Prior Reduced Fill-In in Solving Equations in Interior Point Algorithms

The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric form (i.e., the constraints are Ax b, x > 0 ), then there are two mathematically equivalent forms of the search direction, involving different matrices. One form necessitates factoring a matrix whose sparsity pattern has the same form as that of (A AT). The other form necessitates factoring a matrix whose sparsity pattern has the same form as that of (ATA). Depending on the structure of the matrix A, one of these two forms may produce significantly less fill-in than the other. Furthermore, by analyzing the fill-in of both forms prior to starting the iterative phase of the algorithm, the form with the least fill-in can be computed and used throughout the algorithm. Finally, this methodology can be applied to linear programs that are not in symmetric form, that contain both equality and inequality constraints

Quadratic Electro-Optic Effects in Bacteriorhodopsin: Measurement of γ(-ω;0,0,ω) in Dried Gelatin Thin Films

Quadratic electro-optic effects (dc or low frequency Kerr effect) of bacteriorhodopsin dispersed in dried gelatin thin films are examined in the near resonance region at three wavelengths: 633, 647, and 676 nm. The films show relatively large quadratic electro-optic effects compared to other molecular dispersed systems. The purple membrane is fixed within the polymerized gelatin matrix, and we show that the electronic contribution to γ dominates over possible orientational contributions. At 676 nm. the quadratic electro-optic coefficient s1133( - ω;0,0,ω) is 6.7 × 10-20 m2/V2 and the third order nonlinear susceptibility X1133(3)(-ω;0,0,ω) is 7.0 × 10-13 cm4 statCoulomb-2, with both values obtained for a protein concentration of 6.9 × 1018 cm-3. The orientationally averaged second molecular hyperpolarizability 〈γ(-ω;0.0,ω)〉 determined from the quadratic electro-optic coefficients at 676 nm assuming an Onsager ellipsoidal local field factor is (10.8±5.1)×10-32 cm7 statCoulomb-2 [(1.34±0.63) × 10-56 F3 m4C-2]. The 〈γ(- ω;0,0,ω)〉 value increases roughly tenfold when the probe wavelength is decreased to 633 nm. The behavior of γ(-ω;0,0,ω), when fit to a two-state model, predicts that γ(- ω;0,0,ω) is strongly enhanced via type III processes. Thus, the magnitude of γ(-ω;0,0,ω) is dominated by a term (Δμ210×μ210)/(ω10-ω)3, where Δμ10 is the change in dipole moment, μ10 is the transition moment, and ω10 is the transition energy of the lowest-lying allowed 1Bw*+-like π,π* state. We calculate that Δμ10 is 12.8±1.2 D, in good agreement with previous Stark and two-photon experimental values. Time-dependent Hartree-Fock methods based on the MNDO Hamiltonian yield reasonable agreement with experiment, underestimating γ(-ω;0,0,ω) by factors of only 2-4, with the error increasing as the frequency approaches resonance

Prior reduced fill-in in solving equations in interior point algorithms

The efficiency of interior-point algorithms for linear programming is related to the effort required to factorize the matrix used to solve for the search direction at each iteration. When the linear program is in symmetric form (i.e., the constraints are Ax b, x >= 0), then there are two mathematically equivalent forms of the search direction, involving different matrices. One form necessitates factoring a matrix whose sparsity pattern has the same form as that of (AAT). The other form necessitates factoring a matrix whose sparsity pattern has the same form as that of (ATA). Depending on the structure of the matrix A, one of these two forms may produce significantly less fill-in than the other. Furthermore, by analyzing the fill-in of both forms prior to starting the iterative phase of the algorithm, the form with the least fill-in can be computed and used throughout the algorithm. Finally, this methodology can be applied to linear programs that are not in symmetric form, that contain both equality and inequality constraints.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30071/1/0000441.pd

Nonlinear Optical Properties of Bacteriorhodopsin: Assignment of the Third-order Polarizability Based on Two-photon Absorption Spectroscopy

The third-order (pi) -electron polarizability, (gamma) (pi), of bacteriorhodopsin in the 0.0 - 1.2 eV optical region is assigned based on an analysis of the experimental two-photon properties of the low-lying singlet state manifold. The following selected values of (gamma) (pi) (units of 10-36 esu) are observed: (gamma) (0;0,0,0) equals 2482 +/- 327; (gamma) (-3(omega) ;(omega) ,(omega) ,(omega) ) equals 2976 +/- 385 ((omega) equals 0.25 eV), 5867 +/- 704 ((omega) = 0.5 eV), 14863 +/- 1614 ((omega) = 0.66 eV), 15817 +/- 2314 ((omega) equals 1.0 eV), 10755 +/- 1733 ((omega) equals 1.17 eV). The third-order polarizability of this protein which contains an all-trans retinyl protonated Schiff base chromophore with six double bonds, is comparable to that observed for much longer chain polyenes (for example, dodecapreno (beta) -carotene, a polyene with 19 double bonds, exhibits a third-order (pi) -electron polarizability at 0.66 eV of 17000 +/- 6000 X 10-36 esu. The authors attribute the enhanced third-order nonlinearity associated with the protein bound chromophore of bacteriorhodopsin to two mutually enhancing origins. First, the chromophore is protonated, and the resultant charge reorganization enhances the polarizability in a fashion that is similar to that known to occur for polaronic and bipolaronic chromophores. It is estimated that protonation generates a five-fold enhancement in (gamma) (pi). Second, the protein bound chromophore exhibits a large change in dipole moment upon excitation into the lowest-lying, strongly-allowed 1B*u+-like state ((Delta) (mu) = 13.5 D). The latter property is responsible for a Type III enhancement of the third-order polarizability, and yields at least a 20-fold increase in (gamma) (pi)

Origins of the Quantum Efficiency Duality In the Primary Photochemical Event of Bacteriorhodopsin

Experimental and theoretical evidence is presented which suggests that two distinct forms of light-adapted bacteriorhodopsin may exist. We propose that these two forms have characteristic photocycles with significantly different primary quantum yields. INDO-PSDCI molecular orbital procedures and semiempirical molecular dynamics simulations predict that one ground state geometry of bR undergoes photochemistry with a primary quantum yield, Φ1, of ~ 0.27, and that a second ground state geometry, with a slightly displaced counterion, yields Φ1 ~ 0.74. This theoretical model is supported by the observation that literature measurements of Φ1 tend to fall into one of two categories- those that observe Φ1 ~ 0.33 or below, and those that observe Φ1 ~ 0.6 or above. The observation that all photostationary state measurements of the primary quantum yield give values near 0.3, and all direct measurements of the quantum yield result in values near 0.6, suggests that photochemical back reactions may select the bacteriorhodopsin conformation with the lower quantum yield. The two photocycles may have developed as a natural biological requirement that the bacterium have the capacity to adjust the efficiency of the photocycle in relation to the intensity of light and/or membrane electrochemical gradient

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

A Theoretical Investigation of the One– and Two–photon Properties of Porphyrins

The one‐ and two‐photon properties of free base porphin, free base porphin dianion, and the 2,4‐substituted diformyl and divinyl analogs of these molecules are studied using a semiempirical SCF‐MO formalism (CNDO‐π‐SCF‐MO‐PSDCI) including extensive single and double configuration interaction. Strongly two‐photon allowed states are predicted to lie in the Soret region as well as in the region between the Soret and visible bands. A number of the two‐photon allowed states in the Soret region are predicted to have two‐photon absorptivities exceeding 100×10−50 cm4 s molecule−1 photon−1. The calculations indicate that the visible (Q) states are well characterized by the four orbital model, whereas the Soret (B) states contain significant contributions from configurations comprised of other orbitals. The inclusion of extensive double configuration interaction significantly reduces the Soret‐visible (B–Q) splitting, increases the Qx–Qy splitting, and yields calculated oscillator strengths for the Qbands in better agreement with experiment than values calculated using single CI alone. The effects of conjugation into the porphyrin macrocycle are predicted to be more significant than inductive effects on macrocycle π orbitals due to substituent polarity. The 〈Qx‖r‖S0〉 and 〈Qy‖r‖S0〉 transition moment vectors are predicted to lie approximately through adjacent pyrrole rings in 2‐ and 4‐monoformyl free base porphin dianions and approximately through adjacent methine bridges in 2,4‐diformyl free base porphin dianion

Excited states of linear polyenes

We present density matrix renormalisation group calculations of the Pariser- Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (3Bu+) and even- parity singlet (2Ag+) states have a 2-soliton and 4-soliton form, respectively, both with large relaxation energies. The dipole-allowed (1Bu-) state forms an exciton-polaron and has a very small relaxation energy. The relaxed energy of the 2Ag+ state lies below that of the 1Bu- state. We observe an attraction between the soliton-antisoliton pairs in the 2Ag+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepencies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. The electronic interactions play the key role in determining the ground state dimerisation and the excited state transition energies.Comment: LaTeX, 15 pages, 9 figure

Kentucky UST Field Manual

This study was undertaken to address the removal and closure of defective petroleum underground storage tanks in Kentucky. Goals for the study included: To address standards for levels of contamination requiring corrective action consistent with accepted scientific and technical principles. To recommend a matrix or scoring system to be used for (a) ranking sites as to actual or potential harm to human health and the environment caused by release of petroleum from a petroleum storage tank, and (2) establishing standards and procedures for corrective action that shall adequately protect human health and the environment. To address all compounds individually and collectively known as petroleum. To produce a report that shall be scientifically defensible

Status Report: Identification of Appropriate Standards for Corrective Action for a Release from Petroleum Underground Storage Tanks, Volume 1

This study was undertaken to address the removal and closure of defective petroleum underground storage tanks in Kentucky: To address standards for levels of contamination requiring corrective action consistent with accepted scientific and technical principles. To recommend a matrix or scoring system to be used for (a) ranking sites as to actual or potential harm to human health and the environment caused by a release of petroleum from a petroleum storage tank, and (b) establishing standards and procedures for corrective action that shall adequately protect human health and the environment. To address all compounds individually and collectively known as petroleum. To produce a report that shall be scientifically defensible