pp-adic quotient sets

For $A \subseteq \mathbb{N}$, the question of when $R(A) = \{a/a' : a, a' \in A\}$ is dense in the positive real numbers $\mathbb{R}_+$ has been examined by many authors over the years. In contrast, the $p$-adic setting is largely unexplored. We investigate conditions under which $R(A)$ is dense in the $p$-adic numbers. Techniques from elementary, algebraic, and analytic number theory are employed in this endeavor. We also pose many open questions that should be of general interest.Comment: 24 page

Evolution of the progenitors of SNe 1993J and 2011dh revealed through late time radio and X-ray studies

We perform hydrodynamical simulations of the interaction between supernova (SN) ejecta and circumstellar medium (CSM) for SN 1993J and SN 2011dh, and calculate the radio and X-ray emissions expected from the shocked gas at late epochs ($t$). Considering the ejecta structure from multi-group radiation hydrodynamics simulation, we find that the observed rapid drop in radio and X-ray light curves of SN 1993J at $t>$3000 days can be due to a change in the mass-loss rate ($\dot M$) around $\sim$6500 years prior to the explosion of the SN. The exact epoch scales inversely with the assumed wind velocity of $v_{\rm w}=10~ km~s^{-1}$. The progenitor of this SN very likely belonged to a binary system, where, during its evolution, the primary had transferred material to the secondary. It is argued in the paper that the change in $\dot M$ can happen because of a change in the mass accretion efficiency ($\eta$) of the companion star. It is possible that before $\sim6500~(v_{\rm w}/10~km~s^{-1})^{-1}$years prior to the explosion, $\eta$ was high, thus the CSM was tenuous, which causes the late time downturn in fluxes. In the case of SN 2011dh, the late time evolution is found to be consistent with a wind medium with $\dot M/v_{\rm w}=4\times10^{-6 }~M_{\odot}~ yr^{-1}/10 ~{km ~s^{-1}}$. It is difficult from our analysis to predict whether the progenitor of this SN had a binary companion, however, if future observations show similar decrease in radio and X-ray fluxes, then that would give strong support to a scenario where both SNe had undergone similar kind of binary evolution before explosion.Comment: 13 pages, 10 figures; Accepted for publication in Ap

Energy & Carbon Neutral NYC

In 2016, the world\u27s leading countries signed the Paris Agreement which focused on reducing anthropogenic climate change on the planet. On May 2019, New York State and New York City declared its own ambitious goals aimed at decarbonizing the city and restricting the state’s energy use to relying completely on renewables. Some of these goals specifically target infrastructure in the city since estimates cite buildings as accounting for nearly 70% of New York’s energy use. The main law of New York’s Climate Policy, Local Law 97, requires all buildings over 25,000 sq ft to reduce their CO2 footprint by 40% by 2030 and by 80% by 2050. It also mandates increasing the efficiency of buildings based on the Energy Star rating system. While very ambitious and a step in the right direction for New York, some critics have voiced concern over the comprehensiveness of the Energy Star rating system, how carbon dioxide emissions are calculated and what means and methods building owners will take in order to comply with the law. The legislation will become legally binding in 2024 and owners with buildings meeting the legal requirement will need to move quickly in order ensure their properties meet benchmarks

Modules for Experiments in Stellar Astrophysics (MESA): Convective Boundaries, Element Diffusion, and Massive Star Explosions

We update the capabilities of the software instrument Modules for Experiments in Stellar Astrophysics (MESA) and enhance its ease of use and availability. Our new approach to locating convective boundaries is consistent with the physics of convection, and yields reliable values of the convective core mass during both hydrogen and helium burning phases. Stars with $M<8\,{\rm M_\odot}$ become white dwarfs and cool to the point where the electrons are degenerate and the ions are strongly coupled, a realm now available to study with MESA due to improved treatments of element diffusion, latent heat release, and blending of equations of state. Studies of the final fates of massive stars are extended in MESA by our addition of an approximate Riemann solver that captures shocks and conserves energy to high accuracy during dynamic epochs. We also introduce a 1D capability for modeling the effects of Rayleigh-Taylor instabilities that, in combination with the coupling to a public version of the STELLA radiation transfer instrument, creates new avenues for exploring Type II supernovae properties. These capabilities are exhibited with exploratory models of pair-instability supernova, pulsational pair-instability supernova, and the formation of stellar mass black holes. The applicability of MESA is now widened by the capability of importing multi-dimensional hydrodynamic models into MESA. We close by introducing software modules for handling floating point exceptions and stellar model optimization, and four new software tools -- MESAWeb, MESA-Docker, pyMESA, and mesastar.org -- to enhance MESA's education and research impact.Comment: 64 pages, 61 figures; Accepted to AAS Journal

The WW-HECT protein Smurf2 interacts with the Docking Protein NEDD9/HEF1 for Aurora A activation

The multi-functional adaptor protein NEDD9/HEF1/Cas-L regulates cell motility, invasion and cell cycle progression, and plays key roles in cancer progression and metastasis. NEDD9 is localized to the centrosome and is required for activation of Aurora A kinase in mitosis. Here we demonstrate that the HECT-WW protein Smurf2 physically associates with NEDD9 and is required for the stability of NEDD9 protein. Smurf2 depletion results in a marked decrease in NEDD9 protein levels, by facilitating polyubiquitination and proteasomal degradation of NEDD9. Conversely, forced overexpression of Smurf2 results in upregulation of endogenous NEDD9 protein, confirming the role for Smurf2 in NEDD9 stability. Cells with Smurf2 depletion fail to activate Aurora A at the G2/M boundary, leading to a marked delay in mitotic entry. These observations suggest that the stable complex of Smurf2 and NEDD9 is required for timely entry into mitosis via Aurora A activation

Investigation of Cross-Reactivity of Anti-Ephrin-B2 Antibody to Other Ephrin-B Members in an Immunohistochemical Study in a Cohort of Oral Squamous Cell Carcinoma

Ephrin-B1,-B2 and -B3 proteins share a high degree of sequence similarity. Investigation of these proteins as putative prognostic markers in human cancers including oral squamous cell carcinoma (OSCC) has been limited by challenges in generating specific antibodies against them. The current study examined the reactivity of a polyclonal anti-human ephrin-B2 antibody (HPA008999) against ephrin-B proteins and investigated the prognostic significance of immunoreactivity of the same antibody at different intra-tumor sites in OSCC specimens. By amino acid sequence comparison, immunocytochemistry and Western blot analysis on cell lysates and precipitates from HEK-293T cells transfected with EFNB1, EFNB2, or EFNB3 expression constructs, we demonstrated that HPA008999 reacted to all ephrin-B proteins. Using immunohistochemistry (IHC) with the HPA008999 antibody in a cohort (n = 131) of OSCC, we showed high immunoreactivity at the tumor center, but not at the tumor invading front, was significantly associated with worse 5-year overall survival probabilities. In conclusion, the HPA008999 antibody reacted to all ephrin-B proteins and the immunoreactivity at the tumor center might be useful as a prognostic marker in OSCC. These data underscore the need for the investigation of antibodies for cross-reactivity to similar protein members for obtaining reliable and meaningful results in IHC based biomarker studies.publishedVersio

Investigation of Cross-Reactivity of Anti-Ephrin-B2 Antibody to Other Ephrin-B Members in an Immunohistochemical Study in a Cohort of Oral Squamous Cell Carcinoma

Ephrin-B1,-B2 and -B3 proteins share a high degree of sequence similarity. Investigation of these proteins as putative prognostic markers in human cancers including oral squamous cell carcinoma (OSCC) has been limited by challenges in generating specific antibodies against them. The current study examined the reactivity of a polyclonal anti-human ephrin-B2 antibody (HPA008999) against ephrin-B proteins and investigated the prognostic significance of immunoreactivity of the same antibody at different intra-tumor sites in OSCC specimens. By amino acid sequence comparison, immunocytochemistry and Western blot analysis on cell lysates and precipitates from HEK-293T cells transfected with EFNB1, EFNB2, or EFNB3 expression constructs, we demonstrated that HPA008999 reacted to all ephrin-B proteins. Using immunohistochemistry (IHC) with the HPA008999 antibody in a cohort (n = 131) of OSCC, we showed high immunoreactivity at the tumor center, but not at the tumor invading front, was significantly associated with worse 5-year overall survival probabilities. In conclusion, the HPA008999 antibody reacted to all ephrin-B proteins and the immunoreactivity at the tumor center might be useful as a prognostic marker in OSCC. These data underscore the need for the investigation of antibodies for cross-reactivity to similar protein members for obtaining reliable and meaningful results in IHC based biomarker studies.publishedVersio

The Number Of Titrated Microrna Species Dictates Cerna Regulation

microRNAs (miRNAs) play key roles in cancer, but their propensity to couple their targets as competing endogenous RNAs (ceRNAs) has only recently emerged. Multiple models have studied ceRNA regulation, but these models did not account for the effects of co-regulation by miRNAs with many targets. We modeled ceRNA and simulated its effects using established parameters for miRNA/mRNA interaction kinetics while accounting for co-regulation by multiple miRNAs with many targets. Our simulations suggested that co-regulation by many miRNA species is more likely to produce physiologically relevant context-independent couplings. To test this, we studied the overlap of inferred ceRNA networks from four tumor contexts-our proposed pan-cancer ceRNA interactome (PCI). PCI was composed of interactions between genes that were coregulated by nearly three-times as many miRNAs as other inferred ceRNA interactions. Evidence from expression-profiling datasets suggested that PCI interactions are predictive of gene expression in 12 independent tumor-and non-tumor contexts. Biochemical assays confirmed ceRNA couplings for two PCI subnetworks, including oncogenes CCND1, HIF1A and HMGA2, and tumor suppressors PTEN, RB1 and TP53. Our results suggest that PCI is enriched for context-independent interactions that are coupled by many miRNA species and are more likely to be context independent