Statistical Model Checking of Common Attack Scenarios on Blockchain

Blockchain technology has developed significantly over the last decade. One of the reasons for this is its sustainability architecture, which does not allow modification of the history of committed transactions. That means that developers should consider blockchain vulnerabilities and eliminate them before the deployment of the system. In this paper, we demonstrate a statistical model checking approach for the verification of blockchain systems on three real-world attack scenarios. We build and verify models of DNS attack, double-spending with memory pool flooding, and consensus delay scenario. After that, we analyze experimental results and propose solutions to avoid these kinds of attacks.

Special Bohr-Sommerfeld geometry: variations

In the paper we continue to study Special Bohr-Sommerfeld geometry of compact symplectic manifolds. Using natural deformation parameters we avoid the difficulties appeared in the definition of the moduli space of Special Bohr-Sommerfeld cycles for compact simply connected algebraic varieties. As a byproduct we present certain remarks on the Weinstein structures and Eliashberg conjectures.

On the Decidability of Behavioral Equivalences for (P,P)-PRS

We study resource similarity and resource bisimilarity -- congruent restrictions of the bisimulation equivalence for the (P,P)-class of Process Rewrite Systems (PRS). Both these equivalences coincide with the bisimulation equivalence for (1,P)-subclass of (P,P)-PRS, which is known to be decidable. While it has been shown in the literature that resource similarity is undecidable for (P,P)-PRS, decidability of resource bisimilarity for (P,P)-PRS remained an open question. In this paper, we present an algorithm for checking resource bisimilarity for (P,P)-PRS. We show that although both resource similarity and resource bisimilarity are congruences and have a finite semi-linear basis, only the latter is decidable.

Coalescing primordial binary black holes with log-normal mass spectrum

Primordial black holes created in the early Universe can constitute a substantial fraction of dark matter and serve as seeds for early galaxy formation. Binary primordial black holes with masses of the order of a few dozen solar masses can explain the observed LIGO/Virgo gravitational-wave events. In this Letter, we show that primordial black holes with log-normal mass spectrum centered at $M_0simeq 15-17 M_odot$ simultaneously explain both the chirp mass distribution of the detected LIGO/Virgo binary black holes and the differential chirp mass distribution of merging binaries as inferred from the LIGO/Virgo observations. The obtained parameters of log-normal mass spectrum of primordial black holes also give the fraction of seeds with $Mgtrsim 10^4 M_odot$ required to explain the observed population of supermassive black holes at $z=6-7$.

Classification of bad pixels of the Hawaii-2RG detector of the ASTROnomical NearInfraRed CAMera

ASTRONIRCAM is an infrared camera-spectrograph installed at the 2.5-meter telescope of the CMO SAI. The instrument is equipped with the HAWAII-2RG array. A bad pixels classification of the ASTRONIRCAM detector is proposed. The classification is based on histograms of the difference of consecutive non-destructive readouts of a flat field. Bad pixels are classified into 5 groups: hot (saturated on the first readout), warm (the signal accumulation rate is above the mean value by more than 5 standard deviations), cold (the rate is under the mean value by more than 5 standard deviations), dead (no signal accumulation), and inverse (having a negative signal accumulation in the first readouts). Normal pixels of the ASTRONIRCAM detector account for 99.6% of the total. We investigated the dependence between the amount of bad pixels and the number of cooldown cycles of the instrument. While hot pixels remain the same, the bad pixels of other types may migrate between groups. The number of pixels in each group stays roughly constant. We found that the mean and variance of the bad pixels amount in each group and the transitions between groups do not differ noticeably between normal or slow cooldowns.

Weak Greibach Normal Form for Hyperedge Replacement Grammars

It is known that hyperedge replacement grammars are similar to string context-free grammars in the sense of definitions and properties. Therefore, we expect that there is a generalization of the well-known Greibach normal form from string grammars to hypergraph grammars. Such generalized normal forms are presented in several papers; however, they do not cover a large class of hypergraph languages (e.g. languages consisting of star graphs). In this paper, we introduce a weak Greibach normal form, whose definition corresponds to the lexicalized normal form for string grammars, and prove that every context-free hypergraph language (with nonsubstantial exceptions) can be generated by a grammar in this normal form. The proof presented in this paper generalizes a corresponding one for string grammars with a few more technicalities.

Ruin probabilities with investments: smoothness, IDE and ODE, asymptotic behavior

The study deals with the ruin problem when an insurance company having two business branches, life insurance and non-life insurance, invests its reserve into a risky asset with the price dynamics given by a geometric Brownian motion. We prove a result on smoothness of the ruin probability as a function of the initial capital and obtain for it an integro-differential equation understood in the classical sense. For the case of exponentially distributed jumps we show that the survival probability is a solution of an ordinary differential equation of the 4th order. Asymptotic analysis of the latter leads to the conclusion that the ruin probability decays to zero in the same way as in the already studied cases of models with one-side jumps.

Observations of lenticular galaxies at the 6m telescope of the Special Astrophysical Observatory

This is a historical review covering the last 30 years of the observational study of lenticular galaxies at the 6m telescope BTA of the Special Astrophysical Observatory of the Russian Academy of Sciences. The development of spectroscopic techniques at the BTA has allowed to get comprehensive information about this class of stellar systems, starting from the study of their nuclei in the late 80th towards quite exclusive results obtained in the last years on the outermost parts of their large-scale stellar disks.

Detecting Automatically Managed Accounts in Online Social Networks: Graph Embedding Approach

The widespread of Online Social Networks and the opportunity to commercialize popular accounts have attracted a large number of automated programs, known as artificial accounts. This paper focuses on the classification of human and fake accounts on the social network, by employing several graph neural networks, to efficiently encode attributes and network graph features of the account. Our work uses both network structure and attributes to distinguish human and artificial accounts and compares attributed and traditional graph embeddings. Separating complex, human-like artificial accounts into a standalone task demonstrates significant limitations of profile-based algorithms for bot detection and shows the efficiency of network structure-based methods for detecting sophisticated bot accounts. Experiments show that our approach can achieve competitive performance compared with existing state-of-the-art bot detection systems with only network-driven features. The source code of this paper is available at: http://github.com/karpovilia/botdetection.

Estimation of friction force in an oscillator model of atomic force microscope tip sliding on vibrating surface

We consider an oscillator model to describe qualitatively friction force for an atomic force mi-croscope (AFM) tip driven on a surface described by periodic potential. It is shown that average value of the friction force could be controlled by application of external time-dependent periodic perturbation. Numerical simulation demonstrates significant drop or increase of friction depending on amplitude and frequency of perturbation. Two different oscillating regimes are observed, they determined by frequency and amplitude of perturbation. The first one is regime of mode locking at frequencies multiple to driving frequency. It occurs close to resonance of harmonic perturbation and driving frequencies. Another regime of motion for a driven oscillator is characterized by aperiodic oscillations. It was observed in the numerical experiment for perturbations with large amplitudes and frequencies far from oscillator eigenfrequency. In this regime the oscillator does not follow external driving force, but rather oscillates at several modes which result from interaction of oscillator eigenmode and perturbation frequency.