Multifunctional transducer

Several parameters of a small region of a muscle tissue or other object, can be simultaneously measured using with minimal traumatizing or damage of the object, a trifunctional transducer which can determine the force applied by a muscle fiber, the displacement of the fiber, and the change in thickness of the fiber. The transducer has three legs with inner ends joined together and outer ends formed to piece the tissue and remain within it. Two of the legs are relatively stiff, to measure force applied by the tissue, and a third leg is relatively flexible to measure displacement of the tissue relative to one or both stiff legs, and with the three legs lying in a common plane so that the force and displacement measurements all relate to the same direction of muscle movements. A flexible loop is attached to one of the stiff legs to measure changes in muscle thickness, with the upper end of the loop fixed to the leg and the lower end of the loop bearing against the surface of the tissue and being free to slide on the leg

Virtually Haken fillings and semi-bundles

Suppose that M is a fibered three-manifold whose fiber is a surface of positive genus with one boundary component. Assume that M is not a semi-bundle. We show that infinitely many fillings of M along dM are virtually Haken. It follows that infinitely many Dehn-surgeries of any non-trivial knot in the three-sphere are virtually Haken.Comment: This is the version published by Geometry & Topology on 29 November 200

The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifolds

Recently, Hodgson and Kerckhoff found a small bound on Dehn surgered 3-manifolds from hyperbolic knots not admitting hyperbolic structures using deformations of hyperbolic cone-manifolds. They asked whether the area normalized meridian length squared of maximal tubular neighborhoods of the singular locus of the cone-manifold is decreasing and that summed with the cone angle squared is increasing as we deform the cone-angles. We confirm this near 0 cone-angles for an infinite family of hyperbolic cone-manifolds obtained by Dehn surgeries along the Whitehead link complements. The basic method is based on explicit holonomy computations using the A-polynomials and finding the maximal tubes. One of the key tool is the Taylor expression of a geometric component of the zero set of the A-polynomial in terms of the cone-angles. We also show a sequence of Taylor expressions for Dehn surgered manifolds converges to one for the limit hyperbolic manifold.Comment: 27 pages, 10 figure

Blocked All-Pairs Shortest Paths Algorithm on Intel Xeon Phi KNL Processor: A Case Study

Manycores are consolidating in HPC community as a way of improving performance while keeping power efficiency. Knights Landing is the recently released second generation of Intel Xeon Phi architecture. While optimizing applications on CPUs, GPUs and first Xeon Phi's has been largely studied in the last years, the new features in Knights Landing processors require the revision of programming and optimization techniques for these devices. In this work, we selected the Floyd-Warshall algorithm as a representative case study of graph and memory-bound applications. Starting from the default serial version, we show how data, thread and compiler level optimizations help the parallel implementation to reach 338 GFLOPS.Comment: Computer Science - CACIC 2017. Springer Communications in Computer and Information Science, vol 79

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

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

Computing CMB Anisotropy in Compact Hyperbolic Spaces

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (1) the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (2) an infrared cutoff in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with nontrivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold wrt the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.Comment: 15 pages, LaTeX (IOP style included), 3 color figures (GIF) in separate files. Minor revision to match the version accepted in Class. Quantum Grav.: Proc. of Topology and Cosmology, Cleveland, 1997. The paper can be also downloaded from http://www.cita.utoronto.ca/~pogosyan/cwru_proc.ps.g

The pre-WDVV ring of physics and its topology

We show how a simplicial complex arising from the WDVV (Witten-Dijkgraaf-Verlinde-Verlinde) equations of string theory is the Whitehouse complex. Using discrete Morse theory, we give an elementary proof that the Whitehouse complex $\Delta_n$ is homotopy equivalent to a wedge of $(n-2)!$ spheres of dimension $n-4$. We also verify the Cohen-Macaulay property. Additionally, recurrences are given for the face enumeration of the complex and the Hilbert series of the associated pre-WDVV ring.Comment: 13 pages, 4 figures, 2 table

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