Identifying Novel Leads Using Combinatorial Libraries: Issues and Successes

Chemically generated libraries of small, non-oligomeric compounds are being widely embraced by researchers in both industry and academia. There has been a steady development of new chemistries and equipment applied to library generation so it is now possible to synthesize almost any desired class of compound. However, there are still important issues to consider that range from what specific types of compounds should be made to concerns such as sample resynthesis, structural confirmation of the hit identified, and how to best integrate this technology into a pharmaceutical drug discovery operation. This paper illustrates our approach to new lead discovery (individual, diverse, drug-like molecules of known structural identity using a simple, spatially addressable parallel synthesis approach to prepare Multiple Diverse as well as Universal Libraries) and describes some representative examples of chemistries we had developed within these approaches (preparation of bis-benzamide phenols, thiophenes, pyrrolidines, and highly substituted biphenyls). Finally, the manuscript concludes by addressing some the present concerns that still must be considered in this field

Some homogenization and corrector results for nonlinear monotone operators

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h on $\Omega$ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi$ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ -\limfunc{div}(b(x,Du))=f on $\Omega$. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$

Correctors for some nonlinear monotone operators

In this paper we study homogenization of quasi-linear partial differential equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right) \right) =f_h on $\Omega$ with Dirichlet boundary conditions. Here the sequence $\left( \varepsilon _h\right)$ tends to $0$ as $h\rightarrow \infty$ and the map $a\left( x,y,\xi \right)$ is periodic in $y,$ monotone in $\xi$ and satisfies suitable continuity conditions. We prove that $u_h\rightarrow u$ weakly in $W_0^{1,p}\left( \Omega \right)$ as $h\rightarrow \infty ,$ where $u$ is the solution of a homogenized problem of the form -\mbox{div}\left( b\left( x,Du\right) \right) =f on $\Omega .$ We also derive an explicit expression for the homogenized operator $b$ and prove some corrector results, i.e. we find $\left( P_h\right)$ such that $Du_h-P_h\left( Du\right) \rightarrow 0$ in $L^p\left( \Omega, \mathbf{R}^n\right)$

Coherence-based approaches for estimating the composition of the seismic wavefield

As new techniques exploiting the Earth's ambient seismic noise field are developed and applied, such as for the observation of temporal changes in seismic velocity structure, it is crucial to quantify the precision with which wave‐type measurements can be made. This work uses array data at the Homestake mine in Lead, South Dakota, and an array at Sweetwater, Texas, to consider two aspects that control this precision: the types of seismic wave contributing to the ambient noise field at microseism frequencies and the effect of array geometry. Both are quantified using measurements of wavefield coherence between stations in combination with Wiener filters. We find a strong seasonal change between body‐wave and surface‐wave content. Regarding the inclusion of underground stations, we quantify the lower limit to which the ambient noise field can be characterized and reproduced; the applications of the Wiener filters are about 4 times more successful in reproducing ambient noise waveforms when underground stations are included in the array, resulting in predictions of seismic time series with less than a 1% residual, and are ultimately limited by the geometry and aperture of the array, as well as by temporal variations in the seismic field. We discuss the implications of these results for the geophysics community performing ambient seismic noise studies, as well as for the cancellation of seismic Newtonian gravity noise in ground‐based, sub‐Hertz, gravitational‐wave detectors

Agent-Based Markov Modeling for Improved COVID-19 Mitigation Policies

The year 2020 saw the covid-19 virus lead to one of the worst global pandemics in history. As a result, governments around the world have been faced with the challenge of protecting public health while keeping the economy running to the greatest extent possible. Epidemiological models provide insight into the spread of these types of diseases and predict the e_ects of possible intervention policies. However, to date, even the most data-driven intervention policies rely on heuristics. In this paper, we study how reinforcement learning (RL) and Bayesian inference can be used to optimize mitigation policies that minimize economic impact without overwhelming hospital capacity. Our main contributions are (1) a novel agent-based pandemic simulator which, unlike traditional models, is able to model _ne-grained interactions among people at speci_c locations in a community; (2) an RL- based methodology for optimizing _ne-grained mitigation policies within this simulator; and (3) a Hidden Markov Model for predicting infected individuals based on partial observations regarding test results, presence of symptoms, and past physical contacts

Doping Dependence of Collective Spin and Orbital Excitations in Spin 1 Quantum Antiferromagnet La2−x_{2-x}Srx_xNiO4_4 Observed by X-rays

We report the first empirical demonstration that resonant inelastic x-ray scattering (RIXS) is sensitive to \emph{collective} magnetic excitations in $S=1$ systems by probing the Ni $L_3$-edge of La$_{2-x}$Sr$_x$NiO$_4$ ($x = 0, 0.33, 0.45$). The magnetic excitation peak is asymmetric, indicating the presence of single and multi spin-flip excitations. As the hole doping level is increased, the zone boundary magnon energy is suppressed at a much larger rate than that in hole doped cuprates. Based on the analysis of the orbital and charge excitations observed by RIXS, we argue that this difference is related to the orbital character of the doped holes in these two families. This work establishes RIXS as a probe of fundamental magnetic interactions in nickelates opening the way towards studies of heterostructures and ultra-fast pump-probe experiments.Comment: 8 pages, 4 figures, see ancillary files for the supplemental materia

Stability estimates for resolvents, eigenvalues and eigenfunctions of elliptic operators on variable domains

We consider general second order uniformly elliptic operators subject to homogeneous boundary conditions on open sets $\phi (\Omega)$ parametrized by Lipschitz homeomorphisms $\phi$ defined on a fixed reference domain $\Omega$. Given two open sets $\phi (\Omega)$, $\tilde \phi (\Omega)$ we estimate the variation of resolvents, eigenvalues and eigenfunctions via the Sobolev norm $\|\tilde \phi -\phi \|_{W^{1,p}(\Omega)}$ for finite values of $p$, under natural summability conditions on eigenfunctions and their gradients. We prove that such conditions are satisfied for a wide class of operators and open sets, including open sets with Lipschitz continuous boundaries. We apply these estimates to control the variation of the eigenvalues and eigenfunctions via the measure of the symmetric difference of the open sets. We also discuss an application to the stability of solutions to the Poisson problem.Comment: 34 pages. Minor changes in the introduction and the refercenes. Published in: Around the research of Vladimir Maz'ya II, pp23--60, Int. Math. Ser. (N.Y.), vol. 12, Springer, New York 201

Evolving Clustered Random Networks

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as generic models for studying the impacts of degree distributions and clustering on dynamical processes as well as null models for detecting other structural properties in empirical networks

The importance of major mergers in the build up of stellar mass in brightest cluster galaxies at z=1

Recent independent results from numerical simulations and observations have shown that brightest cluster galaxies (BCGs) have increased their stellar mass by a factor of almost two between z~0.9 and z~0.2. The numerical simulations further suggest that more than half this mass is accreted through major mergers. Using a sample of 18 distant galaxy clusters with over 600 spectroscopically confirmed cluster members between them, we search for observational evidence that major mergers do play a significant role. We find a major merger rate of 0.38 +/- 0.14 mergers per Gyr at z~1. While the uncertainties, which stem from the small size of our sample, are relatively large, our rate is consistent with the results that are derived from numerical simulations. If we assume that this rate continues to the present day and that half of the mass of the companion is accreted onto the BCG during these mergers, then we find that this rate can explain the growth in the stellar mass of the BCGs that is observed and predicted by simulations. Major mergers therefore appear to be playing an important role, perhaps even the dominant one, in the build up of stellar mass in these extraordinary galaxies.Comment: 15 pages, 6 figures, accepted for publication in MNRAS. Reduced data will be made available through the ESO archiv

Uniform Shock Waves in Disordered Granular Matter

The confining pressure $P$ is perhaps the most important parameter controlling the properties of granular matter. Strongly compressed granular media are, in many respects, simple solids in which elastic perturbations travel as ordinary phonons. However, the speed of sound in granular aggregates continuously decreases as the confining pressure decreases, completely vanishing at the jamming-unjamming transition. This anomalous behavior suggests that the transport of energy at low pressures should not be dominated by phonons. In this work we use simulations and theory to show how the response of granular systems becomes increasingly nonlinear as pressure decreases. In the low pressure regime the elastic energy is found to be mainly transported through nonlinear waves and shocks. We numerically characterize the propagation speed, shape, and stability of these shocks, and model the dependence of the shock speed on pressure and impact intensity by a simple analytical approach.Comment: 12 pages, 11 figure