Geographically weighted regression (GWR) is a spatial statistical technique that recognizes that traditional 'global' regression models may be limited when spatial processes vary with spatial context. GWR captures process spatial heterogeneity by allowing effects to vary over space. To do this, GWR calibrates an ensemble of local linear models at any number of locations using 'borrowed' nearby data. This provides a surface of location-specific parameter estimates for each relationship in the model that is allowed to vary spatially, as well as a single bandwidth parameter that provides intuition about the geographic scale of the processes. A recent extension to this framework allows each relationship to vary according to a distinct spatial scale parameter, and is therefore known as multiscale (M)GWR. This paper introduces mgwr, a Python-based implementation of MGWR that explicitly focuses on the multiscale analysis of spatial heterogeneity. It provides novel functionality for inference and exploratory analysis of local spatial processes, new diagnostics unique to multi-scale local models, and drastic improvements to efficiency in estimation routines. We provide two case studies using mgwr, in addition to reviewing core concepts of local models. We present this in a literate programming style, providing an overview of the primary software functionality and demonstrations of suggested usage alongside the discussion of primary concepts and demonstration of the improvements made in mgwr.A recent extension to the GWR framework allows each relationship in the model to vary at a unique spatial scale and is therefore known as multiscale (M)GWR [3]. MGWR is much less restrictive in its assumptions than GWR, since the relationship between the response and a covariate is allowed to vary locally, vary regionally, and or not vary at all. Eliminating the restriction that all relationships vary at the same spatial scale can minimize over-fitting, reduce bias in the parameter estimates, and mitigate concurvity (i.e., collinearity due to similar functional transformations). Therefore, MGWR has been suggested as the default local model specification when using GWR to investigate process spatial heterogeneity and scale. This paper introduces mgwr (throughout this manuscript mgwr refers to the software implementation, while MGWR refers to the technique more generally), a Python-based software package for deploying GWR and MGWR models. Though there are existing software options, they are limited in terms of available functionality, computational efficiency, or both. For example, there is a GWR tool in the spatial analyst toolbox within ArcGIS [4] and there are several options within the R ecosystem, such as spgwr [5] and gwrr [6]. However, none of these implementations offers capabilities to calibrate an MGWR model nor the ability to compute the hat matrix (i.e., projection matrix) and the associated novel model diagnostics described in [7], which includes covariate-specific indicators of scale and inference framework. The R-based GWm...

A recent paper expands the well‐known geographically weighted regression (GWR) framework significantly by allowing the bandwidth or smoothing factor in GWR to be derived separately for each covariate in the model—a framework referred to as multiscale GWR (MGWR). However, one limitation of the MGWR framework is that, until now, no inference about the local parameter estimates was possible. Formally, the so‐called “hat matrix,” which projects the observed response vector into the predicted response vector, was available in GWR but not in MGWR. This paper addresses this limitation by reframing GWR as a Generalized Additive Model, extending this framework to MGWR and then deriving standard errors for the local parameters in MGWR. In addition, we also demonstrate how the effective number of parameters can be obtained for the overall fit of an MGWR model and for each of the covariates within the model. This statistic is essential for comparing model fit between MGWR, GWR, and traditional global models, as well as for adjusting multiple hypothesis tests. We demonstrate these advances to the MGWR framework with both a simulated data set and a real‐world data set and provide a link to new software for MGWR (MGWR1.0) which includes the novel inferential framework for MGWR described here.

We report the first example of Pd(II)-catalyzed γ-C(sp)-H activation of ketones directed by a practical 2,2-dimethyl aminooxyacetic acid auxiliary. 2-Pyridone ligands are identified to enable C(sp)-H activation for the first time. A rare six-membered palladacycle intermediate is isolated and characterized to elucidate the reaction mechanism. Both (hetero)arylation and vinylation of γ-C(sp)-H bonds are demonstrated. Sequential β- and γ-C(sp)-H (hetero)arylation of muscone showcases the utility of this method for late-stage diversification. A convenient Mn(II)-catalyzed auxiliary removal is also developed to further underscore the practicality of this transformation.

Three new polyether‐tethered dinickel–salphen complexes (2 a–c) have been synthesized and fully characterized by NMR spectroscopy, mass spectrometry, and elemental analyses. The binding affinity and selectivity of these complexes and of the parent mono‐nickel complex (1) towards dimeric quadruplex DNA have been determined by UV/Vis titrations, fluorescence spectroscopy, CD spectroscopy, and electrophoresis. These studies have shown that the dinickel–salphen complex with the longest polyether linker (2 c) has higher binding affinity and selectivity towards dimeric quadruplexes (over monomeric quadruplexes) than the dinickel–salphen complexes with the shorter polyether linkers (2 a and 2 b). Complex 2 c also has higher selectivity towards human telomeric dimeric quadruplexes with one TTA linker than the monometallic complex 1. Based on the spectroscopic data, a possible binding mode between complex 2 c and the dimeric G‐quadruplex DNA under study is proposed.

PbS nanocrystals are critical materials for infrared optoelectronics, but the persistent challenge in synthesizing small nanocrystals with narrow line widths demands improved mechanistic understanding. Here, we show that the conventional hot-injection synthesis of PbS nanocrystals per Hines exhibits two-step kinetics involving an intermediate species. The intermediate is small, lead-rich, and has characteristic, reproducible, visible-wavelength emissionall consistent. with a PbS prenucleation cluster (PNC). We then demonstrate that high-pK a amines disrupt the PNC, accelerating nanocrystal nucleation and enabling the synthesis of PbS nanocrystals with diameters as small as ⌀ ∼ 1.7 nm and distinct ensemble absorption peaks (hν = 2.2 eV, λ = 560 nm) in reactions allowed to run to completion. We show that the basicity of the amine additive controls the average size of nanocrystals at reaction completion, which we understand by incorporating metastable PNCs into reaction models that partition monomers between nanocrystal nucleation and nanocrystal growth. This conceptual advance permits the routine synthesis of ultrasmall PbS NCs with excitonic absorption line widths that are up to 25% narrower than previously reported for comparable sizes (⌀: 1.7–3 nm, λpeak,abs: 560–885 nm, hνpeak,abs: 2.2–1.4 eV). This reduced electronic dispersity will enhance device performance, and the underlying insight is further evidence of the exquisite ability of metal-complexing additives to direct the bottom-up syntheses of nanostructured materials.

One of the core challenges in developing C-H activation reactions is to distinguish multiple C-H bonds that are nearly identical in terms of electronic properties and bond strengths. Through recognition of distance and molecular geometry, remote C(sp 2)-H bonds have been selectively activated in the presence of proximate ones 1-2. Yet achieving such unconventional site selectivity with C(sp 3)-H bonds remains a paramount challenge. Here we report a combination of a simple pyruvic acid derived directing group and a 2-pyridione ligand that enables the preferential activation of the distal γ-C(sp 3)-H bond over the proximate β-C(sp 3)-H bonds for a wide range of alcohol derived substrates. Competition experiment of five-and six-membered cyclopalladation step as well as kinetic experiments demonstrate the feasibility of using geometric strain to reverse the conventional site selectivity in C(sp 3)-H activation. Developing C-H activation reactions as new retrosynthetic disconnections could offer a multitude of novel synthetic strategies due to the abundance of positionally diverse C-H bonds 3-4. On the other hand, the great resemblance between these C-H bonds in terms of bond strength and electronic properties presents a tremendous challenge for achieving regioselectivity. This difficulty escalates with metalation chemistry because in such processes, the numerous primary or secondary C-H bonds are nearly indistinguishable by the metal. For example, despite the recent advances in developing a wide range of Pdcatalyzed C(sp 3)-H activation reactions, their regioselectivity is largely restricted to the cleavage of the C-H bond that will result in five-membered cyclopalladation 5-12. Therefore, it is fundamentally important to develop strategies to switch the selectivity of the key metalation step from five-membered to six-membered cyclopalladation (Fig. 1b). Such Reprints and permissions information is available at www.nature.com/reprints.

Herein, we report transition-metal-catalyzed B-H bond insertion reactions between borane adducts and alkynes to afford organoboron compounds in excellent yields under mild reaction conditions. This successful use of alkynes as carbene precursors in these reactions constitutes a new route to organoboron compounds. The starting materials are safe and readily available, and the reaction exhibits 100% atom-economy. Moreover, an asymmetric version catalyzed by chiral dirhodium complexes produced chiral boranes with excellent enantioselectivity (up to 96% ee). This is the first report of highly enantioselective heteroatom-hydrogen bond insertion reactions of metal carbenes generated in situ from alkynes. The chiral products of the reaction could be easily transformed to widely used borates and diaryl methanol compounds without loss of optical purity, which demonstrates its potential utility in organic synthesis. A kinetics study indicated that the Cu-catalyzed B-H bond insertion reaction is first order with respect to the catalyst and the alkyne and zero order with respect to the borane adduct, and no kinetic isotopic effect was observed in the reaction of the adduct. These results, along with density functional theory calculations, suggest that the formation of the Cu carbene is the rate-limiting step and that the B-H bond insertion is a fast, concerted process.

Three polyether-tethered berberine dimers (1a-c) were studied for their binding affinity, selectivity and thermal stabilization towards human telomeric dimeric quadruplex DNA (G2T1). Compound 1a with the shortest polyether linker showed the highest affinity (K > 10 M) and 76-508-fold higher selectivity for mixed-type G2T1 over antiparallel G2T1 and three monomeric G-quadruplexes, which are human telomeric monomeric quadruplex G1, c-kit 1 and c-kit 2. Compound 1a induced the formation of quadruplex structures and showed higher thermal stabilization for mixed-type G2T1 than for anti-parallel G2T1, G1 and ds DNA. Spectroscopic studies suggest that compound 1a could bind to mixed-type G2T1 via end-stacking and external binding modes. These results suggest that the polyether linkers in these compounds play an important role in regulating the binding affinity and selectivity towards mixed-type G2T1 and that compound 1a could target mixed-type G2T1 at other genome regions with antiparallel G2T1 and monomeric G-quadruplexes. These results may provide useful guidance for the rational design of selective multimeric G-quadruplex binders and potential anticancer agents.