Large-scale magnetic field maps using structured kernel interpolation for Gaussian process regression

We present a mapping algorithm to compute large-scale magnetic field maps in indoor environments with approximate Gaussian process (GP) regression. Mapping the spatial variations in the ambient magnetic field can be used for localization algorithms in indoor areas. To compute such a map, GP regression is a suitable tool because it provides predictions of the magnetic field at new locations along with uncertainty quantification. Because full GP regression has a complexity that grows cubically with the number of data points, approximations for GPs have been extensively studied. In this paper, we build on the structured kernel interpolation (SKI) framework, speeding up inference by exploiting efficient Krylov subspace methods. More specifically, we incorporate SKI with derivatives (D-SKI) into the scalar potential model for magnetic field modeling and compute both predictive mean and covariance with a complexity that is linear in the data points. In our simulations, we show that our method achieves better accuracy than current state-of-the-art methods on magnetic field maps with a growing mapping area. In our large-scale experiments, we construct magnetic field maps from up to 40000 three-dimensional magnetic field measurements in less than two minutes on a standard laptop

Exploring Chemical Space for new Substances to stabilize a therapeutic Monoclonal Antibody

The physical stability of therapeutic proteins is a major concern in the development of liquid protein formulations. The number of degrees of freedom to tweak a given protein’s stability is limited to pH, ionic strength and type and concentration of excipient. There are only very few, mostly similar excipients currently in use, limited to the short list of substances generally recognized as safe for human use by the FDA. Opposed to the limited number of molecules the formulation scientist has at hand to stabilize a protein, there is the vastness of chemical space which is hypothesized to consist of 1060 compounds. Its potential to stabilize proteins has never been explored systematically in the context of stabilization of therapeutic proteins. Here we present a screening strategy to discover new excipients to further stabilize an already stable formulation of a therapeutic antibody. We use our data to build a predictive model to evaluate the stabilizing potential of small molecules. We argue that prior to worrying about the hurdles of toxicity and approval of novel excipient candidates, it is mandatory to assess the actual potential hidden in the chemical space

Projecting basis functions with tensor networks for Gaussian process regression

This paper presents a method for approximate Gaussian process (GP) regression with tensor networks (TNs). A parametric approximation of a GP uses a linear combination of basis functions, where the accuracy of the approximation depends on the total number of basis functions $M$. We develop an approach that allows us to use an exponential amount of basis functions without the corresponding exponential computational complexity. The key idea to enable this is using low-rank TNs. We first find a suitable low-dimensional subspace from the data, described by a low-rank TN. In this low-dimensional subspace, we then infer the weights of our model by solving a Bayesian inference problem. Finally, we project the resulting weights back to the original space to make GP predictions. The benefit of our approach comes from the projection to a smaller subspace: It modifies the shape of the basis functions in a way that it sees fit based on the given data, and it allows for efficient computations in the smaller subspace. In an experiment with an 18-dimensional benchmark data set, we show the applicability of our method to an inverse dynamics problem

β-Catenin Directs Nuclear Factor-κB p65 Output via CREB-Binding Protein/p300 in Human Airway Smooth Muscle

β-Catenin is a multifunctional protein that apart from its role in proliferative and differentiation events, also acts upon inflammatory processes, mainly via interaction with nuclear factor-κB (NF-κB). However, there is still controversy as to whether β-catenin facilitates or represses NF-κB output. Insights into the molecular mechanisms underlying the interaction between β-catenin and NF-κB have highlighted the cofactors CREB-binding protein (CBP) and p300 as important candidates. Here, we hypothesized that the interaction of β-catenin with CBP/p300 directs NF-κB output. Using human airway smooth muscle (ASM) cells, we found that β-catenin is essential in interleukin -1β (IL-1β)-mediated expression of interleukin-6 (IL-6) by promoting nuclear translocation of the p65 subunit of NF-κB. These effects were independent from WNT pathway activation or other factors that promote β-catenin signaling. In the nucleus, inhibition of either the CBP- or p300-β-catenin interaction could regulate NF-κB output, by enhancing (CBP inhibition) or inhibiting (p300 inhibition) IL-1β-induced expression of IL-6, respectively. Acetylation of p65 by p300 likely underlies these events, as inhibition of the p300-β-catenin interaction diminished levels of acetylated p65 at lysine 310, thereby reducing p65 transcriptional activity. In conclusion, β-catenin is a critical component of NF-κB-mediated inflammation in human ASM, affecting transcriptional output by interacting with the nuclear cofactors CBP and p300. Targeting β-catenin may be an alternative strategy to treat airway inflammation in patients with airway disease, such as asthma