Representation in the (Artificial) Immune System

Much of contemporary research in Artificial Immune Systems (AIS) has partitioned into either algorithmic machine learning and optimisation, or, modelling biologically plausible dynamical systems, with little overlap between. We propose that this dichotomy is somewhat to blame for the lack of significant advancement of the field in either direction and demonstrate how a simplistic interpretation of Perelson’s shape-space formalism may have largely contributed to this dichotomy. In this paper, we motivate and derive an alternative representational abstraction. To do so we consider the validity of shape-space from both the biological and machine learning perspectives. We then take steps towards formally integrating these perspectives into a coherent computational model of notions such as life-long learning, degeneracy, constructive representations and contextual recognition—rhetoric that has long inspired work in AIS, while remaining largely devoid of operational definition.     

Isotope quantum effects in water around the freezing point

We have measured the difference in electronic structure factors between liquid H(2)O and D(2)O at temperatures of 268 and 273 K with high energy x-ray diffraction. These are compared to our previously published data measured from 279 to 318 K. We find that the total structural isotope effect increases by a factor of 3.5 over the entire range, as the temperature is decreased. Structural isochoric temperature differential and isothermal density differential functions have been used to compare these data to a thermodynamic model based upon a simple offset in the state function. The model works well in describing the magnitude of the structural differences above approximately 310 K, but fails at lower temperatures. The experimental results are discussed in light of several quantum molecular dynamics simulations and are in good qualitative agreement with recent temperature dependent, rotationally quantized rigid molecule simulations.     

Ab initio calculations on the isomerization of alkene radical cations

Ab initio calculations on the isomerization of butene and pentene radical cations indicate that, for all classical ion structures, the lowest barrier for a rearrangement to the most stable ion structure is below the dissociation limit. Isomerizations of linear butene radical cations to the isobutene structure take place via the CH₃CC₂H₅^·+ structure, whereas in the pentene case the connection between linear and branched ion structures proceeds via the 1,2-dimethylcyclopropane radical cation. From the results a qualitative model is derived which suggests that for larger alkene radical cations an isomerization to structures with four alkyl substituents on the double bond may be in close competition with dissociation.     

Optimization of the CHARMM additive force field for DNA: Improved treatment of the BI/BII conformational equilibrium

The B-form of DNA can populate two different backbone conformations: BI and BII, defined by the difference between the torsion angles ε and ζ (BI = ε-ζ < 0 and BII = ε-ζ > 0). BI is the most populated state, but the population of the BII state, which is sequence dependent, is significant and accumulating evidence shows that BII affects the overall structure of DNA, and thus influences protein-DNA recognition. This work presents a reparametrization of the CHARMM27 additive nucleic acid force field to increase the sampling of the BII form in MD simulations of DNA. In addition, minor modifications of sugar puckering were introduced to facilitate sampling of the A form of DNA under the appropriate environmental conditions. Parameter optimization was guided by quantum mechanical data on model compounds, followed by calculations on several DNA duplexes in the condensed phase. The selected optimized parameters were then validated against a number of DNA duplexes, with the most extensive tests performed on the EcoRI dodecamer, including comparative calculations using the Amber Parm99bsc0 force field. The new CHARMM model better reproduces experimentally observed sampling of the BII conformation, including sampling as a function of sequence. In addition, the model reproduces the A form of the 1ZF1 duplex in 75 % ethanol, and yields a stable Z-DNA conformation of duplex (GTACGTAC) in its crystal environment. The resulting model, in combination with a recent reoptimization of the CHARMM27 force field for RNA, will be referred to as CHARMM36.     

Partial information systems and the Smyth powerdomain

The dual of the join semilattice of proper compact Scott open subsets of a domain D is called the Smyth powerdomain of D. The Smyth powerdomain is used in programming semantics as a model for demonic nondeterminism. In this paper, we introduce the concept of partial information systems; and, as an application, show that the Smyth powerdomain of any domain can be realized in terms of the sub partial information systems of the domain??s corresponding information system.     

A geometry optimization framework for photonic crystal design

The performance of photonic crystal devices can depend strongly on their geometry. Alas, their fundamental physics offers relatively little by way of pointers in terms of optimum shapes, so numerical design search techniques must be used in an attempt to determine high performance layouts. We discuss strategies for solving this type of optimization problem, the main challenge of which is the conflict between the enormous size of the space of potentially useful designs and the relatively high computational cost of evaluating the performance of putative shapes. The optimization technique proposed here operates over increasing levels of fidelity, both in terms of the resolution of its non-parametric shape definition and in terms of the resolution of the numerical analysis of the performance of putative designs. This is a generic method, potentially applicable to any type of electromagnetic device shape design problem. We also consider a methodology for assessing the robustness of the optima generated through this process, investigating the impact of manufacturing errors on their performance. As an illustration, we apply this technology to the design of a two-dimensional photonic crystal structure; the result features a large complete band gap structure and a topology that is different from previously published designs.     

Bilinear Square Functions and Vector-Valued Calderón-Zygmund Operators

Boundedness results for bilinear square functions and vector-valued operators on products of Lebesgue, Sobolev, and other spaces of smooth functions are presented. Bilinear vector-valued Calderón-Zygmund operators are introduced and used to obtain bounds for the optimal range of estimates in target Lebesgue spaces including exponents smaller than one.     

Trapping of the putative cationic intermediate in the Morin rearrangement with carbon nucleophiles.

This paper presents reactions in which the putative cationic intermediate in the Morin rearrangement is trapped by aromatic carbon nucleophiles (indoles and furans). For example, reaction of sulfoxide 27 with trifluoroacetic acid in chloroform provides, among other products, indole 29 and indoline 30. The indoline was shown to be in equilibrium with the nine-membered ring bridged indole 31. Other examples of Morin rearrangement-trapping reactions are presented, and mechanisms for these transformations are proposed.