Synthesis, structure and dynamics of NHC-based palladium macrocycles

A series of macrocyclic CNC pincer pro-ligands based on bis(imidazolium)lutidine salts with octa-, deca- and dodecamethylene spacers have been prepared and their coordination chemistry investigated. Using a Ag2O based transmetallation strategy, cationic palladium(II) chloride complexes [PdCl{CNC–(CH2)n}][BArF4] (n = 8, 10, 12; ArF = 3,5-C6H3(CF3)2) were prepared and fully characterised in solution, by NMR spectroscopy and ESI-MS, and in the solid-state, by X-ray crystallography. The smaller macrocyclic complexes (n = 8 and 10) exhibit dynamic behaviour in solution, involving ring flipping of the alkyl spacer across the Pd–Cl bond, which was interrogated by variable temperature NMR spectroscopy. In the solid-state, distorted coordination geometries are observed with the spacer skewed to one side of the Pd–Cl bond. In contrast, a static C2 symmetric structure is observed for the dodecamethylene based macrocycle. For comparison, palladium(II) fluoride analogues [PdF{CNC–(CH2)n}][BArF4] (n = 8, 10, 12) were also prepared and their solution and solid-state structures contrasted with those of the chlorides. Notably, these complexes exhibit very low frequency 19F chemical shifts (ca. −400 ppm) and the presence of C–HF interactions (2hJFC coupling observed by 13C NMR spectroscopy). The dynamic behaviour of the fluoride complexes is largely consistent with the smaller ancillary ligand; [PdF{CNC–(CH2)8}][BArF4] exceptionally shows C2v time averaged symmetry in solution at room temperature (CD2Cl2, 500 MHz) as a consequence of dual fluxional processes of the pincer backbone and alkyl spacer

On the construction of probabilistic Newton-type algorithms

It has recently been shown that many of the existing quasi-Newton algorithms can be formulated as learning algorithms, capable of learning local models of the cost functions. Importantly, this understanding allows us to safely start assembling probabilistic Newton-type algorithms, applicable in situations where we only have access to noisy observations of the cost function and its derivatives. This is where our interest lies. We make contributions to the use of the non-parametric and probabilistic Gaussian process models in solving these stochastic optimisation problems. Specifically, we present a new algorithm that unites these approximations together with recent probabilistic line search routines to deliver a probabilistic quasi-Newton approach. We also show that the probabilistic optimisation algorithms deliver promising results on challenging nonlinear system identification problems where the very nature of the problem is such that we can only access the cost function and its derivative via noisy observations, since there are no closed-form expressions available

Complex-valued Time Series Modeling for Improved Activation Detection in fMRI Studies

A complex-valued data-based model with th order autoregressive errors and general real/imaginary error covariance structure is proposed as an alternative to the commonly used magnitude-only data-based autoregressive model for fMRI time series. Likelihood-ratio-test-based activation statistics are derived for both models and compared for experimental and simulated data. For a dataset from a right-hand finger-tapping experiment, the activation map obtained using complex-valued modeling more clearly identifies the primary activation region (left functional central sulcus) than the magnitude-only model. Such improved accuracy in mapping the left functional central sulcus has important implications in neurosurgical planning for tumor and epilepsy patients. Additionally, we develop magnitude and phase detrending procedures for complex-valued time series and examine the effect of spatial smoothing. These methods improve the power of complex-valued data-based activation statistics. Our results advocate for the use of the complex-valued data and the modeling of its dependence structures as a more efficient and reliable tool in fMRI experiments over the current practice of using only magnitude-valued datasets

How physics instruction impacts students' beliefs about learning physics: A meta-analysis of 24 studies

In this meta-analysis, we synthesize the results of 24 studies using the Colorado Learning Attitudes about Science Survey (CLASS) and the Maryland Physics Expectations Survey (MPEX) to answer several questions: (1) How does physics instruction impact students' beliefs? (2) When do physics majors develop expert-like beliefs? and (3) How do students' beliefs impact their learning of physics? We report that in typical physics classes, students' beliefs deteriorate or at best stay the same. There are a few types of interventions, including an explicit focus on model-building and/or developing expert- like beliefs that lead to significant improvements in beliefs. Further, small courses and those for elementary education and non-science majors also result in improved beliefs. However, because the available data oversamples certain types of classes, it is unclear whether these improvements are actually due to the interventions, or due to the small class size, or student population typical of the kinds of classes in which these interventions are most often used. Physics majors tend to enter their undergraduate education with more expert-like beliefs than non-majors and these beliefs remain relatively stable throughout their undergraduate careers. Thus, typical physics courses appear to be selecting students who already have strong beliefs, rather than supporting students in developing strong beliefs. There is a small correlation between students' incoming beliefs about physics and their gains on conceptual mechanics surveys. This suggests that students with more expert-like incoming beliefs may learn more in their physics courses, but this finding should be further explored and replicated. Some unanswered questions remain. To answer these questions, we advocate several specific types of future studies.Comment: 30 pages. Accepted to Phys Rev ST-PE