In search of Nemesis

The parallax of all stars of visual magnitude greater than about 6.5 has already been measured. If Nemesis is a main-sequence star 1 parsec away, this requires Nemesis's mass to be less than about 0.4 solar masses. If it were less than about 0.05 solar masses its gravity would be too weak to trigger a comet storm. If Nemesis is on the main sequence, this mass range requires it to be a red dwarf. A red dwarf companion would probably have been missed by standard astronomical surveys. Nearby stars are usually found because they are bright or have high proper motion. However, Nemesis's proper motion would now be 0.01 arcsec/yr, and if it is a red dwarf its magnitude is about 10 - too dim to attract attention. Unfortunately, standard four-color photometry does not distinguish between red dwarfs and giants. So although surveys such as the Dearborn Red Star Catalog list stars by magnitude and spectral type, they do not identify the dwarfs. Every star of the correct spectral type and magnitude must be scrutinized. Our candidate list is a hybrid; candidate red stars are identified in the astrometrically poor Dearborn Red Star Catalog and their positions are corrected using the Hubble Guide Star Catalog. When errors in the Dearborn catalog make it impossible to identify the corresponding Hubble star, the fields are split so that we have one centering on each possible candidate. We are currently scrutinizing 3098 fields, which we believe contain all possible red dwarf candidates in the northern hemisphere. Since our last report the analysis and database software has been completely rebuilt to take advantage of updated hardware, to make the data more accessible, and to implement improved methods of data analysis. The software is now completed and we are eliminating stars every clear night

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let T be an ideal triangulation of M. The deformation variety D(T), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T, is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.Comment: 31 pages, 11 figures; minor changes; to appear in Mathematische Zeitschrif

Dimension of the Torelli group for Out(F_n)

Let T_n be the kernel of the natural map from Out(F_n) to GL(n,Z). We use combinatorial Morse theory to prove that T_n has an Eilenberg-MacLane space which is (2n-4)-dimensional and that H_{2n-4}(T_n,Z) is not finitely generated (n at least 3). In particular, this recovers the result of Krstic-McCool that T_3 is not finitely presented. We also give a new proof of the fact, due to Magnus, that T_n is finitely generated.Comment: 27 pages, 9 figure

Subset currents on free groups

We introduce and study the space of \emph{subset currents} on the free group $F_N$. A subset current on $F_N$ is a positive $F_N$-invariant locally finite Borel measure on the space $\mathfrak C_N$ of all closed subsets of $\partial F_N$ consisting of at least two points. While ordinary geodesic currents generalize conjugacy classes of nontrivial group elements, a subset current is a measure-theoretic generalization of the conjugacy class of a nontrivial finitely generated subgroup in $F_N$, and, more generally, in a word-hyperbolic group. The concept of a subset current is related to the notion of an "invariant random subgroup" with respect to some conjugacy-invariant probability measure on the space of closed subgroups of a topological group. If we fix a free basis $A$ of $F_N$, a subset current may also be viewed as an $F_N$-invariant measure on a "branching" analog of the geodesic flow space for $F_N$, whose elements are infinite subtrees (rather than just geodesic lines) of the Cayley graph of $F_N$ with respect to $A$.Comment: updated version; to appear in Geometriae Dedicat

Augmenting forearm crutches with wireless sensors for lower limb rehabilitation

Forearm crutches are frequently used in the rehabilitation of an injury to the lower limb. The recovery rate is improved if the patient correctly applies a certain fraction of their body weight (specified by a clinician) through the axis of the crutch, referred to as partial weight bearing (PWB). Incorrect weight bearing has been shown to result in an extended recovery period or even cause further damage to the limb. There is currently no minimally invasive tool for long-term monitoring of a patient's PWB in a home environment. This paper describes the research and development of an instrumented forearm crutch that has been developed to wirelessly and autonomously monitor a patient's weight bearing over the full period of their recovery, including its potential use in a home environment. A pair of standard forearm crutches are augmented with low-cost off-the-shelf wireless sensor nodes and electronic components to provide indicative measurements of the applied weight, crutch tilt and hand position on the grip. Data are wirelessly transmitted between crutches and to a remote computer (where they are processed and visualized in LabVIEW), and the patient receives biofeedback by means of an audible signal when they put too much or too little weight through the crutch. The initial results obtained highlight the capability of the instrumented crutch to support physiotherapists and patients in monitoring usage

International Union of Basic and Clinical Pharmacology. CV. Somatostatin Receptors: Structure, Function, Ligands, and New Nomenclature.

Somatostatin, also known as somatotropin-release inhibitory factor, is a cyclopeptide that exerts potent inhibitory actions on hormone secretion and neuronal excitability. Its physiologic functions are mediated by five G protein-coupled receptors (GPCRs) called somatostatin receptor (SST)1-5. These five receptors share common structural features and signaling mechanisms but differ in their cellular and subcellular localization and mode of regulation. SST2 and SST5 receptors have evolved as primary targets for pharmacological treatment of pituitary adenomas and neuroendocrine tumors. In addition, SST2 is a prototypical GPCR for the development of peptide-based radiopharmaceuticals for diagnostic and therapeutic interventions. This review article summarizes findings published in the last 25 years on the physiology, pharmacology, and clinical applications related to SSTs. We also discuss potential future developments and propose a new nomenclature

Reshaping Curriculum to Enhance the Relevance of Literary Competence in Children's Education06

Twenty-first century learners face a multi-literacy landscape as they strive to acquire the cognitive skills needed for independent learning, apply linguistic skills to other knowledge base, and become computer literate. This article envisions a combination of skill sets and knowledge bases as the foundation of a literary competence-based curriculum. Such a curriculum would have the goal of enhancing young learners"critical thinking abilities; this would also help them take charge of the cognitive,linguistic, and sociocultural dimensions of written and spoken language in order to make learning transferable and applicable to the real world

Tourism and toponymy: Commodifying and Consuming Place Names

Academic geographers have a long history of studying both tourism and place names, but have rarely made linkages between the two. Within critical toponymic studies there is increasing debate about the commodification of place names, but to date the role of tourism in this process has been almost completely overlooked. In some circumstances, toponyms can become tourist sights based on their extraordinary properties, their broader associations within popular culture, or their role as metanyms for some other aspect of a place. Place names may be sights in their own right or ‘markers’ of a sight and, in some cases, the marker may be more significant than the sight to which it refers. The appropriation of place names through tourism also includes the production and consumption of a broad range of souvenirs based on reproductions or replicas of the material signage that denote place names. Place names as attractions are also associated with a range of performances by tourists, and in some cases visiting a place name can be a significant expression of fandom. In some circumstances, place names can be embraced and promoted by tourism marketing strategies and are, in turn, drawn into broader circuits of the production and consumption of tourist space

Intersection form, laminations and currents on free groups

Let $F_N$ be a free group of rank $N\ge 2$, let $\mu$ be a geodesic current on $F_N$ and let $T$ be an $\mathbb R$-tree with a very small isometric action of $F_N$. We prove that the geometric intersection number $$ is equal to zero if and only if the support of $\mu$ is contained in the dual algebraic lamination $L^2(T)$ of $T$. Applying this result, we obtain a generalization of a theorem of Francaviglia regarding length spectrum compactness for currents with full support. As another application, we define the notion of a \emph{filling} element in $F_N$ and prove that filling elements are "nearly generic" in $F_N$. We also apply our results to the notion of \emph{bounded translation equivalence} in free groups.Comment: revised version, to appear in GAF