The theory and computation of evolutionary distances: Pattern recognition

A method of finding pattern similarities between two sequences is given. Two portions, one from each sequence, are similar if they are close in the metric space of evolutionary distances. The method allows a complete list to be made of all pairs of intervals, one from each of two given sequences, such that each pair displays a maximum local degree of similarity, and, if the lengths of the given sequences are m and n, then the procedure takes on the order of mn computational steps. This result lends itself to finding similarities by computer between pairs of biological sequences, such as proteins and nucleic acids.     

Cubic elliptic functions

The function

Probing the dimensions of semi-rigid inner functionalised U-shaped bis-porphyrin cavities

The synthesis of a series of open U-shaped bis-porphyrin cavity molecules is described, with bridged bicyclic backbones to confer rigidity, and a pendant substituted aromatic probe unit suspended on the inside of the cavity. The dimensions and flexibility of the bis-zincporphyrin cavity were probed using several different techniques. Initially the molecular ruler concept was employed, using flexible bidentate ligands as guests with a range of possible linear dimensions. Secondly, NMR methods were employed with rigid bidentate ligand guests of fixed lengths, and thirdly diffusion based NMR methods were utilised. The range of inter-porphyrin distances estimated by these methods suggests that these types of open-cavity systems have a surprising degree of flexibility.     

Congruences modulo 11 for broken 5-diamond partitions

The notion of broken k-diamond partitions was introduced by Andrews and Paule in 2007. For a fixed positive integer k, let \(\Delta _k(n)\) denote the number of broken k-diamond partitions of n. Recently, Paule and Radu conjectured two relations on \(\Delta _5(n)\) which were proved by Xiong and Jameson, respectively. In this paper, employing these relations, we prove that, for any prime p with \(p\equiv 1\ (\mathrm{mod}\ 4)\), there exists an integer \(\lambda (p)\in \{2,\ 3,\ 5,\ 6,\ 11\}\) such that, for \(n, \alpha \ge 0\), if \(p\not \mid (2n+1)\), then

$$\begin{aligned} \Delta _5\left( 11p^{\lambda (p)(\alpha +1)-1} n+\frac{11p^{\lambda (p)(\alpha +1)-1}+1}{2}\right) \equiv 0\ (\mathrm{mod}\ 11). \end{aligned}$$

Moreover, some non-standard congruences modulo 11 for \(\Delta _5(n)\) are deduced. For example, we prove that, for \(\alpha \ge 0\), \(\Delta _5\left( \frac{11\times 5^{5\alpha }+1}{2}\right) \equiv 7\ (\mathrm{mod}\ 11)\).

     

Controlling the passage of light through metal microchannels by nanocoatings of phospholipids

The flow of polarized light through a metal film with an array of microchannels is controlled by the phase of an optically active, phospholipid nanocoating, even though the coating does not cover the open area of the microchannels. The molecular details of the assembly (DPPC phospholipid monolayer/bilayer on a hexadecanethiol monolayer on a copper- or nickel-coated microarray) were determined using the infrared, surface-plasmon-mediated, extraordinary transmission of the metal microarrays. Infrared absorption spectra with greatly enhanced absorptions by comparison to literature were recorded and used as a diagnostic for the phase, composition, and molecular geometry of these nanocoatings. This approach presents new tools for nanoscale construction in constricted microspaces, which may ultimately be useful with individual microchannels.     

Arithmetic properties of partitions with even parts distinct

In this work, we consider the function ped(n), the number of partitions of an integer n wherein the even parts are distinct (and the odd parts are unrestricted). Our goal is to consider this function from an arithmetical point of view in the spirit of Ramanujan’s congruences for the unrestricted partition function p(n). We prove a number of results for ped(n) including the following: For all n≥0, $$\mathit{ped}(9n+4)\equiv0\pmod{4}$$ and $$\mathit{ped}(9n+7)\equiv0\pmod{12}.$$ Indeed, we compute appropriate generating functions from which we deduce these congruences and find, in particular, the surprising result that $$\sum_{n\geq0}\mathit{ped}(9n+7)q^n=12\frac{ (q^{2};q^{2})_\infty ^{4}(q^{3};q^{3})_\infty ^{6}(q^{4};q^{4})_\infty ^{}}{(q^{};q^{})_\infty ^{11}}.$$ We also show that ped(n) is divisible by 6 at least 1/6 of the time.     

Scalable Biosynthesis of the Seaweed Neurochemical,Kainic Acid

Kainic acid, the flagship member of the kainoid family of natural neurochemicals, is a widely used neuropharmacological agent that helped unravel the key role of ionotropic glutamate receptors, including the kainate receptor, in the central nervous system. Worldwide shortages of this seaweed natural product in the year 2000 prompted numerous chemical syntheses, including scalable preparations with as few as six‐steps. Herein we report the discovery and characterization of the concise two‐enzyme biosynthetic pathway to kainic acid from l ‐glutamic acid and dimethylallyl pyrophosphate in red macroalgae and show that the biosynthetic genes are co‐clustered in genomes of Digenea simplex and Palmaria palmata. Moreover, we applied a key biosynthetic α‐ketoglutarate‐dependent dioxygenase enzyme in a biotransformation methodology to efficiently construct kainic acid on the gram scale. This study establishes both the feasibility of mining seaweed genomes for their biotechnological prowess.     

Extrusion of chalcogenide glass preforms and drawing to multimode optical fibers

We report on viscosity of a Ge₁₇As₁₈Se₆₅ glass over the temperature range of 280-420 °C and the successful co-extrusion and fiber-drawing of two chalcogenide glass boules to form a core/clad. pair. The co-extrusion produces a preform with optimum diameter stability and core/clad. glass ratio, and minimum defects at the core/clad. interface in the middle 120-200 mm region of a 270 mm long preform. Core/clad. fiber is drawn successfully from the extruded preform. An optical loss of 1.7 dB m⁻¹ at 1666 cm⁻¹ (6.0 μm) and 6.7 dB m⁻¹ at 6649 cm⁻¹ (1.55 μm) is reported.     

A temperature dependence kinetic study of O(1D) + CH4: overall rate coefficient and product yields

Using a recently-developed chemiluminescence technique for monitoring O(1D), the rate coefficient, k1, of the important atmospheric reaction O(1D) + CH4 --> products has been determined over a wide temperature range, 227 to 450 K. The rate coefficient was shown to be independent of temperature, having a value of (1.91 +/- 0.08) x 10(-10) cm3 s(-1); the quoted uncertainties are with 95% confidence. This highly precise value, based on an extended set of determinations with very low scatter, is significantly greater, 26%, than current recommended values. Secondly, the fraction of O(1D) quenched to O(3P) by CH4, k(1q)/k1, was precisely determined from chemiluminescence decays over the temperature range 236 to 340 K. A temperature independent value for k(1q)/k1 of 0.002 +/- 0.003 was found. Finally, LIF detection of OH has been applied to accurately determine the product branching fraction to OH of O(1D) + CH4 at room temperature. Our value, k(1a)/k1 = 0.76 +/- 0.08 (95% confidence), is in line with recent determinations by other groups.