Universal Gr\"obner Bases for Binary Linear Codes

Each linear code can be described by a code ideal given as the sum of a toric ideal and a non-prime ideal. In this way, several concepts from the theory of toric ideals can be translated into the setting of code ideals. It will be shown that after adjusting some of these concepts, the same inclusion relationship between the set of circuits, the universal Gr\"obner basis and the Graver basis holds. Furthermore, in the case of binary linear codes, the universal Gr\"obner basis will consist of all binomials which correspond to codewords that satisfy the Singleton bound and a particular rank condition. This will give rise to a new class of binary linear codes denoted as Singleton codes.Comment: Accepted for publication in IJPA

On Binomial Ideals associated to Linear Codes

Recently, it was shown that a binary linear code can be associated to a binomial ideal given as the sum of a toric ideal and a non-prime ideal. Since then two different generalizations have been provided which coincide for the binary case. In this paper, we establish some connections between the two approaches. In particular, we show that the corresponding code ideals are related by elimination. Finally, a new heuristic decoding method for linear codes over prime fields is discussed using Gr\"obner bases

Graver Bases and Universal Gr\"obner Bases for Linear Codes

Two correspondences have been provided that associate any linear code over a finite field with a binomial ideal. In this paper, algorithms for computing their Graver bases and universal Gr\"obner bases are given. To this end, a connection between these binomial ideals and toric ideals will be established.Comment: 18 page

Weighted Automata and Logics on Hierarchical Structures and Graphs

Formal language theory, originally developed to model and study our natural spoken languages, is nowadays also put to use in many other fields. These include, but are not limited to, the definition and visualization of programming languages and the examination and verification of algorithms and systems. Formal languages are instrumental in proving the correct behavior of automated systems, e.g., to avoid that a flight guidance system navigates two airplanes too close to each other. This vast field of applications is built upon a very well investigated and coherent theoretical basis. It is the goal of this dissertation to add to this theoretical foundation and to explore ways to make formal languages and their models more expressive. More specifically, we are interested in models that are able to model quantitative features of the behavior of systems. To this end, we define and characterize weighted automata over structures with hierarchical information and over graphs. In particular, we study infinite nested words, operator precedence languages, and finite and infinite graphs. We show Büchi-like results connecting weighted automata and weighted monadic second order (MSO) logic for the respective classes of weighted languages over these structures. As special cases, we obtain Büchi-type equivalence results known from the recent literature for weighted automata and weighted logics on words, trees, pictures, and nested words. Establishing such a general result for graphs has been an open problem for weighted logics for some time. We conjecture that our techniques can be applied to derive similar equivalence results in other contexts like traces, texts, and distributed systems

Same Old (Macro-) Securitization? A Comparison of Political Reactions to Major Terrorist Attacks in the United States and France

After the November 2015 terror attacks in Paris, the French government reacted swiftly by declaring a state of emergency. This state of emergency remained in place for over two years before it was ended in November 2017, only after being replaced by the new anti-terror legislation. The attacks as well as the government’s reactions evoked parallels to 9/11 and its aftermath. This is a puzzling observation when taking into consideration that the Bush administration’s reactions have been criticized harshly and that the US ‘War on Terror’ (WoT) was initially considered a serious failure in France. We can assume that this adaption of the discourse and practices stems from a successful establishment of the WoT macro-securitization. By using Securitization Theory, we outline the development of this macro-securitization by comparing its current manifestation in France against the backdrop of its origins in the US after 9/11. We analysed securitizing moves in the discourses, as well as domestic and international emergency measure policies. We find extensive similarities with view of both; yet there are differing degrees of securitizing terrorism and the institutionalisation of the WoT in the two states. This suggests that the WoT narrative is still dominant internationally to frame the risk of terrorism as an existential threat, thus enabling repressive actions and the obstruction of a meaningful debate about the underlying problems causing terrorism in the first place

Optimierung des Bestellwesens in einem Dienstleistungsbetrieb

Ein effizientes Bestellwesen kann einen wichtigen Beitrag zur Kostensenkung und Gewinnsteigerung in einer Firma leisten. Hierbei herrscht meist noch Verbesserungspotenzial, was aber von vielen Unternehmen nicht wahrgenommen wird. In dieser Diplomarbeit wurde in Zusammenarbeit mit einem Dienstleistungsbetrieb der Versuch unternommen, das Bestellwesen dieser Firma auf betriebswirtschaftlichen Theorien basierend, zu optimieren. Die Grundlage eines optimalen Bestellwesens liegt in einer aussagekräftigen Prognoserechnung (Forecastrechnung). Durch die Bestimmung der zukünftigen Nachfrage lässt sich ein optimaler Sicherheitsbestand zu einem definierten Servicelevel bestimmen. Durch die genaue Berechnung des Sicherheitsbestandes, lassen sich die Lagerhaltungskosten senken bzw. der Servicegrad verbessern. Weiters beeinflusst auch die Bestellgröße die entstehenden Kosten. Um diese zu minimieren gilt es, die optimale Bestellgröße zu eruieren. Nach diesen Berechnungen wurde in der Arbeit eine effiziente Bestellpolitik entwickelt, um somit Lieferengpässe zu vermeiden und Lagerhaltungskosten zu senken.An effective ordering process can make a major contribution for the cost reduction and profit maximation of a company. Mostly there is still great potential for improving this ordering process, but this opportunity is not seized by most of the companies. This thesis tries to optimize the ordering process of a selected service company based on economic theories. Base for an optimized ordering process is a meaningful forecast calculation. By determining the future demand, an optimum safety stock at a defined servicelevel can be calculated. By exactly calculating the safety stock, storage costs can be reduced and the servicelevel improved. Order quantities also influence the emerging costs. In order to minimize them, the optimal order quantity must be determined. Based on those calculations, an efficient ordering process was established in this thesis in order to avoid a delivery bottleneck and to reduce storage costs

Feministische Klassenpolitiken in Kämpfen um soziale Reproduktion

Der Beitrag beschäftigt sich aus gesellschaftstheoretischer und feministischer Perspektive mit gesellschaftlichen Auseinandersetzungen im Bereich der sozialen Reproduktion. Am Beispiel der Auseinandersetzungen am Berliner Universitätsklinikum Charité soll dabei aufgezeigt werden, dass die Umwälzung sozialer Reproduktionsverhältnisse sowie die gegenwärtig stattfindenden In-Wert-Setzungen im Bereich bezahlter Sorgearbeit nicht nur als ökonomische, sondern auch als politisch-ideologische und subjektivierende Veränderungen zu betrachten sind. Gelingt es, ein neues Verständnis von sozialer Reproduktion und Pflege durchzusetzen, so gelingt es möglicherweise auch, das neoliberale Reproduktionsmodell zu stabilisieren, die ‚Krise der sozialen Reproduktion‘ zu bearbeiten und eine neue Reproduktionsweise zu verallgemeinern, die nicht mehr länger auf einer weiblich* konnotierten, empathischen und zugewandten Vorstellung von ‚Sorge‘ und ‚Fürsorglichkeit‘ basiert