The Spectra of Lamplighter Groups and Cayley Machines

We calculate the spectra and spectral measures associated to random walks on restricted wreath products of finite groups with the infinite cyclic group, by calculating the Kesten-von Neumann-Serre spectral measures for the random walks on Schreier graphs of certain groups generated by automata. This generalises the work of Grigorchuk and Zuk on the lamplighter group. In the process we characterise when the usual spectral measure for a group generated by automata coincides with the Kesten-von Neumann-Serre spectral measure.Comment: 36 pages, improved exposition, main results slightly strengthene

On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page

Janus Scorpionates: Supramolecular Tectons for the Directed Assembly of Hard−Soft Alkali Metallopolymer Chains

A new scorpionate ligand [HB(mtda)3-] containing mercaptothiadiazolyl (mtda) heterocyclic rings with both hard nitrogen donors and soft sulfur donors has been prepared. This new ligand, the Janus scorpionate, is a hybrid of a tris(pyrazolyl)borate and a tris(mercaptoimidazolyl)borate. The differential hard/soft character of the dissimilar donor groups in this bridging ligand was exploited for the controlled solid-state organization of homometallic and heterometallic alkali metal coordination polymers. Remarkably, in the case of sodium, coordination polymers with both acentric (with NaS3N3H kernels) and centric (with alternating NaN6 and NaS6H2 kernels) chains are found in the same crystal (where the centricity is defined by the relative orientations of the B−H bonds of the ligands along the lattice). For the homometallic potassium congener, the larger cation size, compared to sodium, induced significant distortions and favored a polar arrangement of ligands in the resulting coordination polymer chain. An examination of the solid-state structure of the mixed alkali metal salt system revealed that synergistic binding of smaller sodium cations to the nitrogen portion and of the larger potassium cations to the sulfur portion of the ligand minimizes the ligand distortions relative to the homometallic coordination polymer counterparts, a design feature of the ligand that likely assists in thermodynamically driving the self-assembly of the heterometallic chains. The effect of alkali metal complexation on the solution properties of the ligand was studied by comparing NMR chemical shifts, B−H stretching frequencies, and electrochemical properties with those of the noncoordinating tetrabutylammonium salt of the scorpionate. The similarity of these data regardless of cation indicates that the salts are likely dissociated in solution rather than maintaining their solid-state polymeric structures. This data is augmented by the ESI(±) mass spectral data for a series of mixed alkali metal tris(mercaptothiadiazolyl)borates that also indicate that dissociation occurs in solution

Toward Charge-neutral ‘soft scorpionates’: Coordination Chemistry and Lewis Acid Promoted Isomerization of tris(1-organo-imidazol-2-ylthio)methanes

Two tris(1-organo-imidazol-2-ylthio)methanes, HC(S-timR)3 (R = organo = methyl, tert-butyl), have been prepared by a triphasic reaction between chloroform, the appropriate heterocycle, and saturated aqueous solutions of Na2CO3, in the presence of a phase transfer agent, (NBu4)(Br). These ligands have been characterized both spectroscopically and by single crystal X-ray diffraction. The reaction chemistry of these potentially N,N,N-tripodal ligands with AgBF4 was also explored where simple 1:1 coordination complexes could be isolated from reactions performed in THF solution at room temperature. The derivative {Ag[HC(S-timMe)3]}(BF4) was structurally characterized which showed that the ligand binds in a μ–κ2N,κ1N-mode to give a coordination polymer with an interesting layered supramolecular structure. Surprisingly, heating CH3CN solutions of the silver complexes at reflux resulted in decomposition of the complex and concomitant isomerization of the ligands to give metal-free tris(3-organo-1-imidazole-2-thione)methane, HC(N-imtR)3; the heretofore elusive charge-neutral analogues of the well-studied ‘soft scorpionate’ TmR− anions. The solution isomerization of HC(S-timR)3 to HC(N-imtR)3 was found to be general, occurring in a variety of solvents with any of a host of different Lewis acids [para-toluenesulfonic acid, KPF6, and M(CO)5Br (M = Mn, Re)] but did not occur by heating in the absence of Lewis acid. The compound HC(N-imtMe)3 exhibited unusually low solubility in common organic solvents. Single crystal X-ray diffraction of HC(N-imtMe)3 revealed a remarkable honeycomb supramolecular structure with ca. 5 Å channels filled with solvent. The robust nature of this solid is a result of strong dipolar stacking interactions of molecules into polymer chains bolstered by concerted π–π and CH–π interactions involving the heterocycles, holding the chains together in the remaining two dimensions

Ligand-Promoted Solvent-Dependent Ionization and Conformational Equilibria of Re(CO)\u3csub\u3e3\u3c/sub\u3eBr[CH\u3csub\u3e2\u3c/sub\u3e(\u3cem\u3eS\u3c/em\u3e-tim)\u3csub\u3e2\u3c/sub\u3e] (tim = 1-methylthioimidazolyl). Crystal Structures of Re(CO)\u3csub\u3e3\u3c/sub\u3eBr[CH\u3csub\u3e2\u3c/sub\u3e(\u3cem\u3eS\u3c/em\u3e-tim)\u3csub\u3e2\u3c/sub\u3e] and {Re(CO)\u3csub\u3e3\u3c/sub\u3e(CH\u3csub\u3e3\u3c/sub\u3eCN)[CH\u3csub\u3e2\u3c/sub\u3e(S-tim)\u3csub\u3e2\u3c/sub\u3e]}(PF\u3csub\u3e6\u3c/sub\u3e)

The compounds Re(CO)3Br[CH2(S-tim)2] (1) and {Re(CO)3(CH3CN)[CH2(S-tim)2]}(PF6) (2), where tim is 1-methylthioimidazolyl, were prepared in high yields and characterized both in the solid state and in solution. The solid-state structures show that the ligand acts in a chelating binding mode where the eight-member chelate ring adopts twist-boat conformations in both compounds. A comparison of both solid-state IR data for CO stretching frequencies and the solution-phase voltammetric measurements for the Re1+/2+ couples between 1, 2, and related N,N-chelates of the rhenium tricarbonyl moiety indicate that the CH2(S-tim)2 ligand is a stronger donor than even the ubiquitous dipyridyl ligands. A combination of NMR spectroscopic studies and voltammetric studies revealed that compound 1 undergoes spontaneous ionization to form {Re(CO)3(CH3CN)[CH2(S-tim)2]+}(Br-) in acetonitrile. Ionization does not occur in solvents such as CH2Cl2 or acetone that are less polar and Lewis basic (less coordinating). The equilibrium constant at 293 K for the ionization of 1 in CH3CN is 4.3 × 10-3. The eight-member chelate rings in each 1 and 2 were found to be conformationally flexible in all solvents, and boat-chair conformers could be identified. Variable-temperature NMR spectroscopic studies were used to elucidate the various kinetic and thermodynamic parameters associated with the energetically accessible twist-boat to twist-boat and twist-boat to boat-chair interconversions

A Second-Generation Janus Scorpionate Ligand: Controlling Coordination Modes in Iron(II) Complexes by Steric Modulation

The second-generation Janus scorpionate ligand [HB(mtdaMe)3−] containing methyl-mercaptothiadiazolyl (mtdaMe) heterocyclic rings and (N,N,N-) and (S,S,S-) binding pockets has been prepared. The effect of methyl substitution versus the unsubstituted first-generation Janus scorpionate [HB(mtda)3]− on the coordination chemistry with alkali metals and on the binding preferences and on the ground spin state of iron(II) complexes has been studied structurally and by 57Fe Mossbauer Spectroscopy

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references adde

Rehydration behaviour of spray-dried micellar casein concentrates produced using microfiltration of skim milk at cold or warm temperatures

peer-reviewedMicrofiltration (MF) of skim milk, when combined with diafiltration (DF), facilitates the manufacture of liquid micellar casein concentrate (MCC), which can be spray-dried into high-protein (≥80% protein, dry-basis) powders. MCC powders rehydrate slowly, which is typically considered a defect by end-users. This study compared the impact of cold (<10 °C) or warm (50 °C) MF/DF on the rehydration characteristics of MCC powders (MCCcold and MCCwarm, respectively). The wetting properties of the MCC powders, measured using optical tensiometry, were found to be equivalent. However, pronounced differences in dispersion characteristics were measured, and, after 90 min rehydration at 50 °C, liberated casein micelles accounted for only 7.5% of total particle volume in MCCwarm compared with 48% in MCCcold. Due to its superior dispersion characteristics, MCCcold yielded 50–60% less sediment during analytical centrifugation experiments. Cold MF/DF may improve the solubility of MCC powders by accelerating the release of casein micelles from powder particles during rehydration

Calorie restriction alters mitochondrial protein acetylation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72130/1/j.1474-9726.2009.00503.x.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/72130/2/ACEL_503_sm_FigS1.pd

Challenges and opportunities for implementing integrated mental health care: a district level situation analysis from five low- and middle-income countries.

BACKGROUND: Little is known about how to tailor implementation of mental health services in low- and middle-income countries (LMICs) to the diverse settings encountered within and between countries. In this paper we compare the baseline context, challenges and opportunities in districts in five LMICs (Ethiopia, India, Nepal, South Africa and Uganda) participating in the PRogramme for Improving Mental health carE (PRIME). The purpose was to inform development and implementation of a comprehensive district plan to integrate mental health into primary care. METHODS: A situation analysis tool was developed for the study, drawing on existing tools and expert consensus. Cross-sectional information obtained was largely in the public domain in all five districts. RESULTS: The PRIME study districts face substantial contextual and health system challenges many of which are common across sites. Reliable information on existing treatment coverage for mental disorders was unavailable. Particularly in the low-income countries, many health service organisational requirements for mental health care were absent, including specialist mental health professionals to support the service and reliable supplies of medication. Across all sites, community mental health literacy was low and there were no models of multi-sectoral working or collaborations with traditional or religious healers. Nonetheless health system opportunities were apparent. In each district there was potential to apply existing models of care for tuberculosis and HIV or non-communicable disorders, which have established mechanisms for detection of drop-out from care, outreach and adherence support. The extensive networks of community-based health workers and volunteers in most districts provide further opportunities to expand mental health care. CONCLUSIONS: The low level of baseline health system preparedness across sites underlines that interventions at the levels of health care organisation, health facility and community will all be essential for sustainable delivery of quality mental health care integrated into primary care