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std::string view is a reference-like data structure in the C++ Standard Template Library (STL) that enables fast and cheap processing of read-only strings. Due to its wide applicability and performance enhancing power, std::string view has been very popular since its introduction in the C++17 standard. However, its careless use can lead to serious memory management bugs. As the lifetime of a std::string view is not tied to the lifetime of the referenced string in any way, it is the user's responsibility to ensure that the view is only used while the viewed string is live and its buffer is not reallocated. This paper describes a static analysis tool that finds programming errors caused by the incorrect use of std::string view. Our work included modeling std::string view operations in the analysis, defining steps to detect lifetime errors, constructing user-friendly diagnostic messages, and performing an evaluation of the checker.

Static analysis is a method of analyzing source code without executing it. It is widely used to find bugs and code smells in industrial software. Besides other methods, the most important techniques are those based on the abstract syntax tree and those performing symbolic execution. Both of these methods found their role in modern software development as they have different advantages and limitations. In this tutorial, we present two problems from the C++ programming language: the elimination of redundant pointers, and the reporting of dangling pointers originating from incorrect use of the std::string class. These two issues have different theoretical backgrounds and finding them requires different implementation techniques. We will provide a step-by-step guide to implement the checkers (software to identify the aforementioned problems) - one based on the abstract syntax analysis method, the other exploring the possibilities of symbolic execution. The methods are explained in great detail and supported by code examples. The intended audience for this tutorial are both architects of static analysis tools and developers who want to understand the advantages and constraints of the different methods.

CodeChecker is an open source project that integrates different static analysis tools such as the Clang Static Analyzer and Clang-Tidy into the build systems, continuous integration loops, and development workflows of C++ programmers. It has a powerful issue management system to make it easier to evaluate the reports of the static analysis tools. This document was handed out as supportive material for a code analysis lecture at the 2018 3COWS conference in Kosice, Slovakia.

Static analysis is the analysis of a program without executing it, usually carried out by an automated tool. Symbolic execution is a popular static analysis technique used both in program verification and in bug detection software. It works by interpreting the code, introducing a symbol for each value unknown at compile time (e.g. user-given inputs), and carrying out calculations symbolically. The analysis engine strives to explore multiple execution paths simultaneously, although checking all paths is an intractable problem, due to the vast number of possibilities. We focus on an error finding framework called the Clang Static Analyzer, and the infrastructure built around it named CodeChecker. The emphasis is on achieving end-to-end scalability. This includes the run time and memory consumption of the analysis, bug presentation to the users, automatic false positive suppression, incremental analysis, pattern discovery in the results, and usage in continuous integration loops. We also outline future directions and open problems concerning these tools. While a rich literature exists on program verification software, error finding tools normally need to settle for survey papers on individual techniques. In this paper, we not only discuss individual methods, but also how these decisions interact and reinforce each other, creating a system that is greater than the sum of its parts. Although the Clang Static Analyzer can only handle C-family languages, the techniques introduced in this paper are mostly language-independent and applicable to other similar static analysis tools.

Symmetry analysis can provide a suitable change of variables, i.e., in geometric terms, a suitable diffeomorphism that simplifies the given direction field, which can help significantly in solving or studying differential equations. Roughly speaking this is the so-called rectification theorem. The local version of this result is a well-known theorem in the field of ordinary differential equations. In this note we prove a global counterpart when the equation fulfils the Lipschitz condition. Then we use this result to determine the global symmetry group of such an ordinary differential equation. It turns out that, assuming the Lipschitz condition, the full symmetry group is a smooth wreath product of two diffeomorphism groups, and does not depend on the form of the equation, at all., Comment: To appear in Journal of Lie Theory

Space debris larger than 1 cm can damage space instruments and impact Earth. The low-Earth orbits (at heights smaller than 2000 km) and orbits near the geostationary- Earth orbit (at 35786 km height) are especially endangered, because most satellites orbit at these latitudes. With current technology space debris smaller than 10 cm cannot be tracked. Smaller space debris burn up and evaporate in the atmosphere, but larger ones fall to the Earth's surface. For practical reasons it would be important to know the mass, composition, shape, velocity, direction of motion and impact time of space debris re-entering the atmosphere and falling to Earth. Since it is very difficult to measure these physical parameters, almost nothing is known about them. To partly fill this gap, we performed computer modelling with which we studied the celestial mechanics of spherical re-entry particles falling to Earth due to air drag.We determined the time, velocity and angle of impact as functions of the launch height, direction, speed and size of spherical re-entry particles. Our results can also be used for semi-spherical meteoroid particles of the interplanetary dust entering the Earth's atmosphere., Comment: 16 pages, 8 figures

The anomaly detection method presented by this paper has a special feature: it does not only indicate whether an observation is anomalous or not but also tells what exactly makes an anomalous observation unusual. Hence, it provides support to localize the reason of the anomaly. The proposed approach is model-based; it relies on the multivariate probability distribution associated with the observations. Since the rare events are present in the tails of the probability distributions, we use copula functions, that are able to model the fat-tailed distributions well. The presented procedure scales well; it can cope with a large number of high-dimensional samples. Furthermore, our procedure can cope with missing values, too, which occur frequently in high-dimensional data sets. In the second part of the paper, we demonstrate the usability of the method through a case study, where we analyze a large data set consisting of the performance counters of a real mobile telecommunication network. Since such networks are complex systems, the signs of sub-optimal operation can remain hidden for a potentially long time. With the proposed procedure, many such hidden issues can be isolated and indicated to the network operator., Comment: 27 pages, 12 figures, accepted at ACM Transactions on Intelligent Systems and Technology

Telescopes mounted with polarizers can study the neutral points of the Earths atmosphere, the solar corona, the surface of planets/moons of the Solar System, distant stars, galaxies and nebulae. These examples demonstrate well that polarimetry is a useful technique to gather astronomical information from spatially extended phenomena. There are two enigmatic celestial objects that can also effectively be studied with imaging polarimetry, namely the Kordylewski dust clouds (KDCs) positioned around the L4 and L5 triangular Lagrangian libration points of the Earth-Moon system. Although in 1961 the Polish astronomer, Kazimierz Kordylewski had observed two bright patches near the L5 point with photography, many astronomers assume that these dust clouds do not exist, because the gravitational perturbation of the Sun, solar wind and other planets may disrupt the stabilizing effect of the L4 and L5 Lagrange points of the Earth and Moon. Using ground-born imaging polarimetry, we present here new observational evidence for the existence of the KDC around the L5 point of the Earth-Moon system. Excluding artefacts induced by the telescope, cirrus clouds or condensation trails of airplanes, the only explanation remains the polarized scattering of sunlight on the particles collected around the L5 point. By our polarimetric detection of the KDC we think it is appropriate to reconsider the pioneering photometric observation of Kordylewski. Our polarimetric evidence is supported by the results of simulation of dust cloud formation in the L5 point of the Earth-Moon system presented in the first part of this paper.

Since the discovery in 1772 of the triangular Lagrange points L4 and L5 in the gravitational field of two bodies moving under the sole influence of mutual gravitational forces, astronomers found a large number of minor celestial bodies around these points of the Sun-Jupiter, Sun-Earth, Sun-Mars and Sun-Neptune systems. The L4 and L5 points of the Earth and Moon may be empty due to the gravitational perturbation of the Sun. However, in 1961 Kordylewski found two bright patches near the L5 point, which may refer to an accumulation of interplanetary particles. Since that time this formation is called the Kordylewski dust cloud (KDC). Until now only a very few computer simulations studied the formation and characteristics of the KDC. To fill this gap, we investigated a three-dimensional four-body problem consisting of the Sun, Earth, Moon and one test particle, 1860000 times separately. We mapped the size and shape of the conglomeratum of particles not escaped from the system sooner than an integration time of 3650 days around L5. Polarimetric observations of a possible KDC around L5 are presented in the second part of this paper.

We consider the general Lienard-type equation $\ddot{u} = \sum_{k=0}^n f_k \dot{u}^k$ for $n\geq 4$. This equation naturally admits the Lie symmetry $\frac{\partial}{\partial t}$. We completely characterize when this equation admits another Lie symmetry, and give an easily verifiable condition for this on the functions $f_0, \dots , f_n$. Moreover, we give an equivalent characterization of this condition. Similar results have already been obtained previously in the cases $n=1$ or $n=2$. That is, this paper handles all remaining cases except for $n=3$.

We characterize those nilpotent algebras of prime power order and finite type in congruence modular varieties that have infinitely many polynomially inequivalent congruence preserving expansions.

Highly concentrated functions play an important role in many research fields including control system analysis and physics, and they turned out to be the key idea behind inverse Laplace transform methods as well. This paper uses the matrix-exponential family of functions to create highly concentrated functions, whose squared coefficient of variation (SCV) is very low. In the field of stochastic modeling, matrix-exponential functions have been used for decades. They have many advantages: they are easy to manipulate, always non-negative, and integrals involving matrix-exponential functions often have closed-form solutions. For the time being there is no symbolic construction available to obtain the most concentrated matrix-exponential functions, and the numerical optimization-based approach has many pitfalls, too. In this paper, we present a numerical optimization-based procedure to construct highly concentrated matrix-exponential functions. To make the objective function explicit and easy to evaluate we introduce and use a new representation called hyper-trigonometric representation. This representation makes it possible to achieve very low SCV., Comment: Submitted for publication

The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. After collecting together previous partial results, we refine and prove Rhodes's conjecture on the structure of the maximal groups in the flow semigroup for finite, antisymmetric, strongly connected digraphs. Building on this result, we investigate and fully describe the structure and actions of the maximal subgroups of the flow semigroup acting on all but $k$ points for all finite digraphs and graphs for all $k\geq 1$. A linear algorithm (in the number of edges) is presented to determine these so-called `defect $k$ groups' for any finite (di)graph. Finally, we prove that the complexity of the flow semigroup of a 2-vertex connected (and strongly connected di)graph with $n$ vertices is $n-2$, completely confirming Rhodes's conjecture for such (di)graphs., Comment: 25 pages