The Clifford group, stabilizer states, and linear and quadratic operations over GF(2)

We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of a (2n+1)x(2n+1) binary matrix product and binary quadratic forms. As an application we give two schemes to efficiently decompose Clifford group operations into one and two-qubit operations. We also show how the coefficients of stabilizer states and Clifford group operations in a standard basis expansion can be described by binary quadratic forms. Our results are useful for quantum error correction, entanglement distillation and possibly quantum computing.Comment: 9 page

Portfolio Selection in Incomplete Markets with Utility Maximisation

The problem of maximizing the expected utility is well understood in the context of a complete financial market. This dissertation studies the same problem in an arbitrage-free yet incomplete market. Jin and Zhou have characterized the set of the terminal wealths that can be replicated by admissible portfolios. The problem is then transformed into a static optimization problem. It is proved that the terminal wealth is attainable for all utility functions when the market parameters are deterministic. The optimal portfolio is obtained explicitly when the utility function is logarithmic even if the market parameters follow stochastic processes. However we do not succeed in extending this result to the power utility function

The prefigurative power of urban political agroecology: rethinking the urbanisms of agroecological transitions for food system transformation

In recent years, urban contexts and urban-rural linkages have become central for scholars and activists engaged in agrarian questions, agroecological transitions and food system transformation. Grassroots experimentations in urban agroecology and farmers' engagement with urban policies have marked the rise of a new agenda aiming to bridge urban and agrarian movements. Departing from the work of Eric Holt-Gimenez and Annie Shattuck, this paper argues that the way urban-rural links have been conceptualized is occasionally progressive, and that an agroecology-informed food system transformation needs radical approaches. Acknowledging that processes of urbanization are dynamic, driven by specific lifestyles, consumption patterns, and value orientations - producing ongoing suburbanization, land enclosures, farmers displacement and food-knowledge loss - the paper argues that thinking transitions through new rural-urban links is unfit to tackle the evolving nature of these geographies, and reproduces the distinction between consumers and producers, living on either side of what Mindi Schneider and Philip McMichael have described as an epistemic and ecological rift. Building on insights from four case-studies across global north and south, the paper reframes agroecological transitions as a paradigmatic change in biopolitical spatial relations, economic values and planning agency - what we call an 'agroecological urbanism'. The paper articulates a transformation agenda addressing urban nutrients, peri-urban landuse, community food pedagogies and farmers' infrastructure

Unbounded urbanization and the Horizontal Metropolis : the pragmatic program of August Mennes in the Antwerp agglomeration

Parallel to many discussions in other European cities, the debate on a metropolitan Antwerp emerged at the turn of the 20th century, following the decision to tear down the old ramparts around the city in 1904. Once boundless, the old core became for the first time the subject of a contiguous urban expansion at its very fringes. Soon, however, far more loose urbanization processes would wash over the land as the urban territories rapidly expanded beyond what was at first imagined. By consequence, the face of the future Antwerp metropolis would be shaped by a series of interlocking and unbounded urbanization processes. Tracing the interrelated endeavors of the key parties that helped shaping these urbanization processes, ranging from property tycoons, technocrats and architects to key figures in the political world, my PhD research aims at rendering the contours of a long history of the construction of Antwerp’s twentieth century belt within which the notions of urbanism and urbanization are blurred. Through an eclectic catalogue of five ‘urban questions’, this paper investigates the various ways in which the process of territorial rescaling set in motion in 1904 coproduced the features of today’s horizontal metropolis. Based on the activities of engineer August Mennes, the paper will try to conclude that the Antwerp Horizontal Metropolis surfaced as the result of a juxtaposition of urbanization techniques that question and transcend the interpretation of ‘urbanization’ as a process of random and speculative accumulation

Bounding errors of Expectation-Propagation

Expectation Propagation is a very popular algorithm for variational inference, but comes with few theoretical guarantees. In this article, we prove that the approximation errors made by EP can be bounded. Our bounds have an asymptotic interpretation in the number $n$ of datapoints, which allows us to study EP's convergence with respect to the true posterior. In particular, we show that EP converges at a rate of $\mathcal{0}(n^{-2})$ for the mean, up to an order of magnitude faster than the traditional Gaussian approximation at the mode. We also give similar asymptotic expansions for moments of order 2 to 4, as well as excess Kullback-Leibler cost (defined as the additional KL cost incurred by using EP rather than the ideal Gaussian approximation). All these expansions highlight the superior convergence properties of EP. Our approach for deriving those results is likely applicable to many similar approximate inference methods. In addition, we introduce bounds on the moments of log-concave distributions that may be of independent interest.Comment: Accepted and published at NIPS 201

Collective learning experiences in planning: the potential of experimental living labs

‘Living labs’ originate from an R&D environment, and intend to innovate commodities by experience-based knowledge, with a direct involvement of users. Meanwhile, the living labs approach has been shifting into a wider range of applications, and has also ended up in the toolbox of actor- and action-oriented planners. The approach is (implicitly) promoted as a new and better way of combining capacities of different stakeholders by exploring and experimenting in realworld situations. In this paper, we attempt to critically discuss the use of the living lab approach. The first section explores the potential thereof for planning issues: How univocal is the concept of Living Labs? How much do different interpretations and practices of Living Labs resemble in terms of actors involved, actions stimulated, processes promoted and criteria for good practices accepted? The exploration is based on the experience of two experimental living labs, which are compared with a range of international examples. The second section turns to a series of alternative approaches in spatial planning in Flanders: How do the aims and means of these collaborative learning experiences differ? What is the role of users and how important is experimentation? What is the innovative contribution to planning (if any)? How do the practices deal with path dependencies and uncertainties in complex multi-actor settings? We will answer these questions based on research seminars on ‘collective learning’, which are organized for the Policy Research Center Spatial Planning in Flanders, as a part of a work-package which focusses on methodologies for future explorations

Obstetrical aspects in congenital ichtyosis

We present a case of congenital ichthyosis because obstetrical literature is scarce and most obstetricians could need a reminder and update. Congenital ichthyosis (CI) comprises a variety of skin disorders characterised by abnormal keratinization of the epidermis, which are mostly transmitted in an autosomal recessive manner. This condition is rare (seven per million people) with various clinical neonatal expressions and diversified prognosis, from self-healing to lethal. Even less severe phenotypes have significant associated morbidity and mortality. CI babies are often born prematurely and are at highest risk for complications during the postnatal period .CI, while fairly rare, is a condition well described in the literature, mainly from the neonatal point of view. We describe a case in which congenital ichthyosis was diagnosed after birth, and summarise the present literature with particular attention on obstetric implications as the prenatal diagnosis, genetic and ultrasound testing, perinatal complications and care for future pregnancies