Noncyclic covers of knot complements

Hempel has shown that the fundamental groups of knot complements are residually finite. This implies that every nontrivial knot must have a finite-sheeted, noncyclic cover. We give an explicit bound, $\Phi (c)$, such that if $K$ is a nontrivial knot in the three-sphere with a diagram with $c$ crossings and a particularly simple JSJ decomposition then the complement of $K$ has a finite-sheeted, noncyclic cover with at most $\Phi (c)$ sheets.Comment: 29 pages, 8 figures, from Ph.D. thesis at Columbia University; Acknowledgments added; Content correcte

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

Coronavirus Replicase-Reporter Fusions Provide Quantitative Analysis of Replication and Replication Complex Formation

The replication of coronaviruses occurs in association with multiple virus-induced membrane structures that evolve during the course of infection; however, the dynamics of this process remain poorly understood. Previous studies of coronavirus replication complex organization and protein interactions have utilized protein overexpression studies and immunofluorescence of fixed cells. Additionally, live-imaging studies of coronavirus replicase proteins have used fluorescent reporter molecules fused to replicase proteins, but expressed from nonnative locations, mostly late-transcribed subgenomic mRNAs, in the presence or absence of the native protein. Thus, the timing and targeting of native replicase proteins expressed in real time from native locations in the genome remain unknown. In this study, we tested whether reporter molecules could be expressed from the replicase polyprotein of murine hepatitis virus as fusions with nonstructural protein 2 or 3 and whether such reporters could define the targeting and activity of replicase proteins during infection. We demonstrate that the fusion of green fluorescent protein and firefly luciferase with either nonstructural protein 2 or 3 is tolerated and that these reporter-replicase fusions can be used to quantitate replication complex formation and virus replication. The results show that the replicase gene has flexibility to accommodate a foreign gene addition and can be used directly to study replicase complex formation and evolution during infection as well as to provide highly sensitive and specific markers for protein translation and genome replication

Hazards of falling debris to people, aircraft, and watercraft

This report is a collection of studies performed at Sandia National Laboratories in support of Phase One (inert debris) for the Risk and Lethality Commonality Team. This team was created by the Range Safety Group of the Range Commander`s Council to evaluate the safety issues for debris generated during flight tests and to develop debris safety criteria that can be adopted by the national ranges. Physiological data on the effects of debris impacts on people are presented. Log-normal curves are developed to relate the impact kinetic energy of fragments to the probability of fatality for people exposed in standing, sitting, or prone positions. Debris hazards to aircraft resulting from engine ingestion or penetration of a structure or windshield are discussed. The smallest mass fragments of aluminum, steel, and tungsten that may be hazardous to current aircraft are defined. Fragment penetration of the deck of a small ship or a pleasure craft is also considered. The smallest mass fragments of aluminum, steel, or tungsten that can penetrate decks are calculated

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

Implementing Fine/Medium Grained TLP Support in a Many-Core Architecture

Abstract. We believe that future many-core architectures should support a simple and scalable way to execute many threads that are generated by parallel programs. A good candidate to implement an efficient and scalable execution of threads is the DTA (Decoupled Threaded Architecture), which is designed to exploit fine/medium grained Thread Level Parallelism (TLP) by using a hardware scheduling unit and relying on existing simple cores. In this paper, we present an initial implementation of DTA concept in a many-core architecture where it interacts with other architectural components designed from scratch in order to address the problem of scalability. We present initial results that show the scalability of the solution that were obtained using a many-core simulator written in SARCSim (a variant of UNISIM) with DTA support

Effects of Grade Control Structures on Fish Passage, Biological Assemblages and Hydraulic Environments in Western Iowa Streams: A Multidisciplinary Review

Land use changes and channelization of streams in the deep loess region of western Iowa have led to stream channel incision, altered flow regimes, increased sediment inputs, decreased habitat diversity and reduced lateral connectivity of streams and floodplains. Grade control structures (GCSs) are built in streams to prevent further erosion, protect infrastructure and reduce sediment loads. However, GCS can have a detrimental impact on fisheries and biological communities. We review three complementary biological and hydraulic studies on the effects of GCS in these streams. GCS with steep (≥1:4 rise : run) downstream slopes severely limited fish passage, but GCS with gentle slopes (≤1:15) allowed greater passage. Fish assemblages were dominated by species tolerant of degradation, and Index of Biotic Integrity (IBI) scores were indicative of fair or poor biotic integrity. More than 50% of fish species had truncated distributions. After modification of GCS to reduce slopes and permit increased passage, IBI scores increased and several species were detected further upstream than before modification. Total macroinvertebrate density, biomass and taxonomic diversity and abundance of ecologically sensitive taxa were greater at GCS than in reaches immediately upstream, downstream or ≥1 km from GCS. A hydraulic study confirmed results from fish passage studies; minimum depths and maximum current velocities at GCS with gentle slopes (≤1:15) were more likely to meet minimum criteria for catfish passage than GCS with steeper slopes. Multidisciplinary approaches such as ours will increase understanding of GCS-associated factors influencing fish passage, biological assemblage structure and other ecological relationships in streams