Universal Lyndon Words

A word $w$ over an alphabet $\Sigma$ is a Lyndon word if there exists an order defined on $\Sigma$ for which $w$ is lexicographically smaller than all of its conjugates (other than itself). We introduce and study \emph{universal Lyndon words}, which are words over an $n$-letter alphabet that have length $n!$ and such that all the conjugates are Lyndon words. We show that universal Lyndon words exist for every $n$ and exhibit combinatorial and structural properties of these words. We then define particular prefix codes, which we call Hamiltonian lex-codes, and show that every Hamiltonian lex-code is in bijection with the set of the shortest unrepeated prefixes of the conjugates of a universal Lyndon word. This allows us to give an algorithm for constructing all the universal Lyndon words.Comment: To appear in the proceedings of MFCS 201

The complexity of 3-colouring H-colourable graphs.

We study the complexity of approximation on satisfiable instances for graph homomorphism problems. For a fixed graph $H$, the $H$-colouring problem is to decide whether a given graph has a homomorphism to $H$. By a result of Hell and Ne\v{s}et\v{r}il, this problem is NP-hard for any non-bipartite graph $H$. In the context of promise constraint satisfaction problems, Brakensiek and Guruswami conjectured that this hardness result extends to promise graph homomorphism as follows: fix any non-bipartite graph $H$ and another graph $G$ with a homomorphism from $H$ to $G$, it is NP-hard to find a homomorphism to $G$ from a given $H$-colourable graph. Arguably, the two most important special cases of this conjecture are when $H$ is fixed to be the complete graph on 3 vertices (and $G$ is any graph with a triangle) and when $G$ is the complete graph on 3 vertices (and $H$ is any 3-colourable graph). The former case is equivalent to the notoriously difficult approximate graph colouring problem. In this paper, we confirm the Brakensiek-Guruswami conjecture for the latter case. Our proofs rely on a novel combination of the universal-algebraic approach to promise constraint satisfaction, that was recently developed by Barto, Bul\'in and the authors, with some ideas from algebraic topology.Comment: To appear in FOCS 201

Parallelisation Technique for Serial 3D Seismic Codes: SMS Approach

We investigate a fast and easy way to parallelise seismological serial codes mainly oriented for simulating the seismic wave propagation through anelastic dissipative media. Having an efficient modelling tool is important in both assessing strong ground motion and mitigation of seismic hazard when the site effects are considered, and in crustal propagation when the crustal geological structures are of interest. Our chosen case study is repre- sentative of a set of such seismological 3D problems. The Scalable Modelling System (SMS) tool for paralleliza- tion is considered. The IBM SP5 native compiler has been used. Results such as Speed-Up and Efficiency are shown and discussed. SMS can run both in shared and distributed memory environments. The greater advantages of using SMS in such environments become apparent with the utilisation of a higher number of multiprocessor machines arranged in a cluster. We also demonstrate how successful porting from serial to parallel codes is re- alised by way of minimal instructions (6% of the serial original code only) provided that an ad hoc profiling analysis of the serial code is first performed

Local site effects in Ataköy, Istanbul, Turkey, due to a future large earthquake in the Marmara Sea

Since the 1999 Izmit and Düzce earthquakes in northwest Turkey, many seismic hazard studies have focused on the city of Istanbul. An important issue in this respect is local site effects: strong amplifications are expected at a number of locations due to the local geological conditions. In this study we estimate the local site effects in the Ataköy area (southwestern Istanbul) by applying several techniques using synthetic data (hybrid 3-D modelling and 1-D modelling) and comparing to empirical data. We apply a hybrid 3-D finite-difference method that combines a complex source and wave propagation for a regional 1-D velocity model with site effects calculated for a local 3-D velocity structure. The local velocity model is built from geological, geotechnical and geomorphological data. The results indicate that strongest spectral amplifications (SA) in the Ataköy area occur around 1 Hz and that amplification levels are largest for alluvial sites where SA reaching a factor of 1.5-2 can be expected in the case of a large earthquake. We also compare our results to H/V (horizontal to vertical component of the recorded signal) spectral ratios calculated for microtremor data recorded at 30 sites as well as to ambient noise synthetics simulated using a 1-D approach. Because the applied methods complement each other, they provide comprehensive and reliable information about the local site effects in Ataköy. Added to that, our results have significant implications for the southwestern parts of Istanbul built on similar geological formations, for which, therefore, similar SA levels are expecte

Robust algorithms with polynomial loss for near-unanimity CSPs

An instance of the Constraint Satisfaction Problem (CSP) is given by a family of constraints on overlapping sets of variables, and the goal is to assign values from a xed domain to the variables so that all constraints are satised. In the optimization version, the goal is to maximize the number of satised constraints. An approximation algorithm for CSP is called robust if it outputs an assignment satisfying an (1????g("))-fraction of constraints on any (1????")-satisable instance, where the loss function g is such that g(") ! 0 as " ! 0. We study how the robust approximability of CSPs depends on the set of constraint relations allowed in instances, the so-called constraint language. All constraint languages admitting a robust polynomial-time algorithm (with some g) have been characterised by Barto and Kozik, with the general bound on the loss g being doubly exponential, specically g(") = O((log log(1="))= log(1=")). It is natural to ask when a better loss can be achieved: in particular, polynomial loss g(") = O("1=k) for some constant k. In this paper, we consider CSPs with a constraint language having a nearunanimity polymorphism. This general condition almost matches a known necessary condition for having a robust algorithm with polynomial loss. We give two randomized robust algorithms with polynomial loss for such CSPs: one works for any near-unanimity polymorphism and the parameter k in the loss depends on the size of the domain and the arity of the relations in ????, while the other works for a special ternary near-unanimity operation called dual discriminator with k = 2 for any domain size. In the latter case, the CSP is a common generalisation of Unique Games with a xed domain and 2-Sat. In the former case, we use the algebraic approach to the CSP. Both cases use the standard semidenite programming relaxation for CSP

The earthquake of 250 a.d. in Augusta Raurica, A real event with a 3D site-effect?

The Roman city Augusta Raurica is located East of Basel, Switzerland. One important topic of the city's history concerns the hypothesis of an earthquake striking the city in the middle of the third century a.d. This idea had been formulated according to archaeological features and findings, but had not been tested so far. A selection of the archaeological features were reviewed and dated in order to test the hypothesis of a single event. However, archaeological investigations do not draw a conclusive picture; it could not be proven that all features of possible destruction date to the same event. Detailed seismological investigations were performed. These included geological and geotechnical mapping of the unconsolidated sediments. Important parameters such as the thickness and composition of the unconsolidated sediments, the terrain topography and the topography of the bedrock surface were mapped. Ambient vibration H/V measurements provided the fundamental frequency of resonance for the unconsolidated sediments. The velocity of shear waves traveling through sediments is the controlling parameter for amplification of seismic waves. This material property is estimated using the relation between the ellipticity of the fundamental mode Rayleigh wave and the H/V curve. From all information we compiled a three-dimensional model of the surface geology. This model is used to simulate earthquake ground motion and amplification effects in the city, and to map the variability of the amplification. In the part of the city where possible earthquake damage was recognized, amplification occurs in the frequency band of building resonance (2-8Hz). In the other part of the city amplification occurs much above the building's resonance. From 1D modelling we estimate a difference in spectral amplification of about a factor of 2.5 to 3 between the two parts of the city. This corresponds approximately to a difference in macroseismic intensity of one unit. 3D modelling showed a large variability of ground motion within very close distance in the part of the city where possible earthquake damage was recognized. The maximum amplification reaches values up to a factor of nine, which is due to 3D effects and the choice of using vertically incident waves. Finally, all paleoseismological findings in the area of Basel were reviewed in order to find indications of a large event in the time-period of interest. Paleoseismological findings provide no hints to a large earthquake in the third century. If we assume that an earthquake caused at least part of the identified damage in Augusta Raurica, we have to assign to this event a magnitude Mw of about 6.0 or even lower, that is much smaller than the value of 6.9 that is actually in the Swiss earthquake catalogue. The earthquake source of this event must then be very close to the site of Augusta Raurica and a strong site-effect occurred in one part of the cit

Analysis of Socioeconomic Impacts of the FSC and PEFC Certification Systems on Business Entities and Consumers

The article discusses the issues of effectiveness of the FSC (Forest Stewardship Council) and PEFC (Programme for the Endorsement of Forest Certification) certification systems in relation to enterprises and the level to which the systems which present sustainability as a part of their ethos are accepted by consumers. The justifiability and topicality of this issue result from the increasingly strong interest in sustainability of the society as a whole as well as from the long-term vision of sector policies with respect to meeting the objectives of sustainable development. The increasing demand for natural resources exerts pressure on our planet. Sustainability is hence essential for our future and has long been in the centre of the European project. Its economic, social and environmental aspects which form the common objective of society have been acknowledged in EU agreements. A principal document of a global nature is the 2030 UN Agenda for Development, a sustainability programme which has the sustainability of forest ecosystems established in its Goal 15: Protect, restore and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss. Visions, direction and goals of sustainable development have also been stipulated in the Paris Agreement on climate change (COP21), in the Addis Ababa action programme and in The Future We Want declaration, namely in its Chapter II, which appeals to enterprises and industries for developing strategies which would contribute to sustainable development. This study aims to analyse and assess the justifiability of the existence of certification systems in relation to processing operators and end consumers in the Czech Republic. From the results of the study, it can be concluded that, despite the strong representation of selected certification systems in the Czech Republic, their effectiveness in economic, social and environmental terms is not perceived exclusively positive by businesses and consumers.O

Hybrid modeling of seismic waves

Available from STL Prague, CZ / NTK - National Technical LibrarySIGLECZCzech Republi

Transactional replication in a .NET environment

Zsfassung in dt. SpracheReplikation als wichtiger Mechanismus in Erzielung von Zuverlässigkeit verteilter Systeme ist bereits umfangreicher Forschung unterlegt gewesen.Verschiedene Ansätze die Erreichbarkeit während Systemdegradation (z.B.Netzwerktrennung) zu verbessern haben sich traditionell auf pessimistische Replikationsprotokolle konzentriert, welche Update-konflikte während Degradation vermeiden. Vor kurzem wurde eine neue Klasse an optimistischen Replikationsprotokollen vorgestellt, die weniger restriktiv als pessimistische Protokolle ist und die es erlaubt, Erreichbarkeit und Konsistenz eines Systems auszubalancieren. Es können handelbare und nicht-handelbare Konsistenzbedingungen im System definiert werden, wobei die ersten während Systemdegradation gegen Erreichbarkeit gehandelt werden können.Active Replication Per Partition Protocol (ARPPP) ist ein konkretes Replikationsprotokoll, das diese Balancierung anwendet. Es ist eine Modifikation der klassischen aktiven Replikation. In einem gesunden System fordert ARPPP strenge Konsistenz, also erlaubt keine Operation, die gegen eine beliebige Konsistenzbedingung stoßt. Im Falle eines Knotenausfalls oder einer Netzwerktrennung werden vorübergehend alle handelbaren Konsistenzbedingungen von ARPPP aufgehoben und somit alle Operationen, die keine nicht-handelbaren Bedingungen betreffen, erlaubt, auch wenn die handelbaren Bedingungen verletzt werden können. Nachdem das Netzwerk sowie alle Systemknoten heilen, wird strenge Konsistenz im System - während sogenannter Rekonciliation - wiederhergestellt.Die Kontribution dieser Arbeit ist die Prototypimplementierung und -evaluierung des ARPPP Replikationsprotokolls unter Microsoft .NET in der C# Programmiersprache. Basierend auf Eigenschaften des .NET Frameworks 2.0, unterstützt der Prototyp sowohl Transaktionen, als auch geschachtelte Replikaaufrufe.Die Ergebnisse der Evaluierung indizieren, dass der zusätzliche Bedarf an Überprüfen von Konsistenzbedingungen nicht nur einen höheren Aufwand mit sich bringt, sondern auch die Ursache für öftere Transaktionsabbrüche bei manchen gleichlaufenden Operationen ist. Dies ist jedoch das erwartete Verhalten, das auf den Bedarf einer sorgfältigen Definition von Konsistenzbedingungen in jeder Applikation verweist.Replication as an important mechanism in achieving dependability of distributed systems has already been subject to extensive research.Approaches to improve availability in degraded situations (e.g. network partitions) traditionally focus on pessimistic replication protocols, which prevent update conflicts during degradation. Recently, a novel class of optimistic replication protocols has been introduced, which are less restrictive than pessimistic protocols and allow trading consistency against availability. Tradeable and non-tradeable constraints can be defined in the system, while the former will be traded against availability during degradation.The Active Replication Per Partition Protocol (ARPPP) is one concrete protocol applying this trade-off. It is a modification of the standard active replication scheme. In a healthy system, the ARPPP enforces strict constraint consistency and thus does not allow operations violating any of the constraints defined in the system. In case of node failures or network partitions, the ARPPP temporarily relaxes tradeable constraints and allows all operations not affecting non-tradeable constraints, even though tradeable constraints might become violated. After the network and all nodes recover from failures, strict constraint consistency must be reestablished in a process called reconciliation.The contribution of this thesis is a prototype implementation and evaluation of the ARPPP in the Microsoft .NET environment using the C# programming language. Based on the features of the .NET Framework 2.0, the prototype provides full transaction support and allows nested replica calls as well.Evaluation results indicate, that the additional necessity of constraint checking not only causes additional overhead and thus decreases performance, but in some cases also imposes higher transaction abort rates of concurrent operations. This is, however, expected behaviour, that admonishes to a careful constraint definition at application development time.7