Quantifying Complexity: An Object-Relations Approach to Complex Systems

The best way to model, understand, and quantify the information contained in complex systems is an open question in physics, mathematics, and computer science. The uncertain relationship between entropy and complexity further complicates this question. With ideas drawn from the object-relations theory of psychology, this paper develops an object-relations model of complex systems which generalizes to systems of all types, including mathematical operations, machines, biological organisms, and social structures. The resulting Complex Information Entropy (CIE) equation is a robust method to quantify complexity across various contexts. The paper also describes algorithms to iteratively update and improve approximate solutions to the CIE equation, to recursively infer the composition of complex systems, and to discover the connections among objects across different lengthscales and timescales. Applications are discussed in the fields of engineering design, atomic and molecular physics, chemistry, materials science, neuroscience, psychology, sociology, ecology, economics, and medicine.Comment: arXiv admin note: substantial text overlap with arXiv:2210.0720

Kastor-Traschen Black Holes, Null Geodesics and Conformal Circles

The Kastor-Traschen metric is a time-dependent solution of the Einstein-Maxwell equations with positive cosmological constant $\Lambda$ which can be used to describe an arbitrary number of charged dynamical black holes. In this paper, we consider the null geodesic structure of this solution, in particular, focusing on the projection to the space of orbits of the timelike conformal retraction. It is found that these projected light rays arise as integral curves of a system of third order ordinary differential equations. This system is not uniquely defined, however, and we use the inherent freedom to construct a new system whose integral curves coincide with the projection of distinguished null curves of Kastor-Traschen arising from a magnetic flow. We discuss our results in the one-centre case and demonstrate a link to conformal circles in the limit $\Lambda \rightarrow 0$. We also show how to construct analytic expressions for the projected null geodesics of this metric by exploiting a well-known diffeomorphism between the K-T metric and extremal Reissner-Nordstrom deSitter. We make some remarks about the two-centre solution and demonstrate a link with the one-centre case.Comment: 24 pages, 11 figure

Synthesis and Analysis of Copper Beta-Diketonate Complexes

This research addresses the synthesis and characterization of Cu(II) complexes of silicon-based multidentate β-diketonate ligands. The possible products of the synthesis include (where L represents the coordinated ligand) cube Cu12L8, decahedron Cu24L16, and dodecahedron Cu30L20. This study aims to determine the structure of these discrete molecules, which may have applications in drug delivery, fuel storage, and chemical retention. Different techniques were involved in the characterization of Cu(II) complexes: Electrospray Ionization Time of Flight Mass Spectrometry (ESI-TOF MS), Atomic Force Microscopy (AFM) and Analytical Ultracentrifugation (AUC). In ESI-TOF MS, the exact mass of the molecules was attempted to be determined by experimenting if multiply charged ions could occur with these complexes. Although no multiply charged ion peaks were discovered, different experimental conditions yielded different ESI-TOF MS spectra. Additionally in ESI-TOF MS, peaks having large m/z values containing copper atoms were discovered. In AFM studies, heights of multiple copper complexes were measured to see if the discrete molecules of cube (2 nm), decahedron (3.5-4.5 nm), and dodecahedron (5 nm) could be identified. In creating an AFM histogram, the frequency of heights could be used to determine what kind of complexes were being formed and in what percentage. In the studies conducted, there were common occurrences of the samples at or around the heights of the projected structures (e.g. cube, decahedron, and dodecahedron). Additionally, there was a substantial occurrence of measured heights (i.e. 8 nm and 10 nm) that indicated possible aggregation of the discrete molecules. The AUC technique was used to determine whether the samples contained a pure compound or a mixture of discrete molecules, and also to estimate their molecular weight. What was found in the AUC studies of the Cu(II) complexes of silicon-based multidentate β-diketonate ligands were molecular weights similar to the empirical formula of the molecules (i.e. Cu3(MeSi(phac)3)2: 1322.07 g/mol; Cu3(MeSi(phpr)3)2: 1567.80 g/mol) and samples that were polydisperse. No evidence from AUC showed the discovery of compounds which had molecular weights similar to the proposed polyhedra. The numbers are based on assumed densities of 1.138 g/mL

The role of self-objectification and women’s blame, sympathy, and support for a rape victim

Sexual aggression is prevalent and damaging in our culture, and sources of support or blame following an attack of this kind can be important influences on the recovery process. This pair of studies investigate the nature of women's blame reactions towards survivors of sexual aggression, as well as the potential for provision of sympathy and support. Specifically, we focused on the previously neglected role of female self-objectification. It was expected that increased self-objectification would lead to decreased sympathy and support, and more rape victim blame. However, results of Study 1 showed that chronic self-objectification was actually related to higher levels of sympathy and support for a rape victim. Study two built upon the limitations of study one, and examined similar questions. It was expected that women who engaged in greater self-objectification would again show greater sympathy and support for the victim, replicating study one's results, and this was supported with a different scale. The overall relationship between self-objectification and sympathy and support was driven by body-relevant control beliefs. Implications and future directions are discussed

Multiple incidence angle SIR-B experiment over Argentina

The Shuttle Imaging Radar (SIR-B), the second synthetic aperture radar (SAR) to fly aboard a shuttle, was launched on October 5, 1984. One of the primary goals of the SIR-B experiment was to use multiple incidence angle radar images to distinguish different terrain types through the use of their characteristic backscatter curves. This goal was accomplished in several locations including the Chubut Province of southern Argentina. Four descending image acquisitions were collected providing a multiple incidence angle image set. The data were first used to assess stereo-radargrammetric techniques. A digital elevation model was produced using the optimum pair of multiple incidence angle images. This model was then used to determine the local incidence angle of each picture element to generate curves of relative brightness vs. incidence angle. Secondary image products were also generated using the multi-angle data. The results of this work indicate that: (1) various forest species and various structures of a single species may be discriminated using multiple incidence angle radar imagery, and (2) it is essential to consider the variation in backscatter due to a variable incidence angle when analyzing and comparing data collected at varying frequencies and polarizations