Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems

We consider a class of Ising spin systems on a set \Lambda of sites. The sites are grouped into units with the property that each site belongs to either one or two units, and the total internal energy of the system is the sum of the energies of the individual units, which in turn depend only on the number of up spins in the unit. We show that under suitable conditions on these interactions none of the |\Lambda| Lee-Yang zeros in the complex z = exp{2\beta h} plane, where \beta is the inverse temperature and h the uniform magnetic field, touch the positive real axis, at least for large values of \beta. In some cases one obtains, in an appropriately taken \beta to infinity limit, a gas of hard objects on a set \Lambda'; the fugacity for the limiting system is a rescaling of z and the Lee-Yang zeros of the new partition function also avoid the positive real axis. For certain forms of the energies of the individual units the Lee-Yang zeros of both the finite- and zero-temperature systems lie on the negative real axis for all \beta. One zero-temperature limit of this type, for example, is a monomer-dimer system; our results thus generalize, to finite \beta, a well-known result of Heilmann and Lieb that the Lee-Yang zeros of monomer-dimer systems are real and negative.Comment: Plain TeX. Seventeen pages, five figures from .eps files. Version 2 corrects minor errors in version

Patterns in Student Financial Aid at Rural Community Colleges

This article uses the 2005 Basic Classifications of the Carnegie Foundation for the Advancement of Teaching as a framing device through which to examine patterns of student financial aid at America\u27s rural community colleges, which represent 64% of all U.S. community colleges. Rural community colleges serve more first-time, full-time students than suburban and urban community colleges, and their 3.2 million students have different patterns of student financial aid. Rural small and medium colleges have the most aided students, receive more Pell Grants and institutional aid, and have more students incurring loan indebtedness than do other types of community colleges. The article offers recommendations for future research, as well as for policy development and practice

“Some Aspects of Functional Organisation in the Cerebral Cortex”

Stimulation of a sensory receptor initiates a nervous message, which, on arrival in the brain, undergoes modification; and may produce, in the mind, a related sensory experience. Some recent investigations on the vertebrate visual system have shed some light on the peripheral coding and central analysis of this kind of sensory message

Biomimetic spinning of recombinant silk proteins

In the past, we have successfully designed and produced a variety of engineered spider silk-like proteins (eADF3 and eADF4) based upon the primary sequence of the natural dragline proteins ADF3 and ADF4 from the spider Araneus diadematus [1]. Genetically engineered spider silk proteins can be modified at the molecular level to optimize the biochemical and mechanical properties of the final product. Although engineered spider silk proteins can be processed into fibers using different spinning methods, our group is interested in the technical realization of a biomimetic approach. Here, we present an overview over our biomimetic fiber production process

Vortex wandering in a forest of splayed columnar defects

We investigate the scaling properties of single flux lines in a random pinning landscape consisting of splayed columnar defects. Such correlated defects can be injected into Type II superconductors by inducing nuclear fission or via direct heavy ion irradiation. The result is often very efficient pinning of the vortices which gives, e.g., a strongly enhanced critical current. The wandering exponent \zeta and the free energy exponent \omega of a single flux line in such a disordered environment are obtained analytically from scaling arguments combined with extreme-value statistics. In contrast to the case of point disorder, where these exponents are universal, we find a dependence of the exponents on details in the probability distribution of the low lying energies of the columnar defects. The analytical results show excellent agreement with numerical transfer matrix calculations in two and three dimensions.Comment: 11 pages, 9 figure

Utility of the new Movement Disorder Society clinical diagnostic criteria for Parkinson's disease applied retrospectively in a large cohort study of recent onset cases

Objective: To examine the utility of the new Movement Disorder Society (MDS) diagnostic criteria in a large cohort of Parkinson's disease (PD) patients. Methods: Recently diagnosed (<3.5 years) PD cases fulfilling United Kingdom (UK) brain bank criteria in Tracking Parkinson's, a UK multicenter prospective natural history study were assessed by retrospective application of the MDS criteria. Results: In 2000 cases, 1835 (91.7%) met MDS criteria for PD, either clinically established (n = 1261, 63.1%) or clinically probable (n = 574, 28.7%), leaving 165 (8.3%) not fulfilling criteria. Clinically established cases were significantly more likely to have limb rest tremor (89.3%), a good l-dopa response (79.5%), and olfactory loss (71.1%), than clinically probable cases (60.6%, 44.4%, and 34.5% respectively), but differences between probable PD and ‘not PD’ cases were less evident. In cases not fulfilling criteria, the mean MDS UPDRS3 score (25.1, SD 13.2) was significantly higher than in probable PD (22.3, SD 12.7, p = 0.016) but not established PD (22.9, SD 12.0, p = 0.066). The l-dopa equivalent daily dose of 341 mg (SD 261) in non-PD cases was significantly higher than in probable PD (250 mg, SD 214, p < 0.001) and established PD (308 mg, SD 199, p = 0.025). After 30 months' follow-up, 89.5% of clinically established cases at baseline remained as PD (established/probable), and 86.9% of those categorized as clinically probable at baseline remained as PD (established/probable). Cases not fulfilling PD criteria had more severe parkinsonism, in particular relating to postural instability, gait problems, and cognitive impairment. Conclusion: Over 90% of cases clinically diagnosed as early PD fulfilled the MDS criteria for PD. Those not fulfilling criteria may have an atypical parkinsonian disorder or secondary parkinsonism that is not correctly identified by the UK Brain Bank criteria, but possibly by the new criteria

Self-assembly using dendritic building blocks - towards controllable nanomaterials

Dendritic molecules have well defined, three-dimensional branched architectures, and constitute a unique nanoscale toolkit. This review focuses on examples in which individual dendritic molecules are assembled into more complex arrays via non-covalent interactions. In particular, it illustrates how the structural information programmed into the dendritic architecture controls the assembly process, and as a consequence, the properties of the supramolecular structures which are generated. Furthermore, the review emphasises how the use of non-covalent (supramolecular) interactions, provides the assembly process with reversibility, and hence a high degree of control. The review also illustrates how self-assembly offers an ideal approach for amplifying the branching of small, synthetically accessible, relatively inexpensive dendritic systems (e.g. dendrons), into highly branched complex nanoscale assemblies. The review begins by considering the assembly of dendritic molecules to generate discrete, well-defined supramolecular assemblies. The variety of possible assembled structures is illustrated, and the ability of an assembled structure to encapsulate a templating unit is described. The ability of both organic and inorganic building blocks to direct the assembly process is discussed. The review then describes larger discrete assemblies of dendritic molecules, which do not exist as a single well-defined species, but instead exist as statistical distributions. For example, assembly around nanoparticles, the assembly of amphiphilic dendrons and the assembly of dendritic systems in the presence of DNA will all be discussed. Finally, the review examines dendritic molecules, which assemble or order themselves into extended arrays. Such systems extend beyond the nanoscale into the microscale or even the macroscale domain, exhibiting a wide range of different architectures. The ability of these assemblies to act as gel-phase or liquid crystalline materials will be considered. Taken as a whole, this review emphasises the control and tunability that underpins the assembly of nanomaterials using dendritic building blocks, and furthermore highlights the potential future applications of these assemblies at the interfaces between chemistry, biology and materials science

c-axis electrodynamics of ybco

New measurements of surface impedance in ybco show that the c-axis penetration depth and conductivity below Tc exhibit behaviour different from that observed in the planes. The c-axis penetration depth never has the linear temperature dependence seen in the ab-plane. Instead of the conductivity peak seen in the planes, the c-axis microwave conductivity falls to low values in the superconducting state, then rises slightly below 20K. These results show that c-axis transport remains incoherent below Tc, even though this is one of the least anisotropic cuprate superconductors.Comment: 4-page

Tidal Wave II, Community Colleges, and Student Financial Aid

Article examining the impact of "Tidal Wave II" (a bulge of high school graduates wanting access to higher education) on public community colleges for the five-year period from 2000-2001 to 2005-2006

A Mathematical Framework for Agent Based Models of Complex Biological Networks

Agent-based modeling and simulation is a useful method to study biological phenomena in a wide range of fields, from molecular biology to ecology. Since there is currently no agreed-upon standard way to specify such models it is not always easy to use published models. Also, since model descriptions are not usually given in mathematical terms, it is difficult to bring mathematical analysis tools to bear, so that models are typically studied through simulation. In order to address this issue, Grimm et al. proposed a protocol for model specification, the so-called ODD protocol, which provides a standard way to describe models. This paper proposes an addition to the ODD protocol which allows the description of an agent-based model as a dynamical system, which provides access to computational and theoretical tools for its analysis. The mathematical framework is that of algebraic models, that is, time-discrete dynamical systems with algebraic structure. It is shown by way of several examples how this mathematical specification can help with model analysis.Comment: To appear in Bulletin of Mathematical Biolog