Discrete scale invariant fixed point in a quasiperiodic classical dimer model

We study close-packed dimers on the quasiperiodic Ammann-Beenker (AB) graph, that was recently shown to have the unusual feature that hard-core dimer constraints are exactly reproduced at successive discrete length scales. This observation led to a conjecture that it would be possible to construct an exact real-space decimation scheme where each iteration preserves both the quasiperiodic tiling structure and the constraint. Here, we confirm this conjecture by explicitly constructing the corresponding renormalization group transformation and show, using large-scale Monte Carlo simulations, that the dimer distributions flow to a fixed point with non-zero dimer potentials. We use the fixed-point Hamiltonian to demonstrate the existence of slowly decaying dimer correlations. We thus identify a remarkable example of a classical statistical mechanical model whose properties are controlled by the fixed point of an exact renormalization group procedure exhibiting discrete scale invariance but lacking translational and continuous rotational symmetries.Comment: 22 pages, 15 figure

Bayesian Correction Approach for Improving Dual-Frequency Precipitation Radar Rainfall Rate Estimates, A

Includes bibliographical references (pages 14-15).The accurate estimation of precipitation is an important objective for the Dual-frequency Precipitation Radar (DPR), which is located on board the Global Precipitation Measurement (GPM) satellite core observatory. In this study, a Bayesian correction (BC) approach is proposed to improve the DPR’s instantaneous rainfall rate product. Ground dual-polarization radar (GR) observations are used as references, and a log-transformed Gaussian distribution is assumed as the instantaneous rainfall process. Additionally, a generalized regression model is adopted in the BC algorithm. Rainfall intensities such as light, moderate, and heavy rain and their variable influences on the model’s performance are considered. The BC approach quantifies the predictive uncertainties associated with the Bayesiancorrected DPR (DPR_BC) rainfall rate estimates. To demonstrate the concepts developed in this study, data from the GPM overpasses of the Weather Service Surveillance Radar (WSR-88D), KHGX, in Houston, Texas, between April 2014 and June 2018 are used. Observation errors in the DPR instantaneous rainfall rate estimates are analyzed as a function of rainfall intensity. Moreover, the best-performing BC model is implemented in three GPM-overpass cases with heavy rainfall records across the southeastern United States. The results show that the DPR_BC rainfall rate estimates have superior skill scores and are in better agreement with the GR references than with the DPR estimates. This study demonstrates the potential of the proposed BC algorithm for enhancing the instantaneous rainfall rate product from spaceborne radar equipment

Hydrodynamic non-linear response of interacting integrable systems

We develop a formalism for computing the non-linear response of interacting integrable systems. Our results are asymptotically exact in the hydrodynamic limit where perturbing fields vary sufficiently slowly in space and time. We show that spatially resolved nonlinear response distinguishes interacting integrable systems from noninteracting ones, exemplifying this for the Lieb-Liniger gas. We give a prescription for computing finite-temperature Drude weights of arbitrary order, which is in excellent agreement with numerical evaluation of the third-order response of the XXZ spin chain. We identify intrinsically nonperturbative regimes of the nonlinear response of integrable systems.Comment: 6 pages, 3 figures + supplementary material (15 pages, 2 figures

Statistical mechanics of dimers on quasiperiodic tilings

We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Despite the lack of periodicity we prove that each infinite tiling admits 'perfect matchings' in which every vertex is touched by one dimer. We introduce an auxiliary 'AB$^*$' tiling obtained from the AB tiling by deleting all 8-fold coordinated vertices. The AB$^*$ tiling is again two-dimensional, infinite, and quasiperiodic. The AB$^*$ tiling has a single connected component, which admits perfect matchings. We find that in all perfect matchings, dimers on the AB$^*$ tiling lie along disjoint one-dimensional loops and ladders, separated by 'membranes', sets of edges where dimers are absent. As a result, the dimer partition function of the AB$^*$ tiling factorizes into the product of dimer partition functions along these structures. We compute the partition function and free energy per edge on the AB$^*$ tiling using an analytic transfer matrix approach. Returning to the AB tiling, we find that membranes in the AB$^*$ tiling become 'pseudomembranes', sets of edges which collectively host at most one dimer. This leads to a remarkable discrete scale-invariance in the matching problem. The structure suggests that the AB tiling should exhibit highly inhomogenous and slowly decaying connected dimer correlations. Using Monte Carlo simulations, we find evidence supporting this supposition in the form of connected dimer correlations consistent with power law behaviour. Within the set of perfect matchings we find quasiperiodic analogues to the staggered and columnar phases observed in periodic systems.Comment: 33 pages, 26 figure

Saturation genome editing of 11 codons and exon 13 of BRCA2 coupled with chemotherapeutic drug response accurately determines pathogenicity of variants.

The unknown pathogenicity of a significant number of variants found in cancer-related genes is attributed to limited epidemiological data, resulting in their classification as variant of uncertain significance (VUS). To date, Breast Cancer gene-2 (BRCA2) has the highest number of VUSs, which has necessitated the development of several robust functional assays to determine their functional significance. Here we report the use of a humanized-mouse embryonic stem cell (mESC) line expressing a single copy of the human BRCA2 for a CRISPR-Cas9-based high-throughput functional assay. As a proof-of-principle, we have saturated 11 codons encoded by BRCA2 exons 3, 18, 19 and all possible single-nucleotide variants in exon 13 and multiplexed these variants for their functional categorization. Specifically, we used a pool of 180-mer single-stranded donor DNA to generate all possible combination of variants. Using a high throughput sequencing-based approach, we show a significant drop in the frequency of non-functional variants, whereas functional variants are enriched in the pool of the cells. We further demonstrate the response of these variants to the DNA-damaging agents, cisplatin and olaparib, allowing us to use cellular survival and drug response as parameters for variant classification. Using this approach, we have categorized 599 BRCA2 variants including 93-single nucleotide variants (SNVs) across the 11 codons, of which 28 are reported in ClinVar. We also functionally categorized 252 SNVs from exon 13 into 188 functional and 60 non-functional variants, demonstrating that saturation genome editing (SGE) coupled with drug sensitivity assays can enhance functional annotation of BRCA2 VUS

Cross validation of observations from the GPM dual-frequency precipitation radar and dual-polarization S-band ground radars

2018 Spring.Includes bibliographical references.This research presents a comparative study of observations and various products of the Global Precipitation Measurement (GPM) Mission Satellite with dual polarization S-Band Ground Radars. The GPM mission is a joint venture by the NASA and the JAXA. The radar on board the core observatory is a dual-frequency precipitation radar (DPR) capable of simultaneously operating at 13.6 GHz (Ku band) and 35.5 GHz (Ka band). The DPR is expected to revolutionize the way precipitation is measured from space through its dual-frequency observations. Ground Validation is one of the most critical aspects of the GPM mission. The best way of doing this is by direct comparison of the space-based observations with well calibrated dual polarization ground radar measurements. Before any direct comparisons can be made, volume matching of the data is necessary due to the difference in observation geometry and resolution volume of both the system. In this study, a methodology developed by Bolen and Chandrasekar (2001) for aligning TRMM satellite data with ground radar data is followed. This technique was extended by Schwaller and Morris (2011). Radar reflectivity and rainfall rate product comparison study have been performed in detail. Vertical profiles have been studied thoroughly. Various case studies of simultaneous GPM-DPR and ground radar observations have been carefully chosen. Ground validation operational NEXRAD sites have been considered from all over the USA. Comparison studies with research radars such as CSU-CHILL and NASA N-POL have also been conducted. The GPM satellite's profile classification module's products are also evaluated. Results from Hydrometeor classification method by Bechini and Chandrasekar (2015) for ground radars have been extensively used for validating DPR's melting layer detection capability in different types of precipitation system. In this study, a new method developed by Le et al (2017) for identification of snow falling on the ground has been considered. Ground validation comparisons have been performed with observations from ground radars and the results are presented