arXiv subjects
Publications and source records attributed to Andrey Morozov.
In this paper we discuss the principles of measuring topological charge or representation traveling in the set of anyons. We describe the procedure and analyze how it works for the different values of parameters of the theory. We also show how it can be modified to be more effective for different levels of Chern-Simons theory.
This paper presents a new approach to the solution of Probabilistic Risk Assessment (PRA) models using the combination of Reinforcement Learning (RL) and Graph Neural Networks (GNNs). The paper introduces and demonstrates the concept using one of the most popular PRA models - Fault Trees. This paper's original idea is to apply RL algorithms to solve a PRA model represented with a graph model. Given enough training data, or through RL, such an approach helps train generic PRA solvers that can optimize and partially substitute classical PRA solvers that are based on existing formal methods. Such an approach helps to solve the problem of the fast-growing complexity of PRA models of modern technical systems.
AI-controlled robotic systems pose a risk to human workers and the environment. Classical risk assessment methods cannot adequately describe such black box systems. Therefore, new methods for a dynamic risk assessment of such AI-controlled systems are required. In this paper, we introduce the concept of a new dynamic risk assessment approach for AI-controlled robotic systems. The approach pipelines five blocks: (i) a Data Logging that logs the data of the given simulation, (ii) a Skill Detection that automatically detects the executed skills with a deep learning technique, (iii) a Behavioral Analysis that creates the behavioral profile of the robotic systems, (iv) a Risk Model Generation that automatically transforms the behavioral profile and risk data containing the failure probabilities of robotic hardware components into advanced hybrid risk models, and (v) Risk Model Solvers for the numerical evaluation of the generated hybrid risk models. Keywords: Dynamic Risk Assessment, Hybrid Risk Models, M2M Transformation, ROS, AI-Controlled Robotic Systems, Deep Learning, Reinforcement Learning
Robustness is a fundamental property of machine learning classifiers required to achieve safety and reliability. In the field of adversarial robustness of image classifiers, robustness is commonly defined as the stability of a model to all input changes within a p-norm distance. However, in the field of random corruption robustness, variations observed in the real world are used, while p-norm corruptions are rarely considered. This study investigates the use of random p-norm corruptions to augment the training and test data of image classifiers. We evaluate the model robustness against imperceptible random p-norm corruptions and propose a novel robustness metric. We empirically investigate whether robustness transfers across different p-norms and derive conclusions on which p-norm corruptions a model should be trained and evaluated. We find that training data augmentation with a combination of p-norm corruptions significantly improves corruption robustness, even on top of state-of-the-art data augmentation schemes.
Cohesive powers of computable structures are effective analogs of ultrapowers, where cohesive sets play the role of ultrafilters. Let $ω$, $ζ$, and $η$ denote the respective order-types of the natural numbers, the integers, and the rationals when thought of as linear orders. We investigate the cohesive powers of computable linear orders, with special emphasis on computable copies of $ω$. If $\mathcal{L}$ is a computable copy of $ω$ that is computably isomorphic to the usual presentation of $ω$, then every cohesive power of $\mathcal{L}$ has order-type $ω+ ζη$. However, there are computable copies of $ω$, necessarily not computably isomorphic to the usual presentation, having cohesive powers not elementarily equivalent to $ω+ ζη$. For example, we show that there is a computable copy of $ω$ with a cohesive power of order-type $ω+ η$. Our most general result is that if $X \subseteq \mathbb{N} \setminus \{0\}$ is a Boolean combination of $Σ_2$ sets, thought of as a set of finite order-types, then there is a computable copy of $ω$ with a cohesive power of order-type $ω+ σ(X \cup \{ω+ ζη+ ω^*\})$, where $σ(X \cup \{ω+ ζη+ ω^*\})$ denotes the shuffle of the order-types in $X$ and the order-type $ω+ ζη+ ω^*$. Furthermore, if $X$ is finite and non-empty, then there is a computable copy of $ω$ with a cohesive power of order-type $ω+ σ(X)$.
This work is devoted to the capabilities analysis of constellation and small spacecraft developed using CubeSat technology to solve promising problems of the Earth remote sensing in the area of greenhouse gases emissions. This paper presents the scientific needs for such tasks, followed by descriptions and discussions of the micro-technology application both in the small satellite platform design and in the payload design. The overview of analogical spacecraft is carried out. The design of a new spacecraft for determination the oxygen and carbon dioxide concentration in the air column along the line of sight of the spacecraft when it illuminated by reflected sunlight is introduced. A mock-up of the device was made for greenhouse gases remote sensing a Fourier Transform Infrared (FTIR) spectroradiometer is placed in the small spacecraft design. The results of long-term measurements of greenhouse gas concentrations using the developed Fourier spectrometer mock-up is presented.
Racah matrices of quantum algebras are of great interest at present time. These matrices have a relation with $\mathcal{R}$-matrices, which are much simpler than the Racah matrices themselves. This relation is known as the eigenvalue conjecture. In this paper we study symmetries of Racah matrices which follow from the eigenvalue conjecture for multistrand braids.
We present a comprehensive classification of invariants of knots and links associated with irreducible representations of \uqslN{}, when the parameter of quantization $q$ is a root of unity. We demonstrate that, besides the standard HOMFLY-PT invariants, which are associated with representations with highest and lowest weights, non-trivial invariants can be associated only with nilpotent representations with parameters. We define the corresponding invariants and discuss their relations with standard invariants at particular values of parameters.
We improve on and generalize a 1960 result of Maltsev. For a field $F$, we denote by $H(F)$ the Heisenberg group with entries in $F$. Maltsev showed that there is a copy of $F$ defined in $H(F)$, using existential formulas with an arbitrary non-commuting pair $(u,v)$ as parameters. We show that $F$ is interpreted in $H(F)$ using computable $Σ_1$ formulas with no parameters. We give two proofs. The first is an existence proof, relying on a result of Harrison-Trainor, Melnikov, R. Miller, and Montalbán. This proof allows the possibility that the elements of $F$ are represented by tuples in $H(F)$ of no fixed arity. The second proof is direct, giving explicit finitary existential formulas that define the interpretation, with elements of $F$ represented by triples in $H(F)$. Looking at what was used to arrive at this parameter-free interpretation of $F$ in $H(F)$, we give general conditions sufficient to eliminate parameters from interpretations.
Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by sequences of quantum $\mathcal{R}$-matrices. Its dimension and explicit form depend on the parameters of the Chern-Simons theory -- level $k$, gauge group $SU(N)$, and representation, which is chosen to be symmetric representation $[r]$. In this paper, we examine the universality of such a quantum computer. We prove that for sufficiently large $k$ it is universal, and the minimum allowed value of $k$ depends on the remaining parameters $r$ and $N$.
The eigenvalue hypothesis claims that any quantum Racah matrix for finite-dimensional representations of $U_q(sl_N)$ is uniquely determined by eigenvalues of the corresponding quantum $\cal{R}$-matrices. If this hypothesis turns out to be true, then it will significantly simplify the computation of Racah matrices. Also due to this hypothesis various interesting properties of colored HOMFLY-PT polynomials will be proved. In addition, it allows one to discover new symmetries of the quantum 6-j symbols, about which almost nothing is known for $N>2$, with the exception of the tetrahedral symmetries, complex conjugation and transformation $q \longleftrightarrow q^{-1}$. In this paper we prove the eigenvalue hypothesis in $U_q(sl_2)$ case and show that it is equivalent to 6-j symbol symmetries (the Regge symmetry and two argument permutations). Then we apply the eigenvalue hypothesis to inclusive Racah matrices with 3 symmetric incoming representations of $U_q(sl_N)$ and an arbitrary outcoming one. It gives us 8 new additional symmetries that are not tetrahedral ones. Finally, we apply the eigenvalue hypothesis to exclusive Racah matrices with symmetric representations and obtain 4 tetrahedral symmetries.
Model-based fault injection methods are widely used for the evaluation of fault tolerance in safety-critical control systems. In this paper, we introduce a new model-based fault injection method implemented as a highlycustomizable Simulink block called FIBlock. It supports the injection of typical faults of essential heterogeneous components of Cyber-Physical Systems, such as sensors, computing hardware, and network. The FIBlock GUI allows the user to select a fault type and configure multiple parameters to tune error magnitude, fault activation time, and fault exposure duration. Additional trigger inputs and outputs of the block enable the modeling of conditional faults. Furthermore, two or more FIBlocks connected with these trigger signals can model chained errors. The proposed fault injection method is demonstrated with a lower-limb EXO-LEGS exoskeleton, an assistive device for the elderly in everyday life. The EXO-LEGS model-based dynamic control is realized in the Simulink environment and allows easy integration of the aforementioned FIBlocks. Exoskeletons, in general, being a complex CPS with multiple sensors and actuators, are prone to hardware and software faults. In the case study, three types of faults were investigated: 1) sensor freeze, 2) stuck-at-0, 3) bit-flip. The fault injection experiments helped to determine faults that have the most significant effects on the overall system reliability and identify the fine line for the critical fault duration after that the controller could no longer mitigate faults.
Today, Deep Learning (DL) enhances almost every industrial sector, including safety-critical areas. The next generation of safety standards will define appropriate verification techniques for DL-based applications and propose adequate fault tolerance mechanisms. DL-based applications, like any other software, are susceptible to common random hardware faults such as bit flips, which occur in RAM and CPU registers. Such faults can lead to silent data corruption. Therefore, it is crucial to develop methods and tools that help to evaluate how DL components operate under the presence of such faults. In this paper, we introduce two new Fault Injection (FI) frameworks InjectTF and InjectTF2 for TensorFlow 1 and TensorFlow 2, respectively. Both frameworks are available on GitHub and allow the configurable injection of random faults into Neural Networks (NN). In order to demonstrate the feasibility of the frameworks, we also present the results of FI experiments conducted on four VGG-based Convolutional NNs using two image sets. The results demonstrate how random bit flips in the output of particular mathematical operations and layers of NNs affect the classification accuracy. These results help to identify the most critical operations and layers, compare the reliability characteristics of functionally similar NNs, and introduce selective fault tolerance mechanisms.
A closed form expression for multiplicity-free quantum 6-j symbols (MFS) was proposed in arXiv:1302.5143 for symmetric representations of $U_q(sl_N)$, which are the simplest class of multiplicity-free representations. In this paper we rewrite this expression in terms of q-hypergeometric series ${}_4Φ_3$. We claim that it is possible to express any MFS through the 6-j symbol for $U_q(sl_2)$ with a certain factor. It gives us a universal tool for the extension of various properties of the quantum 6-j symbols for $U_q(sl_2)$ to the MFS. We demonstrate this idea by deriving the asymptotics of the MFS in terms of associated tetrahedron for classical algebra $U(sl_N)$. Next we study MFS symmetries using known hypergeometric identities such as argument permutations and Sears' transformation. We describe symmetry groups of MFS. As a result we get new symmetries, which are a generalization of the tetrahedral symmetries and the Regge symmetries for N = 2.
For the verification of systems using model-checking techniques, symbolic representations based on binary decision diagrams (BDDs) often help to tackle the well-known state-space explosion problem. Symbolic BDD-based representations have been also shown to be successful for the analysis of families of systems that arise, e.g., through configurable parameters or following the feature-oriented modeling approach. The state space of such system families face an additional exponential blowup in the number of parameters or features. It is well known that the order of variables in ordered BDDs is crucial for the size of the model representation. Especially for automatically generated models from real-world systems, family models might even be not constructible due to bad variable orders. In this paper we describe a technique, called iterative variable reordering, that can enable the construction of large-scale family models. We exemplify feasibility of our approach by means of an aircraft velocity control system with redundancy mechanisms modeled in the input language of the probabilistic model checker PRISM. We show that standard reordering and dynamic reordering techniques fail to construct the family model due to memory and time constraints, respectively, while the new iterative approach succeeds to generate a symbolic family model.
We study the Chern-Simons approach to the topological quantum computing. We use quantum $\mathcal{R}$-matrices as universal quantum gates and study the approximations of some one-qubit operations. We make some modifications to the known Solovay-Kitaev algorithm suitable for our particular problem.
Modern safety-critical systems are heterogeneous, complex, and highly dynamic. They require reliability evaluation methods that go beyond the classical static methods such as fault trees, event trees, or reliability block diagrams. Promising dynamic reliability analysis methods employ probabilistic model checking on various probabilistic state-based models. However, such methods have to tackle the well-known state-space explosion problem. To compete with this problem, reduction methods such as symmetry reduction and partial-order reduction have been successfully applied to probabilistic models by means of discrete Markov chains or Markov decision processes. Such models are usually specified using probabilistic programs provided in guarded command language. In this paper, we propose two automated reduction methods for probabilistic programs that operate on a purely syntactic level: reset value optimization and register allocation optimization. The presented techniques rely on concepts well known from compiler construction such as live range analysis and register allocation through interference graph coloring. Applied on a redundancy system model for an aircraft velocity control loop modeled in SIMULINK, we show effectiveness of our implementation of the reduction methods. We demonstrate that model-size reductions in three orders of magnitude are possible and show that we can achieve significant speedups for a reliability analysis.
Redundancy mechanisms such as triple modular redundancy protect safety-critical components by replication and thus improve systems fault tolerance. However, the gained fault tolerance comes along with costs to be invested, e.g., increasing execution time, energy consumption, or packaging size, for which constraints have to be obeyed during system design. This turns the question of finding suitable combinations of components to be protected into a challenging task as the number of possible protection combinations grows exponentially in the number of components. We propose family-based approaches to tackle the combinatorial blowup in redundancy systems modeling and analysis phases. Based on systems designed in SIMULINK we show how to obtain models that include all possible protection combinations and present a tool chain that, given a probabilistic error model, generates discrete Markov chain families. Using symbolic techniques that enable concise family representation and analysis, we show how SIMULINK models of realistic size can be protected and analyzed with a single family-based analysis run while a one-by-one analysis of each protection combination would clearly exceed any realistic time constraints.