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Multifractality is a concept that helps compactly grasping the most essential features of the financial dynamics. In its fully developed form, this concept applies to essentially all mature financial markets and even to more liquid cryptocurrencies traded on the centralized exchanges. A new element that adds complexity to cryptocurrency markets is the possibility of decentralized trading. Based on the extracted tick-by-tick transaction data from the Universal Router contract of the Uniswap decentralized exchange, from June 6, 2023, to June 30, 2024, the present study using Multifractal Detrended Fluctuation Analysis (MFDFA) shows that even though liquidity on these new exchanges is still much lower compared to centralized exchanges convincing traces of multifractality are already emerging on this new trading as well. The resulting multifractal spectra are however strongly left-side asymmetric which indicates that this multifractality comes primarily from large fluctuations and small ones are more of the uncorrelated noise type. What is particularly interesting here is the fact that multifractality is more developed for time series representing transaction volumes than rates of return. On the level of these larger events a trace of multifractal cross-correlations between the two characteristics is also observed.

An efficient method of exploring the effects of anisotropy in the fractal properties of 2D surfaces and images is proposed. It can be viewed as a direction-sensitive generalization of the multifractal detrended fluctuation analysis (MFDFA) into 2D. It is tested on synthetic structures to ensure its effectiveness, with results indicating consistency. The interdisciplinary potential of this method in describing real surfaces and images is demonstrated, revealing previously unknown directional multifractality in data sets from the Martian surface and the Crab Nebula. The multifractal characteristics of Jackson Pollock's paintings are also analyzed. The results point to their evolution over the time of creation of these works., Comment: 20 pages, 7 figures

As the recent studies indicate, the structure imposed onto written texts by the presence of punctuation develops patterns which reveal certain characteristics of universality. In particular, based on a large collection of classic literary works, it has been evidenced that the distances between consecutive punctuation marks, measured in terms of the number of words, obey the discrete Weibull distribution - a discrete variant of a distribution often used in survival analysis. The present work extends the analysis of punctuation usage patterns to more experimental pieces of world literature. It turns out that the compliance of the the distances between punctuation marks with the discrete Weibull distribution typically applies here as well. However, some of the works by James Joyce are distinct in this regard - in the sense that the tails of the relevant distributions are significantly thicker and, consequently, the corresponding hazard functions are decreasing functions not observed in typical literary texts in prose. "Finnegans Wake" - the same one to which science owes the word "quarks" for the most fundamental constituents of matter - is particularly striking in this context. At the same time, in all the studied texts, the sentence lengths - representing the distances between sentence-ending punctuation marks - reveal more freedom and are not constrained by the discrete Weibull distribution. This freedom in some cases translates into long-range nonlinear correlations, which manifest themselves in multifractality. Again, a text particularly spectacular in terms of multifractality is "Finnegans Wake".

Noise is a fundamental problem in learning theory with huge effects in the application of Machine Learning (ML) methods, due to real world data tendency to be noisy. Additionally, introduction of malicious noise can make ML methods fail critically, as is the case with adversarial attacks. Thus, finding and developing alternatives to improve robustness to noise is a fundamental problem in ML. In this paper, we propose a method to deal with noise: mitigating its effect through the use of data abstractions. The goal is to reduce the effect of noise over the model's performance through the loss of information produced by the abstraction. However, this information loss comes with a cost: it can result in an accuracy reduction due to the missing information. First, we explored multiple methodologies to create abstractions, using the training dataset, for the specific case of numerical data and binary classification tasks. We also tested how these abstractions can affect robustness to noise with several experiments that explore the robustness of an Artificial Neural Network to noise when trained using raw data \emph{vs} when trained using abstracted data. The results clearly show that using abstractions is a viable approach for developing noise robust ML methods.

We report the study of a huge optical intraday flare on November 12, 2021, at 2 am UT, in the blazar OJ287. In the binary black hole model it is associated with an impact of the secondary black hole on the accretion disk of the primary. Our multifrequency observing campaign was set up to search for such a signature of the impact, based on a prediction made eight years earlier. The first I-band results of the flare have already been reported by \cite{2024ApJ...960...11K}. Here we combine these data with our monitoring in the R-band. There is a big change in the R-I spectral index by $1.0\pm0.1$ between the normal background and the flare, suggesting a new component of radiation. The polarization variation during the rise of the flare suggests the same. The limits on the source size place it most reasonably in the jet of the secondary black hole. We then ask why we have not seen this phenomenon before. We show that OJ287 was never before observed with sufficient sensitivity on the night when the flare should have happened according to the binary model. We also study the probability that this flare is just an oversized example of intraday variability, using the Krakow-dataset of intense monitoring between 2015 and 2023. We find that the occurrence of a flare of this size and rapidity is unlikely. In the Appendix, we give the full orbit-linked historical light curve of OJ287 as well as the dense monitoring sample of Krakow., Comment: to Appear in Astrophysical Journal Letters

The non-fungible token (NFT) market emerges as a recent trading innovation leveraging blockchain technology, mirroring the dynamics of the cryptocurrency market. The current study is based on the capitalization changes and transaction volumes across a large number of token collections on the Ethereum platform. In order to deepen the understanding of the market dynamics, the collection-collection dependencies are examined by using the multivariate formalism of detrended correlation coefficient and correlation matrix. It appears that correlation strength is lower here than that observed in previously studied markets. Consequently, the eigenvalue spectra of the correlation matrix more closely follow the Marchenko-Pastur distribution, still, some departures indicating the existence of correlations remain. The comparison of results obtained from the correlation matrix built from the Pearson coefficients and, independently, from the detrended cross-correlation coefficients suggests that the global correlations in the NFT market arise from higher frequency fluctuations. Corresponding minimal spanning trees (MSTs) for capitalization variability exhibit a scale-free character while, for the number of transactions, they are somewhat more decentralized.

Magnetic vortices are topological spin structures frequently found in ferromagnets, yet novel to antiferromagnets. By combining experiment and theory, we demonstrate that in a nanostructured antiferromagnetic-ferromagnetic NiO(111)-Fe(110) bilayer, a magnetic vortex is naturally stabilized by magnetostatic interactions in the ferromagnet and is imprinted onto the adjacent antiferromagnet via interface exchange coupling. We use micromagnetic simulations to construct a corresponding phase diagram of the stability of the imprinted antiferromagnetic vortex state. Our in depth analysis reveals that the interplay between interface exchange coupling and the antiferromagnet magnetic anisotropy plays a crucial role in locally reorienting the N\'eel vector out-of-plane in the prototypical in-plane antiferromagnet NiO and thereby stabilizing the vortices in the antiferromagnet.

The review summarizes the main methodological concepts used in studying natural language from the perspective of complexity science and documents their applicability in identifying both universal and system-specific features of language in its written representation. Three main complexity-related research trends in quantitative linguistics are covered. The first part addresses the issue of word frequencies in texts and demonstrates that taking punctuation into consideration restores scaling whose violation in the Zipf's law is often observed for the most frequent words. The second part introduces methods inspired by time series analysis, used in studying various kinds of correlations in written texts. The related time series are generated on the basis of text partition into sentences or into phrases between consecutive punctuation marks. It turns out that these series develop features often found in signals generated by complex systems, like long-range correlations or (multi)fractal structures. Moreover, it appears that the distances between punctuation marks comply with the discrete variant of the Weibull distribution. In the third part, the application of the network formalism to natural language is reviewed, particularly in the context of the so-called word-adjacency networks. Parameters characterizing topology of such networks can be used for classification of texts, for example, from a stylometric perspective. Network approach can also be applied to represent the organization of word associations. Structure of word-association networks turns out to be significantly different from that observed in random networks, revealing genuine properties of language. Finally, punctuation seems to have a significant impact not only on the language's information-carrying ability but also on its key statistical properties, hence it is recommended to consider punctuation marks on a par with words., Comment: 113 pages, 49 figures

A non-fungible token (NFT) market is a new trading invention based on the blockchain technology which parallels the cryptocurrency market. In the present work we study capitalization, floor price, the number of transactions, the inter-transaction times, and the transaction volume value of a few selected popular token collections. The results show that the fluctuations of all these quantities are characterized by heavy-tailed probability distribution functions, in most cases well described by the stretched exponentials, with a trace of power-law scaling at times, long-range memory, and in several cases even the fractal organization of fluctuations, mostly restricted to the larger fluctuations, however. We conclude that the NFT market - even though young and governed by a somewhat different mechanisms of trading - shares several statistical properties with the regular financial markets. However, some differences are visible in the specific quantitative indicators.

As evidenced by recent survey results, majority of asteroids are slow rotators (P>12 h), but lack spin and shape models due to selection bias. This bias is skewing our overall understanding of the spins, shapes, and sizes of asteroids, as well as of their other properties. Also, diameter determinations for large (>60km) and medium-sized asteroids (between 30 and 60 km) often vary by over 30% for multiple reasons. Our long-term project is focused on a few tens of slow rotators with periods of up to 60 hours. We aim to obtain their full light curves and reconstruct their spins and shapes. We also precisely scale the models, typically with an accuracy of a few percent. We used wide sets of dense light curves for spin and shape reconstructions via light-curve inversion. Precisely scaling them with thermal data was not possible here because of poor infrared data: large bodies are too bright for WISE mission. Therefore, we recently launched a campaign among stellar occultation observers, to scale these models and to verify the shape solutions, often allowing us to break the mirror pole ambiguity. The presented scheme resulted in shape models for 16 slow rotators, most of them for the first time. Fitting them to stellar occultations resolved previous inconsistencies in size determinations. For around half of the targets, this fitting also allowed us to identify a clearly preferred pole solution, thus removing the ambiguity inherent to light-curve inversion. We also address the influence of the uncertainty of the shape models on the derived diameters. Overall, our project has already provided reliable models for around 50 slow rotators. Such well-determined and scaled asteroid shapes will, e.g. constitute a solid basis for density determinations when coupled with mass information. Spin and shape models continue to fill the gaps caused by various biases., Comment: Accepted to Astronomy & Astrophysics. 12 pages + appendices

Intense outbursts in blazars are among the most extreme phenomena seen in extragalactic objects. Studying these events can offer important information about the energetic physical processes taking place within the innermost regions of blazars, which are beyond the resolution of current instruments. This work presents some of the largest and most rapid flares detected in the optical band from the sources 3C 279, OJ 49, S4 0954+658, Ton 599, and PG 1553+113, which are mostly TeV blazars. The source flux increased by nearly ten times within a few weeks, indicating the violent nature of these events. Such energetic events might originate from magnetohydrodynamical instabilities near the base of the jets, triggered by processes modulated by the magnetic field of the accretion disc. We explain the emergence of flares owing to the injection of high-energy particles by the shock wave passing along the relativistic jets. Alternatively, the flares may have also arisen due to geometrical effects related to the jets. We discuss both source-intrinsic and source-extrinsic scenarios as possible explanations for the observed large amplitude flux changes., Comment: 8 pages, 2 figures, 38th International Cosmic Ray Conference (ICRC2023) proceedings

The highly variable blazar OJ~287 is commonly discussed as an example of a binary black hole system. The 130 year long optical light curve is well explained by a model where the central body is a massive black hole of 18.35$\times$10$^9$ solar mass that supports a thin accretion disc. The secondary black hole of 0.15$\times$10$^9$ solar mass impacts the disc twice during its 12 year orbit, and causes observable flares. Recently, it has been argued that an accretion disc with a typical AGN accretion rate and above mentioned central body mass should be at least six magnitudes brighter than OJ~287's host galaxy and would therefore be observationally excluded. Based on the observations of OJ~287's radio jet, detailed in Marscher and Jorstad (2011), and up-to-date accretion disc models of Azadi et al. (2022), we show that the V-band magnitude of the accretion disc is unlikely to exceed the host galaxy brightness by more than one magnitude, and could well be fainter than the host. This is because accretion power is necessary to launch the jet as well as to create electromagnetic radiation, distributed across many wavelengths, and not concentrated especially on the optical V-band. Further, we note that the claimed V-band concentration of accretion power leads to serious problems while interpreting observations of other Active Galactic Nuclei. Therefore, we infer that the mass of the primary black hole and its accretion rate do not need to be smaller than what is determined in the standard model for OJ~287.

We present a summary of the results of the OJ 287 observational campaign, which was carried out during the 2021/2022 observational season. This season is special in the binary model because the major axis of the precessing binary happens to lie almost exactly in the plane of the accretion disc of the primary. This leads to pairs of almost identical impacts between the secondary black hole and the accretion disk in 2005 and 2022. In 2005, a special flare called "blue flash" was observed 35 days after the disk impact, which should have also been verifiable in 2022. We did observe a similar flash and were able to obtain more details of its properties. We describe this in the framework of expanding cloud models. In addition, we were able to identify the flare arising exactly at the time of the disc crossing from its photo-polarimetric and gamma-ray properties. This is an important identification, as it directly confirms the orbit model. Moreover, we saw a huge flare that lasted only one day. We may understand this as the lighting up of the jet of the secondary black hole when its Roche lobe is suddenly flooded by the gas from the primary disk. Therefore, this may be the first time we directly observed the secondary black hole in the OJ 287 binary system., Comment: 24 pages, 13 figures, published in Galaxies as part of the Special Issue Distant Glowing Objects: Quest for Quasars

This paper investigates the temporal patterns of activity in the cryptocurrency market with a focus on Bitcoin, Ethereum, Dogecoin, and WINkLink from January 2020 to December 2022. Market activity measures - logarithmic returns, volume, and transaction number, sampled every 10 seconds, were divided into intraday and intraweek periods and then further decomposed into recurring and noise components via correlation matrix formalism. The key findings include the distinctive market behavior from traditional stock markets due to the nonexistence of trade opening and closing. This was manifest in three enhanced-activity phases aligning with Asian, European, and U.S. trading sessions. An intriguing pattern of activity surge in 15-minute intervals, particularly at full hours, was also noticed, implying the potential role of algorithmic trading. Most notably, recurring bursts of activity in bitcoin and ether were identified to coincide with the release times of significant U.S. macroeconomic reports such as Nonfarm payrolls, Consumer Price Index data, and Federal Reserve statements. The most correlated daily patterns of activity occurred in 2022, possibly reflecting the documented correlations with U.S. stock indices in the same period. Factors that are external to the inner market dynamics are found to be responsible for the repeatable components of the market dynamics, while the internal factors appear to be substantially random, which manifests itself in a good agreement between the empirical eigenvalue distributions in their bulk and the random matrix theory predictions expressed by the Marchenko-Pastur distribution. The findings reported support the growing integration of cryptocurrencies into the global financial markets.

In relation to the traditional financial markets, the cryptocurrency market is a recent invention and the trading dynamics of all its components are readily recorded and stored. This fact opens up a unique opportunity to follow the multidimensional trajectory of its development since inception up to the present time. Several main characteristics commonly recognized as financial stylized facts of mature markets were quantitatively studied here. In particular, it is shown that the return distributions, volatility clustering effects, and even temporal multifractal correlations for a few highest-capitalization cryptocurrencies largely follow those of the well-established financial markets. The smaller cryptocurrencies are somewhat deficient in this regard, however. They are also not as highly cross-correlated among themselves and with other financial markets as the large cryptocurrencies. Quite generally, the volume V impact on price changes R appears to be much stronger on the cryptocurrency market than in the mature stock markets, and scales as $R(V) \sim V^{\alpha}$ with $\alpha \gtrsim 1$.

The bright blazar OJ~287 routinely parades high brightness bremsstrahlung flares, which are explained as being a result of a secondary supermassive black hole (SMBH) impacting the accretion disc of a more massive primary SMBH in a binary system. The accretion disc is not rigid but rather bends in a calculable way due to the tidal influence of the secondary. Below we refer to this phenomenon as a variable disc level. We begin by showing that these flares occur at times predicted by a simple analytical formula, based on general relativity inspired modified Kepler equation, which explains impact flares since 1888. The 2022 impact flare, namely flare number 26, is rather peculiar as it breaks the typical pattern of two impact flares per 12-year cycle. This is the third bremsstrahlung flare of the current cycle that follows the already observed 2015 and 2019 impact flares from OJ~287. It turns out that the arrival epoch of flare number 26 is sensitive to the level of primary SMBH's accretion disc relative to its mean level in our model. We incorporate these tidally induced changes in the level of the accretion disc to infer that the thermal flare should have occurred during July-August 2022, when it was not possible to observe it from the Earth. Thereafter, we explore possible observational evidence for certain pre-flare activity by employing spectral and polarimetric data from our campaigns in 2004/05 and 2021/22. We point out theoretical and observational implications of two observed mini-flares during January-February 2022., Comment: 29 pages, 6 figures, 1 table. arXiv admin note: text overlap with arXiv:2209.08360

In this study the cross-correlations between the cryptocurrency market represented by the two most liquid and highest-capitalized cryptocurrencies: bitcoin and ethereum, on the one side, and the instruments representing the traditional financial markets: stock indices, Forex, commodities, on the other side, are measured in the period: January 2020--October 2022. Our purpose is to address the question whether the cryptocurrency market still preserves its autonomy with respect to the traditional financial markets or it has already aligned with them in expense of its independence. We are motivated by the fact that some previous related studies gave mixed results. By calculating the $q$-dependent detrended cross-correlation coefficient based on the high frequency 10 s data in the rolling window, the dependence on various time scales, different fluctuation magnitudes, and different market periods are examined. There is a strong indication that the dynamics of the bitcoin and ethereum price changes since the March 2020 Covid-19 panic is no longer independent. Instead, it is related to the dynamics of the traditional financial markets, which is especially evident now in 2022, when the bitcoin and ethereum coupling to the US tech stocks is observed during the market bear phase. It is also worth emphasizing that the cryptocurrencies have begun to react to the economic data such as the Consumer Price Index readings in a similar way as traditional instruments. Such a spontaneous coupling of the so far independent degrees of freedom can be interpreted as a kind of phase transition that resembles the collective phenomena typical for the complex systems. Our results indicate that the cryptocurrencies cannot be considered as a safe haven for the financial investments.

Flaring episodes in blazars represent one of the most violent processes observed in extra-galactic objects. Studies of such events shed light on the energetics of the physical processes occurring in the innermost regions of blazars, which cannot otherwise be resolved by any current instruments. In this work, we present some of the largest and most rapid flares captured in the optical band in the blazars 3C 279, OJ 49, S4 0954+658, TXS 1156+295 and PG 1553+113. The source flux was observed to increase by nearly ten times within a timescale of a few weeks. We applied several methods of time series analysis and symmetry analysis. Moreover, we also performed searches for periodicity in the light curves of 3C 279, OJ 49 and PG 1553+113 using the Lomb-Scargle method and found plausible indications of quasi-periodic oscillations (QPOs). In particular, the 33- and 22-day periods found in 3C 279, i.e. a 3:2 ratio, are intriguing. These violent events might originate from magnetohydrodynamical instabilities near the base of the jets, triggered by processes modulated by the magnetic field of the accretion disc. We present a qualitative treatment as the possible explanation for the observed large amplitude flux changes in both the source-intrinsic and source-extrinsic scenarios., Comment: 11 pages, 6 figures, MNRAS accepted

The celebrated proverb that "speech is silver, silence is golden" has a long multinational history and multiple specific meanings. In written texts punctuation can in fact be considered one of its manifestations. Indeed, the virtue of effectively speaking and writing involves - often decisively - the capacity to apply the properly placed breaks. In the present study, based on a large corpus of world-famous and representative literary texts in seven major Western languages, it is shown that the distribution of intervals between consecutive punctuation marks in almost all texts can universally be characterised by only two parameters of the discrete Weibull distribution which can be given an intuitive interpretation in terms of the so-called hazard function. The values of these two parameters tend to be language-specific, however, and even appear to navigate translations. The properties of the computed hazard functions indicate that among the studied languages, English turns out to be the least constrained by the necessity to place a consecutive punctuation mark to partition a sequence of words. This may suggest that when compared to other studied languages, English is more flexible, in the sense of allowing longer uninterrupted sequences of words. Spanish reveals similar tendency to only a bit lesser extent.

The convection velocity ($U_C$) of turbulent structures has been studied in adverse-pressure-gradient (APG) turbulent boundary layers (TBLs) for a wide range of Reynolds numbers $Re_\tau = 1400 - 4000$. The study is based on estimation of the convection velocity using decomposed streamwise skewness factor introduced in (Drozdz A., Elsner W., Int. J. of Heat and Fluid Flow. 63 (2017) 67\-74) and verified by means of two-point correlation method. It was shown that in the overlapping region of APG flows, the convection velocity profiles (when scaled in viscous units) reassemble the universal logarithmic law characteristic for the ZPG flows up to Clauser-Rota pressure gradient parameter $\beta \lesssim 19$ for the considered range of Reynolds number, what means that in the inner region of TBL the friction velocity in APG is not proportional to $U$ (as in ZPG) but to $U_C$ instead. The physical mechanism that explains the impact of increased convection velocity on the mean flow is proposed. The difference between $U_C$ and $U$ increases as a function of APG, which causes the stronger sweeping that enhances momentum transfer to the wall and compensates the weaker mean shear profile that is created by lower vorticity near the wall. This effect is a result of an enhancement of amplitude modulation of the small scales by large scale motion. The process becomes more pronounced as eddy density grows, so with increasing Re. The proposed model addresses a number of literature observations found in adverse pressure gradient flows which have been so far left without a well-founded explanation., Comment: 25 pages, 11 figures

Based on the mathematical arguments formulated within the Multifractal Detrended Fluctuation Analysis (MFDFA) approach it is shown that in the uncorrelated time series from the Gaussian basin of attraction the effects resembling multifractality asymptotically disappear for positive moments when the length of time series increases. A hint is given that this applies to the negative moments as well and extends to the L\'evy stable regime of fluctuations. The related effects are also illustrated and confirmed by numerical simulations. This documents that the genuine multifractality in time series may only result from the long-range temporal correlations and the fatter distribution tails of fluctuations may broaden the width of singularity spectrum only when such correlations are present. The frequently asked question of what makes multifractality in time series - temporal correlations or broad distribution tails - is thus ill posed. In the absence of correlations only the bifractal or monofractal cases are possible. The former corresponds to the L\'evy stable regime of fluctuations while the latter to the ones belonging to the Gaussian basin of attraction in the sense of the Central Limit Theorem.

We characterize the optical variability properties of eight lobe-dominated radio quasars (QSOs): B2 0709$+$37, FBQS J095206.3$+$235245, PG 1004$+$130, [HB89] 1156$+$631, [HB89] 1425$+$267, [HB89] 1503$+$691, [HB89] 1721$+$343, 4C $+$74.26, systematically monitored for a duration of 13 years since 2009. The quasars are radio-loud objects with extended radio lobes that indicate their orientation close to the sky plane. Five of the eight QSOs are classified as giant radio quasars. All quasars showed variability during our monitoring, with magnitude variations between 0.3 and 1 mag for the least variable and the most variable QSO, respectively. We performed both structure function (SF) analysis and power spectrum density (PSD) analysis for the variability characterization and search for characteristic timescales and periodicities. As a result of our analysis, we obtained relatively steep SF slopes ($\alpha$ ranging from 0.49 to 0.75) that are consistent with the derived PSD slopes ($\sim$2--3). All the PSDs show a good fit to single power law forms, indicating a red-noise character of variability between $\sim$13 years and weeks timescales. We did not measure reliable characteristic timescales of variability from the SF analysis which indicates that the duration of the gathered data is too short to reveal them. The absence of bends in the PSDs (change of slope from $\geq$1 to $\sim$0) on longer timescales indicates that optical variations are most likely caused by thermal instabilities in the accretion disk., Comment: Accepted for publication in ApJS; 17 pages, 5 figures, 5 tables

The bright blazar OJ~287 routinely parades high brightness bremsstrahlung flares which are explained as being a result of a secondary supermassive black hole (SMBH) impacting the accretion disk of a primary SMBH in a binary system. We begin by showing that these flares occur at times predicted by a simple analytical formula, based on the Kepler equation, which explains flares since 1888. The next impact flare, namely the flare number 26, is rather peculiar as it breaks the typical pattern of two impact flares per 12 year cycle. This will be the third bremsstrahlung flare of the current cycle that follows the already observed 2015 and 2019 impact flares from OJ~287. Unfortunately, astrophysical considerations make it difficult to predict the exact arrival epoch of the flare number 26. In the second part of the paper, we describe our recent OJ~287 observations. They show that the pre-flare light curve of flare number 22, observed in 2005, exhibits similar activity as the pre-flare light curve in 2022, preceding the expected flare number 26 in our model. We argue that the pre-flare activity most likely arises in the primary jet whose activity is modulated by the transit of the secondary SMBH through the accretion disk of the primary. Observing the next impact flare of OJ~287 in October 2022 will substantiate the theory of disk impacts in binary black hole systems., Comment: 16 pages, 2 figures

Unlike price fluctuations, the temporal structure of cryptocurrency trading has seldom been a subject of systematic study. In order to fill this gap, we analyse detrended correlations of the price returns, the average number of trades in time unit, and the traded volume based on high-frequency data representing two major cryptocurrencies: bitcoin and ether. We apply the multifractal detrended cross-correlation analysis, which is considered the most reliable method for identifying nonlinear correlations in time series. We find that all the quantities considered in our study show an unambiguous multifractal structure from both the univariate (auto-correlation) and bivariate (cross-correlation) perspectives. We looked at the bitcoin--ether cross-correlations in simultaneously recorded signals, as well as in time-lagged signals, in which a time series for one of the cryptocurrencies is shifted with respect to the other. Such a shift suppresses the cross-correlations partially for short time scales, but does not remove them completely. We did not observe any qualitative asymmetry in the results for the two choices of a leading asset. The cross-correlations for the simultaneous and lagged time series became the same in magnitude for the sufficiently long scales.

Historically, FU Orionis-type stars are low-mass, pre-main sequence stars. The members of this class experience powerful accretion outbursts and remain in an enhanced accretion state for decades or centuries. V1515 Cyg, a classical FUor, started brightening in the 1940s and reached its peak brightness in the late 1970s. Following a sudden decrease in brightness it stayed in a minimum state for a few months, then started a brightening for several years. We present results of our ground-based photometric monitoring complemented with optical/NIR spectroscopic monitoring. Our light curves show a long-term fading with strong variability on weekly and monthly time scales. The optical spectra show P Cygni profiles and broad blue-shifted absorption lines, common properties of FUors. However, V1515 Cyg lacks the P Cygni profile in the Ca II 8498 \r{A} line, a part of the Ca infrared triplet (IRT), formed by an outflowing wind, suggesting that the absorbing gas in the wind is optically thin. The newly obtained near-infrared spectrum shows the strengthening of the CO bandhead and the FeH molecular band, indicating that the disk has become cooler since the last spectroscopic observation in 2015. The current luminosity of the accretion disk dropped from the peak value of 138 $L_{\odot}$ to about 45 $L_{\odot}$, suggesting that the long-term fading is also partly caused by the dropping of the accretion rate., Comment: 26 pages, 19 figure, accepted for publication in The Astrophysical Journal

We analyse tick-by-tick data representing major cryptocurrencies traded on some different cryptocurrency trading platforms. We focus on such quantities like the inter-transaction times, the number of transactions in time unit, the traded volume, and volatility. We show that the inter-transaction times show long-range power-law autocorrelations. These lead to multifractality expressed by the right-side asymmetry of the singularity spectra $f(\alpha)$ indicating that the periods of increased market activity are characterised by richer multifractality compared to the periods of quiet market. We also show that neither the stretched exponential distribution nor the power-law-tail distribution are able to model universally the cumulative distribution functions of the quantities considered in this work. For each quantity, some data sets can be modeled by the former, some data sets by the latter, while both fail in other cases. An interesting, yet difficult to account for, observation is that parallel data sets from different trading platforms can show disparate statistical properties.