Beautiful, simple, exact, crazy

This is a review of the book “Beautiful, Simple, Exact, Crazy” written by Apoorva Khare and Anna Lachowska. The authors write in the preface that this book arose out of an introductory course called Mathematics in the Real World which they co-designed (and taught at Stanford and Yale University, respectively). The target audience of that course consisted mainly of undergraduates of humanities and social sciences – students whose principal interests lay outside of mathematics and the sciences

Arithmetically Cohen-Macaulay Bundles on complete intersection varieties of sufficiently high multidegree

Recently it has been proved that any arithmetically Cohen-Macaulay (ACM) bundle of rank two on a general, smooth hypersurface of degree at least three and dimension at least four is a sum of line bundles. When the dimension of the hypersurface is three, a similar result is true provided the degree of the hypersurface is at least six. We extend these results to complete intersection subvarieties by proving that any ACM bundle of rank two on a general, smooth complete intersection subvariety of sufficiently high multi-degree and dimension at least four splits. We also obtain partial results in the case of threefolds.Comment: 15 page

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

Beautiful, simple, exact, crazy

This is a review of the book “Beautiful, Simple, Exact, Crazy” written by Apoorva Khare and Anna Lachowska. The authors write in the preface that this book arose out of an introductory course called Mathematics in the Real World which they co-designed (and taught at Stanford and Yale University, respectively). The target audience of that course consisted mainly of undergraduates of humanities and social sciences – students whose principal interests lay outside of mathematics and the sciences

Genetic and phylogenetic analysis of the outer capsid protein genes of Indian isolates of bluetongue virus serotype-16

Aim: The aim of the study was to characterize bluetongue virus serotype 16 (BTV-16), recently isolated from different states of India. The evolutionary relationship of newly isolated BTV-16 and previously reported Indian and global BTV-16 isolates were compared using molecular analysis. Materials and Methods: In the present study, five (n=5) BTV-16 isolates were used to amplify gene segment-2 and segment-6 encoding the outer capsid proteins VP2 and VP5, respectively. The amplified products were purified and sequenced by the Sanger sequencing method. The phylogenetic relationship and nucleotide identity of all five BTV-16 isolates were compared with previously reported Indian and global BTV-16 isolates. Nucleotide sequence data were aligned using the CLUSTAL W algorithm implemented in the MegAlign of DNASTAR program package (MegAlign 5.00, DNASTAR Inc., Madison, USA). Phylogenetic analyses were carried out using MEGA version 6.0 software with the best nucleotide substitution model. Results: Phylogenetic analysis based on the VP2 and VP5 encoding genes, segregates Indian BTV-16 isolates in a distinct cluster with proximity to the Eastern topotype. Indian isolates make a monophyletic cluster with Eastern topotypes with Western topotype BTV-16 (BTV-16/NIG/AJ586694) occupying a separate cluster. Indian isolates were found to share 91.5%- 97.5% and 96.5%-98.9% identity at the nucleotide and deduced amino acid (aa) level, respectively, to the global BTV-16 isolates. There is a high degree of variation with the Nigerian isolate with 27.0-27.7% and 26.0-26.9% at the nucleotide and aa sequence level, respectively. These data suggest that Indian BTV-16 isolates might have evolved separately within the Eastern BTV topotype. Conclusion: Phylogenetic analyses and nucleotide identity of BTV-16 isolates at the VP2 and VP5 gene encoded level indicate that isolates used in the present study might have evolved from a common Eastern topotype ancestor. The data presented in this study will be helpful for future selection of reference strains in a serological and molecular epidemiology study

Search for intermediate-mass black hole binaries in the third observing run of Advanced LIGO and Advanced Virgo

International audienceIntermediate-mass black holes (IMBHs) span the approximate mass range 100−105 M⊙, between black holes (BHs) that formed by stellar collapse and the supermassive BHs at the centers of galaxies. Mergers of IMBH binaries are the most energetic gravitational-wave sources accessible by the terrestrial detector network. Searches of the first two observing runs of Advanced LIGO and Advanced Virgo did not yield any significant IMBH binary signals. In the third observing run (O3), the increased network sensitivity enabled the detection of GW190521, a signal consistent with a binary merger of mass ∼150 M⊙ providing direct evidence of IMBH formation. Here, we report on a dedicated search of O3 data for further IMBH binary mergers, combining both modeled (matched filter) and model-independent search methods. We find some marginal candidates, but none are sufficiently significant to indicate detection of further IMBH mergers. We quantify the sensitivity of the individual search methods and of the combined search using a suite of IMBH binary signals obtained via numerical relativity, including the effects of spins misaligned with the binary orbital axis, and present the resulting upper limits on astrophysical merger rates. Our most stringent limit is for equal mass and aligned spin BH binary of total mass 200 M⊙ and effective aligned spin 0.8 at 0.056 Gpc−3 yr−1 (90% confidence), a factor of 3.5 more constraining than previous LIGO-Virgo limits. We also update the estimated rate of mergers similar to GW190521 to 0.08 Gpc−3 yr−1.Key words: gravitational waves / stars: black holes / black hole physicsCorresponding author: W. Del Pozzo, e-mail: [email protected]† Deceased, August 2020