Collisions at infinity in hyperbolic manifolds

For a complete, finite volume real hyperbolic n-manifold M, we investigate the map between homology of the cusps of M and the homology of $M$. Our main result provides a proof of a result required in a recent paper of Frigerio, Lafont, and Sisto

Columnar phases exhibited by some polycatenar ligands and a few related metal complexes

The synthesis and characterization of some polycatenar ligands which exhibit hexagonal columnar and cubic phases are reported. A pentacatenar with only four phenyl rings in the core and exhibiting a mesophase is also reported. A few copper (II) and palladium (II) complexes have been synthesized using these ligands and the mesomorphic properties exhibited by them are described. The hexagonal columnar phase exhibited by some of the complexes can be cooled down to room temperature. The mesophases have been characterized using a combination of polarized light microscopy, differential scanning calorimetry and X-ray diffraction methods

Extending Johnson's and Morita's homomorphisms to the mapping class group

We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every $k\geq 2$, we construct a crossed homomorphism $\epsilon_k$ which extends Morita's homomorphism $\tilde \tau_k$ to the entire mapping class group. From this crossed homomorphism we also obtain a crossed homomorphism extending the $k$th Johnson homomorphism $\tau_k$ to the mapping class group. D. Johnson and S. Morita obtained their respective homomorphisms by considering the action of the mapping class group on the nilpotent truncations of the surface group; our approach is to mimic Morita's construction topologically by using nilmanifolds associated to these truncations. This allows us to take the ranges of these crossed homomorphisms to be certain finite-dimensional real vector spaces associated to these nilmanifolds.Comment: 32 pages; cleaned up and minor corrections to proofs; updated to agree with version published by Alg. & Geom. Top at: http://msp.warwick.ac.uk/agt/2007/07/p050.xhtm

ReverseCloak: A Reversible Multi-level Location Privacy Protection System

With the fast popularization of mobile devices and wireless networks, along with advances in sensing and positioning technology, we are witnessing a huge proliferation of Location-based Services (LBSs). Location anonymization refers to the process of perturbing the exact location of LBS users as a cloaking region such that a user's location becomes indistinguishable from the location of a set of other users. However, existing location anonymization techniques focus primarily on single level unidirectional anonymization, which fails to control the access to the cloaking data to let data requesters with different privileges get information with varying degrees of anonymity. In this demonstration, we present a toolkit for ReverseCloak, a location perturbation system to protect location privacy over road networks in a multi-level reversible manner, consisting of an 'Anonymizer' GUI to adjust the anonymization settings and visualize the multilevel cloaking regions over road network for location data owners and a 'De-anonymizer' GUI to de-anonymize the cloaking region and display the reduced region over road network for location data requesters. With the toolkit, we demonstrate the practicality and effectiveness of the ReverseCloak approach

19-Ferrocenyl-18-oxa-8,16-diaza­penta­cyclo­[8.6.3.01,10.02,7.012,16]nona­deca-2(7),3,5-triene-9,17-dione

In the title compound, [Fe(C5H5)(C21H19N2O3)], both pyrrol­idine rings of the pyrrolizine substructure show an envelope conformation. In the ferrocenyl moiety, the unsubstituted cyclo­penta­dienyl ring is disordered over two orientations with site occupancies of 0.64 (2) and 0.36 (2). In the pyrrolizine ring, one C atom is disordered over two positions, with site occupancies of 0.71 (1) and 0.29 (1). Intra­molecular C—H⋯O inter­actions occur. The crystal packing is established through weak inter­molecular C—H⋯O and N—H⋯O inter­actions

4′-Ferrocenyl-1′-methylacenapthylene-1-spiro-2′-pyrrolidine-3′-spiro-2′′-indane-2,1′′,3′′(1H)-trione

In the title compound, [Fe(C5H5)(C29H20NO3)], the acenaphthyl­ene ring system makes a dihedral angle of 83.77 (3)° with the indane-1,3-dione ring system. The central pyrrolidine ring exhibits a twist conformation. In the crystal, mol­ecules are linked by a weak inter­molecular C—H⋯O inter­action into a chain along the b axis. Two weak intra­molecular C—H⋯O inter­actions are also present

Methyl 9-p-tolyl-8a,9,9a,10,11,12,13,14a-octa­hydro-8H-benzo[f]chromeno[3,4-b]indolizine-8a-carboxyl­ate

In the title compound, C28H29NO3, the fused pyrrolidine and piperidine rings of the octa­hydro­indolizine unit exhibit envelope and chair conformations, respectively. The dihedral angle between the naphthalene ring system and the benzene ring is 40.37 (5)°. The crystal packing is stabilized by weak inter­molecular C—H⋯O inter­actions

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules

We introduce machine learning models of quantum mechanical observables of atoms in molecules. Instant out-of-sample predictions for proton and carbon nuclear chemical shifts, atomic core level excitations, and forces on atoms reach accuracies on par with density functional theory reference. Locality is exploited within non-linear regression via local atom-centered coordinate systems. The approach is validated on a diverse set of 9k small organic molecules. Linear scaling of computational cost in system size is demonstrated for saturated polymers with up to sub-mesoscale lengths

SARAS 2: A Spectral Radiometer for probing Cosmic Dawn and the Epoch of Reionization through detection of the global 21 cm signal

The global 21 cm signal from Cosmic Dawn (CD) and the Epoch of Reionization (EoR), at redshifts $z \sim 6-30$, probes the nature of first sources of radiation as well as physics of the Inter-Galactic Medium (IGM). Given that the signal is predicted to be extremely weak, of wide fractional bandwidth, and lies in a frequency range that is dominated by Galactic and Extragalactic foregrounds as well as Radio Frequency Interference, detection of the signal is a daunting task. Critical to the experiment is the manner in which the sky signal is represented through the instrument. It is of utmost importance to design a system whose spectral bandpass and additive spurious can be well calibrated and any calibration residual does not mimic the signal. SARAS is an ongoing experiment that aims to detect the global 21 cm signal. Here we present the design philosophy of the SARAS 2 system and discuss its performance and limitations based on laboratory and field measurements. Laboratory tests with the antenna replaced with a variety of terminations, including a network model for the antenna impedance, show that the gain calibration and modeling of internal additives leave no residuals with Fourier amplitudes exceeding 2~mK, or residual Gaussians of 25 MHz width with amplitudes exceeding 2~mK. Thus, even accounting for reflection and radiation efficiency losses in the antenna, the SARAS~2 system is capable of detection of complex 21-cm profiles at the level predicted by currently favoured models for thermal baryon evolution.Comment: 44 pages, 17 figures; comments and suggestions are welcom