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Understanding causal relationships within a system is crucial for uncovering its underlying mechanisms. Causal discovery methods, which facilitate the construction of such models from time-series data, hold the potential to significantly advance scientific and engineering fields. This study introduces the Cross-Mapping Coherence (CMC) method, designed to reveal causal connections in the frequency domain between time series. CMC builds upon nonlinear state-space reconstruction and extends the Convergent Cross-Mapping algorithm to the frequency domain by utilizing coherence metrics for evaluation. We tested the Cross-Mapping Coherence method using simulations of logistic maps, Lorenz systems, Kuramoto oscillators, and the Wilson-Cowan model of the visual cortex. CMC accurately identified the direction of causal connections in all simulated scenarios. When applied to the Wilson-Cowan model, CMC yielded consistent results similar to spectral Granger causality. Furthermore, CMC exhibits high sensitivity in detecting weak connections, demonstrates sample efficiency, and maintains robustness in the presence of noise. In conclusion, the capability to determine directed causal influences across different frequency bands allows CMC to provide valuable insights into the dynamics of complex, nonlinear systems.

We study the spatially homogeneous granular medium equation \[\partial_t\mu=\rm{div}(\mu\nabla V)+\rm{div}(\mu(\nabla W \ast \mu))+\Delta\mu\,,\] within a large and natural class of the confinement potentials $V$ and interaction potentials $W$. The considered problem do not need to assume that $\nabla V$ or $\nabla W$ are globally Lipschitz. With the aim of providing particle approximation of solutions, we design efficient forward-backward splitting algorithms. Sharp convergence rates in terms of the Wasserstein distance are provided.

Gaze-based interactions offer a potential way for users to naturally engage with mixed reality (XR) interfaces. Black-box machine learning models enabled higher accuracy for gaze-based interactions. However, due to the black-box nature of the model, users might not be able to understand and effectively adapt their gaze behaviour to achieve high quality interaction. We posit that explainable AI (XAI) techniques can facilitate understanding of and interaction with gaze-based model-driven system in XR. To study this, we built a real-time, multi-level XAI interface for gaze-based interaction using a deep learning model, and evaluated it during a visual search task in XR. A between-subjects study revealed that participants who interacted with XAI made more accurate selections compared to those who did not use the XAI system (i.e., F1 score increase of 10.8%). Additionally, participants who used the XAI system adapted their gaze behavior over time to make more effective selections. These findings suggest that XAI can potentially be used to assist users in more effective collaboration with model-driven interactions in XR.

The physical parameters of the sunspot are not fully understood, especially the height dependence of the magnetic field. So far, it is also an open question as to which heights the He I 1083 nm spectral line is formed at. Our aim is to investigate the magnetic and dynamical properties in the atmosphere above a sunspot, from the photosphere to the chromosphere. We analyzed the photospheric and chromospheric magnetic field properties of a stable sunspot in AR 12553 on June 20, 2016 using spectropolarimetric observations obtained with GRIS at GREGOR. A spectral-line inversion technique was used to infer the magnetic field vector and Doppler velocities from the full Stokes profiles. In total, three spectral lines were inverted and the variation of the magnetic properties was qualified using the average values of the radial circles. The sunspot is located close to the solar limb, and thus this allows us to make a geometrical determination of the height of the spectral line He I 1083 nm. We find the height of helium spectral line to be 970 km above the photospheric spectral lines directly from observation at a stable sunspot. The total magnetic field strength decreases with height over the sunspot; the rates are -0.34 G/km for the umbra and -0.28 G/km for the penumbra. The inclination increases with increasing height in the umbra, but decreases in the penumbra. In the umbra, the vertical component ($B_z$) decreases with height, while the horizontal component ($B_{hor}$) remains almost constant. In the penumbra this is reversed, as $B_z$ remains nearly constant over height, while $B_{hor}$ decreases. We also observe fast velocities with 30 km/s in small chromospheric patches on the central side of the spot. The key parameters depending on height in the sunspot are the $B_{z}$ component of the magnetic field for the umbra and the $B_{hor}$ component of the magnetic field for the penumbra., Comment: Accepted for publication in Astronomy & Astrophysics, 11 pages, 9 figures

Extended Reality (XR) interfaces offer engaging user experiences, but their effective design requires a nuanced understanding of user behavior and preferences. This knowledge is challenging to obtain without the widespread adoption of XR devices. We introduce MineXR, a design mining workflow and data analysis platform for collecting and analyzing personalized XR user interaction and experience data. MineXR enables elicitation of personalized interfaces from participants of a data collection: for any particular context, participants create interface elements using application screenshots from their own smartphone, place them in the environment, and simultaneously preview the resulting XR layout on a headset. Using MineXR, we contribute a dataset of personalized XR interfaces collected from 31 participants, consisting of 695 XR widgets created from 178 unique applications. We provide insights for XR widget functionalities, categories, clusters, UI element types, and placement. Our open-source tools and data support researchers and designers in developing future XR interfaces., Comment: 17 pages, 18 figures, Proceedings of the 2024 CHI Conference on Human Factors in Computing Systems

As a starting point of our research, we show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$), satisfies stationarity conditions in terms of a coderivative construction of order $\gamma$, or is asymptotically stationary with respect to a critical direction as well as order $\gamma$ in a certain sense. By ruling out the latter case with a constraint qualification not stronger than directional metric subregularity, we end up with new necessary optimality conditions comprising a mixture of limiting variational tools of orders $1$ and $\gamma$. These abstract findings are carved out for the broad class of geometric constraints and $\gamma:=2$, and visualized by examples from complementarity-constrained and nonlinear semidefinite optimization. As a byproduct of the particular setting $\gamma:=1$, our general approach yields new so-called directional asymptotic regularity conditions which serve as constraint qualifications guaranteeing M-stationarity of local minimizers. We compare these new regularity conditions with standard constraint qualifications from nonsmooth optimization. Further, we extend directional concepts of pseudo- and quasi-normality to arbitrary set-valued mappings. It is shown that these properties provide sufficient conditions for the validity of directional asymptotic regularity. Finally, a novel coderivative-like variational tool is used to construct sufficient conditions for the presence of directional asymptotic regularity. For geometric constraints, it is illustrated that all appearing objects can be calculated in terms of initial problem data., Comment: 78 pages. arXiv admin note: text overlap with arXiv:2205.00775, arXiv:2204.13932

In data science, hypergraphs are natural models for data exhibiting multi-way relations, whereas graphs only capture pairwise. Nonetheless, many proposed hypergraph neural networks effectively reduce hypergraphs to undirected graphs via symmetrized matrix representations, potentially losing important information. We propose an alternative approach to hypergraph neural networks in which the hypergraph is represented as a non-reversible Markov chain. We use this Markov chain to construct a complex Hermitian Laplacian matrix - the magnetic Laplacian - which serves as the input to our proposed hypergraph neural network. We study HyperMagNet for the task of node classification, and demonstrate its effectiveness over graph-reduction based hypergraph neural networks., Comment: 9 pages, 1 figure

In this paper, we characterize Lipschitzian properties of different multiplier-free and multiplier-dependent perturbation mappings associated with the stationarity system of a so-called generalized nonlinear program popularized by Rockafellar. Special emphasis is put on the investigation of the isolated calmness property at and around a point. The latter is decisive for the locally fast convergence of the so-called semismooth* Newton-type method by Gfrerer and Outrata. Our central result is the characterization of the isolated calmness at a point of a multiplier-free perturbation mapping via a combination of an explicit condition and a rather mild assumption, automatically satisfied e.g. for standard nonlinear programs. Isolated calmness around a point is characterized analogously by a combination of two stronger conditions. These findings are then related to so-called criticality of Lagrange multipliers, as introduced by Izmailov and extended to generalized nonlinear programming by Mordukhovich and Sarabi. We derive a new sufficient condition (a characterization for some problem classes) of nonexistence of critical multipliers, which has been also used in the literature as an assumption to guarantee local fast convergence of Newton-, SQP-, or multiplier-penalty-type methods. The obtained insights about critical multipliers seem to complement the vast literature on the topic., Comment: 35 pages

Much is known about when a locally optimal solution depends in a single-valued Lipschitz continuous way on the problem's parameters, including tilt perturbations. Much less is known, however, about when that solution and a uniquely determined multiplier vector associated with it exhibit that dependence as a primal-dual pair. In classical nonlinear programming, such advantageous behavior is tied to the combination of the standard strong second-order sufficient condition (SSOC) for local optimality and the linear independent gradient condition (LIGC) on the active constraint gradients. But although second-order sufficient conditions have successfully been extended far beyond nonlinear programming, insights into what should replace constraint gradient independence as the extended dual counterpart have been lacking. The exact answer is provided here for a wide range of optimization problems in finite dimensions. Behind it are advances in how coderivatives and strict graphical derivatives can be deployed. New results about strong metric regularity in solving variational inequalities and generalized equations are obtained from that as well.

Up to now, it seemed that the additional frequencies in the fundamental mode (RRab) and in the overtone mode pulsating (RRc and RRd) RR Lyrae stars have different nature. RRab stars show frequencies associated with periodic doubling, as well as frequencies at the first and second radial overtones, and linear combinations of these. RRc stars show frequencies with specific ratios ($f_1/f_x\sim$0.61, or $\sim$0.63) which are explained by non-radial modes and frequencies with $f_x/f_1\sim0.68$ ratio which have no currently accepted explanation. To search for similarities in spectral content, we compared the Fourier spectra of the recently published TESS and K2 data of RRc stars with the spectra of Kepler RRab stars that do not show the Blazhko effect but contain additional frequencies. The time series data have been analysed using standard Fourier methods, and the possibility of the excitation of the second radial overtone mode in RRab stars has also been tested using numerical hydrodynamical codes. We show that the additional frequencies appear in non-Blazhko RRab stars at the position of the second radial overtone mode, and the pattern they create, is very similar to that caused by the additional frequencies with the period ratio $\sim0.68$ in RRc stars. The former explanation of the additional frequencies of these RRab stars by a second radial overtone is unlikely., Comment: 5 pages, 4 tables, 2 figures, accepted for publication in Astronomy & Astrophysics Letters

RR Lyrae stars are pulsating stars, many of which also show a long-term variation called the Blazhko effect which is a modulation of amplitude and phase of the lightcurve. In this work, we searched for the incidence rate of the Blazhko effect in the first-overtone pulsating RR Lyrae (RRc) stars of the Galactic halo. The focus was on the Stripe 82 region in the Galactic halo which was studied by Sesar et al using the Sloan Digital Sky Survey (SDSS) data. In their work, 104 RR Lyrae stars were classified as RRc type. We combined their SDSS light curves with Zwicky Transient Facility (ZTF) data, and use them to document the Blazhko properties of these RRc stars. Our analysis showed that among the 104 RRc stars, 8 were rather RRd stars, and were excluded from the study. Out of remaining 96, 34 were Blazhko type, 62 were non-Blazhko type, giving the incidence rate of 35.42% for Blazhko RRc stars. The shortest Blazhko period found was 12.808 +/- 0.001 d for SDSS 747380, while the longest was 3100 +/- 126 d for SDSS 3585856. Combining SDSS and ZTF data sets increased the probability of detecting the small variations due to the Blazhko effect, and thus provided a unique opportunity to find longer Blazhko periods. We found that 85% of RRc stars had the Blazhko period longer than 200 d., Comment: 9 pages, 2 tables, 8 figures, AJ accepted

Explainable AI (XAI) has established itself as an important component of AI-driven interactive systems. With Augmented Reality (AR) becoming more integrated in daily lives, the role of XAI also becomes essential in AR because end-users will frequently interact with intelligent services. However, it is unclear how to design effective XAI experiences for AR. We propose XAIR, a design framework that addresses "when", "what", and "how" to provide explanations of AI output in AR. The framework was based on a multi-disciplinary literature review of XAI and HCI research, a large-scale survey probing 500+ end-users' preferences for AR-based explanations, and three workshops with 12 experts collecting their insights about XAI design in AR. XAIR's utility and effectiveness was verified via a study with 10 designers and another study with 12 end-users. XAIR can provide guidelines for designers, inspiring them to identify new design opportunities and achieve effective XAI designs in AR., Comment: Proceedings of the 2023 CHI Conference on Human Factors in Computing Systems

Additional low-amplitude signals are observed in many RR Lyrae stars, beside the pulsations in radial modes. The most common ones are short-period signals forming a period ratio of around 0.60--0.65 with the first overtone, or long-period signals forming a period ratio of around 0.68. The RR Lyrae stars may also exhibit quasi-periodic modulation of the light curves, known as the Blazhko effect. We used the extensive sample of the first-overtone RR Lyrae stars observed by the Kepler telescope during the K2 mission to search for and characterize these low-amplitude additional signals. K2 data provides space-based photometry for a statistically significant sample. Hence this data is excellent to study in detail pulsation properties of RR Lyrae stars. We used K2 space-based photometry for RR Lyrae candidates from Campaigns 0-19. We selected RR Lyrae stars pulsating in the first overtone and performed a frequency analysis for each star to characterize their frequency contents. We classified 452 stars as first-overtone RR Lyrae. From that sample, we selected 281 RR$_{0.61}$ stars, 67 RR$_{0.68}$ stars, and 68 Blazhko stars. We found particularly interesting stars which show all of the above phenomena simultaneously. We detected signals in RR$_{0.61}$ stars that form period ratios lower than observed for the majority of stars. These signals likely form a new sequence in the Petersen diagram, around a period ratio of 0.60. In 32 stars we detected additional signals that form a period ratio close to that expected in RRd stars, but the classification of these stars as RRd is uncertain. We also report a discovery of additional signals in eight stars that form a new group in the Petersen diagram around the period ratio of 0.465-0.490. The nature of this periodicity remains unknown., Comment: 29 pages, 29 figures, 4 tables, accepted for publication in A&A, full tables are available upon request before publication

Using two years of data from the TESS space telescope, we have investigated the time series of 633 overtone pulsating field RR Lyrae (RRc) stars. The majority of stars (82.8 per cent) contain additional frequencies beyond the main pulsation. In addition to the frequencies previously explained by the $\ell = 8$ and $\ell = 9$ non-radial modes, we have identified a group of stars where the additional frequencies may belong to the $\ell = 10$ non-radial modes. We found that stars with no additional frequencies are more common among stars with shorter periods, while stars with longer periods almost always show additional frequencies. The incidence rate and this period distribution both agree well with the predictions of recent theoretical models. The amplitude and phase of additional frequencies are varying in time. The frequencies of different non-radial modes appearing in a given star seem to vary on different timescales. We have determined a 10.4 per cent incidence rate for the Blazhko effect. For several stars we have detected continuous annual-scale phase change without significant amplitude variation. This type of variation offers a plausible explanation for the `phase jump' phenomenon reported in many RRc stars. The main pulsation frequency could show quasi-periodic phase and amplitude fluctuations. This fluctuation is clearly related to additional frequencies present in the star: stars with two non-radial modes show the strongest fluctuations, while stars with no such modes show no fluctuations at all. The summation of the phase fluctuation over time may explain the O-C variations that have long been known for many non-Blazhko RRc stars., Comment: 20 pages, 20 figures, accepted for publication in MNRAS

In this paper, we readdress the classical topic of second-order sufficient optimality conditions for optimization problems with nonsmooth structure. Based on the so-called second subderivative of the objective function and of the indicator function associated with the feasible set, one easily obtains second-order sufficient optimality conditions of abstract form. In order to exploit further structure of the problem, e.g., composite terms in the objective function or feasible sets given as (images of) pre-images of closed sets under smooth transformations, to make these conditions fully explicit, we study calculus rules for the second subderivative under mild conditions. To be precise, we investigate a chain rule and a marginal function rule, which then also give a pre-image and image rule, respectively. As it turns out, the chain rule and the pre-image rule yield lower estimates desirable in order to obtain sufficient optimality conditions for free. Similar estimates for the marginal function and the image rule are valid under a comparatively mild inner calmness* assumption. Our findings are illustrated by several examples including problems from composite, disjunctive, and nonlinear second-order cone programming., Comment: 44 pages

During the last years, asymptotic (or sequential) constraint qualifications, which postulate upper semicontinuity of certain set-valued mappings and provide a natural companion of asymptotic stationarity conditions, have been shown to be comparatively mild, on the one hand, while possessing inherent practical relevance from the viewpoint of numerical solution methods, on the other one. Based on recent developments, the theory in this paper enriches asymptotic constraint qualifications for very general nonsmooth optimization problems over inverse images of set-valued mappings by incorporating directional data. We compare these new directional asymptotic regularity conditions with standard constraint qualifications from nonsmooth optimization. Further, we introduce directional concepts of pseudo- and quasi-normality which apply to set-valued mappings. It is shown that these properties provide sufficient conditions for the validity of directional asymptotic regularity. Finally, a novel coderivative-like variational tool is introduced which allows to study the presence of directional asymptotic regularity. For geometric constraints, it is illustrated that all appearing objects can be calculated in terms of initial problem data., Comment: 38 pages

We show that, for a fixed order $\gamma\geq 1$, each local minimizer of a rather general nonsmooth optimization problem in Euclidean spaces is either M-stationary in the classical sense (corresponding to stationarity of order $1$), satisfies stationarity conditions in terms of a coderivative construction of order $\gamma$, or is approximately stationary with respect to a critical direction as well as $\gamma$ in a certain sense. By ruling out the latter case with a constraint qualification not stronger than directional metric subregularity, we end up with new necessary optimality conditions comprising a mixture of limiting variational tools of order $1$ and $\gamma$. These abstract findings are carved out for the broad class of geometric constraints. As a byproduct, we obtain new constraint qualifications ensuring M-stationarity of local minimizers. The paper closes by illustrating these results in the context of standard nonlinear, complementarity-constrained, and nonlinear semidefinite programming., Comment: 41 pages

In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our conditions prove to be sufficient, for an essential local minimizer of second order, under merely basic smoothness and closedness assumptions on the data defining the problem.In the second part, we propose a comprehensive first- and second-order variational analysis of disjunctive systems and demonstrate how the second-order objects appearing in the optimality conditions can be effectively computed in this case.

The TESS space telescope is collecting continuous, high-precision optical photometry of stars throughout the sky, including thousands of RR Lyrae stars. In this paper, we present results for an initial sample of 118 nearby RR Lyrae stars observed in TESS Sectors 1 and 2. We use differential-image photometry to generate light curves and analyse their mode content and modulation properties. We combine accurate light curve parameters from TESS with parallax and color information from the Gaia mission to create a comprehensive classification scheme. We build a clean sample, preserving RR Lyrae stars with unusual light curve shapes, while separating other types of pulsating stars. We find that a large fraction of RR Lyrae stars exhibit various low-amplitude modes, but the distribution of those modes is markedly different from those of the bulge stars. This suggests that differences in physical parameters have an observable effect on the excitation of extra modes, potentially offering a way to uncover the origins of these signals. However, mode identification is hindered by uncertainties when identifying the true pulsation frequencies of the extra modes. We compare mode amplitude ratios in classical double-mode stars to stars with extra modes at low amplitudes and find that they separate into two distinct groups. Finally, we find a high percentage of modulated stars among the fundamental-mode pulsators, but also find that at least 28% of them do not exhibit modulation, confirming that a significant fraction of stars lack the Blazhko effect., Comment: 35 pages, 26 figures, and a 19-page appendix. Accepted for publication in ApJS. Light curve data temporarily available: https://konkoly.hu/staff/lmolnar/tess_rrl_firstlight_all_lcs.txt

Determining hidden shared patterns behind dynamic phenomena can be a game-changer in multiple areas of research. Here we present the principles and show a method to identify hidden shared dynamics from time series by a two-module, feedforward neural network architecture: the Mapper-Coach network. We reconstruct unobserved, continuous latent variable input, the time series generated by a chaotic logistic map, from the observed values of two simultaneously forced chaotic logistic maps. The network has been trained to predict one of the observed time series based on its own past and conditioned on the other observed time series by error-back propagation. It was shown, that after this prediction have been learned successfully, the activity of the bottleneck neuron, connecting the mapper and the coach module, correlated strongly with the latent shared input variable. The method has the potential to reveal hidden components of dynamical systems, where experimental intervention is not possible.

This article commences a study of convergence of discretized point-object configurations, which we call Brill-Lindquist-Riemann sums, towards a charged dust continuum from the perspective of relativistic initial data. We are motivated by the interpretation of Brill-Lindquist-Riemann sums as collections of relatively isolated astrophysical bodies such as stars and galaxies in the universe, and the interpretation of the dust continuum as the universe itself. Our work begins by establishing the existence and the uniqueness of horizons/minimal surfaces of Brill-Lindquist metrics in the vicinity of the point-sources ("stars"). We then study the geometries of the regions exterior to said minimal surfaces, and discuss their Gromov-Hausdorff and intrinsic flat limit. An interesting and purely geometric byproduct of our work are examples in which the scalar curvature jumps upon taking Gromov-Hausdorff and /or intrinsic flat limits.

By analyzing photometric and spectroscopic time series in this paper, we show that the pulsator V764 Mon, assumed to be the brightest RR Lyrae star in the sky, is in fact a rapidly rotating delta Scuti star with an unusually long dominant period (P1=0.29 d). Our spectroscopy confirmed the discovery of the Gaia satellite about the binarity of V764 Mon. In the case of HY Com, a `bona fide' RRc star, we present its first complete radial velocity curve. Additionally, we found that the star continues its strong phase variation reported before., Comment: 18 pages, 7 figures, 6 tables. To appear in Acta Astron

We present the first analysis of Cepheid stars observed by the TESS space mission in Sectors 1 to 5. Our sample consists of 25 pulsators: ten fundamental mode, three overtone and two double-mode classical Cepheids, plus three Type II and seven anomalous Cepheids. The targets were chosen from fields with different stellar densities, both from the Galactic field and from the Magellanic System. Three targets have 2-minute cadence light curves available by the TESS Science Processing Operations Center: for the rest, we prepared custom light curves from the full-frame images with our own differential photometric FITSH pipeline. Our main goal was to explore the potential and the limitations of TESS concerning the various subtypes of Cepheids. We detected many low amplitude features: weak modulation, period jitter, and timing variations due to light-time effect. We also report signs of non-radial modes and the first discovery of such a mode in an anomalous Cepheid, the overtone star XZ Cet, which we then confirmed with ground-based multicolor photometric measurements. We prepared a custom photometric solution to minimize saturation effects in the bright fundamental-mode classical Cepheid, $\beta$ Dor with the lightkurve software, and we revealed strong evidence of cycle-to-cycle variations in the star. In several cases, however, fluctuations in the pulsation could not be distinguished from instrumental effects, such as contamination from nearby sources which also varies between sectors. Finally, we discuss how precise light curve shapes will be crucial not only for classification purposes but also to determine physical properties of these stars., Comment: 30 pages, 18 figures, accepted for publication in ApJS

We present spectroscopic time series observations on one of the brightest northern RRc star, T Sex. Additionally, we also analysed extended photometric data sets, particularly the recent observations of the TESS space telescope. The main findings of our studies are as follows: T Sex, unlike all RRc stars whose space photometry has been analysed, shows only the $0.5f_x$ frequency as an additional pulsation frequency. With this, T Sex may be the first represent of such rare RRc stars found from space photometry. The spectroscopic data show a periodic distortion of the H$\alpha$ line with the pulsation phase. This phenomenon has not been reported for any RR Lyrae stars. The characteristic line distortion is probably caused by the turbulent convection, which resulted in higher macroturbulent velocity for T Sex than for typical RRab stars. Line doubling of the Na D line was observed between the 0.37 and 0.80 pulsation phases. The explanation of this phenomenon is that the two absorption components originate from different sources. The redder component comes from the pulsating atmosphere of the star, while the bluer one from the interstellar space. At phase 0.438, we detected emission on the Na D line, which may indicate a weak shock wave., Comment: 11 pages. 10 figures, accepted for publication in MNRAS

Implicit variables of a mathematical program are variables which do not need to be optimized but are used to model feasibility conditions. They frequently appear in several different problem classes of optimization theory comprising bilevel programming, evaluated multiobjective optimization, or nonlinear optimization problems with slack variables. In order to deal with implicit variables, they are often interpreted as explicit ones. Here, we first point out that this is a light-headed approach which induces artificial locally optimal solutions. Afterwards, we derive various Mordukhovich-stationarity-type necessary optimality conditions which correspond to treating the implicit variables as explicit ones on the one hand, or using them only implicitly to model the constraints on the other. A detailed comparison of the obtained stationarity conditions as well as the associated underlying constraint qualifications will be provided. Overall, we proceed in a fairly general setting relying on modern tools of variational analysis. Finally, we apply our findings to different well-known problem classes of mathematical optimization in order to visualize the obtained theory., Comment: 34 pages

We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed troughout the pile of calculus rules. These estimates also illustrate the role of the essential assumptions that accompany these two patters, namely calmness on the one hand and (fuzzy) inner calmness* on the other. Afterwards, we study the relationship between and sufficient conditions for the various notions of (inner) calmness. The aforementioned estimates are applied in order to recover several prominent calculus rules for tangents and normals as well as generalized derivatives of marginal functions and compositions as well as Cartesian products of set-valued mappings under mild conditions. We believe that our enhanced approach puts the overall generalized calculus into some other light. Some applications of our findings are presented which exemplary address necessary optimality conditions for minimax optimization problems as well as the calculus related to the recently introduced semismoothness* property., Comment: 38 pages, 1 figure

Data dimensionality informs us about data complexity and sets limit on the structure of successful signal processing pipelines. In this work we revisit and improve the manifold-adaptive Farahmand-Szepesv\'ari-Audibert (FSA) dimension estimator, making it one of the best nearest neighbor-based dimension estimators available. We compute the probability density function of local FSA estimates, if the local manifold density is uniform. Based on the probability density function, we propose to use the median of local estimates as a basic global measure of intrinsic dimensionality, and we demonstrate the advantages of this asymptotically unbiased estimator over the previously proposed statistics: the mode and the mean. Additionally, from the probability density function, we derive the maximum likelihood formula for global intrinsic dimensionality, if i.i.d. holds. We tackle edge and finite-sample effects with an exponential correction formula, calibrated on hypercube datasets. We compare the performance of the corrected-median-FSA estimator with kNN estimators: maximum likelihood (ML, Levina-Bickel) and two implementations of DANCo (R and matlab). We show that corrected-median-FSA estimator beats the ML estimator and it is on equal footing with DANCo for standard synthetic benchmarks according to mean percentage error and error rate metrics. With the median-FSA algorithm, we reveal diverse changes in the neural dynamics while resting state and during epileptic seizures. We identify brain areas with lower-dimensional dynamics that are possible causal sources and candidates for being seizure onset zones.

Recognition of anomalous events is a challenging but critical task in many scientific and industrial fields, especially when the properties of anomalies are unknown. In this paper, we introduce a new anomaly concept called "unicorn" or unique event and present a new, model-free, unsupervised detection algorithm to detect unicorns. The key component of the new algorithm is the Temporal Outlier Factor (TOF) to measure the uniqueness of events in continuous data sets from dynamic systems. The concept of unique events differs significantly from traditional outliers in many aspects: while repetitive outliers are no longer unique events, a unique event is not necessarily an outlier; it does not necessarily fall out from the distribution of normal activity. The performance of our algorithm was examined in recognizing unique events on different types of simulated data sets with anomalies and it was compared with the Local Outlier Factor (LOF) and discord discovery algorithms. TOF had superior performance compared to LOF and discord algorithms even in recognizing traditional outliers and it also recognized unique events that those did not. The benefits of the unicorn concept and the new detection method were illustrated by example data sets from very different scientific fields. Our algorithm successfully recognized unique events in those cases where they were already known such as the gravitational waves of a binary black hole merger on LIGO detector data and the signs of respiratory failure on ECG data series. Furthermore, unique events were found on the LIBOR data set of the last 30 years.

In this paper, we study continuity and Lipschitzian properties of set-valued mappings, focusing on inner-type conditions. We introduce new notions of inner calmness* and, its relaxation, fuzzy inner calmness*. We show that polyhedral maps enjoy inner calmness* and examine (fuzzy) inner calmness* of a multiplier mapping associated with constraint systems in depth. Then we utilize these notions to develop some new rules of generalized differential calculus, mainly for the primal objects (e.g. tangent cones). In particular, we propose an exact chain rule for graphical derivatives. We apply these results to compute the derivatives of the normal cone mapping, essential e.g. for sensitivity analysis of variational inequalities., Comment: 27 pages

Modern deep artificial neural networks have achieved great success in the domain of computer vision and beyond. However, their application to many real-world tasks is undermined by certain limitations, such as overconfident uncertainty estimates on out-of-distribution data or performance deterioration under data distribution shifts. Several types of deep learning models used for density estimation through probabilistic generative modeling have been shown to fail to detect out-of-distribution samples by assigning higher likelihoods to anomalous data. We investigate this failure mode in Variational Autoencoder models, which are also prone to this, and improve upon the out-of-distribution generalization performance of the model by employing an alternative training scheme utilizing negative samples. We present a fully unsupervised version: when the model is trained in an adversarial manner, the generator's own outputs can be used as negative samples. We demonstrate empirically the effectiveness of the approach in reducing the overconfident likelihood estimates of out-of-distribution inputs on image data.

This paper is devoted to the study of the metric subregularity constraint qualification (MSCQ) for general optimization problems, with the emphasis on the nonconvex setting. We elaborate on notions of directional pseudo- and quasi-normality, recently introduced by Bai et al. (SIAM J. Opt., 2019), which combine the standard approach via pseudo- and quasi-normality with modern tools of directional variational analysis. We focus on applications to disjunctive programs, where (directional) pseudo-normality is characterized via an extremal condition. This, in turn, yields efficient tools to verify pseudo-normality and MSCQ, which include, but are not limited to, Robinson's result on polyhedral multifunctions and Gfrerer's second-order sufficient condition for metric subregularity. Finally, we refine our study by defining the new class of ortho-disjunctive programs which comprises prominent optimization problems such as mathematical programs with complementarity, vanishing or switching constraints., Comment: 27 pages

The purpose of this work is twofold. First, we aim to extend for $0

We analyzed the long and short cadence light curves of the Kepler non-Blazhko RRab stars. We prepared the Fourier spectra, the Fourier amplitude and phase variation functions, time-frequency representation, the O-C diagrams and their Fourier contents. Our main findings are: (i) All stars which are brighter a certain magnitude limit show significant cycle-to-cycle light curve variations. (ii) We found permanently excited additional modes for at least one third of the sample and some other stars show temporarily excited additional modes. (iii) The presence of the Blazhko effect was carefully checked and identified one new Blazhko candidate but for at least 16 stars the effect can be excluded. This fact has important consequences. Either the cycle-to-cycle variation phenomenon is independent from the Blazhko effect and the Blazhko incidence ratio is still much lower (51%-55%) than the extremely large (>90%) ratio published recently. The connection between the extra modes and the cycle-to-cycle variations is marginal., Comment: 18 pages, 14 figures, 4 tables; Accepted for publication in MNRAS

Estimating the regular normal cone to constraint systems plays an important role for the derivation of sharp necessary optimality conditions. We present two novel approaches and introduce a new stationarity concept which is stronger than M-stationarity. We apply our theory to three classes of mathematical programs frequently arising in the literature., Comment: 35 pages

In the paper we provide new conditions ensuring the isolated calmness property and the Aubin property of parameterized variational systems with constraints depending, apart from the parameter, also on the solution itself. Such systems include, e.g., quasi-variational inequalities and implicit complementarity problems. Concerning the Aubin property, possible restrictions imposed on the parameter are also admitted. Throughout the paper, tools from the directional limiting generalized differential calculus are employed enabling us to impose only rather weak (non-restrictive) qualification conditions. Despite the very general problem setting, the resulting conditions are workable as documented by some academic examples, Comment: 26 pages

It was empirically determined that the umbra-penumbra boundaries of stable sunspots are characterized by a constant value of the vertical magnetic field. We analyzed the evolution of the photospheric magnetic field properties of a decaying sunspot belonging to NOAA 11277 between August 28 - September 3, 2011. The observations were acquired with the spectropolarimeter on-board of the Hinode satellite. We aim to proof the validity of the constant vertical magnetic-field boundary between the umbra and penumbra in decaying sunspots. A spectral-line inversion technique was used to infer the magnetic field vector from the full-Stokes profiles. In total, eight maps were inverted and the variation of the magnetic properties in time were quantified using linear or quadratic fits. We found a linear decay of the umbral vertical magnetic field, magnetic flux, and area. The penumbra showed a linear increase of the vertical magnetic field and a sharp decay of the magnetic flux. In addition, the penumbral area quadratically decayed. The vertical component of the magnetic field is weaker on the umbra-penumbra boundary of the studied decaying sunspot compared to stable sunspots. Its value seem to be steadily decreasing during the decay phase. Moreover, at any time of the shown sunspot decay, the inner penumbra boundary does not match with a constant value of the vertical magnetic field, contrary to what was seen in stable sunspots. During the decaying phase of the studied sunspot, the umbra does not have a sufficiently strong vertical component of the magnetic field and is thus unstable and prone to be disintegrated by convection or magnetic diffusion. No constant value of the vertical magnetic field was found for the inner penumbral boundary., Comment: Accepted for publication in Astronomy & Astrophysics, 6 pages, 7 figures