Post-Brexit implications for transboundary groundwater management along the Northern Ireland and the Republic of Ireland border

There are multiple transboundary groundwater bodies shared between Northern Ireland and the Republic of Ireland that are currently managed jointly through the EU Water Framework Directive. In 2016 the United Kingdom voted to leave the European Union and consequently, there are uncertainties regarding the future status of groundwater management between Northern Ireland and the Republic of Ireland in regards to future UK environmental policy. This paper explores the post 'Brexit' transboundary groundwater implications, if a transboundary groundwater agreement is required between Northern Ireland and the Republic of Ireland, and, should it transpire, what form should it take

Optimal non-perfect uniform secret sharing schemes

A secret sharing scheme is non-perfect if some subsets of participants that cannot recover the secret value have partial information about it. The information ratio of a secret sharing scheme is the ratio between the maximum length of the shares and the length of the secret. This work is dedicated to the search of bounds on the information ratio of non-perfect secret sharing schemes. To this end, we extend the known connections between polymatroids and perfect secret sharing schemes to the non-perfect case. In order to study non-perfect secret sharing schemes in all generality, we describe their structure through their access function, a real function that measures the amount of information that every subset of participants obtains about the secret value. We prove that there exists a secret sharing scheme for every access function. Uniform access functions, that is, the ones whose values depend only on the number of participants, generalize the threshold access structures. Our main result is to determine the optimal information ratio of the uniform access functions. Moreover, we present a construction of linear secret sharing schemes with optimal information ratio for the rational uniform access functions.Peer ReviewedPostprint (author's final draft

What is the topology of a Schwarzschild black hole?

We investigate the topology of Schwarzschild's black hole through the immersion of this space-time in spaces of higher dimension. Through the immersions of Kasner and Fronsdal we calculate the extension of the Schwarzschild's black hole.Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1102.446

Ideal hierarchical secret sharing schemes

Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft

The complications of ‘hiring a hubby’: gender relations and the commoditisation of home maintenance in New Zealand

This paper examines the commoditization of traditionally male domestic tasks through interviews with handymen who own franchises in the company ‘Hire a Hubby’ in New Zealand and homeowners who have paid for home repair tasks to be done. Discussions of the commoditization of traditionally female tasks in the home have revealed the emotional conflicts of paying others to care as well as the exploitative and degrading conditions that often arise when work takes place behind closed doors. By examining the working conditions and relationships involved when traditionally male tasks are paid for, this paper raises important questions about the valuing of reproductive labour and the production of gendered identities. The paper argues that while working conditions and rates of pay for ‘hubbies’ are better than those for people undertaking commoditized forms of traditionally female domestic labour, the negotiation of this work is still complex and implicated in gendered relations and identities. Working on the home was described by interviewees as an expression of care for family and a performance of the ‘right’ way to be a ‘Kiwi bloke’ and a father. Paying others to do this labour can imply a failure in a duty of care and in the performance of masculinity

Time evolution and observables in constrained systems

The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework. The existence of reasonable true, or physical, degrees of freedom is rigorously defined and called {\em local reducibility}. A proof is given that any locally reducible system admits a complete set of perennials. For locally reducible systems, the most general construction of time evolution in the Schroedinger and Heisenberg form that uses only geometry of the phase space is described. The time shifts are not required to be 1symmetries. A relation between perennials and observables of the Schroedinger or Heisenberg type results: such observables can be identified with certain classes of perennials and the structure of the classes depends on the time evolution. The time evolution between two non-global transversal surfaces is studied. The problem is posed and solved within the framework of the ordinary quantum mechanics. The resulting non-unitarity is different from that known in the field theory (Hawking effect): state norms need not be preserved so that the system can be lost during the evolution of this kind.Comment: 31 pages, Latex fil

Combinatorial Bounds and Characterizations of Splitting Authentication Codes

We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a combinatorial characterization of optimal splitting authentication codes that are multi-fold secure against spoofing attacks. The characterization is based on a new type of combinatorial designs, which we introduce and for which basic necessary conditions are given regarding their existence.Comment: 13 pages; to appear in "Cryptography and Communications

On the optimization of bipartite secret sharing schemes

Optimizing the ratio between the maximum length of the shares and the length of the secret value in secret sharing schemes for general access structures is an extremely difficult and long-standing open problem. In this paper, we study it for bipartite access structures, in which the set of participants is divided in two parts, and all participants in each part play an equivalent role. We focus on the search of lower bounds by using a special class of polymatroids that is introduced here, the bipartite ones. We present a method based on linear programming to compute, for every given bipartite access structure, the best lower bound that can be obtained by this combinatorial method. In addition, we obtain some general lower bounds that improve the previously known ones, and we construct optimal secret sharing schemes for a family of bipartite access structures.Postprint (author’s final draft

Secure multiparty PageRank algorithm for collaborative fraud detection

Collaboration between financial institutions helps to improve detection of fraud. However, exchange of relevant data between these institutions is often not possible due to privacy constraints and data confidentiality. An important example of relevant data for fraud detection is given by a transaction graph, where the nodes represent bank accounts and the links consist of the transactions between these accounts. Previous works show that features derived from such graphs, like PageRank, can be used to improve fraud detection. However, each institution can only see a part of the whole transaction graph, corresponding to the accounts of its own customers. In this research a new method is described, making use of secure multiparty computation (MPC) techniques, allowing multiple parties to jointly compute the PageRank values of their combined transaction graphs securely, while guaranteeing that each party only learns the PageRank values of its own accounts and nothing about the other transaction graphs. In our experiments this method is applied to graphs containing up to tens of thousands of nodes. The execution time scales linearly with the number of nodes, and the method is highly parallelizable. Secure multiparty PageRank is feasible in a realistic setting with millions of nodes per party by extrapolating the results from our experiments