How does aromaticity rule the thermodynamic stability of hydroporphyrins?

Several measures of aromaticity including energetic, magnetic, and electron density criteria are employed to show how aromatic stabilization can explain the stability sequence of hydroporphyrins, ranging from porphin to octahydroporphin, and their preferred hydrogenation paths. The methods employed involve topological resonance energies and their circuit energy effects, bond resonance energies, multicenter delocalization indices, ring current maps, magnetic susceptibilities, and nuclear-independent chemical shifts. To compare the information obtained by the different methods, the results have been put in the same scale by using recently proposed approaches. It is found that all of them provide essentially the same information and lead to similar conclusions. Also, hydrogenation energies along different hydrogenation paths connecting porphin with octahydroporphin have been calculated with density functional theory. It is shown by using the methods mentioned above that the relative stability of different hydroporphyrin isomers and the observed inaccessibility of octahydroporphin both synthetically and in nature can be perfectly rationalized in terms of aromaticity

Reducible Configurations and So On: The Final Years of the Four Color Theorem

The Four Color Theorem is in a set of mathematical questions that are very simple to state but amazingly complex to answer. It goes as follows, "given any map, are any more than 4 colors required to color the map in such a way that no two areas which share a border also share a color?"(2). It was thought to be proven by Alfred Kempe for nearly a decade using a unique but unsuccessful process later referred to as Kempe chains. It wasn't until 1913, with George Birkhoff's treatment of reducibility, was true progress from the "proof" of Kempe to be made. From here, Heinrich Heesch explored reducibility with an improvement on the established A, B, and C-reducibilities, finding something algorithmically sound in D-reducibility and his subsequent discharging methods. Then Karl Durre introduced the first, somewhat rudimentary, computer program of D-reducibility. From here the extensive use of the super computers of the era helped seal the fate of the long unfinished theorem, with Wolfgang Haken and Kenneth Appel at the helm. We seek to examine the history of this theorem from the proof of Kempe to the utilization of reducible configurations and discharging methods of Durre and Heesch and into the eventual proof of the theorem itself

Interactive specification of data displays

On-line graphical language for computer data displa

Gate-Level Simulation of Quantum Circuits

While thousands of experimental physicists and chemists are currently trying to build scalable quantum computers, it appears that simulation of quantum computation will be at least as critical as circuit simulation in classical VLSI design. However, since the work of Richard Feynman in the early 1980s little progress was made in practical quantum simulation. Most researchers focused on polynomial-time simulation of restricted types of quantum circuits that fall short of the full power of quantum computation. Simulating quantum computing devices and useful quantum algorithms on classical hardware now requires excessive computational resources, making many important simulation tasks infeasible. In this work we propose a new technique for gate-level simulation of quantum circuits which greatly reduces the difficulty and cost of such simulations. The proposed technique is implemented in a simulation tool called the Quantum Information Decision Diagram (QuIDD) and evaluated by simulating Grover's quantum search algorithm. The back-end of our package, QuIDD Pro, is based on Binary Decision Diagrams, well-known for their ability to efficiently represent many seemingly intractable combinatorial structures. This reliance on a well-established area of research allows us to take advantage of existing software for BDD manipulation and achieve unparalleled empirical results for quantum simulation

An Interactive Graph Theory System

The medium of computer graphics provides a capability for dealing with pictures in man-machine communication. Graph Theory is used to model relationships which are represented by pictures and is therefore an appropriate discipline for the application of an interactive computer graphics system. Previous efforts to solve Graph Theoretic problems by computer have usually involved specialized programs written in a symbolic assembly language or algebraic compiler language. In recent years, graphics equipment with processing power has been commercially available for use as a remote terminal to a large central computer. Although these terminals typically include a small general purpose computer, the potential of using one as programmable subsystem has received little attention. These motivations have led to the design and implementation of an interactive graphics system for solving Graph Theoretic problems. The system operates on an IBM 7040 with a DEC-338 graphics terminal connected by voice-grade telephone line. To provide effective response times, computing power is appropriately divided between the two machines. The remote computer graphics terminal is controlled by a special-purpose executive program. This executive includes an interpreter of a command language oriented towards the control of existence and display of graphs. Several interactive functions such as graph drawing and editing are available to a user through light button and pushbutton selection. These functions which are local to the terminal are programmed in a mixture of the terminal computer\u27s machine language and the interpreted command language. For more significant computational requirements the central computer is used, but response time for interactive operation is then diminished. In order to overcome the speed of the telephone link, the central computer may call upon a program at the terminal as a subroutine. Based on the mathematical terminology used to define graphs, a high level language was developed for the specification of interactive algorithms. A growing library of these algorithms provides routines to aid in the construction and recognition of various types of graphs. Other routines are used for computing certain properties of graphs. Graphs may be transformed by some routines with respect to both connectivity and layout. Any number of graphs my be saved and later restored. A programmer using the terminal as an alphanumeric console may call upon the programming features of the system to develop new interactive algorithms and add them to the library. Programs may also be created for the display terminal, using the central computer for assembly. Examples of system use which are presented include finding a shortest path between any pair of vertices in a weighted directed graph, determining the maximally complete subgraphs of an arbitrary graph, interpreting a graph as a Mealy model of a finite state machine, and laying out a tree for aesthetic presentation

Size-Dependent Scattering Properties of Planetary Regolith Analogs

The physics of the interaction of light with a particulate surface are important to understanding and analyzing remote sensing data from planetary surfaces. An examination of the angular scattering properties of powder samples with known compositions and particle sizes was undertaken to try and further understand the interaction of light with a closely packed particulate medium. The samples range in size from smaller than to larger than the wavelength(l) of incident light (0.05 - 30.09 µm in diameter, l=0.635 µm). Based on a rich history of both theoretical treatments and laboratory measurements, results would be expected to show any dependence of scattering parameters on composition and/or particle size. Scanning electron microscope analyses of the powders were done to characterize particle size, composition, and shape as the major contributors to observed trends in scattering parameters. Models currently in wide use to describe light scattering by planetary regoliths make two important assumptions: (1) the propagation of light through the medium can be described by the equation of radiative transfer, which treats the medium as if it were made up of a continuous distribution of independent scatterers and absorbers; and (2) these fundamental scatterers are the individual particles that make up the medium. Models based on the radiative transfer equation were found to provide good empirical descriptions of the light scattering properties of particulate media composed of complex particles, such as planetary regoliths. However, the results reported here show that changes in scattering parameters predicted by the assumption that the particles are the scatterers are not observed in these samples, and that such models do not accurately predict the transport mean free path, scattering coefficient, or extinction coefficient of such media. In particular, the transport mean free path shows remarkably little dependence on particle size over the size ranges studied, whereas the particle scattering assumption predicts a large variation. Theoretical models based on the second assumption should only be used with great caution when analyzing data taken on particulate surfaces