Unification modulo a partial theory of exponentiation

Modular exponentiation is a common mathematical operation in modern cryptography. This, along with modular multiplication at the base and exponent levels (to different moduli) plays an important role in a large number of key agreement protocols. In our earlier work, we gave many decidability as well as undecidability results for multiple equational theories, involving various properties of modular exponentiation. Here, we consider a partial subtheory focussing only on exponentiation and multiplication operators. Two main results are proved. The first result is positive, namely, that the unification problem for the above theory (in which no additional property is assumed of the multiplication operators) is decidable. The second result is negative: if we assume that the two multiplication operators belong to two different abelian groups, then the unification problem becomes undecidable.Comment: In Proceedings UNIF 2010, arXiv:1012.455

A combined experimental and computational fluid dynamics analysis of the dynamics of drop formation

This article presents a complementary experimental and computational investigation of the effect of viscosity and flowrate on the dynamics of drop formation in the dripping mode. In contrast to previous studies, numerical simulations are performed with two popular commercial computational fluid dynamics (CFD) packages, CFX and FLOW-3D, both of which employ the volume of fluid (VOF) method. Comparison with previously published experimental and computational data and new experimental results reported here highlight the capabilities and limitations of the aforementioned packages

Three Cuts for Accelerated Interval Propagation

This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here

Imipramine blue sensitively and selectively targets FLT3-ITD positive acute myeloid leukemia cells.

Aberrant cytokine signaling initiated from mutant receptor tyrosine kinases (RTKs) provides critical growth and survival signals in high risk acute myeloid leukemia (AML). Inhibitors to FLT3 have already been tested in clinical trials, however, drug resistance limits clinical efficacy. Mutant receptor tyrosine kinases are mislocalized in the endoplasmic reticulum (ER) of AML and play an important role in the non-canonical activation of signal transducer and activator of transcription 5 (STAT5). Here, we have tested a potent new drug called imipramine blue (IB), which is a chimeric molecule with a dual mechanism of action. At 200-300 nM concentrations, IB is a potent inhibitor of STAT5 through liberation of endogenous phosphatase activity following NADPH oxidase (NOX) inhibition. However, at 75-150 nM concentrations, IB was highly effective at killing mutant FLT3-driven AML cells through a similar mechanism as thapsigargin (TG), involving increased cytosolic calcium. IB also potently inhibited survival of primary human FLT3/ITD+ AML cells compared to FLT3/ITDneg cells and spared normal umbilical cord blood cells. Therefore, IB functions through a mechanism involving vulnerability to dysregulated calcium metabolism and the combination of fusing a lipophilic amine to a NOX inhibiting dye shows promise for further pre-clinical development for targeting high risk AML

Do GPs want or need formal support following a patient suicide?: a mixed methods study.

BACKGROUND: Patient suicide can be a devastating event for some general practitioners (GPs). Few guidelines exist to aid or support GPs in the aftermath of patient suicide. AIM: To explore GPs views on how they are affected by a patient suicide and the formal support available to them following a patient suicide. DESIGN: Questionnaires and semi-structured interviews. SETTING: General practices in the northwest of England. METHODS: About 198 semi-structured interviews were conducted as part of a retrospective study. Interviews were transcribed verbatim and analysed using descriptive statistics and a framework thematic approach. RESULTS: GPs were aged between 31 and 67 years, 144 (73%) were male and the number of years in practice varied between 8 and 40 years (median = 24 years). GPs were based at 133 (67%) urban and 65 (33%) rural practices, 30 (15%) were single-handed GP practices and 168 (85%) practices had two or more GPs. About 131 (66%) GPs reported being affected by patient suicide through feelings of grief, guilt and self-scrutiny. A greater number of years in practice may have been protective against these effects. About 54 (27%) GPs reported having mostly 'informal' support from peers or colleagues and support was less available to younger and single handed GPs. CONCLUSIONS: Our findings suggest that the majority of GPs are affected by patient suicide and most seek informal support from their peers and colleagues. Although many indicated that informal support systems were adequate and provided a protective environment, procedures should be developed to ensure the availability of guidelines for those who may require formal support

Information entropy and nucleon correlations in nuclei

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. It is found that $S_r$ depends strongly on $\ln A$ and does not depend very much on the model. The behaviour of $S_k$ is opposite. The various cases we consider can be classified according to either the quantity of the experimental data we use or by the values of $S$, i.e., the increase of the quality of the density and of the momentum distributions leads to an increase of the values of $S$. In all cases, apart from the linear relation $S=a+b\ln A$, the linear relation $S=a_V+b_V \ln V$ also holds. V is the mean volume of the nucleus. If $S$ is considered as an ensemble entropy, a relation between $A$ or $V$ and the ensemble volume can be found. Finally, comparing different electron scattering experiments for the same nucleus, it is found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that $S$ could be used to compare different experiments for the same nucleus and to choose the most reliable one.Comment: 14 pages, 4 figures, 2 table