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Let $\mathcal{F}$ and $\mathcal{K}$ be commuting $C^\infty$ diffeomorphisms of the cylinder $\mathbb{T}\times\mathbb{R}$ that are, respectively, close to $\mathcal{F}_0 (x, y)=(x+\omega(y), y)$ and $T_\alpha (x, y)=(x+\alpha, y)$, where $\omega(y)$ is non-degenerate and $\alpha$ is Diophantine. Using the KAM iterative scheme for the group action we show that $\mathcal{F}$ and $\mathcal{K}$ are simultaneously $C^\infty$-linearizable if $\mathcal{F}$ has the intersection property (including the exact symplectic maps) and $\mathcal{K}$ satisfies a semi-conjugacy condition. We also provide examples showing necessity of these conditions. As a consequence, we get local rigidity of certain class of $\mathbb{Z}^2$-actions on the cylinder, generated by commuting twist maps., Comment: 35 pages, 1 figure

A weakly interacting Bose gas with a single static impurity is studied in one dimension. The local spectral density is evaluated and an analytic expression valid for positive strengths of the impurity coupling to the bosons, at all distances and at all frequencies is obtained using the Bogoliubov-de Gennes approximation., Comment: 14 pages, 4 figures

We study a weakly-interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary coupling and separation $r$. At $r\lesssim \xi$, where $\xi$ denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of $r$ at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for $r\gg\xi$. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as $1/r^3$, while at strong coupling we find an intermediate distance regime with a slower decay, $1/r$. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy., Comment: 6 pages, 2 figures

We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on computation rules, where both kinds of rules are defined using the type-theoretic concept of object-invertible rules. We also give sufficient syntactic criteria for recognizing such rules, as well as a simple pattern-matching algorithm for applying them. A third component of the algorithm is a suitable notion of principal arguments, which determines a notion of normal form. By varying these, we obtain known notions, such as weak head-normal and strong normal forms. We prove that our algorithm is sound. We implemented it in the Andromeda 2 proof assistant, which supports user-definable type theories. The user need only provide the equality rules they wish to use, which the algorithm automatically classifies as computation or extensionality rules, and select appropriate principal arguments.

Missing mass spectroscopy with the $(e,e^{\prime}K^{+})$ reaction was performed at Jefferson Laboratory's Hall C for the neutron rich $\Lambda$ hypernucleus $^{9}_{\Lambda}{\rm Li}$. The ground state energy was obtained to be $B_{\Lambda}^{\rm g.s.}=8.84\pm0.17^{\rm stat.}\pm0.15^{\rm sys.}~{\rm MeV}$ by using shell model calculations of a cross section ratio and an energy separation of the spin doublet states ($3/2^{+}_1$ and $5/2^{+}_1$). In addition, peaks that are considered to be states of [$^{8}{\rm Li}(3^{+})\otimes s_{\Lambda}=3/2^{+}_{2}, 1/2^{+}$] and [$^{8}{\rm Li}(1^{+})\otimes s_{\Lambda}=5/2^{+}_{2}, 7/2^{+}$] were observed at $E_{\Lambda}({\rm no.~2})=1.74\pm0.27^{\rm stat.}\pm0.11^{\rm sys.}~{\rm MeV}$ and $E_{\Lambda}({\rm no.~3})=3.30\pm0.24^{\rm stat.}\pm0.11^{\rm sys.}~{\rm MeV}$, respectively. The $E_{\Lambda}({\rm no.~3})$ is larger than shell model predictions by a few hundred keV, and the difference would indicate that a ${\rm ^{5}He}+t$ structure is more developed for the $3^{+}$ state than those for the $2^{+}$ and $1^{+}$ states in a core nucleus $^{8}{\rm Li}$ as a cluster model calculation suggests., Comment: 5 pages, 3 figures

Automatic programming, the task of generating computer programs compliant with a specification without a human developer, is usually tackled either via genetic programming methods based on mutation and recombination of programs, or via neural language models. We propose a novel method that combines both approaches using a concept of a virtual neuro-genetic programmer: using evolutionary methods as an alternative to gradient descent for neural network training}, or scrum team. We demonstrate its ability to provide performant and explainable solutions for various OpenAI Gym tasks, as well as inject expert knowledge into the otherwise data-driven search for solutions., Comment: Source code is available at https://github.com/vadim0x60/cibi

Feature ranking has been widely adopted in machine learning applications such as high-throughput biology and social sciences. The approaches of the popular Relief family of algorithms assign importances to features by iteratively accounting for nearest relevant and irrelevant instances. Despite their high utility, these algorithms can be computationally expensive and not-well suited for high-dimensional sparse input spaces. In contrast, recent embedding-based methods learn compact, low-dimensional representations, potentially facilitating down-stream learning capabilities of conventional learners. This paper explores how the Relief branch of algorithms can be adapted to benefit from (Riemannian) manifold-based embeddings of instance and target spaces, where a given embedding's dimensionality is intrinsic to the dimensionality of the considered data set. The developed ReliefE algorithm is faster and can result in better feature rankings, as shown by our evaluation on 20 real-life data sets for multi-class and multi-label classification tasks. The utility of ReliefE for high-dimensional data sets is ensured by its implementation that utilizes sparse matrix algebraic operations. Finally, the relation of ReliefE to other ranking algorithms is studied via the Fuzzy Jaccard Index.

Most state of the art decision systems based on Reinforcement Learning (RL) are data-driven black-box neural models, where it is often difficult to incorporate expert knowledge into the models or let experts review and validate the learned decision mechanisms. Knowledge-insertion and model review are important requirements in many applications involving human health and safety. One way to bridge the gap between data and knowledge driven systems is program synthesis: replacing a neural network that outputs decisions with a symbolic program generated by a neural network or by means of genetic programming. We propose a new programming language, BF++, designed specifically for automatic programming of agents in a Partially Observable Markov Decision Process (POMDP) setting and apply neural program synthesis to solve standard OpenAI Gym benchmarks., Comment: 8+2 pages (paper+references)

As robots are becoming more and more ubiquitous in human environments, it will be necessary for robotic systems to better understand and predict human actions. However, this is not an easy task, at times not even for us humans, but based on a relatively structured set of possible actions, appropriate cues, and the right model, this problem can be computationally tackled. In this paper, we propose to use an ensemble of long-short term memory (LSTM) networks for human action prediction. To train and evaluate models, we used the MoGaze dataset - currently the most comprehensive dataset capturing poses of human joints and the human gaze. We have thoroughly analyzed the MoGaze dataset and selected a reduced set of cues for this task. Our model can predict (i) which of the labeled objects the human is going to grasp, and (ii) which of the macro locations the human is going to visit (such as table or shelf). We have exhaustively evaluated the proposed method and compared it to individual cue baselines. The results suggest that our LSTM model slightly outperforms the gaze baseline in single object picking accuracy, but achieves better accuracy in macro object prediction. Furthermore, we have also analyzed the prediction accuracy when the gaze is not used, and in this case, the LSTM model considerably outperformed the best single cue baseline

In this work, we propose two novel (groups of) methods for unsupervised feature ranking and selection. The first group includes feature ranking scores (Genie3 score, RandomForest score) that are computed from ensembles of predictive clustering trees. The second method is URelief, the unsupervised extension of the Relief family of feature ranking algorithms. Using 26 benchmark data sets and 5 baselines, we show that both the Genie3 score (computed from the ensemble of extra trees) and the URelief method outperform the existing methods and that Genie3 performs best overall, in terms of predictive power of the top-ranked features. Additionally, we analyze the influence of the hyper-parameters of the proposed methods on their performance, and show that for the Genie3 score the highest quality is achieved by the most efficient parameter configuration. Finally, we propose a way of discovering the location of the features in the ranking, which are the most relevant in reality., Comment: 20 pages, 5 figures

In this paper, we analyze human male and female sex recognition problem and present a fully automated classification system using only 2D keypoints. The keypoints represent human joints. A keypoint set consists of 15 joints and the keypoint estimations are obtained using an OpenPose 2D keypoint detector. We learn a deep learning model to distinguish males and females using the keypoints as input and binary labels as output. We use two public datasets in the experimental section - 3DPeople and PETA. On PETA dataset, we report a 77% accuracy. We provide model performance details on both PETA and 3DPeople. To measure the effect of noisy 2D keypoint detections on the performance, we run separate experiments on 3DPeople ground truth and noisy keypoint data. Finally, we extract a set of factors that affect the classification accuracy and propose future work. The advantage of the approach is that the input is small and the architecture is simple, which enables us to run many experiments and keep the real-time performance in inference. The source code, with the experiments and data preparation scripts, are available on GitHub (https://github.com/kristijanbartol/human-sex-classifier)., Comment: There was an error in the implementation of the base experiment (#1), i.e., the data preparation step. More specifically, the labels used both for training and evaluation were wrong, thus making the conclusions invalid

Time-of-flight (ToF) cameras are becoming increasingly popular for 3D imaging. Their optimal usage has been studied from the several aspects. One of the open research problems is the possibility of a multicamera interference problem when two or more ToF cameras are operating simultaneously. In this work we present an efficient method to synchronize multiple operating ToF cameras. Our method is based on the time-division multiplexing, but unlike traditional time multiplexing, it does not decrease the effective camera frame rate. Additionally, for unsynchronized cameras, we provide a robust method to extract from their corresponding video streams, frames which are not subject to multicamera interference problem. We demonstrate our approach through a series of experiments and with a different level of support available for triggering, ranging from a hardware triggering to purely random software triggering.

This paper proposes to use keypoints as a self-supervision clue for learning depth map estimation from a collection of input images. As ground truth depth from real images is difficult to obtain, there are many unsupervised and self-supervised approaches to depth estimation that have been proposed. Most of these unsupervised approaches use depth map and ego-motion estimations to reproject the pixels from the current image into the adjacent image from the image collection. Depth and ego-motion estimations are evaluated based on pixel intensity differences between the correspondent original and reprojected pixels. Instead of reprojecting the individual pixels, we propose to first select image keypoints in both images and then reproject and compare the correspondent keypoints of the two images. The keypoints should describe the distinctive image features well. By learning a deep model with and without the keypoint extraction technique, we show that using the keypoints improve the depth estimation learning. We also propose some future directions for keypoint-guided learning of structure-from-motion problems.

The last decade has witnessed a rapid growth of the field of exoplanet discovery and characterisation. However, several big challenges remain, many of which could be addressed using machine learning methodology. For instance, the most prolific method for detecting exoplanets and inferring several of their characteristics, transit photometry, is very sensitive to the presence of stellar spots. The current practice in the literature is to identify the effects of spots visually and correct for them manually or discard the affected data. This paper explores a first step towards fully automating the efficient and precise derivation of transit depths from transit light curves in the presence of stellar spots. The methods and results we present were obtained in the context of the 1st Machine Learning Challenge organized for the European Space Agency's upcoming Ariel mission. We first present the problem, the simulated Ariel-like data and outline the Challenge while identifying best practices for organizing similar challenges in the future. Finally, we present the solutions obtained by the top-5 winning teams, provide their code and discuss their implications. Successful solutions either construct highly non-linear (w.r.t. the raw data) models with minimal preprocessing -deep neural networks and ensemble methods- or amount to obtaining meaningful statistics from the light curves, constructing linear models on which yields comparably good predictive performance., Comment: 20 pages, 7 figures, 2 tables, Submitted to The Astrophysics Journal (ApJ)

The data made available for analysis are becoming more and more complex along several directions: high dimensionality, number of examples and the amount of labels per example. This poses a variety of challenges for the existing machine learning methods: coping with dataset with a large number of examples that are described in a high-dimensional space and not all examples have labels provided. For example, when investigating the toxicity of chemical compounds there are a lot of compounds available, that can be described with information rich high-dimensional representations, but not all of the compounds have information on their toxicity. To address these challenges, we propose semi-supervised learning of feature ranking. The feature rankings are learned in the context of classification and regression as well as in the context of structured output prediction (multi-label classification, hierarchical multi-label classification and multi-target regression). To the best of our knowledge, this is the first work that treats the task of feature ranking within the semi-supervised structured output prediction context. More specifically, we propose two approaches that are based on tree ensembles and the Relief family of algorithms. The extensive evaluation across 38 benchmark datasets reveals the following: Random Forests perform the best for the classification-like tasks, while for the regression-like tasks Extra-PCTs perform the best, Random Forests are the most efficient method considering induction times across all tasks, and semi-supervised feature rankings outperform their supervised counterpart across a majority of the datasets from the different tasks., Comment: Submitted to: Special Issue on Discovery Science of the Machine Learning Journal

We propose Fuzzy Jaccard Index (FUJI) -- a scale-invariant score for assessment of the similarity between two ranked/ordered lists. FUJI improves upon the Jaccard index by incorporating a membership function which takes into account the particular ranks, thus producing both more stable and more accurate similarity estimates. We provide theoretical insights into the properties of the FUJI score as well as propose an efficient algorithm for computing it. We also present empirical evidence of its performance on different synthetic scenarios. Finally, we demonstrate its utility in a typical machine learning setting -- comparing feature ranking lists relevant to a given machine learning task. In real-life, and in particular high-dimensional domains, where only a small percentage of the whole feature space might be relevant, a robust and confident feature ranking leads to interpretable findings as well as efficient computation and good predictive performance. In such cases, FUJI correctly distinguishes between existing feature ranking approaches, while being more robust and efficient than the benchmark similarity scores., Comment: 29 pages, 30 figures

We study the effect of the boundary on a system of weakly interacting bosons in one dimension. It strongly influences the boson density which is completely suppressed at the boundary position. Away from it, the density is depleted over the distances on the order of the healing length at the mean-field level. Quantum fluctuations modify the density profile considerably. The local density approaches the average one as an inverse square of the distance from the boundary. We calculate an analytic expression for the density profile at arbitrary separations from the boundary. We then consider the problem of localization of a foreign quantum particle (impurity) in the potential created by the inhomogeneous boson density. At the mean-field level, we find exact results for the energy spectrum of the bound states, the corresponding wave functions, and the condition for interaction-induced localization. The quantum contribution to the boson density gives rise to small corrections of the bound state energy levels. However, it is fundamentally important for the existence of a long-range Casimir-like interaction between the impurity and the boundary., Comment: 10 pages, 5 figures

The purpose of this study is to give a performance comparison between several classic hand-crafted and deep key-point detector and descriptor methods. In particular, we consider the following classical algorithms: SIFT, SURF, ORB, FAST, BRISK, MSER, HARRIS, KAZE, AKAZE, AGAST, GFTT, FREAK, BRIEF and RootSIFT, where a subset of all combinations is paired into detector-descriptor pipelines. Additionally, we analyze the performance of two recent and perspective deep detector-descriptor models, LF-Net and SuperPoint. Our benchmark relies on the HPSequences dataset that provides real and diverse images under various geometric and illumination changes. We analyze the performance on three evaluation tasks: keypoint verification, image matching and keypoint retrieval. The results show that certain classic and deep approaches are still comparable, with some classic detector-descriptor combinations overperforming pretrained deep models. In terms of the execution times of tested implementations, SuperPoint model is the fastest, followed by ORB. The source code is published on \url{https://github.com/kristijanbartol/keypoint-algorithms-benchmark}.

This note describes moduli spaces of complexes in the derived category of a Veronese double cone $Y$. Focusing on objects with the same class $\kappa_1$ as ideal sheaves of lines, we describe the moduli space of Gieseker stable sheaves and show that it has two components. Then, we study the moduli space of stable complexes in the Kuznetsov component of $Y$ of the same class, which also has two components. One parametrizes ideal sheaves of lines and it appears in both moduli spaces. The other components are not directly related by a wall-crossing: we show this by describing an intermediate moduli space of complexes as a space of stable pairs in the sense of Pandharipande and Thomas., Comment: V2: 19 pages. Substantially rewritten. Added results on Hilbert scheme of lines, improved exposition, strengthened arguments. References and acknowledgments updated. V3: Final version, to appear in J. Pure Appl. Algebra. The statement of theorem 5.1 contained an imprecision, now corrected. All comments very welcome!

Understanding the reactions in M-O2 cells (M = Li or Na) is of great importance for further advancement of this promising technology. Computational modelling can be helpful along this way, but an adequate approach is needed to model such complex systems. We propose a new scheme for modelling processes in M-O2 cells, where reference energies are obtained from high-level theory, CCSD(T), while the interactions of reaction intermediates with catalyst surfaces are extracted from computationally less expensive DFT. The approach is demonstrated for the case of graphene-based surfaces as model catalysts in Li-O2 and Na-O2 cells using the minimum viable mechanism. B-doped graphene was identified as the best catalyst among considered surfaces, while pristine graphene performs poorly. Moreover, we show that the inclusion of dispersion corrections for DFT has a significant impact on calculated discharge and charge potentials and suggests that long-range dispersion interactions should always be considered when graphene-based materials are modelled as electrocatalysts. Finally, we offer general guidelines for designing new ORR catalysts for M-O2 cells in terms of the optimization of the interactions of catalyst surface with reaction intermediates., Comment: 27 pages, including supplementary information, 7 figures in the main text, 1 table, 66 references, 5 figures in supplementary information

With the substantial growth of logistics businesses the need for larger and more automated warehouses increases, thus giving rise to fully robotized shop-floors with mobile robots in charge of transporting and distributing goods. However, even in fully automatized warehouse systems the need for human intervention frequently arises, whether because of maintenance or because of fulfilling specific orders, thus bringing mobile robots and humans ever closer in an integrated warehouse environment. In order to ensure smooth and efficient operation of such a warehouse, paths of both robots and humans need to be carefully planned; however, due to the possibility of humans deviating from the assigned path, this becomes an even more challenging task. Given that, the supervising system should be able to recognize human intentions and its alternative paths in real-time. In this paper, we propose a framework for human deviation detection and intention recognition which outputs the most probable paths of the humans workers and the planner that acts accordingly by replanning for robots to move out of the human's path. Experimental results demonstrate that the proposed framework increases total number of deliveries, especially human deliveries, and reduces human-robot encounters., Comment: To be presented in 28th Mediterranean Conference on Control and Automation (MED'2020) conference

A semiconductor transmon with an epitaxial Al shell fully surrounding an InAs nanowire core is investigated in the low $E_J/E_C$ regime. Little-Parks oscillations as a function of flux along the hybrid wire axis are destructive, creating lobes of reentrant superconductivity separated by a metallic state at a half-quantum of applied flux. In the first lobe, phase winding around the shell can induce topological superconductivity in the core. Coherent qubit operation is observed in both the zeroth and first lobes. Splitting of parity bands by coherent single-electron coupling across the junction is not resolved beyond line broadening, placing a bound on Majorana coupling, $E_M/h$ < 10 MHz, much smaller than the Josephson coupling $E_J/h$ ~ 4.7 GHz.

Black-box neural network models are widely used in industry and science, yet are hard to understand and interpret. Recently, the attention mechanism was introduced, offering insights into the inner workings of neural language models. This paper explores the use of attention-based neural networks mechanism for estimating feature importance, as means for explaining the models learned from propositional (tabular) data. Feature importance estimates, assessed by the proposed Self-Attention Network (SAN) architecture, are compared with the established ReliefF, Mutual Information and Random Forest-based estimates, which are widely used in practice for model interpretation. For the first time we conduct scale-free comparisons of feature importance estimates across algorithms on ten real and synthetic data sets to study the similarities and differences of the resulting feature importance estimates, showing that SANs identify similar high-ranked features as the other methods. We demonstrate that SANs identify feature interactions which in some cases yield better predictive performance than the baselines, suggesting that attention extends beyond interactions of just a few key features and detects larger feature subsets relevant for the considered learning task., Comment: Accepted for publication in ECAI 2020

In this paper we address the problem of representing 3D visual data with parameterized volumetric shape primitives. Specifically, we present a (two-stage) approach built around convolutional neural networks (CNNs) capable of segmenting complex depth scenes into the simpler geometric structures that can be represented with superquadric models. In the first stage, our approach uses a Mask RCNN model to identify superquadric-like structures in depth scenes and then fits superquadric models to the segmented structures using a specially designed CNN regressor. Using our approach we are able to describe complex structures with a small number of interpretable parameters. We evaluated the proposed approach on synthetic as well as real-world depth data and show that our solution does not only result in competitive performance in comparison to the state-of-the-art, but is able to decompose scenes into a number of superquadric models at a fraction of the time required by competing approaches. We make all data and models used in the paper available from https://lmi.fe.uni-lj.si/en/research/resources/sq-seg., Comment: 8 pages, in Computer Vision Winter Workshop, 2020