A Distributed Algorithm for Gathering Many Fat Mobile Robots in the Plane

In this work we consider the problem of gathering autonomous robots in the plane. In particular, we consider non-transparent unit-disc robots (i.e., fat) in an asynchronous setting. Vision is the only mean of coordination. Using a state-machine representation we formulate the gathering problem and develop a distributed algorithm that solves the problem for any number of robots. The main idea behind our algorithm is for the robots to reach a configuration in which all the following hold: (a) The robots' centers form a convex hull in which all robots are on the convex, (b) Each robot can see all other robots, and (c) The configuration is connected, that is, every robot touches another robot and all robots together form a connected formation. We show that starting from any initial configuration, the robots, making only local decisions and coordinate by vision, eventually reach such a configuration and terminate, yielding a solution to the gathering problem.Comment: 39 pages, 5 figure

Foreign Market Entry and Exit Process: the Case of BP Lubricants in Europe and Africa

Foreign market entry strategies are considered critical for organisations looking to expand their operations to other countries abroad, as these require significant commitments, financial and other, which are more often than not, irreversible in the short and medium term. It is not surprising, therefore, that the area of foreign market entry is receiving considerable and growing academic attention over the last twenty years. In fact, the subject of international market entry is the third most researched area in international management, following the related fields of foreign market investments and internationalization. The overall aim of this thesis is to explore, analyse, and understand the foreign market entry and exit process that the business unit of BP Lubricants in Europe and Africa is following and identify strengths and weaknesses. A systematic literature review showed that there is a plethora of empirical evidence on foreign market research that provide useful insights into this important strategic process, however, the findings are often conflicting which makes it difficult to draw conclusions that can be generalized. The review identified the main theories and constructs for foreign market entry and highlighted certain gaps in the theory that the research evidence from this study has aimed to bridge. Using case study methodology and exploring in depth two contrasting cases (the Libyan entry and the Cyprus exit), the foreign market entry and exit processes within BP Lubricants in Europe and Africa have been established. Collection of evidence was achieved through three different methods, questionnaire, focused interviews, and documentation review. The detailed analysis of the foreign market entry process that BP Lubricants in Europe and Africa follows, has led to the development of a model that describes the process. This model depicts the complex nature of the process and recognises that a number of variables play an important role in the decision making process

New Constructions for Quantum Money

We propose an information theoretically secure secret-key quantum money scheme in which the verification of a coin is classical and consists of only one round; namely, a classical query from the user to the bank and an accept/reject answer from the bank to the user. A coin can be verified polynomially (on the number of its qubits) many times before it expires. Our scheme is an improvement on Gavinsky\u27s scheme [Gavinsky, Computational Complexity, 2012], where three rounds of interaction are needed and is based on the notion of quantum retrieval games. Moreover, we propose a public-key quantum money scheme which uses one-time memories as a building block and is computationally secure in the random oracle model. This construction is derived naturally from our secret-key scheme using the fact that one-time memories are a special case of quantum retrieval games

Unclonable Secret Keys

We propose a novel concept of securing cryptographic keys which we call “Unclonable Secret Keys,” where any cryptographic object is modified so that its secret key is an unclonable quantum bit-string whereas all other parameters such as messages, public keys, ciphertexts, signatures, etc., remain classical. We study this model in the authentication and encryption setting giving a plethora of definitions and positive results as well as several applications that are impossible in a purely classical setting. In the authentication setting, we define the notion of one-shot signatures, a fundamental element in building unclonable keys, where the signing key not only is unclonable, but also is restricted to signing only one message even in the paradoxical scenario where it is generated dishonestly. We propose a construction relative to a classical oracle and prove its unconditional security. Moreover, we provide numerous applications including a signature scheme where an adversary can sign as many messages as it wants and yet it cannot generate two signing keys for the same public key. We show that one-shot signatures are sufficient to build a proof-of-work-based decentralized cryptocurrency with several ideal properties: it does not make use of a blockchain, it allows sending money over insecure classical channels and it admits several smart contracts. Moreover, we demonstrate that a weaker version of one-shot signatures, namely privately verifiable tokens for signatures, are sufficient to reduce any classically queried stateful oracle to a stateless one. This effectively eliminates, in a provable manner, resetting attacks to hardware devices (modeled as oracles). In the encryption setting, we study different forms of unclonable decryption keys. We give constructions that vary on their security guarantees and their flexibility. We start with the simplest setting of secret key encryption with honestly generated keys and show that it exists in the quantum random oracle model. We provide a range of extensions, such as public key encryption with dishonestly generated keys, predicate encryption, broadcast encryption and more

Contribution of Ref(2)p to regulation of Drosophila notum epithelial cell apico-basal polarity and phenotype

Cell polarity impacts on the maintenance of cell shape, cell-cell junction integrity, and protrusion formation and dynamics. Further, polarity additionally regulates cell movement, proliferation and differentiation. Conversely when cells lose their polarity they may be susceptible to dysfunction that may underlie degenerative disorders. Cell polarity and polarity protein complexes are highly conserved between different organisms from unicellular to multi-cellular, and from invertebrates to vertebrates. The focus of this study is the apico-basal polarity that is established normally in epithelial cells. p62 is a multifunctional scaffold protein which acts as a signalling hub for different pathways, and through interactions with the polarity protein aPKC we hypothesise that it may regulate apico-basal polarity. Ref(2)p is the Drosophila homologue of p62 and using Drosophila as a model system we are investigating the effects of Ref(2)p mutation or expression levels on apico-basal polarity, cell shape and protrusion dynamics in the epithelial cells of the dorsal thorax. Our preliminary data suggest that Ref(2)p is required to maintain normal cell size, cell-cell junctions and protrusion dynamics. Mechanistically, these phenotypes may be due to Ref(2)p’s interaction with polarity proteins or broader changes in Ref(2)p-mediated autophagy