Next Level Of Complexity Research Articles

Polynomial invariants of links satisfying cubic skein relations

The aim of this paper is to define two link invariants satisfying cubic skein relations. In the hierarchy of polynomial invariants determined by explicit skein relations they are the next level of complexity after Jones, HOMFLY, Kauffman and Kuperberg's G2 quantum invariants. Our method consists of the study of Markov traces on a suitable tower of quotients of cubic Hecke algebras extending Jones approach.

Meeting report--44th Annual Drosophila Research Conference.

The ability to compare the genetics of aging in multiple model organisms is a powerful tool to dissect the biology of aging. Although the fruit fly has only about half again as many genes as the nematode worm, its tissue organization is much more complex. The emerging importance of tissue specificity and endocrine signaling in aging makes the fly a natural choice for many researchers interested in unraveling the next level of complexity of the aging process. This Perspective provides an overview of research related to aging that was described at the annual Drosophila conference held in Chicago in March 2003.

Processing and characterization of silicon carbon-nitride ceramics: application of electrical properties towards MEMS thermal actuators

Abstract This paper reports the development of electrically conductive silicon carbon-nitride (SiCN) for harsh-environment MEMS applications. SiCN is a new class of polymer-derived bulk ceramics for ultra-high temperature and corrosive environment applications; however, as-pyrolyzed SiCN is electrically insulating. Through post-pyrolysis annealing at 1400 °C in a hot isostatic press in a nitrogen atmosphere poly(urea-methyl-vinyl)silazane-derived SiCN MEMS devices were fabricated that exhibit a room temperature electrical resistivity of 2–5.5 Ω cm. The material was examined using linear four-probe, X-ray diffraction, Fourier transform infrared spectroscopy and SEM. This integrated materials/micromachining process enables the realization of a new class of (electro-thermo-mechanical) devices not previously possible in SiCN, and thus takes polymer-derived ceramic (PDC) microsystems technology to the next level of complexity. SiCN lateral thermal actuators and micro-grippers for moving chip-sized objects were fabricated to demonstrate an application of this functionalized material. This work is the first to demonstrate electro-thermo-mechanical transducers fabricated from polymer-derived SiCN.

NMR analysis of lignins in CAD-deficient plants. Part 1. Incorporation of hydroxycinnamaldehydes and hydroxybenzaldehydes into lignins.

Peroxidase/H2O2-mediated radical coupling of 4-hydroxycinnamaldehydes produces 8-O-4-, 8-5-, and 8-8-coupled dehydrodimers as has been documented earlier, as well as the 5-5-coupled dehydrodimer. The 8-5-dehydrodimer is however produced kinetically in its cyclic phenylcoumaran form at neutral pH. Synthetic polymers produced from mixtures of hydroxycinnamaldehydes and normal monolignols provide the next level of complexity. Spectral data from dimers, oligomers, and synthetic polymers have allowed a more substantive assignment of aldehyde components in lignins isolated from a CAD-deficient pine mutant and an antisense-CAD-downregulated transgenic tobacco. CAD-deficient pine lignin shows enhanced levels of the typical benzaldehyde and cinnamaldehyde end-groups, along with evidence for two types of 8-O-4-coupled coniferaldehyde units. The CAD-downregulated tobacco also has higher levels of hydroxycinnamaldehyde and hydroxybenzaldehyde (mainly syringaldehyde) incorporation, but the analogous two types of 8-O-4-coupled products are the dominant features. 8-8-Coupled units are also clearly evident. There is clear evidence for coupling of hydroxycinnamaldehydes to each other and then incorporation into the lignin, as well as for the incorporation of hydroxycinnamaldehyde monomers into the growing lignin polymer. Coniferaldehyde and sinapaldehyde (as well as vanillin and syringaldehyde) co-polymerize with the traditional monolignols into lignins and do so at enhanced levels when CAD-deficiency has an impact on the normal monolignol production. The implication is that, particularly in angiosperms, the aldehydes behave like the traditional monolignols and should probably be regarded as authentic lignin monomers in normal and CAD-deficient plants.

A BASIS OF THE BASIC $\mathfrak{sl} ({\bf 3}, {\mathbb C})^~$-MODULE

J. Lepowsky and R. L. Wilson initiated the approach to combinatorial Rogers–Ramanujan type identities via the vertex operator constructions of representations of affine Lie algebras. In this approach the first new combinatorial identities were discovered by S. Capparelli through the construction of the level 3 standard [Formula: see text]-modules. We obtained several infinite series of new combinatorial identities through the construction of all standard [Formula: see text]-modules; the identities associated to the fundamental modules coincide with the two Capparelli identities. In this paper we extend our construction to the basic [Formula: see text]-module and, by using the principal specialization of the Weyl–Kac character formula, we obtain a Rogers–Ramanujan type combinatorial identity for colored partitions. The new combinatorial identity indicates the next level of complexity which one should expect in Lepowsky–Wilson's approach for affine Lie algebras of higher ranks, say for [Formula: see text], n ≥ 2, in a way parallel to the next level of complexity seen when passing from the Rogers–Ramanujan identities (for modulus 5) to the Gordon identities for odd moduli ≥7.

Probability density function computations of a strongly swirling nonpremixed flame stabilized on a new burner

Turbulent nonpremixed swirl-stabilized flames are common in practical combustors and form the next level of complexity after piloted and bluff-body stabilized flames. Modeling swirling flows remains a challenge especially when the swirl level is high enough to induce vortex breakdown and recirculation. This paper presents experimental results on the velocity field and the stability characteristics of a new swirl burner which has well-defined boundary conditions. This burner is capable of stabilizing turbulent nonpremixed flames which have high swirl numbers and which may have a significant degree of turbulence-chemistry interactions. A Monte Carlo-based probability density function (PDF) method is also used to compute the same turbulent, highly swirling flame using the simplest models for velocity (SLM), turbulent frequency (JPM), and molecular mixing (IEM). A single flamelet library is used here to represent chemistry. These simple computations reproduce the correct flow structure and compare well with the measured velocity field. Refinements to the computations and more extensive measurements in such flows are forthcoming.

The Physics and Chemistry of Small Translucent Molecular Clouds. XII. More Complex Species Explainable by Gas‐Phase Processes

We have observed 10 molecular species of complexity (four to seven atoms) in three translucent clouds and in TMC-1 and L183. Of these species HNCO, HOCO+, H2CCO, CCH, and CH3CCH are detected in all five objects, while HCOOH, CH3CHO, CH3CN, CH2NH, and VyCN are detected in fewer objects. These species are chosen because they are expected to mark the transition between simpler species that are formed in the gas phase and complex hydrogenated species [NH2CHO, EtOH, EtCN, (CH3)2O, and CH3OCHO] that are believed to form by grain chemistry. The C/O ratio and the metal abundances are determining factors in the abundances of most of the species. The gas-phase chemistry of HNCO is set out for the first time. HNCO, H2CCO, CCH, and CH3CCH are successfully modeled for a wide range of C/O, metals, and cloud conditions. HOCO+, HCOOH, CH3CN, and VyCN are well modeled under fewer conditions, while CH3CHO and CH2NH are fitted in only a small range of conditions. For most species, the models tend to underestimate the observed abundances. By introducing or modifying a number of gas-phase reactions in the New Standard Model we are able to explain the abundances of most species for specific sets of physical conditions (density, temperature, extinction), abundances (metals, C/O), and time epoch. The parameter sets for the different species are largely non overlapping. However, we have been able to find a single, unique set of parameters including a specific epoch for each of TMC-1, L183, and the translucent clouds that explains eight of the 10 species. The exceptions are CH2NH, which requires higher C/O than other species, and CH3CHO, which is possibly modeled in dark clouds but not in translucent objects. For the eight well-fitted species, C/O=0.4 is favored, and the time epoch is 5(5)±4(5) yr for each type of object. In this exercise we cannot distinguish between high and low metals. Previously studied species (HCN, C3H2, CCS, and HC3N) fit the same set of conditions. It is possible that all 10 species may be explained by gas-phase chemistry, perhaps when suitable neutral-neutral reactions are found for species such as CH3CHO and CH2NH. Until then, grain processes cannot be ruled out for these and other species such as HOCO+ (formed from desorbed CO2) or VyCN (highly saturated). Ortho/para and E/A ratios are found to lie within the thermal limits for all cases except O/P (H2CCO), whose value of 5.9 in TMC-1 exceeds the limit of 3.0, which confirms an earlier result by Ohishi. This result cannot be explained by grain interactions. Nevertheless, in the species of intermediate complexity, we may be encountering the boundary between gas and grain chemistry for partly hydrogen-saturated species. The transition to grain chemistry seems clearly to occur at the next level of complexity, which includes NH2CHO, EtOH, EtCN, (CH3)2O, and CH3OCHO, species we have failed to detect after exhaustive searches in translucent and dark clouds.

Experiments and Simulations by Self-Consistent Models of Texture Development in Cu–Fe Powder Composites

Two-Sites Self-Consistent (2-SSC) models have been used for simulation of texture development of two-phase materials (Bolmaro and Lebensohn, 1996; Bolmaro et al., 1997). When both phases are plastically deforming the co-deformation and sharing of spins have to be taken into account via interaction among phases. One-Site Self-Consistent (1-SSC) models are able to consider interaction among each grain and the rest of surrounding grains through a mean field calculated over the “matrix grains”. The next level of complexity, i.e., 2-SSC models, is appropriate to capture some interaction features between phases. In the current paper, starting from well-defined microstructures and textures of Cu–Fe powder composites, the textures obtained after wire-drawing are simulated taking into account codeformation and sharing of rotations. The results are shown agreeing with experimental ones provided that, depending on volume fraction and relative strength of both phases, different ad-hoc strain rate sensitivities are used.

The Stellar Populations in Local Group Dwarf Galaxies

The aim of the study of the populations in a stellar system is to understand and be able to describe the stellar content of a system in terms of physical parameters such as the age, star formation history, chemical enrichment history, initial mass function (IMF), environment, and dynamical history of the system. This is done given an understanding of stellar evolution and the ability to express the outcome in “observer parameters”, particularly a color-magnitude diagram (CMD), kinematics, and metallicity. From this perspective, the simplest systems are the galactic clusters and the globular clusters, where all the component stars are coeval and of the same metallicity. The current state of knowledge for these are discussed by others in this conference. We proceed to the next level of complexity (where metallicities are not necessarily all the same, and nor are the stars all coeval), and try to decompose their stellar content, particularly in terms of star formation rate and metallicity. In this regard the two classes of objects that come to mind are the dwarf spheroidals, and the dwarf irregulars. Both these classes of objects are more massive than the open clusters and globular clusters, and show evidence of complexities in their star formation histories, without being so convolved as to make such a study intractable. As we shall see, recent studies along these lines have presented some puzzling problems. Moreover, these are the smallest independent galaxies, and the study of star formation in these is likely to shed light on the history and formation of larger and more complex galaxies.

The Stellar Populations in Local Group Dwarf Galaxies

The aim of the study of the populations in a stellar system is to understand and be able to describe the stellar content of a system in terms of physical parameters such as the age, star formation history, chemical enrichment history, initial mass function (IMF), environment, and dynamical history of the system. This is done given an understanding of stellar evolution and the ability to express the outcome in “observer parameters”, particularly a color-magnitude diagram (CMD), kinematics, and metallicity. From this perspective, the simplest systems are the galactic clusters and the globular clusters, where all the component stars are coeval and of the same metallicity. The current state of knowledge for these are discussed by others in this conference. We proceed to the next level of complexity (where metallicities are not necessarily all the same, and nor are the stars all coeval), and try to decompose their stellar content, particularly in terms of star formation rate and metallicity. In this regard the two classes of objects that come to mind are the dwarf spheroidals, and the dwarf irregulars. Both these classes of objects are more massive than the open clusters and globular clusters, and show evidence of complexities in their star formation histories, without being so convolved as to make such a study intractable. As we shall see, recent studies along these lines have presented some puzzling problems. Moreover, these are the smallest independent galaxies, and the study of star formation in these is likely to shed light on the history and formation of larger and more complex galaxies.

Peptide models of protein folding initiation sites. 3. The G-H helical hairpin of myoglobin.

As part of an extensive dissection of the folding pathway of myoglobin, a series of peptides corresponding to fragments of sperm whale myoglobin have been synthesized, and their conformational preferences investigated using circular dichroism and nuclear magnetic resonance spectroscopy in aqueous solution and in solvent mixtures containing water and trifluoroethanol. The behavior of short fragments corresponding to the sequences of the G- and H-helices of myoglobin and to the turn region between these helices has been described in accompanying papers. At the next level of complexity, peptide model compounds have been synthesized to explore the longer-range interactions which may take place in protein folding after initial secondary structure formation has occurred. A series of disulfide-bridged dimeric peptides containing the complete sequences of the G- and H-helices of myoglobin were synthesized and their conformational preferences examined. CD spectra indicate that disulfide-bridged peptides consisting of two H-helix sequences (Mb-HssH) and of one G- and one H-helix (Mb-GssH) are highly helical in water solution, as a result of intermolecular association. A 51-residue peptide, Mb-GH51, encompassing the entire G-H helical hairpin of myoglobin, including the turn sequence between the two helices, has been successfully synthesized by standard methods. This peptide was designed to be monomeric in aqueous solution. Mb-GH51 does not appear from CD spectra to contain any additional helix in water solution above what would be expected from an equimolar mixture of the G- and H-helix peptides. NMR spectra indicate that the turn conformation observed in shorter peptide fragments is retained in Mb-GH51 in high population.(ABSTRACT TRUNCATED AT 250 WORDS)

A hierarchy of performance analysis techniques for adaptive active control of sound and vibration

Active control for silencing sound and vibration has recently become the subject of much investigation and is now being enhanced by the advent of adaptive filtering techniques. In this paper, an approach to adaptive active control performance analysis is developed that involves a hierarchy of techniques, starting with an ideal simplified problem and progressively adding practical constraints and other complexities. Four levels of performance analysis are defined: Level I derives fundamental performance limits given continuous measurements over the entire performance surface; level II brings in the practical constraint of a fixed number of sensors at discrete locations; level III incorporates knowledge of the transfer function structure; and, level IV adds in all of the other practical effects and design constraints required for detailed performance calculations. At each step, a degree of confidence is gained and a benchmark is established for comparison and cross-checking with the next level of complexity. Following this methodical process leads to a baseline architecture, which can then be subjected to detailed performance analysis in order to arrive at a final design. The four levels of performance analysis are discussed in detail and are illustrated by numerical example for a vibrating cantilever beam using a graphics display that was developed for real-time interactive design.

A simple model of flow—Sediment—Organism interaction

Previous models of organism-sediment interaction have been limited primarily to eddy diffusion-type mixing. While such models are useful in interpreting some stratigraphic records, they cannot be expected to provide mechanistic insights into the diversity of interactions among sedimentary processes, organism activities, and boundary layer flows. To provide a more general formulation capable of dealing with all three types of processes in concert, a simple, discrete-time Markov model is generated. This version of the model deals explicitly only with particulate and not liquid phases. The initial formulation is a two-compartment, ergodic model of deposit feeding. Particle selection by deposit feeders results in incorporation of the selected particles into fecal pellets, and fecal pellet disaggregation completes the cycle. Particles which are more strongly selected or which are incorporated into more robust pellets thus spend more time and reach higher relative concentration in the fecal-pellet compartment. The next level of complexity is achieved by adding burial from the “free” sediment (non-fecal-pellet) compartment. This model predicts that particles which are more strongly selected or incorporated into more robust fecal pellets will have greater residence times in surficial sediments (both pellets and “free” sediments) before they become part of the stratigraphic record, and will therefore achieve higher concentrations in surficial sediments than will less preferred particles. The full flow-sediment-organism system is reached by adding the potential for lateral advection of particles. The probability of such advection is allowed to differ between pellets and “free” sediments. Increasing selection and robustness of fecal pellets then can either increase or decrease relative concentration and residence time of a given particle type in surficial sediments. The model thus provides a means of explaining differences in stratigraphic patterns among materials deposited simultaneously. It also suggests that deposit-feeder selection may increase the average age (i.e., time since initial deposition) of surficial sediments by maintaining preferred particle types near the surface. Selection may likewise control the texture of surficial sediments-in a manner which is easily confused with purely physical sorting. Parameters which require careful measurement in testing these simple predictions are selectivity by deposit feeders (probability of selection), rate of fecal-pellet breakdown under realistically simulated conditions (probability of pelletal disaggregation), differential erodibilities of pellets versus “free” sediments (relative probabilities of lateral advection), and rates of burial of “free” sediments versus pelletized sediments (probabilities of burial).

Construction of isology functors

This paper is, hopefully, a step in the direction of obtaining a complete system of algebraic invariants for the isotopy classes of finitely triangulable spaces. We construct a large family of isotopy functors defined on a category of embeddings of topological pairs and having values in the category of homomorphisms of graded abelian groups. These functors are formally like homotopy and homology functors, having a boundary operator and satisfying an exactness axiom, and some of them are especially well behaved: they are isologyfunctors, which is to say, they satisfy an excision axiom. These functors are defined in the first three sections and their basic properties are established. The rest of the paper is concerned with testing whether these functors can tell one space from another. Ideally, one should construct a functor T with the property that if f is an embedding and if T(f) is an isomorphism, then f is an isotopy equivalence. In fact, somewhat less than this has happened. The ideal situation holds for embeddings of 1-dimensional finitely triangulable spaces, but at the next level of complexity, embeddings of 2-dimensional finitely triangulable cone spaces, there are nonequivalences which induce isomorphisms. This gap may be partially closed by employing the deleted product functor, but there still remain some spaces which look alike to all of the functors that the author knows how to deal with gracefully. However, it should be noted that the remaining cone spaces are quite simple and it seems unlikely that they will resist algebraic analysis for long. 1. The basic functors. If X is a topological space, let cX= X*p be the join of X with a point p = aX not in X. The pair (cX, aX) is called a cone over X, cX is the space of the cone and aX is the apex. The space X is naturally embedded in cX and is called the base of the cone. A mapf: X -+ Y induces a map cf: cX, aX -? c Y, a Y such that each segment from x E X to aX is mapped linearly onto the segment from f(x) to a Y. Any two cones over the same space are topologically equivalent pairs, and we choose to ignore the difference between them. In this spirit, we demand that if Yc X, then a Y= aX and c Yc cX, so that c is now regarded as a covariant functor from maps between topological pairs to maps between pairs with basepoint. If f is an embedding, then cf is also an embedding, and if f is isotopic to g, then cf is isotopic to cg; the second isotopy leaves the apex fixed. If X and K are topological spaces, let m(X; K) be the following subspace of K,