Large N reduction on a twisted torus

We consider SU(N) lattice gauge theory at infinite N defined on a torus with a CP invariant twist. Massless fermions are incorporated in an elegant way, while keeping them quenched. We present some numerical results which suggest that twisting can make numerical simulations of planar QCD more efficient.Comment: 14 pages, 2 figures, 1 tabl

Numerical solution of open string field theory in Schnabl gauge

Using traditional Virasoro $L_0$ level-truncation computations, we evaluate the open bosonic string field theory action up to level $(10,30)$. Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value $-1$ at level $L=6$. Extrapolating the level-truncation data for $L\leq 10$ to estimate the vacuum energies for $L > 10$, we predict that the energy reaches a minimum value at $L \sim 12$, and then turns back to approach $-1$ asymptotically as $L \rightarrow \infty$. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at $L \sim 26$, and then turns back to approach the expected analytical result as $L \rightarrow \infty$.Comment: 37 pages, 9 figures, some typos correcte

Convex drawings of the complete graph: topology meets geometry

In this work, we introduce and develop a theory of convex drawings of the complete graph $K_n$ in the sphere. A drawing $D$ of $K_n$ is convex if, for every 3-cycle $T$ of $K_n$, there is a closed disc $\Delta_T$ bounded by $D[T]$ such that, for any two vertices $u,v$ with $D[u]$ and $D[v]$ both in $\Delta_T$, the entire edge $D[uv]$ is also contained in $\Delta_T$. As one application of this perspective, we consider drawings containing a non-convex $K_5$ that has restrictions on its extensions to drawings of $K_7$. For each such drawing, we use convexity to produce a new drawing with fewer crossings. This is the first example of local considerations providing sufficient conditions for suboptimality. In particular, we do not compare the number of crossings {with the number of crossings in} any known drawings. This result sheds light on Aichholzer's computer proof (personal communication) showing that, for $n\le 12$, every optimal drawing of $K_n$ is convex. Convex drawings are characterized by excluding two of the five drawings of $K_5$. Two refinements of convex drawings are h-convex and f-convex drawings. The latter have been shown by Aichholzer et al (Deciding monotonicity of good drawings of the complete graph, Proc.~XVI Spanish Meeting on Computational Geometry (EGC 2015), 2015) and, independently, the authors of the current article (Levi's Lemma, pseudolinear drawings of $K_n$, and empty triangles, \rbr{J. Graph Theory DOI: 10.1002/jgt.22167)}, to be equivalent to pseudolinear drawings. Also, h-convex drawings are equivalent to pseudospherical drawings as demonstrated recently by Arroyo et al (Extending drawings of complete graphs into arrangements of pseudocircles, submitted)

A new Viola (Violaceae) from the Argentinian Andes

Viola beati, a hitherto unknown species of V. sect. Andinium (Violaceae) is described and illustrated. It is an inconspicuous, diminutive, perennial forb currently known from only one locality in NW Argentina. We draw attention to its morphology, ecology, rarity and endemism. The differences between V. beati and its apparently only close relative, V. singularis J. M. Watson & A. R. Flores, are defined

Large NN reduction with the Twisted Eguchi-Kawai model

We examine the breaking of $Z_N$ symmetry recently reported for the Twisted Eguchi-Kawai model (TEK). We analyse the origin of this behaviour and propose simple modifications of twist and lattice action that could avoid the problem. Our results show no sign of symmetry breaking and allow us to obtain values of the large $N$ infinite volume string tension in agreement with extrapolations from results based upon straightforward methods.Comment: latex file 14 pages, 4 figure

Geminiviral protein Rep interferes in PCNA sumoylation

Rep is a multifunctional protein essential for replication of geminivirus that interferes with the sumoylation of a key protein in the DNA replication, PCNA (Proliferating Cell Nuclear Antigen). It is known that Rep is capable of interacting with a plethora of plant proteins, including PCNA. Despite the biological significance remains unknown, it’s thought that this interaction should play a key role for generating new copies of the virus genome. Therefore, in order to characterize this interaction, we study which lysines are sumoylated in tomato PCNA (SlPCNA). Considering conservation, location and presence of sumoylation domain criteria, we have identified some candidate lysines and studied how its mutation affects this protein sumoylation in Escherichia coli assays. Finally, we plan to confirm and characterize the Rep interference on SlPCNA sumoylation and determine if this interference occurs in planta.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Calibration of piezoelectric positioning actuators using a reference voltage-to-displacement transducer based on quartz tuning forks

We use a piezoelectric quartz tuning fork to calibrate the displacement of ceramic piezoelectric scanners which are widely employed in scanning probe microscopy. We measure the static piezoelectric response of a quartz tuning fork and find it to be highly linear, non-hysteretic and with negligible creep. These performance characteristics, close to those of an ideal transducer, make quartz transducers superior to ceramic piezoelectric actuators. Furthermore, quartz actuators in the form of a tuning fork have the advantage of yielding static displacements comparable to those of local probe microscope scanners. We use the static displacement of a quartz tuning fork as a reference to calibrate the three axis displacement of a ceramic piezoelectric scanner. Although this calibration technique is a non-traceable method, it can be more versatile than using calibration grids because it enables to characterize the linear and non-linear response of a piezoelectric scanner in a broad range of displacements, spanning from a fraction of a nanometer to hundreds of nanometers. In addition, the creep and the speed dependent piezoelectric response of ceramic scanners can be studied in detail.Comment: 9 pages, 3 figure