A Proof of Convergence of the B-RED and P-RED Algorithms for Random Early Detection

In [8], we recently presented two computationally efficient algorithms named B-RED and P-RED for random early detection. In this letter, we present the mathematical proof of convergence of these algorithms under general conditions to local minima.

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

Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of llostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein esponsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

1H NMR study of internal motions and quantum rotational tunneling in (CH3)4NGeCl3

(CH3)4NGeCl3 is prepared, characterized and studied using 1H NMR spin lattice relaxation time and second moment to understand the internal motions and quantum rotational tunneling. Proton second moment is measured at 7 MHz as function of temperature in the range 300-77 K and spin lattice relaxation time (T1) is measured at two Larmor frequencies, as a function of temperature in the range 270-17 K employing a homemade wide-line/pulsed NMR spectrometers. T1 data are analyzed in two temperature regions using relevant theoretical models. The relaxation in the higher temperatures (270-115 K) is attributed to the hindered reorientations of symmetric groups (CH3 and (CH3)4N). Broad asymmetric T1 minima observed below 115 K down to 17 K are attributed to quantum rotational tunneling of the inequivalent methyl groups.

Structure and Bonding in Cyclic Isomers of B2AlHnm (n = 3−6, m = −2 to +1): A Comparative Study with B3Hnm, BAl2Hnm and Al3Hnm†

The structure, bonding and energetics of B2AlHnm (n = 3−6, m = −2 to +1) are compared with corresponding homocyclic boron, aluminum analogues and BAl2Hnm using density functional theory (DFT). Divalent to hexacoordinated boron and aluminum atoms are found in these species. The geometrical and bonding pattern in B2AlH4− is similar to that for B2SiH4. Species with lone pairs on the divalent boron and aluminum atoms are found to be minima on the potential energy surface of B2AlH32−. A dramatic structural diversity is observed in going from B3Hnm to B2AlHnm, BAl2Hnm and Al3Hnm and this is attributable to the preference of lower coordination on aluminum, higher coordination on boron and the higher multicenter bonding capability of boron. The most stable structures of B3H6+, B2AlH5 and BAl2H4− and the trihydrogen bridged structure of Al3H32− show an isostructural relationship, indicating the isolobal analogy between trivalent boron and divalent aluminum anion.

Structure and bonding of MCB5H7 and its sandwiched dimer CB5H6M–MCB5H6 (M = Si, Ge, Sn): Isomer stability and preference for slip distorted structure

We find sandwiched metal dimers CB5H6M–MCB5H6 (M = Si, Ge, Sn) which are minima in the potential energy surface with a characteristic M–M single bond. The NBO analysis and the M–M distances (Å) (2.3, 2.44 and 2.81 for M = Si, Ge, Sn) indicate substantial M–M bonding. Formal generation of CB5H6M–MCB5H6 has been studied theoretically. Consecutive substitution of two boron atoms in B7H−27 by M (Si, Ge, Sn) and carbon, respectively followed by dehydrogenation may lead to our desired CB5H6M–MCB5H6. We find that the slip distorted geometry is preferred for MCB5H7 and its dehydrogenated dimer CB5H6M–MCB5H6. The slip-distortion of M–M bond in CB5H6M–MCB5H6 is more than the slip distortion of M–H bond in MCB5H7. Molecular orbital analysis has been done to understand the slip distortion. Larger M–M bending (CB5H6M–MCB5H6) in comparison with M–H bending (MCB5H7) is suspected to be encouraged by stabilization of one of the M–M π bonding MO’s. Preference of M to occupy the apex of pentagonal skeleton of MCB5H7 over its icosahedral analogue MCB10H11 has been observed.

Vibrational dynamics and boson peak in a supercooled polydisperse liquid

Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

A genetic algorithm with characteristic amplification through multiple geographically isolated populations and varied fitness landscapes

This paper proposes a new approach, wherein multiple populations are evolved on different landscapes. The problem statement is broken down, to describe discrete characteristics. Each landscape, described by its fitness landscape is used to optimize or amplify a certain characteristic or set of characteristics. Individuals from each of these populations are kept geographically isolated from each other Each population is evolved individually. After a predetermined number of evolutions, the system of populations is analysed against a normalized fitness function. Depending on this score and a predefined merging scheme, the populations are merged, one at a time, while continuing evolution. Merging continues until only one final population remains. This population is then evolved, following which the resulting population will contain the optimal solution. The final resulting population will contain individuals which have been optimized against all characteristics as desired by the problem statement. Each individual population is optimized for a local maxima. Thus when populations are merged, the effect is to produce a new population which is closer to the global maxima.

Raman and infra-red spectra of crystalline ammonium sulphamate

Raman spectrum of a single crystal of ammonium sulphamate has been recorded for the two different orientations using λ 2537 resonance radiation of the mercury as the exciter. Thirty-four Raman lines have been observed of which eight belong to the lattice oscillations. Weak hydrogen bonding of NH2 group in the crystal was predicted. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc, using Carl Zeiss UR10 IR spectrometer. Thirty-five absorption maxima could be identified.

Raman and infra-red spectra of crystalline potassium sulphamate

Raman spectrum of a single crystal of potassium sulphamate has been recorded for the first time using λ 2536 radiation of mercury as the exciter. Thirty-three Raman lines have been observed of which nine belong to the lattice oscillations. The infra-red absorption spectrum of the substance was taken in the powder form in potassium bromide disc using Carl Zeiss UR 10 IR spectrometer. Thirty-six absorption maxima could be identified of which twenty-five have been recorded for the first time. The analysis clearly shows that the N-H bond in the crystalline potassium sulphamate is not hydrogen-bonded to any appreciable extent.

Applicability of partition ratios, mercuric chloride complexes, and chromatographic behavior for the identification of carotenoids

Partition ratios and M50 values of different carotenoids in hexaneaqueous methanol were determined. Mercuric chloride complexes of 14 epoxy carotenoids were prepared and their absorption maxima in acetone were estimated. The difference in chromatographic behavior of carotenoid epoxides on alumina and magnesium oxide-Celite columns is discussed. It is shown that the magnesium oxide-Celite column behaves as a reverse-phase chromatographic column to alumina column.

Evaluation of solute-solvent interactions from solvent blue-shifts of n → π* transitions of C=O, C=S, NO2 and N=N groups: hydrogen bond energies of various donor-acceptor systems

Effects of non-polar, polar and proton-donating solvents on the n → π* transitions of C=O, C=S, NO2 and N=N groups have been investigated. The shifts of the absorption maxima in non-polar and polar solvents have been related to the electrostatic interactions between solute and solvent molecules, by employing the theory of McRAE. In solvents which can donate protons the solvent shifts are mainly determined by solute-solvent hydrogen bonding. Isobestic points have been found in the n → π* bonds of ethylenetrithio-carbonate in heptane-alcohol and heptane-chloroform solvent systems, indicating the existence of equilibria between the hydrogen bonded and the free species of the solute. Among the different proton-donating solvents studied water produces the largest blue-shifts. The blue-shifts in alcohols decrease in the order 2,2,2-trifluoroethanol, methanol, ethanol, isopropanol and t-butanol, the blue-shift in trifluoroethanol being nearly equal to that in water. This trend is exactly opposite to that for the self-association of alcohols. It is suggested that electron-withdrawing groups not merely decrease the extent of self-association of alcohols, but also increase the ability to donate hydrogen bonds. The approximate hydrogen-bond energies for several donor-acceptor systems have been estimated. In a series of aliphatio ketones and nitro compounds studied, the blue-shifts and consequently the hydrogen bond energies decrease with the decrease in the electron-withdrawing power of the alkyl groups. It is felt that electron-withdrawing groups render the chromophores better proton acceptors, and the alcohols better donors. A linear relationship between n → π* transition frequency and the infrared frequency of ethylenetrithiocarbonate has been found. It is concluded that stabilization of the electronic ground states of solute molecules by electrostatic and/or hydrogen-bond interactions determines the solvent shifts.

Studies on phosphorus oxychloride and aluminium chloride complex

1. Anhydrous aluminium chloride reacts with phosphorus oxychloride to give a complex with a composition AlCl3.2 POCl3 which can be prepared in the form of a free flowing powder. 2. The phosphorus oxychloride-aluminium chloride complex in nitrobenzene dissociates into AlCl3.POCl3 and POCl3 as indicated by the cryoscopic measurements. 3. The solution of the complex in nitrobenzene has a higher specific conductivity than the corresponding electrical conductivities of individual components. Similar higher electrical conductance is observed when the two components are mixed in nitrobenzene in different proportions. 4.When a solution of anhydrous aluminium chloride in nitrobenzene is titrated conductometrically against a solution of phosphorus oxychloride in nitrobenzene, a limiting value in the conductivity is reached at point corresponding to the molecular composition, the components in the ratio of 1:2 AlCl3: POCl3 in solution. 5. The absorption maxima of the complex in nitrobenzene solution differ from the absorption maximum of the individual components.

Energy landscape view of phase transitions and slow dynamics in thermotropic liquid crystals

Thermotropic liquid crystals are known to display rich phase behavior on temperature variation. Although the nematic phase is orientationally ordered but translationally disordered, a smectic phase is characterized by the appearance of a partial translational order in addition to a further increase in orientational order. In an attempt to understand the interplay between orientational and translational order in the mesophases that thermotropic liquid crystals typically exhibit upon cooling from the high-temperature isotropic phase, we investigate the potential energy landscapes of a family of model liquid crystalline systems. The configurations of the system corresponding to the local potential energy minima, known as the inherent structures, are determined from computer simulations across the mesophases. We find that the depth of the potential energy minima explored by the system along an isochor grows through the nematic phase as temperature drops in contrast to its insensitivity to temperature in the isotropic and smectic phases. The onset of the growth of the orientational order in the parent phase is found to induce a translational order, resulting in a smectic-like layer in the underlying inherent structures; the inherent structures, surprisingly, never seem to sustain orientational order alone if the parent nematic phase is sandwiched between the high-temperature isotropic phase and the low-temperature smectic phase. The Arrhenius temperature dependence of the orientational relaxation time breaks down near the isotropic-nematic transition. We find that this breakdown occurs at a temperature below which the system explores increasingly deeper potential energy minima.