We extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard trees in the strict ...traditional sense, as invariant compact trees embedded in
$\mathbb {C}$
, do not exist even for post-singularly finite exponential maps; the difficulty lies in the existence of asymptotic values. We therefore introduce the concept of a homotopy Hubbard tree that takes care of these difficulties. Specifically for the family of exponential maps, we show that every post-singularly finite map has a homotopy Hubbard tree that is unique up to homotopy, and that post-singularly finite exponential maps can be classified in terms of homotopy Hubbard trees, using a transcendental analogue of Thurston’s topological characterization theorem of rational maps.
Dreadlocks are a natural generalization of the well-known concept of dynamic
rays in complex dynamics. In this article we investigate which periodic or
preperiodic dreadlocks land together for ...arbitrary post-singularly finite
transcendental entire functions. Our main result is a combinatorial description
of the landing relation of dreadlocks in terms of the dynamic partitions of the
space of external addresses. One of the main difficulties deals with taming the
more complicated topology of dreadlocks. In the end, dreadlocks possess all the
topological properties of dynamic rays that are essential for the construction
of dynamic partitions. The results of this paper are the foundation for the
development of combinatorial models, in particular homotopy Hubbard trees, for
arbitrary post-singularly finite transcendental entire functions.
We extend the concept of a Hubbard tree, well established and useful in the theory of polynomial dynamics, to the dynamics of transcendental entire functions. We show that Hubbard trees in the strict ...traditional sense, as invariant compact trees embedded in \(\mathbb{C}\), do not exist even for post-singularly finite exponential maps; the difficulty lies in the existence of asymptotic values. We therefore introduce the concept of a Homotopy Hubbard Tree that takes care of these difficulties. Specifically for the family of exponential maps, we show that every post-singularly finite map has a Homotopy Hubbard tree that is unique up to homotopy, and we show that post-singulary finite exponential maps can be classified in terms of Homotopy Hubbard Trees, using a transcendental analogue of Thurston's topological characterization theorem of rational maps.
Modern industrial facilities consist of controllers, actuators and sensors that are connected via traditional IT equipment. The ongoing integration of these systems into the communication network ...yields to new threats and attack possibilities. In industrial networks, often distinct communication protocols like
Profinet IO (PNIO)
are used. These protocols are often not supported by typical network security tools. In this work, we present two attack techniques that allow to take over the control of a PNIO device, enabling an attacker to replay previously recorded traffic. We model attack detection rules and propose an intrusion detection system (IDS) for industrial networks which is capable of detecting those replay attacks by correlating alerts from traditional IT IDS with specific PNIO alarms. As an additional effort, we introduce defense in depth mechanisms in order to prevent those attacks from taking effect in the physical world. Thereafter, we evaluate our IDS in a physical demonstrator and compare it with another IDS dedicated to securing PNIO networks. In a conceptual design, we show how network segmentation with flow control allows for preventing some, but not all of the attacks.
A neutrino with energy ∼290 TeV, IceCube-170922A, was detected in coincidence with the BL Lac object TXS 0506+056 during enhanced gamma-ray activity, with chance coincidence being rejected at ∼3 ...level. We monitored the object in the very-high-energy (VHE) band with the Major Atmospheric Gamma-ray Imaging Cherenkov (MAGIC) telescopes for ∼41 hr from 1.3 to 40.4 days after the neutrino detection. Day-timescale variability is clearly resolved. We interpret the quasi-simultaneous neutrino and broadband electromagnetic observations with a novel one-zone lepto-hadronic model, based on interactions of electrons and protons co-accelerated in the jet with external photons originating from a slow-moving plasma sheath surrounding the faster jet spine. We can reproduce the multiwavelength spectra of TXS 0506+056 with neutrino rate and energy compatible with IceCube-170922A, and with plausible values for the jet power of . The steep spectrum observed by MAGIC is concordant with internal γγ absorption above ∼100 GeV entailed by photohadronic production of a ∼290 TeV neutrino, corroborating a genuine connection between the multi-messenger signals. In contrast to previous predictions of predominantly hadronic emission from neutrino sources, the gamma-rays can be mostly ascribed to inverse Compton upscattering of external photons by accelerated electrons. The X-ray and VHE bands provide crucial constraints on the emission from both accelerated electrons and protons. We infer that the maximum energy of protons in the jet comoving frame can be in the range ∼1014 - 1018 eV.
Industrial automation and control systems (IACS) play a key role in modern production facilities. On the one hand, they provide real-time functionality to the connected field devices. On the other ...hand, they get more and more connected to local networks and the internet in order to facilitate use cases promoted by "Industry 4.0". This makes IACS susceptible to cyber-attacks which exploit vulnerabilities, for example in order to interrupt the automation process. Security testing targets at discovering those vulnerabilities before they are exploited. In order to enable IACS manufacturers and integrators to perform security testing for their devices, we present ISuTest, a modular security testing framework for IACS. ISuTest is designed to be extendable regarding all kinds of automation protocols, different connection paths as well as evaluating arbitrary outputs of the tested devices. This paper describes the fundamental ideas behind ISuTest, its design and a basic evaluation in which the ISuTest framework was able to discover a vulnerability in a programmable logic controller (PLC). The paper concludes with a broad overview of the planned future work.
Industrial automation and control systems (IACS) play a key role in modern production facilities. On the one hand, they provide real-time functionality to the connected field devices. On the other ...hand, they get more and more connected to local networks and the internet in order to facilitate use cases promoted by “Industrie 4.0”. A lot of IACS are equipped with web servers that provide web applications for configuration and management purposes. If an attacker gains access to such a web application operated on an IACS, he can exploit vulnerabilities and possibly interrupt the critical automation process. Cyber security research for web applications is well-known in the office IT. There exist a lot of best practices and tools for testing web applications for different kinds of vulnerabilities. Security testing targets at discovering those vulnerabilities before they can get exploited. In order to enable IACS manufacturers and integrators to perform security tests for their devices, ISuTest was developed, a modular security testing framework for IACS.
This paper provides a classification of known types of web application vulnerabilities. Therefore, it makes use of the worst direct impact of a vulnerability. Based on this analysis, a subset of open-source vulnerability scanners to detect such vulnerabilities is selected to be integrated into ISuTest. Subsequently, the integration is evaluated. This evaluation is twofold: At first, willful vulnerable web applications are used. In a second step, seven real IACS, like a programmable logic controller, industrial switches and cloud gateways, are used. Both evaluation steps start with the manual examination of the web applications for vulnerabilities. They conclude with an automated test of the web applications using the vulnerability scanners automated by ISuTest.
The results show that the vulnerability scanners detected 53 % of the existing vulnerabilities. In a former study using commercial vulnerability scanners, 54 % of the security flaws could be found. While performing the analysis, 45 new vulnerabilities were detected. Some of them did not only break the web server but crashed the whole IACS, stopping the critical automation process. This shows that security testing is crucial in the industrial domain and needs to cover all services provided by the devices.
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