The virtual Haken conjecture: Experiments and examples

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture says that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. Here, we discuss two interrelated topics concerning this conjecture. First, we describe computer experiments which give strong evidence that the Virtual Haken Conjecture is true for hyperbolic 3-manifolds. We took the complete Hodgson-Weeks census of 10,986 small-volume closed hyperbolic 3-manifolds, and for each of them found finite covers which are Haken. There are interesting and unexplained patterns in the data which may lead to a better understanding of this problem. Second, we discuss a method for transferring the virtual Haken property under Dehn filling. In particular, we show that if a 3-manifold with torus boundary has a Seifert fibered Dehn filling with hyperbolic base orbifold, then most of the Dehn filled manifolds are virtually Haken. We use this to show that every non-trivial Dehn surgery on the figure-8 knot is virtually Haken.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper12.abs.htm

Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras

We construct an explicit isomorphism between blocks of cyclotomic Hecke algebras and (sign-modified) Khovanov-Lauda algebras in type A. These isomorphisms connect the categorification conjecture of Khovanov and Lauda to Ariki's categorification theorem. The Khovanov-Lauda algebras are naturally graded, which allows us to exhibit a non-trivial Z-grading on blocks of cyclotomic Hecke algebras, including symmetric groups in positive characteristic.Comment: 32 pages; minor changes to section

Costs analysis of a population level rabies control programme in Tamil Nadu, India

The study aimed to determine costs to the state government of implementing different interventions for controlling rabies among the entire human and animal populations of Tamil Nadu. This built upon an earlier assessment of Tamil Nadu’s efforts to control rabies. Anti-rabies vaccines were made available at all health facilities. Costs were estimated for five different combinations of animal and human interventions using an activity-based costing approach from the provider perspective. Disease and population data were sourced from the state surveillance data, human census and livestock census. Program costs were extrapolated from official documents. All capital costs were depreciated to estimate annualized costs. All costs were inflated to 2012 Rupees. Sensitivity analysis was conducted across all major cost centres to assess their relative impact on program costs. It was found that the annual costs of providing Anti-rabies vaccine alone and in combination with Immunoglobulins was \$0.7 million (Rs 36 million) and \$2.2 million (Rs 119 million), respectively. For animal sector interventions, the annualised costs of rolling out surgical sterilisation-immunization, injectable immunization and oral immunizations were estimated to be \$ 44 million (Rs 2,350 million), \$23 million (Rs 1,230 million) and \$ 11 million (Rs 590 million), respectively. Dog bite incidence, health systems coverage and cost of rabies biologicals were found to be important drivers of costs for human interventions. For the animal sector interventions, the size of dog catching team, dog population and vaccine costs were found to be driving the costs. Rabies control in Tamil Nadu seems a costly proposition the way it is currently structured. Policy makers in Tamil Nadu and other similar settings should consider the long-term financial sustainability before embarking upon a state or nation-wide rabies control programme

Allopregnanolone preclinical acute pharmacokinetic and pharmacodynamic studies to predict tolerability and efficacy for Alzheimer's disease.

To develop allopregnanolone as a therapeutic for Alzheimer's disease, we investigated multiple formulations and routes of administration in translationally relevant animal models of both sexes. Subcutaneous, topical (transdermal and intranasal), intramuscular, and intravenous allopregnanolone were bolus-administered. Pharmacokinetic analyses of intravenous allopregnanolone in rabbit and mouse indicated that peak plasma and brain levels (3-fold brain/plasma ratios) at 5min were sufficient to activate neuroregenerative responses at sub-sedative doses. Slow-release subcutaneous suspension of allopregnanolone displayed 5-fold brain/plasma ratio at Cmax at 30min. At therapeutic doses by either subcutaneous or intravenous routes, allopregnanolone mouse plasma levels ranged between 34-51ng/ml by 30min, comparable to published endogenous human level in the third trimester of pregnancy. Exposure to subcutaneous, topical, intramuscular, and intravenous allopregnanolone, at safe and tolerable doses, increased hippocampal markers of neurogenesis including BrdU and PCNA in young 3xTgAD and aged wildtype mice. Intravenous allopregnanolone transiently and robustly phosphorylated CREB within 5min and increased levels of neuronal differentiation transcription factor NeuroD within 4h. Neurogenic efficacy was achieved with allopregnanolone brain exposure of 300-500hr*ng/g. Formulations were tested to determine the no observable adverse effect level (NOAEL) and maximally tolerated doses (MTD) in male and female rats by sedation behavior time course. Sex differences were apparent, males exhibited ≥40% more sedation time compared to females. Allopregnanolone formulated in sulfobutyl-ether-beta-cyclodextrin at optimized complexation ratio maximized allopregnanolone delivery and neurogenic efficacy. To establish the NOAEL and MTD for Allo-induced sedation using a once-per-week intravenous regenerative treatment regimen: In female rats the NOAEL was 0.5mg/kg and MTD 2mg/kg. The predicted MTD in human female is 0.37mg/kg. In male rats the NOAEL and MTD were less than those determined for female. Outcomes of these PK/PD studies predict a safe and efficacious dose range for initial clinical trials of allopregnanolone for Alzheimer's disease. These findings have translational relevance to multiple neurodegenerative conditions

Global Jacquet-Langlands correspondence, multiplicity one and classification of automorphic representations

In this paper we show a local Jacquet-Langlands correspondence for all unitary irreducible representations. We prove the global Jacquet-Langlands correspondence in characteristic zero. As consequences we obtain the multiplicity one and strong multiplicity one theorems for inner forms of GL(n) as well as a classification of the residual spectrum and automorphic representations in analogy with results proved by Moeglin-Waldspurger and Jacquet-Shalika for GL(n).Comment: 49 pages; Appendix by N. Grba

On the Exploitation of a High-throughput SHA-256 FPGA Design for HMAC

High-throughput and area-efficient designs of hash functions and corresponding mechanisms for Message Authentication Codes (MACs) are in high demand due to new security protocols that have arisen and call for security services in every transmitted data packet. For instance, IPv6 incorporates the IPSec protocol for secure data transmission. However, the IPSec's performance bottleneck is the HMAC mechanism which is responsible for authenticating the transmitted data. HMAC's performance bottleneck in its turn is the underlying hash function. In this article a high-throughput and small-size SHA-256 hash function FPGA design and the corresponding HMAC FPGA design is presented. Advanced optimization techniques have been deployed leading to a SHA-256 hashing core which performs more than 30% better, compared to the next better design. This improvement is achieved both in terms of throughput as well as in terms of throughput/area cost factor. It is the first reported SHA-256 hashing core that exceeds 11Gbps (after place and route in Xilinx Virtex 6 board)

Cherednik algebras and Zhelobenko operators

We study canonical intertwining operators between induced modules of the trigonometric Cherednik algebra. We demonstrate that these operators correspond to the Zhelobenko operators for the affine Lie algebra of type A. To establish the correspondence, we use the functor of Arakawa, Suzuki and Tsuchiya which maps certain modules of the affine Lie algebra to modules of the Cherednik algebra