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Statistical insignificance does not suggest the absence of effect, yet scientists must often use null results as evidence of negligible (near-zero) effect size to falsify scientific hypotheses. Doing so must assess a result's null strength, defined as the evidence for a negligible effect size. Such an assessment would differentiate strong null results that suggest a negligible effect size from weak null results that suggest a broad range of potential effect sizes. We propose the most difference in means ($\delta_M$) as a two-sample statistic that can both quantify null strength and perform a hypothesis test for negligible effect size. To facilitate consensus when interpreting results, our statistic allows scientists to conclude that a result has negligible effect size using different thresholds with no recalculation required. To assist with selecting a threshold, $\delta_M$ can also compare null strength between related results. Both $\delta_M$ and the relative form of $\delta_M$ outperform other candidate statistics in comparing null strength. We compile broadly related results and use the relative $\delta_M$ to compare null strength across different treatments, measurement methods, and experiment models. Reporting the relative $\delta_M$ may provide a technical solution to the file drawer problem by encouraging the publication of null and near-zero results.

Advances in biomedicine are largely fueled by exploring uncharted territories of human biology. Machine learning can both enable and accelerate discovery, but faces a fundamental hurdle when applied to unseen data with distributions that differ from previously observed ones -- a common dilemma in scientific inquiry. We have developed a new deep learning framework, called {\textit{Portal Learning}}, to explore dark chemical and biological space. Three key, novel components of our approach include: (i) end-to-end, step-wise transfer learning, in recognition of biology's sequence-structure-function paradigm, (ii) out-of-cluster meta-learning, and (iii) stress model selection. Portal Learning provides a practical solution to the out-of-distribution (OOD) problem in statistical machine learning. Here, we have implemented Portal Learning to predict chemical-protein interactions on a genome-wide scale. Systematic studies demonstrate that Portal Learning can effectively assign ligands to unexplored gene families (unknown functions), versus existing state-of-the-art methods, thereby allowing us to target previously "undruggable" proteins and design novel polypharmacological agents for disrupting interactions between SARS-CoV-2 and human proteins. Portal Learning is general-purpose and can be further applied to other areas of scientific inquiry., Comment: 18 pages, 6 figures

Recent observations of Seyfert galaxies indicate that low power, misaligned jets can undergo significant interaction with the gas in the galactic disc and may be able to drive large-scale, multiphase outflows. We apply our novel sub-grid model for Blandford-Znajek jets to simulations of the central regions of Seyferts, in which a black hole is embedded in a dense, sub-kpc circumnuclear disc (CND) and surrounded by a dilute circumgalactic medium (CGM). We find that the variability of the accretion flow is highly sensitive both to the jet power and to the CND thermodynamics and, ultimately, is determined by the complex interplay between jet-driven outflows and backflows. Even at moderate Eddington ratios, AGN jets are able to significantly alter the thermodynamics and kinematics of CNDs and entrain up to 10% of their mass in the outflow. Mass outflow rates and kinetic powers of the warm outflowing component are in agreement with recent observations for black holes with similar bolometric luminosities, with outflow velocities that are able to reach 500 km/s. Depending on their power and direction, jets are able to drive a wide variety of large-scale outflows, ranging from light, hot and collimated structures to highly mass-loaded, multiphase, bipolar winds. This diversity of jet-driven outflows highlights the importance of applying physically motivated models of AGN feedback to realistic galaxy formation contexts. Such simulations will play a crucial role in accurately interpreting the wealth of data that next generation facilities such as JWST, SKA and Athena will provide., Comment: 25 pages, 12 figures, 2 appendices, MNRAS accepted

Implementation plans for the National Institutes of Health policy for data management and sharing, which takes effect in 2023, provide an opportunity to reflect on the stakeholders, infrastructures, practice, economics, and sustainability of data sharing. Responsibility for fulfilling data sharing requirements tends to fall on principal investigators, whereas it takes a village of stakeholders to construct, manage, and sustain the necessary knowledge infrastructure for disseminating data products. Individual scientists have mixed incentives, and many disincentives to share data, all of which vary by research domain, methods, resources, and other factors. Motivations and investments for data sharing also vary widely among academic institutional stakeholders such as university leadership, research computing, libraries, and individual schools and departments. Stakeholder concerns are interdependent along many dimensions, seven of which are explored: what data to share; context and credit; discovery; methods and training; intellectual property; data science programs; and international tensions. Data sharing is not a simple matter of individual practice, but one of infrastructure, institutions, and economics. Governments, funding agencies, and international science organizations all will need to invest in commons approaches for data sharing to develop into a sustainable international ecosystem., Comment: 22 pages, Changing the Culture of Data Management and Sharing: A Workshop. https://www.nationalacademies.org/event/04-29-2021/changing-the-culture-of-data-management-and-sharing-a-workshop. Sponsored by National Institutes of Health; preprint version of manuscript accepted for the Harvard Data Science Review. To appear in summer, 2022

We consider quasifree ground states of Araki's self-dual CAR algebra from the viewpoint of index theory and symmetry protected topological (SPT) phases. We first review how Clifford module indices characterise a topological obstruction to connect pairs of symmetric gapped ground states. This construction is then generalised to give invariants in $KO_\ast(A^\mathfrak{r})$ with $A$ a $C^{*,\mathfrak{r}}$-algebra of allowed deformations. When $A=C^*(X)$, the Roe algebra of a coarse space $X$, and we restrict to gapped ground states that are locally equivalent with respect $X$, a $K$-homology class is also constructed. The coarse assembly map relates these two classes and clarifies the relevance of $K$-homology to free-fermionic SPT phases., Comment: v3: Final version to appear in J. Phys A, 31 pages

Reversible covalent kinase inhibitors (RCKIs) are a class of novel kinase inhibitors attracting increasing attention because they simultaneously show the selectivity of covalent kinase inhibitors, yet avoid permanent protein-modification-induced adverse effects. Over the last decade, RCKIs have been reported to target different kinases, including atypical kinases. Currently, three RCKIs are undergoing clinical trials to treat specific diseases, for example, Pemphigus, an autoimmune disorder. In this perspective, first, RCKIs are systematically summarized, including characteristics of electrophilic groups, chemical scaffolds, nucleophilic residues, and binding modes. Second, we provide insights into privileged electrophiles, the distribution of nucleophiles and hence effective design strategies for RCKIs. Finally, we provide a brief perspective on future design strategies for RCKIs, including those that target proteins other than kinases., Comment: 55 pages; 12 figures

This paper explores whether graph embedding methods can be used as a tool for analysing the robustness of power-grids within the framework of network science. The paper focuses on the strain elevation tension spring embedding (SETSe) algorithm and compares it to node2vec and Deep Graph Infomax, and the measures mean edge capacity and line load. These five methods are tested on how well they can predict the collapse point of the giant component of a network under random attack. The analysis uses seven power-grid networks, ranging from 14 to 2000 nodes. In total, 3456 load profiles are created for each network by loading the edges of the network to have a range of tolerances and concentrating network capacity into fewer edges. One hundred random attack sequences are generated for each load profile, and the mean number of attacks required for the giant component to collapse for each profile is recorded. The relationship between the embedding values for each load profile and the mean collapse point is then compared across all five methods. It is found that only SETSe and line load perform well as proxies for robustness with $R^2 = 0.89$ for both measures. When tested on a time series normal operating conditions line load performs exceptionally well ($R=0.99$). However, the SETSe algorithm provides valuable qualitative insight into the state of the power-grid by leveraging its method local smoothing and global weighting of node features to provide an interpretable geographical embedding. This paper shows that graph representation algorithms can be used to analyse network properties such as robustness to cascading failure attacks, even when the network is embedded at node level., Comment: 5 figures 21 pages

Kinase-targeted drug design is challenging. It requires designing inhibitors that can bind to specific kinases when all kinase catalytic domains share a common folding scaffold that binds ATP. Thus, obtaining the desired selectivity, given the whole human kinome, is a fundamental task during early-stage drug discovery. This begins with deciphering the kinase-ligand characteristics, analyzing the structure-activity relationships, and prioritizing the desired drug molecules across the whole kinome. Currently, there are more than 300 kinases with released PDB structures, which provides a substantial structural basis to gain these necessary insights. Here, we review in silico structure-based methods - notably, a function-site interaction fingerprint approach used in exploring the complete human kinome. In silico methods can be explored synergistically with multiple cell-based or protein-based assay platforms such as KINOMEscan. We conclude with new drug discovery opportunities associated with kinase signaling networks and using machine/deep learning techniques broadly referred to as structural biomedical data science., Comment: 22 pages, 2 figures, 3 tables

We consider the recent surge of information on the potential benefits of acid-suppression drugs in the context of COVID-19, with an eye on the variability (and confusion) across the reported findings--at least as regards the popular antacid famotidine. The inconsistencies reflect contradictory conclusions from independent clinical-based studies that took roughly similar approaches, in terms of experimental design (retrospective, cohort-based, etc.) and statistical analyses (propensity-score matching and stratification, etc.). The confusion has significant ramifications in choosing therapeutic interventions: e.g., do potential benefits of famotidine indicate its use in a particular COVID-19 case? Beyond this pressing therapeutic issue, conflicting information on famotidine must be resolved before its integration in ontological and knowledge graph-based frameworks, which in turn are useful in drug repurposing efforts. To begin systematically structuring the rapidly accumulating information, in the hopes of clarifying and reconciling the discrepancies, we consider the contradictory information along three proposed 'axes': (1) a context-of-disease axis, (2) a degree-of-[therapeutic]-benefit axis, and (3) a mechanism-of-action axis. We suspect that incongruencies in how these axes have been (implicitly) treated in past studies has led to the contradictory indications for famotidine and COVID-19. We also trace the evolution of information on acid-suppression agents as regards the transmission, severity, and mortality of COVID-19, given the many literature reports that have accumulated. By grouping the studies conceptually and thematically, we identify three eras in the progression of our understanding of famotidine and COVID-19. Harmonizing these findings is a key goal for both clinical standards-of-care (COVID and beyond) as well as ontological and knowledge graph-based approaches., Comment: 10 pages, 1 figure

Any periodic variations of earthquake occurrence rates in response to small, known, periodic stress variations provide important opportunities to learn about the earthquake nucleation process. Yet, reliable detection of earthquake periodicity is complicated by the presence of earthquake clustering due to aftershocks and foreshocks. Existing methods for detecting periodicity in an earthquake catalogue typically require the prior removal of these clustered events. Declustering is a highly uncertain process, so declustering methods are inherently non-unique. Incorrect declustering may remove some independent events, or fail to remove some aftershocks or foreshocks, or both. These two types of error could respectively lead to false negative or false positive reporting of periodic seismicity. To overcome these limitations, we propose a new method for detecting earthquake periodicity that does not require declustering. Our approach is to modify the existing Schuster Spectrum Test (SST) by adapting a test statistic for periodic seismicity to account for the presence of clustered earthquakes within the catalogue without requiring their identification and removal., Comment: 55 pages, 9 figures

We prove an asymptotic crystallization result in two dimensions for a class of nonlocal particle systems. To be precise, we consider the best approximation with respect to the 2-Wasserstein metric of a given absolutely continuous probability measure $f \mathrm{d}x$ by a discrete probability measure $\sum_i m_i \delta_{z_i}$, subject to a constraint on the particle sizes $m_i$. The locations $z_i$ of the particles, their sizes $m_i$, and the number of particles are all unknowns of the problem. We study a one-parameter family of constraints. This is an example of an optimal location problem (or an optimal sampling or quantization problem) and it has applications in economics, signal compression, and numerical integration. We establish the asymptotic minimum value of the (rescaled) approximation error as the number of particles goes to infinity. In particular, we show that for the constrained best approximation of the Lebesgue measure by a discrete measure, the discrete measure whose support is a triangular lattice is asymptotically optimal. In addition, we prove an analogous result for a problem where the constraint is replaced by a penalization. These results can also be viewed as the asymptotic optimality of the hexagonal tiling for an optimal partitioning problem. They generalise the crystallization result of Bourne, Peletier and Theil (Communications in Mathematical Physics, 2014) from a single particle system to a class of particle systems, and prove a case of a conjecture by Bouchitt\'{e}, Jimenez and Mahadevan (Journal de Math\'ematiques Pures et Appliqu\'ees, 2011). Finally, we prove a crystallization result which states that optimal configurations with energy close to that of a triangular lattice are geometrically close to a triangular lattice.

Delta-self-consistent field theory (delta-SCF) is a conceptually simple and computationally inexpensive method for finding excited states. Using the maximum overlap method to guide optimization of the excited state, delta-SCF has been shown to predict excitation energies with a level of accuracy that is competitive with, and sometimes better than, that of TDDFT. Here we benchmark delta-SCF on a larger set of molecules than has previously been considered, and, in particular, we examine the performance of delta-SCF in predicting transition dipole moments, the essential quantity for spectral intensities. A potential downfall for delta-SCF transition dipoles is origin dependence induced by the nonorthogonality of delta-SCF ground and excited states. We propose and test the simplest correction for this problem, based on symmetric orthogonalization of the states, and demonstrate its use on bacteriochlorophyll structures sampled from the photosynthetic antenna in purple bacteria., Comment: 24 pages, 4 figure, 1 excel spreadsheet containing supplementary material

Jets launched by active galactic nuclei (AGN) are believed to play a significant role in shaping the properties of galaxies and provide an energetically viable mechanism through which galaxies can become quenched. Here we present a novel AGN feedback model, which we have incorporated into the AREPO code, that evolves the black hole mass and spin as the accretion flow proceeds through a thin $\alpha$-disc which we self-consistently couple to a Blandford-Znajek jet. We apply our model to the central region of a typical radio-loud Seyfert galaxy embedded in a hot circumgalactic medium (CGM). We find that jets launched into high pressure environments thermalise efficiently due to the formation of recollimation shocks and the vigorous instabilities that these shocks excite increase the efficiency of the mixing of CGM and jet material. The beams of more overpressured jets, however, are not as readily disrupted by instabilities so the majority of the momentum flux at the jet base is retained out to the head, where the jet terminates in a reverse shock. All jets entrain a significant amount of cold circumnuclear disc material which, while energetically insignificant, dominates the lobe mass together with the hot, entrained CGM material. The jet power evolves significantly due to effective self-regulation by the black hole, fed by secularly-driven, intermittent mass flows. The direction of jets launched directly into the circumnuclear disc changes considerably due to effective Bardeen-Petterson torquing. Interestingly, these jets obliterate the innermost regions of the disc and drive large-scale, multi-phase, turbulent, bipolar outflows., Comment: 33 pages, 12 figures, 2 appendices, published in MNRAS

Artificial potential fields (APFs) and their variants have been a staple for collision avoidance of mobile robots and manipulators for almost 40 years. Its model-independent nature, ease of implementation, and real-time performance have played a large role in its continued success over the years. Control barrier functions (CBFs), on the other hand, are a more recent development, commonly used to guarantee safety for nonlinear systems in real-time in the form of a filter on a nominal controller. In this paper, we address the connections between APFs and CBFs. At a theoretic level, we prove that APFs are a special case of CBFs: given a APF one obtains a CBFs, while the converse is not true. Additionally, we prove that CBFs obtained from APFs have additional beneficial properties and can be applied to nonlinear systems. Practically, we compare the performance of APFs and CBFs in the context of obstacle avoidance on simple illustrative examples and for a quadrotor, both in simulation and on hardware using onboard sensing. These comparisons demonstrate that CBFs outperform APFs., Comment: 8 pages, submitted to RA-L

Following the operator algebraic approach to Gabor analysis, we construct frames of translates for the Hilbert space localisation of the Morita equivalence bimodule arising from a groupoid equivalence between Hausdorff groupoids, where one of the groupoids is \'{e}tale and with a compact unit space. For finitely generated and projective submodules, we show these frames are orthonormal bases if and only if the module is free. We then apply this result to the study of localised Wannier bases of spectral subspaces of Schr\"{o}dinger operators with atomic potentials supported on (aperiodic) Delone sets. The noncommutative Chern numbers provide a topological obstruction to fast-decaying Wannier bases and we show this result is stable under deformations of the underlying Delone set., Comment: v2: name changed and other minor changes. To appear in J. Fourier Anal. Appl. 28 pages

We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver., Comment: 35 pages, 2 figures

While there is overwhelming observational evidence of AGN-driven jets in galaxy clusters and groups, if and how the jet energy is delivered to the ambient medium remains unanswered. Here we perform very high resolution AGN jet simulations within a live, cosmologically evolved cluster with the moving mesh code AREPO. We find that mock X-ray and radio lobe properties are in good agreement with observations with different power jets transitioning from FR-I to FR-II-like morphologies. During the lobe inflation phase, heating by both internal and bow shocks contributes to lobe energetics, and $\sim 40$ per cent of the feedback energy goes into the $PdV$ work done by the expanding lobes. Low power jets are more likely to simply displace gas during lobe inflation, but higher power jets become more effective at driving shocks and heating the intracluster medium (ICM), although shocks rarely exceed $\mathcal{M}\sim 2-3$. Once the lobe inflation phase ceases, cluster weather significantly impacts the lobe evolution. Lower power jet lobes are more readily disrupted and mixed with the ICM, depositing up to $\sim 70$ per cent of the injected energy, however, ultimately the equivalent of $\gtrsim 50$ per cent of the feedback energy ends up as potential energy of the system. Even though the mean ICM entropy is increased up to $80$~Myr after the jets switch off, AGN heating is gentle, inducing no large variations in cluster radial profiles in accord with observations., Comment: 29 pages, 14 figures, accepted for publication in MNRAS

This paper introduces the Strain Elevation Tension Spring embedding (SETSe) algorithm, a graph embedding method that uses a physics model to create node and edge embeddings in undirected attribute networks. Using a low-dimensional representation, SETSe is able to differentiate between graphs that are designed to appear identical using standard network metrics such as number of nodes, number of edges and assortativity. The embeddings generated position the nodes such that sub-classes, hidden during the embedding process, are linearly separable, due to the way they connect to the rest of the network. SETSe outperforms five other common graph embedding methods on both graph differentiation and sub-class identification. The technique is applied to social network data, showing its advantages over assortativity as well as SETSe's ability to quantify network structure and predict node type. The algorithm has a convergence complexity of around $\mathcal{O}(n^2)$, and the iteration speed is linear ($\mathcal{O}(n)$), as is memory complexity. Overall, SETSe is a fast, flexible framework for a variety of network and graph tasks, providing analytical insight and simple visualisation for complex systems., Comment: 27 pages; 7000 words

We introduce an index for symmetry protected topological (SPT) phases of infinite fermionic chains with an on-site symmetry given by a finite group $G$. This index takes values in $\mathbb{Z}_2 \times H^1(G,\mathbb{Z}_2) \times H^2(G, U(1)_{\mathfrak{p}})$ with a generalized Wall group law under stacking. We show that this index is an invariant of the classification of SPT phases. When the ground state is translation invariant and has reduced density matrices with uniformly bounded rank on finite intervals, we derive a fermionic matrix product representative of this state with on-site symmetry., Comment: To appear in Forum of Mathematics, Sigma

Recent computational advances in the accurate prediction of protein three-dimensional (3D) structures from amino acid sequences now present a unique opportunity to decipher the interrelationships between proteins. This task entails--but is not equivalent to--a problem of 3D structure comparison and classification. Historically, protein domain classification has been a largely manual and subjective activity, relying upon various heuristics. Databases such as CATH represent significant steps towards a more systematic (and automatable) approach, yet there still remains much room for the development of more scalable and quantitative classification methods, grounded in machine learning. We suspect that re-examining these relationships via a Deep Learning (DL) approach may entail a large-scale restructuring of classification schemes, improved with respect to the interpretability of distant relationships between proteins. Here, we describe our training of DL models on protein domain structures (and their associated physicochemical properties) in order to evaluate classification properties at CATH's "homologous superfamily" (SF) level. To achieve this, we have devised and applied an extension of image-classification methods and image segmentation techniques, utilizing a convolutional autoencoder model architecture. Our DL architecture allows models to learn structural features that, in a sense, 'define' different homologous SFs. We evaluate and quantify pairwise 'distances' between SFs by building one model per SF and comparing the loss functions of the models. Hierarchical clustering on these distance matrices provides a new view of protein interrelationships--a view that extends beyond simple structural/geometric similarity, and towards the realm of structure/function properties., Comment: 6 pages, 3 figures, 1 table; IEEE SIEDS conference submission