Equilibrium-independent passivity: A new definition and numerical certification

We extend the traditional notion of passivity to a forced system whose equilibrium is dependent on the control input by defining equilibrium-independent passivity, a system property characterized by a dissipation inequality centered at an arbitrary equilibrium point. We provide a necessary input/output condition which can be tested for systems of arbitrary dimension and sufficient conditions to certify this property for scalar systems. An example from network stability analysis is presented which demonstrates the utility of this new definition. We then proceed to numerical certification of equilibrium-independent passivity using sum-of-squares programming. Finally, through numerical examples we show that equilibrium-independent passivity is less restrictive than incremental passivity.     

SODA: A new method of in-scene atmospheric water vapor estimation and post-flight spectral recalibration for hyperspectral sensors: Application to the HyMap sensor at two locations

A new method of estimating per-pixel atmospheric column water vapor (ACWV) and potential differences in the reported band center wavelengths of the HyMap sensor has been developed. The new method uses variations of a second order derivative algorithm (SODA) to assess the impact of atmospheric residual features on calculated surface reflectance spectra after atmospheric compensation. The SODA method provides an alternative to the current band ratio techniques of ACWV estimation and also allows the same form of algorithm to be used for the estimation of possible band shifts. A comparison of in-situ measured surface reflectance at two field sites in Western Australia demonstrates improvement in the resulting spectra when post-flight updates are made to the reported HyMap band center wavelengths and applied during the atmospheric compensation process. The same SODA methodology was varied to estimate the ACWV on a per-pixel basis and found to significantly reduce the appearance of the underlying surface structure on the resulting ACWV images as well as improve the overall accuracy of the estimation. The ACWV estimated from the HyMap imagery at the two field sites was found to agree with in-situ atmospheric ACWV measurements to within 2% and represented a two fold increase in accuracy over a 3 band ratio Continuum Interpolated Band Ratio (CIBR) technique of ACWV estimation.     

Approximate steady-state analysis of large Markov models based on the structure of their decision diagram encoding

We propose a new approximate numerical algorithm for the steady-state solution of general structured ergodic Markov models. The approximation uses a state-space encoding based on multiway decision diagrams and a transition rate encoding based on a new class of edge-valued decision diagrams. The new method retains the favorable properties of a previously proposed Kronecker-based approximation, while eliminating the need for a Kronecker-consistent model decomposition. Removing this restriction allows for a greater utilization of event locality, which facilitates the generation of both the state-space and the transition rate matrix, thus extends the applicability of this algorithm to larger and more complex models.     

Efficiently Testing Sparse <Emphasis Type="Italic">GF</Emphasis>(2) Polynomials

We give the first algorithm that is both query-efficient and time-efficient for testing whether an unknown function f:{0,1} ⁿ →{−1,1} is an s-sparse GF(2) polynomial versus ε-far from every such polynomial. Our algorithm makes poly(s,1/ε) black-box queries to f and runs in time n⋅poly(s,1/ε). The only previous algorithm for this testing problem (Diakonikolas et al. in Proceedings of the 48th Annual Symposium on Foundations of Computer Science, FOCS, pp. 549–558, 2007) used poly(s,1/ε) queries, but had running time exponential in s and super-polynomial in 1/ε.     

Guarding a set of line segments in the plane

We consider the following problem: Given a finite set of straight line segments in the plane, find a set of points of minimum size, so that every segment contains at least one point in the set. This problem can be interpreted as looking for a minimum number of locations of policemen, guards, cameras or other sensors, that can observe a network of streets, corridors, tunnels, tubes, etc. We show that the problem is strongly NP-complete even for a set of segments with a cubic graph structure, but in P for tree structures.     

Visualizing multiwavelength astrophysical data

With recent advances in the measurement technology for allsky astrophysical imaging, our view of the sky is no longer limited to the tiny visible spectral range over the 2D Celestial sphere. We now can access a third dimension corresponding to a broad electromagnetic spectrum with a wide range of allsky surveys; these surveys span frequency bands including long wavelength radio, microwaves, very short X-rays, and gamma rays. These advances motivate us to study and examine multiwavelength visualization techniques to maximize our capabilities to visualize and exploit these informative image data sets. In this work, we begin with the processing of the data themselves, uniformizing the representations and units of raw data obtained from varied detector sources. Then we apply tools to map, convert, color-code, and format the multiwavelength data in forms useful for applications. We explore different visual representations for displaying the data, including such methods as textured image stacks, the horseshoe representation, and GPU-based volume visualization. A family of visual tools and analysis methods is introduced to explore the data, including interactive data mapping on the graphics processing unit (GPU), the mini-map explorer, and GPU-based interactive feature analysis.     

The Other Mathematical Bridge

This paper contextualises, describes and discusses a student project which takes a particular exploratory approach to using mathematical surface definition as a language and vehicle for co-rational design co-authorship for architecture and engineering. The project has two authors, one from an architectural and one from an engineering educational background. It investigates the metaphorical and operational role of mathematics in the design process and outcomes.     

Constructing malware normalizers using term rewriting

A malware mutation engine is able to transform a malicious program to create a different version of the program. Such mutation engines are used at distribution sites or in self-propagating malware in order to create variation in the distributed programs. Program normalization is a way to remove variety introduced by mutation engines, and can thus simplify the problem of detecting variant strains. This paper introduces the “normalizer construction problem” (NCP), and formalizes a restricted form of the problem called “NCP=”, which assumes a model of the engine is already known in the form of a term rewriting system. It is shown that even this restricted version of the problem is undecidable. A procedure is provided that can, in certain cases, automatically solve NCP= from the model of the engine. This procedure is analyzed in conjunction with term rewriting theory to create a list of distinct classes of normalizer construction problems. These classes yield a list of possible attack vectors. Three strategies are defined for approximate solutions of NCP=, and an analysis is provided of the risks they entail. A case study using the virus suggests the approximations may be effective in practice for countering mutated malware. R. Mathur is presently at McAfee AVERT Labs.     

Semiempirical and ab initio conformational analysis of 2-methylene-8,8-dimethyl-1,4,6,10-tetraoxaspiro[4.5] decane with application of GIAO-SCF methods to NMR spectrum interpretation

The GIAO-SCF method for calculating isotropic nuclear magnetic shielding values has been utilized to explain certain features in the ¹H-NMR spectrum of 2-methylene-8,8-dimethyl-1,4,6,10-tetraoxaspiro[4.5] decane. Population distributions of the low-energy conformers based on their ab initio energies were used to produce weighting factors for the individual calculated shielding values to calculate the weighted average of the shielding values for a complete set of conformers. The differences in ¹H chemical shifts between the hydrogens of the two methyl groups and between the axial and equatorial hydrogens in 2-methylene-8,8-dimethyl-1,4,6,10-tetraoxaspiro[4.5] decane were shown to be due to energy differences between the chair and boat orientations of the six-membered ring and contribution from a twist-boat conformation. Results suggest a hypothesis that intramolecular differences in chemical shift might be calculated to a greater degree of accuracy than chemical shifts calculated relative to a standard.