Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

We report a detailed physical analysis on a family of isolated, antiferro-magnetically (AF) coupled, chromium(III) finite chains, of general formula (Cr(RCO(2))(2)F)(n) where the chain length n = 6 or 7. Additionally, the chains are capped with a selection of possible terminating ligands, including hfac (= 1,1,1,5,5,5-hexafluoropentane-2,4-dionate(1-)), acac (= pentane-2,4-dionate(1-)) or (F)(3). Measurements by inelastic neutron scattering (INS), magnetometery and electron paramagnetic resonance (EPR) spectroscopy have been used to study how the electronic properties are affected by n and capping ligand type. These comparisons allowed the subtle electronic effects the choice of capping ligand makes for odd member spin 3/2 ground state and even membered spin 0 ground state chains to be investigated. For this investigation full characterisation of physical properties have been performed with spin Hamiltonian parameterisation, including the determination of Heisenberg exchange coupling constants and single ion axial and rhombic anisotropy. We reveal how the quantum spin energy levels of odd or even membered chains can be modified by the type of capping ligand terminating the chain. Choice of capping ligands enables Cr-Cr exchange coupling to be adjusted by 0, 4 or 24%, relative to Cr-Cr exchange coupling within the body of the chain, by the substitution of hfac, acac or (F)(3) capping ligands to the ends of the chain, respectively. The manipulation of quantum spin levels via ligands which play no role in super-exchange, is of general interest to the practise of spin Hamilton modelling, where such second order effects are generally not considered of relevance to magnetic properties.

Multilead quantitative electroencephalogram profile and cognitive evoked potentials (P300) in healthy subjects after a single dose of olanzapine

RATIONALE: Olanzapine is an atypical antipsychotic drug with a more favourable safety profile than typical antipsychotics with a hitherto unknown topographic quantitative electroencephalogram (QEEG) profile. OBJECTIVES: We investigated electrical brain activity (QEEG and cognitive event related potentials, ERPs) in healthy subjects who received olanzapine. METHODS: Vigilance-controlled, 19-channel EEG and ERP in an auditory odd-ball paradigm were recorded before and 3 h, 6 h and 9 h after administration of either a single dose of placebo or olanzapine (2.5 mg and 5 mg) in ten healthy subjects. QEEG was analysed by spectral analysis and evaluated in nine frequency bands. For the P300 component in the odd-ball ERP, the amplitude and latency was analysed. Statistical effects were tested using a repeated-measurement analysis of variance. RESULTS: For the interaction between time and treatment, significant effects were observed for theta, alpha-2, beta-2 and beta-4 frequency bands. The amplitude of the activity in the theta band increased most significantly 6 h after the 5-mg administration of olanzapine. A pronounced decrease of the alpha-2 activity especially 9 h after 5 mg olanzapine administration could be observed. In most beta frequency bands, and most significantly in the beta-4 band, a dose-dependent decrease of the activity beginning 6 h after drug administration was demonstrated. Topographic effects could be observed for the beta-2 band (occipital decrease) and a tendency for the alpha-2 band (frontal increase and occipital decrease), both indicating a frontal shift of brain electrical activity. There were no significant changes in P300 amplitude or latency after drug administration. Conclusion: QEEG alterations after olanzapine administration were similar to EEG effects gained by other atypical antipsychotic drugs, such as clozapine. The increase of theta activity is comparable to the frequency distribution observed for thymoleptics or antipsychotics for which treatment-emergent somnolence is commonly observed, whereas the decrease of beta activity observed after olanzapine administration is not characteristic for these drugs. There were no clear signs for an increased cerebral excitability after a single-dose administration of 2.5 mg and 5 mg olanzapine in healthy controls.

Hamilton decompositions of 6-regular abelian Cayley graphs

In 1969, Lovasz asked whether every connected, vertex-transitive graph has a Hamilton path. This question has generated a considerable amount of interest, yet remains vastly open. To date, there exist no known connected, vertex-transitive graph that does not possess a Hamilton path. For the Cayley graphs, a subclass of vertex-transitive graphs, the following conjecture was made: Weak Lovász Conjecture: Every nontrivial, finite, connected Cayley graph is hamiltonian. The Chen-Quimpo Theorem proves that Cayley graphs on abelian groups flourish with Hamilton cycles, thus prompting Alspach to make the following conjecture: Alspach Conjecture: Every 2k-regular, connected Cayley graph on a finite abelian group has a Hamilton decomposition. Alspach’s conjecture is true for k = 1 and 2, but even the case k = 3 is still open. It is this case that this thesis addresses. Chapters 1–3 give introductory material and past work on the conjecture. Chapter 3 investigates the relationship between 6-regular Cayley graphs and associated quotient graphs. A proof of Alspach’s conjecture is given for the odd order case when k = 3. Chapter 4 provides a proof of the conjecture for even order graphs with 3-element connection sets that have an element generating a subgroup of index 2, and having a linear dependency among the other generators. Chapter 5 shows that if Γ = Cay(A, {s1, s2, s3}) is a connected, 6-regular, abelian Cayley graph of even order, and for some1 ≤ i ≤ 3, Δi = Cay(A/(si), {sj1 , sj2}) is 4-regular, and Δi ≄ Cay(ℤ3, {1, 1}), then Γ has a Hamilton decomposition. Alternatively stated, if Γ = Cay(A, S) is a connected, 6-regular, abelian Cayley graph of even order, then Γ has a Hamilton decomposition if S has no involutions, and for some s ∈ S, Cay(A/(s), S) is 4-regular, and of order at least 4. Finally, the Appendices give computational data resulting from C and MAGMA programs used to generate Hamilton decompositions of certain non-isomorphic Cayley graphs on low order abelian groups.

Hamilton-Waterloo problem with triangle and C9 factors

The Hamilton-Waterloo problem and its spouse-avoiding variant for uniform cycle sizes asks if Kv, where v is odd (or Kv - F, if v is even), can be decomposed into 2-factors in which each factor is made either entirely of m-cycles or entirely of n-cycles. This thesis examines the case in which r of the factors are made up of cycles of length 3 and s of the factors are made up of cycles of length 9, for any r and s. We also discuss a constructive solution to the general (m,n) case which fixes r and s.

Crystal structure of the alpha(6)beta(6) holoenzyme of propionyl-coenzyme A carboxylase.

Propionyl-coenzyme A carboxylase (PCC), a mitochondrial biotin-dependent enzyme, is essential for the catabolism of the amino acids Thr, Val, Ile and Met, cholesterol and fatty acids with an odd number of carbon atoms. Deficiencies in PCC activity in humans are linked to the disease propionic acidaemia, an autosomal recessive disorder that can be fatal in infants. The holoenzyme of PCC is an alpha(6)beta(6) dodecamer, with a molecular mass of 750 kDa. The alpha-subunit contains the biotin carboxylase (BC) and biotin carboxyl carrier protein (BCCP) domains, whereas the beta-subunit supplies the carboxyltransferase (CT) activity. Here we report the crystal structure at 3.2-A resolution of a bacterial PCC alpha(6)beta(6) holoenzyme as well as cryo-electron microscopy (cryo-EM) reconstruction at 15-A resolution demonstrating a similar structure for human PCC. The structure defines the overall architecture of PCC and reveals unexpectedly that the alpha-subunits are arranged as monomers in the holoenzyme, decorating a central beta(6) hexamer. A hitherto unrecognized domain in the alpha-subunit, formed by residues between the BC and BCCP domains, is crucial for interactions with the beta-subunit. We have named it the BT domain. The structure reveals for the first time the relative positions of the BC and CT active sites in the holoenzyme. They are separated by approximately 55 A, indicating that the entire BCCP domain must translocate during catalysis. The BCCP domain is located in the active site of the beta-subunit in the current structure, providing insight for its involvement in the CT reaction. The structural information establishes a molecular basis for understanding the large collection of disease-causing mutations in PCC and is relevant for the holoenzymes of other biotin-dependent carboxylases, including 3-methylcrotonyl-CoA carboxylase (MCC) and eukaryotic acetyl-CoA carboxylase (ACC).

Minimizing the Threat of a Positive Majority Deficit in Two-tier Voting Systems with Equipopulous Units

The mean majority deficit in a two-tier voting system is a function of the partition of the population. We derive a new square-root rule: For odd-numbered population sizes and equipopulous units the mean majority deficit is maximal when the member size of the units in the partition is close to the square root of the population size. Furthermore, within the partitions into roughly equipopulous units, partitions with small even numbers of units or small even-sized units yield high mean majority deficits. We discuss the implications for the winner-takes-all system in the US Electoral College.