between three and seven fused rings when the compounds were pumped in the resonance and pre-resonance regions, a simple mixture of three PAHs could be optically separated through the wavelength selectivity of the resonant enhancement process. The spectrum from a component in the mixture and the spectrum of each pure component showed no significant differences when pumped at the same wavelength. Finally, lineshape analysis performed on the CARS spectra facilitated comparisons between classes of compounds and for quantitative purposes.     

Models and algorithms to improve earthwork operations in road design using mixed integer linear programming

In road construction, earthwork operations account for about 25% of the construction costs. Existing linear programming models for earthwork optimization are designed to minimize the hauling costs and to balance the earth across the construction site. However, these models do not consider the removal of physical blocks that may influence the earthwork process. As such, current models may result in inaccurate estimates of optimal earthwork costs, leading to poor choices in road design. In this research, we extend the classical linear program model of earthwork operations to a mixed integer linear program model that accounts for blocks. We examine the economic impact of incorporating blocks via mixed integer linear programming, and find significant savings for most road designs in our test-set. However, the resulting model is considerably harder to solve than the original linear program. Based on structural observations, we introduce a set of algorithms that theoretically reduce the solving time of the model. We confirm this reduction in solve time with numerical experiments.     

The set of values of b for which there exist block designs with b blocks

Let B denote the set of values of b for which there exists a block design with b blocks and for k3, let B_k denote the subset of B determined by the designs with block size k. We present some information about B and the sets B_k. In particular, we discuss, for certain integers h, the question as to whether there exist integers k and k^′ such that the equation b^′=b+h has infinitely many solutions b,b^′ satisfying bB_k and b^′B_k^′. The study is restricted to the case λ=1.     

Improved measurement of the positive-muon lifetime and determination of the Fermi constant

The mean life of the positive muon has been measured to a precision of 11 ppm using a low-energy, pulsed muon beam stopped in a ferromagnetic target, which was surrounded by a scintillator detector array. The result, tau(micro)=2.197 013(24) micros, is in excellent agreement with the previous world average. The new world average tau(micro)=2.197 019(21) micros determines the Fermi constant G(F)=1.166 371(6)x10(-5) GeV-2 (5 ppm). Additionally, the precision measurement of the positive-muon lifetime is needed to determine the nucleon pseudoscalar coupling g(P).     

Curvature driven transport of mouse macrophages in a pulsating magnetic garnet film ratchet

Magnetic fields varying on the colloidal length scale are used for the directed transport of magnetically labeled biological cells. The transport is achieved by using the ratchet effect which relies on an asymmetric, symmetry broken periodic potential where nonequilibrium fluctuations or oscillations generate a net cell current. Ferrofluid ingested mouse macrophages were placed on a magnetic garnet film with alternating stripe domain patterns, and a pulsating magnetic potential is provided by superposing an oscillating magnetic field normal to the film. The symmetry of the resulting periodic stripe potential is broken locally by the curvature of the stripes. We show, both experimentally and theoretically, the curvature of such stripes required for inducing directed transport of the macrophages in the ratchet. This may be useful for microfluidic devices such as a digital colloidal shift register for magnetically labeled biological cells.     

Accurate predictions of crystal densities using quantum mechanical molecular volumes

A quantum mechanically based procedure for estimation of crystal densities of neutral and ionic crystals is presented. In this method, volumes within 0.001 electrons/bohr3 isosurfaces of electron density for the constituent isolated neutral and ionic molecules are calculated to define the molecular volume or formula unit volumes used in predicting the crystal density. The B3LYP density functional theory in conjunction with the 6-31G** basis set were employed to generate the electron densities. The suitability of this method of crystal density prediction was assessed by subjecting a large number (289) of molecular and ionic crystals to the procedure and comparing results with experimental information. The results indicate that, for neutral molecular crystals, the root-mean-square (rms) deviation from experiment is within 4%, whereas the rms deviation is somewhat larger for the 71 ionic crystals evaluated (within 5%).