Topology of ambient manifolds of non-singular Morse – Smale flows with three periodic orbits

The purpose of this study is to establish the topological properties of three-dimensional manifolds which admit Morse – Smale flows without fixed points (non-singular or NMS-flows) and give examples of such manifolds that are not lens spaces. Despite the fact that it is known that any such manifold is a union of circular handles, their topology can be investigated additionally and refined in the case of a small number of orbits. For example, in the case of a flow with two non-twisted (having a tubular neighborhood homeomorphic to a solid torus) orbits, the topology of such manifolds is established exactly: any ambient manifold of an NMS-flow with two orbits is a lens space. Previously, it was believed that all prime manifolds admitting NMS-flows with at most three non-twisted orbits have the same topology. Methods. In this paper, we consider suspensions over Morse – Smale diffeomorphisms with three periodic orbits. These suspensions, in turn, are NMS-flows with three periodic trajectories. Universal coverings of the ambient manifolds of these flows and lens spaces are considered. Results. In this paper, we present a countable set of pairwise distinct simple 3-manifolds admitting NMS-flows with exactly three non-twisted orbits. Conclusion. From the results of this paper it follows that there is a countable set of pairwise distinct three-dimensional manifolds other than lens spaces, which refutes the previously published result that any simple orientable manifold admitting an NMS-flow with at most three orbits is lens space.

Recommended conventions for reporting results from direct dark matter searches

The field of dark matter detection is a highly visible and highly competitive one. In this paper, we propose recommendations for presenting dark matter direct detection results particularly suited for weak-scale dark matter searches, although we believe the spirit of the recommendations can apply more broadly to searches for other dark matter candidates, such as very light dark matter or axions. To translate experimental data into a final published result, direct detection collaborations must make a series of choices in their analysis, ranging from how to model astrophysical parameters to how to make statistical inferences based on observed data. While many collaborations follow a standard set of recommendations in some areas, for example the expected flux of dark matter particles (to a large degree based on a paper from Lewin and Smith in 1995), in other areas, particularly in statistical inference, they have taken different approaches, often from result to result by the same collaboration. We set out a number of recommendations on how to apply the now commonly used Profile Likelihood Ratio method to direct detection data. In addition, updated recommendations for the Standard Halo Model astrophysical parameters and relevant neutrino fluxes are provided. The authors of this note include members of the DAMIC, DarkSide, DARWIN, DEAP, LZ, NEWS-G, PandaX, PICO, SBC, SENSEI, SuperCDMS, and XENON collaborations, and these collaborations provided input to the recommendations laid out here. Wide-spread adoption of these recommendations will make it easier to compare and combine future dark matter results.

Eye tracking based dyslexia detection using a holistic approach

A new detection method for cognitive impairments is presented utilizing an eye tracking signals in a text reading test. This research enhances published articles that extract combination of various features. It does so by processing entire eye-tracking records either in time or frequency whereas applying only basic signal pre-processing. Such signals were classified as a whole by Convolutional Neural Networks (CNN) that hierarchically extract substantial features scatter either in time or frequency and nonlinearly binds them using machine learning to minimize a detection error. In the experiments we used a 100 fold cross validation and a dataset containing signals of 185 subjects (88 subjects with low risk and 97 subjects with high risk of dyslexia). In a series of experiments it was found that magnitude spectrum based representation of time interpolated eye-tracking signals recorded the best results, i.e. an average accuracy of 96.6% was reached in comparison to 95.6% that is the best published result on the same database. These findings suggest that a holistic approach involving small but complex enough CNNs applied to properly pre-process and expressed signals provides even better results than a combination of meticulously selected well-known features.

Sample Efficient Decentralized Stochastic Frank-Wolfe Methods for Continuous DR-Submodular Maximization

Continuous DR-submodular maximization is an important machine learning problem, which covers numerous popular applications. With the emergence of large-scale distributed data, developing efficient algorithms for the continuous DR-submodular maximization, such as the decentralized Frank-Wolfe method, became an important challenge. However, existing decentralized Frank-Wolfe methods for this kind of problem have the sample complexity of $\mathcal{O}(1/\epsilon^3)$, incurring a large computational overhead. In this paper, we propose two novel sample efficient decentralized Frank-Wolfe methods to address this challenge. Our theoretical results demonstrate that the sample complexity of the two proposed methods is $\mathcal{O}(1/\epsilon^2)$, which is better than $\mathcal{O}(1/\epsilon^3)$ of the existing methods. As far as we know, this is the first published result achieving such a favorable sample complexity. Extensive experimental results confirm the effectiveness of the proposed methods.

Building Service Compositions Based on data on Use of Services by Users

The automatic service composition is discussed in the article. The method is proposed for building the service composition based on the processing of statistical data on individual applying services (tasks) by users. The method is based on linking tasks to each other, determining data dependencies, parameters of services whose values are rigidly set by the composition of services, and parameters whose values can be changed by the user are highlighted. Service compositions are built in the form of a directed graph of DAG. The methods have been developed for reducing the set of obtained service compositions, which allow us to highlight useful ones and rank them by degree of use. In particular, equivalent service compositions based on isomorphism of DAG graphs are determined, trivial ones are discarded, and only compositions that lead to the published result are left behind.

Homoclinic orbits of sub-linear Hamiltonian systems with perturbed terms

By using variational methods, we obtain the existence of homoclinic orbits for perturbed Hamiltonian systems with sub-linear terms. To the best of our knowledge, there is no published result focusing on the perturbed and sub-linear Hamiltonian systems.

Improved Mekong Basin Runoff Estimate and Its Error Characteristics Using Pure Remotely Sensed Data Products

Basin runoff is a quantity of river discharge per unit basin area monitored close to an estuary mouth, essential for providing information on the flooding and drought conditions of an entire river basin. Owing to a decreasing number of in situ monitoring stations since the late 1970s, basin runoff estimates using remote sensing have been advocated. Previous runoff estimates of the entire Mekong Basin calculated from the water balance equation were achieved through the hybrid use of remotely sensed and model-predicted data products. Nonetheless, these basin runoff estimates revealed a weak consistency with the in situ ones. To address this issue, we provide a newly improved estimate of the monthly Mekong Basin runoff by using the terrestrial water balance equation, purely based on remotely sensed water balance component data products. The remotely sensed water balance component data products used in this study included the satellite precipitation from the Tropical Rainfall Measuring Mission (TRMM), the satellite evapotranspiration from the Moderate Resolution Imaging Spectroradiometer (MODIS), and the inferred terrestrial water storage from the Gravity Recovery and Climate Experiment (GRACE). A comparison of our new estimate and previously published result against the in situ runoff indicated a marked improvement in terms of the Pearson’s correlation coefficient (PCC), reaching 0.836 (the new estimate) instead of 0.621 (the previously published result). When a three-month moving-average process was applied to each data product, our new estimate further reached a PCC of 0.932, along with the consistent improvement revealed from other evaluation metrics. Conducting an error analysis of the estimated mean monthly runoff for the entire data timespan, we found that the usage of different evapotranspiration data products had a substantial influence on the estimated runoff. This indicates that the choice of evapotranspiration data product is critical in the remotely sensed runoff estimation.

RetroPrime: A Chemistry-Inspired and Transformer-based Method for Retrosynthesis Predictions

Retrosynthesis prediction is a crucial task for organic synthesis. In this work, we propose a template-free and Transformer-based method dubbed RetroPrime, integrating chemists’ retrosynthetic strategy of (1) decomposing a molecule into synthons then (2) generating reactants by attaching leaving groups. These two steps are accomplished with versatile Transformer models, respectively. While RetroPrime performs competitively against all state-of-the art models on the standard USPTO-50K dataset, it manifests remarkable generalizability and outperforms the only published result by a non-trivial margin of 4.8% for the Top-1 accuracy on the large-scale USPTO-full dataset. It is known that outputs of Transformer-based retrosynthesis model tend to suffer from insufficient diversity and high invalidity. These problems may limit the potential of Transformer-based methods in real practice, yet no prior works address both issues simultaneously. RetroPrime is designed to tackle these challenges. Finally, we provide convincing results to support the claim that RetromPrime can more effectively generalize across chemical space.

RetroPrime: A Chemistry-Inspired and Transformer-based Method for Retrosynthesis Predictions

Retrosynthesis prediction is a crucial task for organic synthesis. In this work, we propose a template-free and Transformer-based method dubbed RetroPrime, integrating chemists’ retrosynthetic strategy of (1) decomposing a molecule into synthons then (2) generating reactants by attaching leaving groups. These two steps are accomplished with versatile Transformer models, respectively. While RetroPrime performs competitively against all state-of-the art models on the standard USPTO-50K dataset, it manifests remarkable generalizability and outperforms the only published result by a non-trivial margin of 4.8% for the Top-1 accuracy on the large-scale USPTO-full dataset. It is known that outputs of Transformer-based retrosynthesis model tend to suffer from insufficient diversity and high invalidity. These problems may limit the potential of Transformer-based methods in real practice, yet no prior works address both issues simultaneously. RetroPrime is designed to tackle these challenges. Finally, we provide convincing results to support the claim that RetromPrime can more effectively generalize across chemical space.

RetroPrime: A Chemistry-Inspired and Transformer-based Method for Retrosynthesis Predictions

Retrosynthesis prediction is a crucial task for organic synthesis. In this work, we propose a template-free and Transformer-based method dubbed RetroPrime, integrating chemists’ retrosynthetic strategy of (1) decomposing a molecule into synthons then (2) generating reactants by attaching leaving groups. These two steps are accomplished with versatile Transformer models, respectively. While RetroPrime performs competitively against all state-of-the art models on the standard USPTO-50K dataset, it manifests remarkable generalizability and outperforms the only published result by a non-trivial margin of 4.8% for the Top-1 accuracy on the large-scale USPTO-full dataset. It is known that outputs of Transformer-based retrosynthesis model tend to suffer from insufficient diversity and high invalidity. These problems may limit the potential of Transformer-based methods in real practice, yet no prior works address both issues simultaneously. RetroPrime is designed to tackle these challenges. Finally, we provide convincing results to support the claim that RetromPrime can more effectively generalize across chemical space.