Symmetry properties of one- and two- electron molecular integrals

The maximum numbers of distinct one- and two-electron integrals that arise in calculating the electronic energy of a molecule are discussed. It is shown that these may be calculated easily using the character table of the symmetry group of the set of basis functions used to express the wave function. Complications arising from complex group representations and from a conflict of symmetry between the basis set and the nuclear configuration are considered and illustrated by examples.

Fast assembly of fock matrices utilising symmetry properties of the basis set

A method of assembling the elements of the Fock matrix is described which is a modification of that due to Dacre. Lists of symmetry equivalent one-electron integrals are used as pointers to abbreviate the process of collecting two-electron integrals into the Fock matrix.

Intercepting Cyclic Dinucleotide Signaling with Small Molecules

Bacterial infections, especially the ones that are caused by multidrug-resistant strains, are becoming increasingly difficult to treat and put enormous stress on healthcare systems. Recently President Obama announced a new initiative to combat the growing problem of antibiotic resistance. New types of antibiotic drugs are always in need to catch up with the rapid speed of bacterial drug-resistance acquisition. Bacterial second messengers, cyclic dinucleotides, play important roles in signal transduction and therefore are currently generating great buzz in the microbiology community because it is believed that small molecules that inhibit cyclic dinucleotide signaling could become next-generation antibacterial agents. The first identified cyclic dinucleotide, c-di-GMP, has now been shown to regulate a large number of processes, such as virulence, biofilm formation, cell cycle, quorum sensing, etc. Recently, another cyclic dinucleotide, c-di-AMP, has emerged as a regulator of key processes in Gram-positive and mycobacteria. C-di-AMP is now known to regulate DNA damage sensing, fatty acid synthesis, potassium ion transport, cell wall homeostasis and host type I interferon response induction. Due to the central roles that cyclic dinucleotides play in bacteria, we are interested in small molecules that intercept cyclic dinucleotide signaling with the hope that these molecules would help us learn more details about cyclic dinucleotide signaling or could be used to inhibit bacterial viability or virulence. This dissertation documents the development of several small molecule inhibitors of a cyclic dinucleotide synthase (DisA from B. subtilis) and phosphodiesterases (RocR from P. aeruginosa and CdnP from M. tuberculosis). We also demonstrate that an inhibitor of RocR PDE can inhibit bacterial swarming motility, which is a virulence factor.

A SUBSET OF 3´ TO 5´ EXORIBONUCLEASES ARE THE PRIMARY ENZYMES RESPONSIBLE FOR THE DEGRADATION OF PGPG IN CYCLIC DI-GMP SIGNALING

Bis-(3´-5´)-cyclic dimeric guanosine monophosphate, or cyclic di-GMP (c-di-GMP) is a ubiquitous bacterial second messenger that regulates processes such biofilm formation, motility, and virulence. C-di-GMP is synthesized by diguanylate cyclases (DGCs), while phosphodiesterases (PDE-As) end signaling by linearizing c-di-GMP to 5ʹ-phosphoguanylyl-(3ʹ,5ʹ)-guanosine (pGpG), which is then hydrolyzed to two GMPs by previously unidentified enzymes termed PDE-Bs. To identify the PDE-B responsible for pGpG turnover, a screen for pGpG binding proteins in a Vibrio cholerae open reading frame library was conducted to identify potential pGpG binding proteins. This screen led to identification of oligoribonuclease (Orn). Purified Orn binds to pGpG and can cleave pGpG to GMP in vitro. A deletion mutant of orn in Pseudomonas aeruginosa was highly defective in pGpG turnover and accumulated pGpG. Deletion of orn also resulted in accumulation c-di-GMP, likely through pGpG-mediated inhibition of the PDE-As, causing an increase in c-di-GMP-governed auto-aggregation and biofilm. Thus, we found that Orn serves as the primary PDE-B enzyme in P. aeruginosa that removes pGpG, which is necessary to complete the final step in the c-di-GMP degradation pathway. However, not all bacteria that utilize c-di-GMP signaling also have an ortholog of orn, suggesting that other PDE-Bs must be present. Therefore, we asked whether RNases that cleave small oligoribonucleotides in other species could also act as PDE-Bs. NrnA, NrnB, and NrnC can rapidly degrade pGpG to GMP. Furthermore, they can reduce the elevated aggregation and biofilm formation in P. aeruginosa ∆orn. Together, these results indicate that rather than having a single dedicated PDE-B, different bacteria utilize distinct RNases to cleave pGpG and complete c-di-GMP signaling. The ∆orn strain also has a growth defect, indicating changes in other regulatory processes that could be due to pGpG accumulation, c-di-GMP accumulation, or another effect due to loss of Orn. We sought to investigate the genetic pathways responsible for these growth defect phenotypes by use of a transposon suppressor screen, and also investigated transcriptional changes using RNA-Seq. This work identifies that c-di-GMP degradation intersects with RNA degradation at the point of the Orn and the functionally related RNases.

2-categories and cyclic homology

The topic of this thesis is the application of distributive laws between comonads to the theory of cyclic homology. The work herein is based on the three papers 'Cyclic homology arising from adjunctions', 'Factorisations of distributive laws', and 'Hochschild homology, lax codescent,and duplicial structure', to which the current author has contributed. Explicitly, our main aims are: 1) To study how the cyclic homology of associative algebras and of Hopf algebras in the original sense of Connes and Moscovici arises from a distributive law, and to clarify the role of different notions of bimonad in this generalisation. 2) To extend the procedure of twisting the cyclic homology of a unital associative algebra to any duplicial object defined by a distributive law. 3) To study the universality of Bohm and Stefan’s approach to constructing duplicial objects, which we do in terms of a 2-categorical generalisation of Hochschild (co)homology. 4) To characterise those categories whose nerve admits a duplicial structure.

Leader Based Cyclic Pursuit

In this work a system of autonomous agents engaged in cyclic pursuit (under constant bearing (CB) strategy) is considered, for which one informed agent (the leader) also senses and responds to a stationary beacon. Building on the framework proposed in a previous work on beacon-referenced cyclic pursuit, necessary and suffi- cient conditions for the existence of circling equilibria in a system with one informed agent are derived, with discussion of stability and performance. In a physical testbed, the leader (robot) is equipped with a sound sensing apparatus composed of a real time embedded system, estimating direction of arrival of sound by an Interaural Level and Phase Difference Algorithm, using empirically determined phase and level signatures, and breaking front-back ambiguity with appropriate sensor placement. Furthermore a simple framework for implementing and evaluating the performance of control laws with the Robot Operating System (ROS) is proposed, demonstrated, and discussed.

Symmetry reduction due to gallium substitution in the garnet Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12

Single-crystal structure refinements on lithium lanthanum zirconate (LLZO; Li7La3Zr2O12) substituted with gallium were successfully carried out in the cubic symmetry space group I [Formula: see text]3d. Gallium was found on two lithium sites as well as on the lanthanum position. Due to the structural distortion of the resulting Li6.43(2)Ga0.52(3)La2.67(4)Zr2O12 (Ga-LLZO) single crystals, a reduction of the LLZO cubic garnet symmetry from Ia[Formula: see text] d to I [Formula: see text]3d was necessary, which could hardly be analysed from X-ray powder diffraction data.

Calculable lepton masses, seesaw relations, and four neutrino mixings in a 3-3-1 model with an extra U(1) symmetry

We propose a scheme in which the masses of the heavier leptons obey seesaw type relations. The light lepton masses, except the electron and the electron neutrino ones, are generated by one loop level radiative corrections. We work in a version of the 3-3-1 electroweak model that predicts singlets (charged and neutral) of heavy leptons beyond the known ones. An extra U(1)(Omega) symmetry is introduced in order to avoid the light leptons getting masses at the tree level. The electron mass induces an explicit symmetry breaking at U(1)(Omega). We discuss also the mixing matrix among four neutrinos. The new energy scale required is not higher than a few TeV.

Symmetry-breaking in chiral polymerisation

We propose a model for chiral polymerisation and investigate its symmetric and asymmetric solutions. The model has a source species which decays into left- and right-handed types of monomer, each of which can polymerise to form homochiral chains; these chains are susceptible to `poisoning' by the opposite handed monomer. Homochiral polymers are assumed to influence the proportion of each type of monomer formed from the precursor. We show that for certain parameter values a positive feedback mechanism makes the symmetric steady-state solution unstable. The kinetics of polymer formation are then analysed in the case where the system starts from zero concentrations of monomers and chains. We show that following a long induction time, extremely large concentrations of polymers are formed for a short time, during this time an asymmetry introduced into the system by a random external perturbation may be massively amplified. The system then approaches one of the steady-state solutions described above.

Aerosol transport in a bifurcating tube at cyclic flow

Branching tube flow is a common feature of many fields of science and technology, and occurs both in animate and inanimate systems [1]. The transport of aerosol particles is of particular importance in industrial flow networks but also for the respiratory tree [2]. In this analysis a 3-D numerical study is performed to investigate transport and deposition of aerosol particles in branching tubes. Bifurcation tubes designed according to Hess-Murray law [3] but with different branching angles are analyzed. This study covers cyclic flow conditions at frequencies of 0.25 Hz, 0.50 Hz and 0.75 Hz, Stokes numbers ranging between 0.03 and 0.25, and Reynolds numbers up to 3000.

Tabu search for the cyclic bandwidth problem

International audience

Impact of the cation symmetry on the mutual solubilities between water and imidazolium-based ionic liquids

Aiming at the evaluation of the impact of the ionic liquids (ILs) cation symmetry on their phase behaviour, in this work, novel mutual solubilities with water of the symmetric series of [C(n)C(n)im][NTf2] (with n=1-5) were determined and compared with their isomeric forms of the asymmetric [C(n)C(1)im][NTf2] group. While the solubility of isomeric ILs in water was found to be similar, the solubility of water in ILs follows the same trend up to a maximum cation alkyl side chain length. For n >= 4 in [C(n)C(n)im][NTf2] the solubility of water in the asymmetric ILs is slightly higher than that observed in the symmetric counterparts. The thermodynamic properties of solution and solvation derived from the experimental solubility data of ILs in water at infinite dilution, namely the Gibbs energy, enthalpy and entropy were used to evaluate the cation symmetry effect on the ILs solvation. It is shown that the solubility of ILs in water is entropically driven and highly influenced by the cation size. Accordingly, it was found that the ILs solubility in water of both symmetric and asymmetric series depends on their molecular volume. Based on these findings, a linear correlation between the logarithm of the solubility of ILs in water and their molar volume is here proposed for the [NTf2]-based ILs at a fixed temperature.

Analysis of cyclic variations during mode switching between spark ignition and controlled auto-ignition combustion operations

© IMechE 2014. Controlled auto-ignition, also known as homogeneous charge compression ignition, has been the subject of extensive research because of their ability to provide simultaneous reductions in fuel consumption and NOx emissions from a gasoline engine. However, due to its limited operation range, switching between controlled auto-ignition and spark ignition combustion is needed to cover the complete operating range of a gasoline engine for passenger car applications. Previous research has shown that the spark ignition -controlled auto-ignition hybrid combustion (SCHC) has the potential to control the ignition timing and heat release process during the mode transition operations. However, it was found that the SCHC is often characterized with large cycle-to-cycle variations. The cyclic variations in the in-cylinder pressure are particularly noticeable in terms of both their peak values and timings while the coefficient of variation in the indicated mean effective pressure is much less. In this work, the cyclic variations in SCHC operations were analyzed by means of in-cylinder pressure and heat release analysis in a single-cylinder gasoline engine equipped with Variable Valve Actuation (VVA) systems. First, characteristics of the in-cylinder pressure traces during the spark ignition-controlled auto-ignition hybrid combustion operation are presented and their heat release processes analyzed. In order to clarify the contribution to heat release and cyclic variation in SCHC, a new method is introduced to identify the occurrence of auto-ignition combustion and its subsequent heat release process. Based on the new method developed, the characteristics of cyclic variations in the maximum rate of pressure rise and different stages of heat release process have been analyzed and discussed.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.

STRUCTURAL AND FUNCTIONAL STUDIES OF CYCLIC K48-LINKED DIUBIQUITIN

K48-linked di-ubiquitin exists in a dynamic equilibrium between open and closed states. The structure of K48-Ub2 in the closed conformation features a hydrophobic interface formed between the two Ub domains. The same hydrophobic residues at the interface are involved in binding to ubiquitin-associated (UBA) domains. Cyclization of K48-Ub2 should limit the range of conformations available for such interactions. Interestingly, cyclic K48-linked Ub2 (cycUb2) has been found in vivo and can be isolated in vitro to study its structure and dynamics. In this study, a crystal structure of cycUb2 was obtained, and the dynamics of cycUb2 were characterized by solution NMR. The crystal structure of cycUb2, which is in agreement with solution NMR data, is closed with the hydrophobic patches of each Ub domain buried at the interface. Despite its structural constraints, cycUb2 was still able to interact with UBA domains, albeit with lower affinity.