Numerical computation of an Evans function for travelling waves

We demonstrate a geometrically inspired technique for computing Evans functions for the linearised operators about travelling waves. Using the examples of the F-KPP equation and a Keller–Segel model of bacterial chemotaxis, we produce an Evans function which is computable through several orders of magnitude in the spectral parameter and show how such a function can naturally be extended into the continuous spectrum. In both examples, we use this function to numerically verify the absence of eigenvalues in a large region of the right half of the spectral plane. We also include a new proof of spectral stability in the appropriate weighted space of travelling waves of speed c≥sqrt(2δ) in the F-KPP equation.

1H and 13C NMR spectra of some unsymmetric N,N-dipyridyl ureas: spectral assignments and molecular conformation

Abstract: The H-1 NMR spectra of N-(2-pyridyl), N'-(3-pyridyl)ureas and N-(2-pyridyl), N'-(4-pyridyl)ureas in CDCl3 and (CD3)(2)CO have been assigned with the aid of COSY and NOE experiments and chemical shift and coupling constant correlations, The C-13 NMR spectra in CDCl3 were analysed utilizing the HETCOR and proton coupled spectra, The H-1 NMR spectra, NOE effects and MINDO/3 calculations have been utilized to show that the molecular conformation of these compounds has the 2-pyridyl ring coplanar with the urea plane with the N-H group hydrogen bonded to the nitrogen of the 2-pyridyl group on the other urea nitrogen while the 3/4-pyridyl group rotates rapidly about the N-C-3/N-C-4 bond.

Conformation of some N,N'-arylalkyl thioureas by 1H-NMR and infrared spectral analysis

Several N,N-²-arylalkyl thioureas were examined with 1H-NMR and i.r. spectra in order to study the conformation of the -NHCSNH- group. The influence of temperature and substituents on the chemical shift of the N---H protons has been investigated. Formation of a strong intramolecular hydrogen bond stabilizes the trans-cis conformation for most systems, while for the others the prevalence of different rotational isomers can be postulated. The influence of the steric effect on hydrogen bonding and molecular conformation is discussed.

Spectral analysis of pair-correlation bandwidth: Application to cell biology images

Images from cell biology experiments often indicate the presence of cell clustering, which can provide insight into the mechanisms driving the collective cell behaviour. Pair-correlation functions provide quantitative information about the presence, or absence, of clustering in a spatial distribution of cells. This is because the pair-correlation function describes the ratio of the abundance of pairs of cells, separated by a particular distance, relative to a randomly distributed reference population. Pair-correlation functions are often presented as a kernel density estimate where the frequency of pairs of objects are grouped using a particular bandwidth (or bin width), Δ>0. The choice of bandwidth has a dramatic impact: choosing Δ too large produces a pair-correlation function that contains insufficient information, whereas choosing Δ too small produces a pair-correlation signal dominated by fluctuations. Presently, there is little guidance available regarding how to make an objective choice of Δ. We present a new technique to choose Δ by analysing the power spectrum of the discrete Fourier transform of the pair-correlation function. Using synthetic simulation data, we confirm that our approach allows us to objectively choose Δ such that the appropriately binned pair-correlation function captures known features in uniform and clustered synthetic images. We also apply our technique to images from two different cell biology assays. The first assay corresponds to an approximately uniform distribution of cells, while the second assay involves a time series of images of a cell population which forms aggregates over time. The appropriately binned pair-correlation function allows us to make quantitative inferences about the average aggregate size, as well as quantifying how the average aggregate size changes with time.

1H and 13C NMR spectral studies of C-2 substituted isomeric exo- and endo-5-methyl-bicyclo[3.2.1]octane-6,8-diones

A detailed analysis of the 1H and 13C NMR spectra of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones is presented. The chemical shift of the C-5 angular methyl, the C-2 alkyl/olefinic (C-10)/C-2 methine protons, the aromatic proton shieldings and the characteristic AMX and ABX spectral pattern of the ketomethylene and bridgehead protons were found to be sensitive to the phenyl ring orientation (anisotropy). These distinctive features could be used for configurational distinction for this class of compounds. With increasing ortho-methoxy substitution on the phenyl ring, considerable deshilelding of the bridgehead proton was observed (ca. 0.6 ppm). Absence of the C-2 alkyl group in the desalkyl isomers resulted in substantial changes in the chemical shifts of different protons. A study of the NMR spectra of the corresponding bicyclic compounds with C-2 methoxy/hydroxy substitution instead of the aryl group revealed that the anisotropy of the phenyl ring and the electronegative oxygen substituents have opposite effects. The 13C NMR spectral assignment of each carbon resonance of C-2 aryl and alkyl/desalkyl substituted isomeric exo- and endo-5-methylbicyclo[3.2.1]octane-6,8-diones and the corresponding C-2 methoxy/hydroxy/chloro and methyl bicyclic compounds are reported. Additional ortho-methoxy substitution on the phenyl ring was found to produce considerable high field shifts of the C-10 and C-1 carbon resonances. A high-field shift was observed for the C-6 and C-8 carbonyl carbons, presumably due to 1,3-dicarbonyl interactions. The chemical shifts of C-1 aromatic, C-10 alkyl and C-2 carbons, which are sensitive to exo/endo isomerism, could be utilized in differentiating a pair of isomers.

Adsorption of carbon monoxide on the surfaces of polycrystalline transition metals and alloys: electron energy loss and ultraviolet photoelectron spectral studies1

Adsorption of CO has been investigated on the surfaces of polycrystalline transition metals as well as alloys by employing electron energy loss spectroscopy (eels) and ultraviolet photoelectron spectroscopy (ups). CO adsorbs on polycrystalline transition metal surfaces with a multiplicity of sites, each being associated with a characteristic CO stretching frequency; the relative intensities vary with temperature as well as coverage. Whilst at low temperatures (80- 120 K), low coordination sites are stabilized, the higher coordination sites are stabilized at higher temperatures (270-300 K). Adsorption on surfaces of polycrystalline alloys gives characteristic stretching frequencies due to the constituent metal sites. Alloying, however, causes a shift in the stretching frequencies, indicating the effect of the band structure on the nature of adsorption. The up spectra provide confirmatory evidence for the existence of separate metal sites in the alloys as well as for the high-temperature and low-temperature phases of adsorbed CO.

Urban energy fluxes in Helsinki and their high frequency spectral corrections

Inadvertent climate modification has led to an increase in urban temperatures compared to the surrounding rural area. The main reason for the temperature rise is the altered energy portioning of input net radiation to heat storage and sensible and latent heat fluxes in addition to the anthropogenic heat flux. The heat storage flux and anthropogenic heat flux have not yet been determined for Helsinki and they are not directly measurable. To the contrary, turbulent fluxes of sensible and latent heat in addition to net radiation can be measured, and the anthropogenic heat flux together with the heat storage flux can be solved as a residual. As a result, all inaccuracies in the determination of the energy balance components propagate to the residual term and special attention must be paid to the accurate determination of the components. One cause of error in the turbulent fluxes is the fluctuation attenuation at high frequencies which can be accounted for by high frequency spectral corrections. The aim of this study is twofold: to assess the relevance of high frequency corrections to water vapor fluxes and to assess the temporal variation of the energy fluxes. Turbulent fluxes of sensible and latent heat have been measured at SMEAR III station, Helsinki, since December 2005 using the eddy covariance technique. In addition, net radiation measurements have been ongoing since July 2007. The used calculation methods in this study consist of widely accepted eddy covariance data post processing methods in addition to Fourier and wavelet analysis. The high frequency spectral correction using the traditional transfer function method is highly dependent on relative humidity and has an 11% effect on the latent heat flux. This method is based on an assumption of spectral similarity which is shown not to be valid. A new correction method using wavelet analysis is thus initialized and it seems to account for the high frequency variation deficit. Anyhow, the resulting wavelet correction remains minimal in contrast to the traditional transfer function correction. The energy fluxes exhibit a behavior characteristic for urban environments: the energy input is channeled to sensible heat as latent heat flux is restricted by water availability. The monthly mean residual of the energy balance ranges from 30 Wm-2 in summer to -35 Wm-2 in winter meaning a heat storage to the ground during summer. Furthermore, the anthropogenic heat flux is approximated to be 50 Wm-2 during winter when residential heating is important.

Brillouin Scattering by Phonons Renormalized by Two-Magnon Excitations in Ferromagnetic Dielectrics

Brillouin scattering by one-phonon-two-magnon interacting excitations in ferromagnetic dielectrics is discussed. The basic light scattering mechanism is taken to be the modulation of the density-dependent optical dielectric polarizability of the medium by the dynamic strain field generated by the longitudinal acoustic (LA) phonons. The renormalization effects arising from the scattering of phonons by the two-magnon creation-annihilation processes have, however, been taken into account. Via these interactions, the Brillouin components corresponding to the two-magnon excitations are reflected indirectly in the spectrum of the phonon scattered light as line-broadening of the otherwise relatively sharp Brillouin doublet. The present mechanism is shown to be dominant in a clean saturated ferromagnetic dielectric with large magneto-strictive coupling constant, and with the magnetic ions in the orbitally quenched states. Following the linear response theory, an expression has been derived for the spectral density of the scattered light as a function of temperature, scattering angle, and the strength of the externally applied magnetic field. Some estimates are given for the line-width and line-shift of the Brillouin components for certain typical choice of parameters involved. The results are discussed in relation to some available calculations on the ultrasonic attenuation in ferromagnetic insulators at low temperatures.

Use of protein A gene fusions for the analysis of structure-function relationship of the transactivator protein C of bacteriophage Mu

A sensitive dimerization assay for DNA binding proteins has been developed using gene fusion technology. For this purpose, we have engineered a gene fusion using protein A gene of Staphylococcus aureus and C gene, the late gene transactivator of bacteriophage Mu. The C gene was fused to the 3' end of the gene for protein A to generate an A- C fusion. The overexpressed fusion protein was purified in a single step using immunoglobulin affinity chromatography. Purified fusion protein exhibits DNA binding activity as demonstrated by electrophoretic mobility shift assays. When the fusion protein A-C was mixed with C and analyzed for DNA binding, in addition to C and A-C specific complexes, a single intermediate complex comprising of a heterodimer of C and A-C fusion proteins was observed. Further, the protein A moiety in the fusion protein A-C does not contribute to DNA binding as demonstrated by proteolytic cleavage and circular dichroism (CD) analysis. The assay has also been applied to analyze the DNA binding domain of C protein by generating fusions between protein A and N- and C-terminal deletion mutants of C. The results indicate a role for the region towards the carboxy terminal of the protein in DNA binding. The general applicability of this method is discussed.

Spectral and thermal data on polystyrene peroxide

Poly(styrene peroxide) has been prepared and characterized. Nuclear magnetlc resonance (NMR) spectra Of the polymer show the shift Of aliphatic protons. Differential scanning calorimetric (DSC) and differential thermal analysis (DTA) results show anexothermic peak around 110 OC which is characteristic of peroxide decomposition.

Spectral Tuning and Adaptation to Different Light Environments of Mysid Visual Pigments

In the present thesis, questions of spectral tuning, the relation of spectral and thermal properties of visual pigments, and evolutionary adaptation to different light environments were addressed using a group of small crustaceans of the genus Mysis as a model. The study was based on microspectrophotometric measurements of visual pigment absorbance spectra, electrophysiological measurements of spectral sensitivities of dark-adapted eyes, and sequencing of the opsin gene retrieved through PCR. The spectral properties were related to the spectral transmission of the respective light environments, as well as to the phylogentic histories of the species. The photoactivation energy (Ea) was estimated from temperature effects on spectral sensitivity in the long-wavelength range, and calculations were made for optimal quantum catch and optimal signal-to-noise ratio in the different light environments. The opsin amino acid sequences of spectrally characterized individuals were compared to find candidate residues for spectral tuning. The general purpose was to clarify to what extent and on what time scale adaptive evolution has driven the functional properties of (mysid) visual pigments towards optimal performance in different light environments. An ultimate goal was to find the molecular mechanisms underlying the spectral tuning and to understand the balance between evolutionary adaptation and molecular constraints. The totally consistent segregation of absorption maxima (λmax) into (shorter-wavelength) marine and (longer-wavelength) freshwater populations suggests that truly adaptive evolution is involved in tuning the visual pigment for optimal performance, driven by selection for high absolute visual sensitivity. On the other hand, the similarity in λmax and opsin sequence between several populations of freshwater M. relicta in spectrally different lakes highlights the limits to adaptation set by evolutionary history and time. A strong inverse correlation between Ea and λmax was found among all visual pigments studied in these respects, including those of M. relicta and 10 species of vertebrate pigments, and this was used to infer thermal noise. The conceptual signal-to-noise ratios thus calculated for pigments with different λmax in the Baltic Sea and Lake Pääjärvi light environments supported the notion that spectral adaptation works towards maximizing the signal-to-noise ratio rather than quantum catch as such. Judged by the shape of absorbance spectra, the visual pigments of all populations of M. relicta and M. salemaai used exclusively the A2 chromophore (3, 4-dehydroretinal). A comparison of amino acid substitutions between M. relicta and M. salemaai indicated that mysid shrimps have a small number of readily available tuning sites to shift between a shorter - and a longer -wavelength opsin. However, phylogenetic history seems to have prevented marine M. relicta from converting back to the (presumably) ancestral opsin form, and thus the more recent reinvention of marine spectral sensitivity has been accomplished by some other novel mechanism, yet to be found

When and why threats go undetected: Impacts of event rate and shift length on threat detection accuracy during airport baggage screening

Objective: We aimed to assess the impact of task demands and individual characteristics on threat detection in baggage screeners. Background: Airport security staff work under time constraints to ensure optimal threat detection. Understanding the impact of individual characteristics and task demands on performance is vital to ensure accurate threat detection. Method: We examined threat detection in baggage screeners as a function of event rate (i.e., number of bags per minute) and time on task across 4 months. We measured performance in terms of the accuracy of detection of Fictitious Threat Items (FTIs) randomly superimposed on X-ray images of real passenger bags. Results: Analyses of the percentage of correct FTI identifications (hits) show that longer shifts with high baggage throughput result in worse threat detection. Importantly, these significant performance decrements emerge within the first 10 min of these busy screening shifts only. Conclusion: Longer shift lengths, especially when combined with high baggage throughput, increase the likelihood that threats go undetected. Application: Shorter shift rotations, although perhaps difficult to implement during busy screening periods, would ensure more consistently high vigilance in baggage screeners and, therefore, optimal threat detection and passenger safety.

Vibrational phase relaxation of O–H stretch in bulk water: Role of large amplitude angular jumps and negative cross-correlations among the forces on the O–H bond

The ultrafast vibrational phase relaxation of O–H stretch in bulk water is investigated in molecular dynamics simulations. The dephasing time (T2) of the O–H stretch in bulk water calculated from the frequency fluctuation time correlation function (Cω(t)) is in the range of 70–80 femtosecond (fs), which is comparable to the characteristic timescale obtained from the vibrational echo peak shift measurements using infrared photon echo [W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, Ann. Rev. Phys. Chem. 49 (1998) 99]. The ultrafast decay of Cω(t) is found to be responsible for the ultrashort T2 in bulk water. Careful analysis reveals the following two interesting reasons for the ultrafast decay of Cω(t). (A) The large amplitude angular jumps of water molecules (within 30–40 fs time duration) provide a large scale contribution to the mean square vibrational frequency fluctuation and gives rise to the rapid spectral diffusion on 100 fs time scale. (B) The projected force, due to all the atoms of the solvent molecules on the oxygen (FO(t)) and hydrogen (FH(t)) atom of the O–H bond exhibit a large negative cross-correlation (NCC). We further find that this NCC is partly responsible for a weak, non-Arrhenius temperature dependence of the dephasing rate.

Spectral states and accretion geometries in Galactic black hole binaries

Black hole X-ray binaries, binary systems where matter from a companion star is accreted by a stellar mass black hole, thereby releasing enormous amounts of gravitational energy converted into radiation, are seen as strong X-ray sources in the sky. As a black hole can only be detected via its interaction with its surroundings, these binary systems provide important evidence for the existence of black holes. There are now at least twenty cases where the measured mass of the X-ray emitting compact object in a binary exceeds the upper limit for a neutron star, thus inferring the presence of a black hole. These binary systems serve as excellent laboratories not only to study the physics of accretion but also to test predictions of general relativity in strongly curved space time. An understanding of the accretion flow onto these, the most compact objects in our Universe, is therefore of great importance to physics. We are only now slowly beginning to understand the spectra and variability observed in these X-ray sources. During the last decade, a framework has developed that provides an interpretation of the spectral evolution as a function of changes in the physics and geometry of the accretion flow driven by a variable accretion rate. This doctoral thesis presents studies of two black hole binary systems, Cygnus~X-1 and GRS~1915+105, plus the possible black hole candidate Cygnus~X-3, and the results from an attempt to interpret their observed properties within this emerging framework. The main result presented in this thesis is an interpretation of the spectral variability in the enigmatic source Cygnus~X-3, including the nature and accretion geometry of its so-called hard spectral state. The results suggest that the compact object in this source, which has not been uniquely identified as a black hole on the basis of standard mass measurements, is most probably a massive, ~30 Msun, black hole, and thus the most massive black hole observed in a binary in our Galaxy so far. In addition, results concerning a possible observation of limit-cycle variability in the microquasar GRS~1915+105 are presented as well as evidence of `mini-hysteresis' in the extreme hard state of Cygnus X-1.

Structure determination and biochemical studies on Bacillus stearothermophilus E53Q serine hydroxymethyltransferase and its complexes provide insights on function and enzyme memory

Serine hydroxymethyltransferase (SHMT) belongs to the alpha-family of pyridoxal 5'-phosphate-dependent enzymes and catalyzes the reversible conversion of L-Ser and etrahydrofolate to Gly and 5,10-methylene tetrahydrofolate. 5,10-Methylene tetrahydrofolate serves as a source of one-carbon fragment in many biological processes. SHMT also catalyzes the tetrahydrofolate-independent conversion of L-allo-Thr to Gly and acetaldehyde. The crystal structure of Bacillus stearothermophilus SHMT (bsSHMT) suggested that E53 interacts with the substrate, L-Ser and etrahydrofolate. To elucidate the role of E53, it was mutated to Q and structural and biochemical studies were carried out with the mutant enzyme. The internal aldimine structure of E53QbsSHMT was similar to that of the except for significant changes at Q53, Y60 and Y61. The wild-type enzyme, carboxyl of Gly and side chain of L-Ser were in two conformations in the respective external aldimine structures. The mutant enzyme was completely inactive for tetrahydrofolate-depen dent cleavage of L-Ser, whereas there was a 1.5-fold increase in the rate of tetrahydrofolate-independent reaction with L-allo-Thr. The results obtained from these studies suggest that E53 plays an essential role in tetrahydrofolate/5-formyl tetrahydrofolate binding and in the proper positioning of C beta of L-Ser for direct attack by N5 of tetrahydrofolate. Most interestingly, the structure of the complex obtained by cocrystallization of E53QbsSHMT with Gly and 5-formyl tetrahydrofolate revealed the gem-diamine form of pyridoxal 5'-phosphate bound to Gly and active site Lys. However, density for 5-formyl tetrahydrofolate was not observed. Gly carboxylate was in a single conformation, whereas pyridoxal 5'-phosphate had two distinct conformations. The differences between the structures of this complex and Gly external aldimine suggest that the changes induced by initial binding of 5-formyl tetrahydrofolate are retained even though 5-formyl tetrahydrofolate is absent in the final structure. Spectral studies carried out with this mutant enzyme also suggest that 5-formyl tetrahydrofolate binds to the E53QbsSHMT-Gly complex forming a quinonoid intermediate and falls off within 4 h of dialysis, leaving behind the mutant enzyme in the gemdiamine form. This is the first report to provide direct evidence for enzyme memory based on the crystal structure of enzyme complexes.