Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Three-Body Recombination with Two-Channel Contact Interactions

We use a two-channel contact interaction model to describe a system of three identical bosons. The two-channel model quantitatively describes the phenomena of Feshbach resonance in agreement with the phenomenological expression relating scattering length to magnetic detuning. The model also has a finite effective range. We investigate finite range effects in three-body recombination. The simpler one-channel contact interaction model predicts a characteristic geometric scaling of minima in the recombination coefficient as a function of scattering length with scaling parameter 22.7. We show that this factor is reduced when the effective range is included. We compare calculations to experiment.     

Thermodynamics of Dipolar Chain Systems

The thermodynamics of a quantum system of layers containing perpendicularly oriented dipolar molecules is studied within an oscillator approximation for both bosonic and fermionic species. The system is assumed to be built from chains with one molecule in each layer. We consider the effects of the intralayer repulsion and quantum statistical requirements in systems with more than one chain. Specifically, we consider the case of two chains and solve the problem analytically within the harmonic Hamiltonian approach which is accurate for large dipole moments. The case of three chains is calculated numerically. Our findings indicate that thermodynamic observables, such as the heat capacity, can be used to probe the signatures of the intralayer interaction between chains. This should be relevant for near future experiments on polar molecules with strong dipole moments.     

Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

Disjoint Paths in Decomposable Digraphs

The k‐linkage problem is as follows: given a digraph and a collection of k terminal pairs such that all these vertices are distinct; decide whether D has a collection of vertex disjoint paths such that is from to for . A digraph is k‐linked if it has a k‐linkage for every choice of 2k distinct vertices and every choice of k pairs as above. The k‐linkage problem is NP‐complete already for [11] and there exists no function such that every ‐strong digraph has a k‐linkage for every choice of 2k distinct vertices of D [17]. Recently, Chudnovsky et al. [9] gave a polynomial algorithm for the k‐linkage problem for any fixed k in (a generalization of) semicomplete multipartite digraphs. In this article, we use their result as well as the classical polynomial algorithm for the case of acyclic digraphs by Fortune et al. [11] to develop polynomial algorithms for the k‐linkage problem in locally semicomplete digraphs and several classes of decomposable digraphs, including quasi‐transitive digraphs and directed cographs. We also prove that the necessary condition of being ‐strong is also sufficient for round‐decomposable digraphs to be k‐linked, obtaining thus a best possible bound that improves a previous one of . Finally we settle a conjecture from [3] by proving that every 5‐strong locally semicomplete digraph is 2‐linked. This bound is also best possible (already for tournaments) [1].     

Substrates and Cyclic Peptide Inhibitors of the Oligonucleotide-Activated Sirtuin 7**

The sirtuins are NAD⁺-dependent lysine deacylases, comprising seven isoforms (SIRT1–7) in humans, which are involved in the regulation of a plethora of biological processes, including gene expression and metabolism. The sirtuins share a common hydrolytic mechanism but display preferences for different ϵ-N-acyllysine substrates. SIRT7 deacetylates targets in nuclei and nucleoli but remains one of the lesser studied of the seven isoforms, in part due to a lack of chemical tools to specifically probe SIRT7 activity. Here we expressed SIRT7 and, using small-angle X-ray scattering, reveal SIRT7 to be a monomeric enzyme with a low degree of globular flexibility in solution. We developed a fluorogenic assay for investigation of the substrate preferences of SIRT7 and to evaluate compounds that modulate its activity. We report several mechanism-based SIRT7 inhibitors as well as de novo cyclic peptide inhibitors selected from mRNA-display library screening that exhibit selectivity for SIRT7 over other sirtuin isoforms, stabilize SIRT7 in cells, and cause an increase in the acetylation of H3 K18.     

Highly selective micro-sequential injection lab-on-valve (μSI-LOV) method for the determination of ultra-trace concentrations of nickel in saline matrices using detection by electrothermal atomic absorption spectrometry

A highly selective procedure is proposed for the determination of ultra-trace level concentrations of nickel in saline aqueous matrices exploiting a micro-sequential injection Lab-On-Valve (μSI-LOV) sample pretreatment protocol comprising bead injection separation/pre-concentration and detection by electrothermal atomic absorption spectrometry (ETAAS). Based on the dimethylglyoxime (DMG) reaction used for nickel analysis, the sample, as contained in a pH 9.0 buffer, is, after on-line merging with the chelating reagent, transported to a reaction coil attached to one of the external ports of the LOV to assure sufficient reaction time for the formation of Ni(DMG)₂ chelate. The non-ionic coordination compound is then collected in a renewable micro-column packed with a reversed-phase copolymeric sorbent [namely, poly(divinylbenzene-co-N-vinylpyrrolidone)] containing a balanced ratio of hydrophilic and lipophilic monomers. Following elution by a 50-μL methanol plug in an air-segmented modality, the nickel is finally quantified by ETAAS. Under the optimized conditions and for a sample volume of 1.8 mL, a retention efficiency of 70 % and an enrichment factor of 25 were obtained. The proposed methodology showed a high tolerance to the commonly encountered alkaline earth matrix elements in environmental waters, that is, calcium and magnesium, and was successfully applied for the determination of nickel in an NIST standard reference material (NIST 1640-Trace elements in natural water), household tap water of high hardness and local seawater. Satisfying recoveries were achieved for all spiked environmental water samples with maximum deviations of 6 %. The experimental results for the standard reference material were not statistically different to the certified value at a significance level of 0.05.     

Watching nanoparticles form: an in situ (small-/wide-angle X-ray scattering/total scattering) study of the growth of yttria-stabilised zirconia in supercritical fluids

Understanding nanoparticle-formation reactions requires multi-technique in situ characterisation, since no single characterisation technique provides adequate information. Here, the first combined small-angle X-ray scattering (SAXS)/wide-angle X-ray scattering (WAXS)/total-scattering study of nanoparticle formation is presented. We report on the formation and growth of yttria-stabilised zirconia (YSZ) under the extreme conditions of supercritical methanol for particles with Y(2)O(3) equivalent molar fractions of 0, 4, 8, 12 and 25 %. Simultaneous in situ SAXS and WAXS reveals a quick formation (seconds) of sub-nanometre amorphous material forming larger agglomerates with subsequent slow crystallisation (minutes) into nanocrystallites. The amount of yttria dopant is shown to strongly affect the crystallite size and unit-cell dimensions. At yttria-doping levels larger than 8 %, which is known to be the stoichiometry with maximum ionic conductivity, the strain on the crystal lattice is significantly increased. Time-resolved nanoparticle size distributions are calculated based on whole-powder-pattern modelling of the WAXS data, which reveals that concurrent with increasing average particle sizes, a broadening of the particle-size distributions occur. In situ total scattering provides structural insight into the sub-nanometre amorphous phase prior to crystallite growth, and the data reveal an atomic rearrangement from six-coordinated zirconium atoms in the initial amorphous clusters to eight-coordinated zirconia atoms in stable crystallites. Representative samples prepared ex situ and investigated by transmission electron microscopy confirm a transformation from an amorphous material to crystalline nanoparticles upon increased synthesis duration.     

Electron detachment and relaxation of OH-(aq)

Femtosecond transient absorption spectroscopy is used to study the primary reaction dynamics of photoinduced electron detachment of the hydroxide ion in water, OH- (aq). The electron is detached by excitation of OH- (aq) to the charge-transfer-to-solvent (CTTS) state at 200 nm. The subsequent relaxation processes are probed in the spectral range from 193 to 800 nm with femtosecond time resolution. We determine both the time-dependent quantum yields of OH- (aq), OH(aq), and e-(aq), and we observe a transient spectral signature which is assigned to relaxation of hot (OH-)* ions formed via solvent-assisted conversion of the excited CTTS state to OH-. The primary quantum yield of OH(aq) is 65 +/- 5%, while recombination with e-(aq) reduces the yield to 34% after 5 ps and 12% after 200 ps. The yield of hot (OH-)* ions is 35 +/- 5%. Rotational anisotropy measurements of OH- (aq) and OH(aq) indicate a reorientation time for OH- (aq) of 1.9 ps, while no rotational anisotropy is resolved for the OH(aq) radical within our time resolution of 0.3 ps. This is consistent with the notion that OH(aq) radicals formed after electron detachment are only weakly bound to the hydrogen bond network of water. The assignment of the experimental data is supported by a series of electronic structure calculations of simple complexes of OH- (H(2)O)(n).