The Generalized Ricci Flow for 3D Manifolds with One Killing Vector

We consider 3D flow equations inspired by the renormalization group (RG) equations of string theory with a three dimensional target space. By modifying the flow equations to include a U(1) gauge field, and adding carefully chosen De Turck terms, we are able to extend recent 2D results of Bakas to the case of a 3D Riemannian metric with one Killing vector. In particular, we show that the RG flow with De Turck terms can be reduced to two equations: the continual Toda flow solved by Bakas, plus its linearizaton. We find exact solutions which flow to homogeneous but not always isotropic geometries

The XPF-ERCC1 endonuclease and homologous recombination contribute to the repair of minor groove DNA interstrand crosslinks inmammalian cells produced by the pyrrolo[2,1-c][1,4]benzodiazepine dimer SJG-136

SJG-136, a pyrrolo[2,1-c][1,4]benzodiazepine (PBD) dimer, is a highly efficient interstrand crosslinking agent that reacts with guanine bases in a 5'-GATC-3' sequence in the DNA minor groove. SJG-136 crosslinks form rapidly and persist compared to those produced by conventional crosslinking agents such as nitrogen mustard, melphalan or cisplatin which bind in the DNA major groove. A panel of Chinese hamster ovary (CHO) cells with defined defects in specific DNA repair pathways were exposed to the bi-functional agents SJG-136 and melphalan, and to their mono-functional analogues mmy-SJG and mono-functional melphalan. SJG-136 was >100 times more cytotoxic than melphalan, and the bi-functional agents were much more cytotoxic than their respective mono-functional analogues. Cellular sensitivity of both SJG-136 and melphalan was dependent on the XPF-ERCC1 heterodimer, and homologous recombination repair factors XRCC2 and XRCC3. The relative level of sensitivity of these repair mutant cell lines to SJG-136 was, however, significantly less than with major groove crosslinking agents. In contrast to melphalan, there was no clear correlation between sensitivity to SJG-136 and crosslink unhooking capacity measured using a modified comet assay. Furthermore, repair of SJG-136 crosslinks did not involve the formation of DNA double-strand breaks. SJG-136 cytotoxicity is likely to result from the poor recognition of DNA damage by repair proteins resulting in the slow repair of both mono-adducts and more importantly crosslinks in the minor groove

MACH-T: A Behavior-based Mobile Node Trust Evaluation Algorithm

Resiliency and availability in community and public service networks may be economically enhanced by building new ad hoc networks of private mobile devices and joining these to public service networks at specific trusted points. Resiliency in such ad hoc networks relies on the afforded increased availability but also on security which is in turn built on trust. In this article, we describe MACH-T, a novel behavior-based algorithm for mobile ad hoc network node trust building. MACH-T uses historical mobile node geographic location traces to incrementally calculate node trust values based on the concepts of node capability, commitment, and consistency. We describe experiments and results from evaluating MACH-T using real GPS traces from the Microsoft Research Geolife and University of Rome Tor Vergata Roma Taxi datasets. Our results show that MACH-T builds a reliable trust value and corresponding confidence value based on learned patterns of time spent in qualifying geographic locations

The rationality of Sol manifolds

Let $\Gamma$ be the fundamental group of a manifold modeled on three dimensional Sol geometry. We prove that $\Gamma$ has a finite index subgroup $G$ which has a rational growth series with respect to a natural generating set. We do this by enumerating $G$ by a regular language. However, in contrast to most earlier proofs of this sort our regular language is not a language of words in the generating set, but rather reflects a different geometric structure in $G$.Comment: 30 pages; author's name changed to agree with published version; to appear in Journal of Algebr

Dual Garside structure and reducibility of braids

Benardete, Gutierrez and Nitecki showed an important result which relates the geometrical properties of a braid, as a homeomorphism of the punctured disk, to its algebraic Garside-theoretical properties. Namely, they showed that if a braid sends a curve to another curve, then the image of this curve after each factor of the left normal form of the braid (with the classical Garside structure) is also standard. We provide a new simple, geometric proof of the result by Benardete-Gutierrez-Nitecki, which can be easily adapted to the case of the dual Garside structure of braid groups, with the appropriate definition of standard curves in the dual setting. This yields a new algorithm for determining the Nielsen-Thurston type of braids

How to Avoid the Ambiguity in Applying the Copernican Principle for Cosmic Topology: Take the Observational Approach

It is often stated that homogeneity and isotropy of the Universe are assumptions of the almost Friedmann-Lema^itre (FL) model (the hot big bang model), inspired from the Copernican Principle. However, only local homogeneity and isotropy are required by the model: multiply connected almost FL models are locally homogeneous and isotropic, but they can be globally anisotropic and/or globally inhomogeneous. Toy models are used here to show how global anisotropy and/or global inhomogeneity of an almost FL model could be shown directly in observations. This approach may avoid having to make any assumptions regarding global anisotropy and inhomogeneity.Comment: 9 pages, 6 figures, accepted for Advances in Space Researc

Quadri-tilings of the plane

We introduce {\em quadri-tilings} and show that they are in bijection with dimer models on a {\em family} of graphs $\{R^*\}$ arising from rhombus tilings. Using two height functions, we interpret a sub-family of all quadri-tilings, called {\em triangular quadri-tilings}, as an interface model in dimension 2+2. Assigning "critical" weights to edges of $R^*$, we prove an explicit expression, only depending on the local geometry of the graph $R^*$, for the minimal free energy per fundamental domain Gibbs measure; this solves a conjecture of \cite{Kenyon1}. We also show that when edges of $R^*$ are asymptotically far apart, the probability of their occurrence only depends on this set of edges. Finally, we give an expression for a Gibbs measure on the set of {\em all} triangular quadri-tilings whose marginals are the above Gibbs measures, and conjecture it to be that of minimal free energy per fundamental domain.Comment: Revised version, minor changes. 30 pages, 13 figure

Absolute Determination of Stress in Textured Materials

The continuum theory of elastic wave propagation in deformed, anisotropic solids is reviewed with emphasis on those features which might be used to distinguish between stress induced changes in ultrasonic velocity and changes due to material anisotropy, such as would be produced by preferred grain orientation in a polycrystalline metal As noted by previous authors, one such feature is the difference in velocity of two shear waves, whose directions of propagation and polarization have been interchanged. In particular, when these directions fall along the symmetry axes of a rolled plate (assuming orthorhombic symmetry) and these are also the directions of principal stress, then the theory predicts that ρ(V 12 2−V 21 2) = T1−T2 where ρ is the density, Vij is the velocity of a shear wave propagating along the i-axis and polarized along the j-axis, and Ti is a principal stress component. In addition to being independent of the degree of texture, this relationship has the advantage that no microstructurally dependent acoustoelastic coefficient is involved. The applicability of this prediction of continuum theory to heterogeneous engineering materials such as metal polycrystals is discussed using previously reported stress dependencies of ultrasonic velocities, and new experiments to answer some remaining questions are described. A possible configuration for using the effect to measure the value of a uniform stress in a plate of unknown texture is proposed

Self-harm & suicide: encouraging social support to reduce risk

Within HMPPS, rates of self-harm and suicide continue to be high. Managing self-harm and suicide in prison is challenging and can have negative impacts on both prison staff and residents. Research has shown that social support, such as contact with friends and family, can reduce the risk of self-harm and suicide. This report presents an overview of the current evidence, bringing together information from a wide range of high-quality academic sources, including peer-reviewed papers, reports, and research with people living in the community. It aims to give a clear outline of the primary evidence and suggest how social support can be applied in a prison setting to inform practice in HMPPS

Randomized comparison of ultrasonic aspiration versus conventional electrocautery for dissection of the human internal thoracic artery

AbstractThe most common technique currently employed to harvest the internal thoracic artery for coronary artery bypass grafting is conventional electrocautery. This study compared an alternative method, electrocautery with an ultrasonic aspirator, for harvesting the internal thoracic artery. Patients were randomly assigned to one of six experimental groups (conventional electrocautery, ultrasonic aspirator at settings of 60%, 80%, and 100% power output, and ultrasonic aspirator in 100% CAVI-Pulse modes 1 and 3). Ring segments of internal thoracic artery were studied in an organ bath. Contraction responses were elicited with 123 mmol/L potassium physiologic salt solution, KPSS, KPSS solution containing noradrenaline, and a cumulative noradrenaline dose-contraction curve. Relaxation studies were performed with the vasodilators acetylcholine, bradykinin, and sodium nitroprusside. Forty percent of the electrocauterized vessels were traumatized or damaged and failed to respond to contractile stimuli, whereas only 10% of the vessels in ultrasonic aspirator groups 60%, 80%, and 100% failed to respond. All vessels in the group harvested by ultrasonic aspirator in 100% CAVI-Pulse mode 1 responded, whereas 20% of the vessels in the group harvested by ultrasonic aspirator in 100% CAVI-Pulse mode 3 failed to respond. All settings of electrocautery with an ultrasonic aspirator produced a greater contractile response to KPSS and noradrenaline. Acetylcholine and sodium nitroprusside produced similar relaxations in all groups, but the bradykinin responses were significantly improved in all groups undergoing 100% electrocautery with an ultrasonic aspirator. These results suggest that 100% electrocautery with an ultrasonic aspirator, particularly in 100% CAVI-Pulse mode 1, resulted in less damage and trauma than conventional electrocautery during harvesting of the internal thoracic artery. (J T HORAC CARDIOVASC SURG 1996;111:1194-9