Coherent Spaces Research Articles

Anthropocene Crisis: Climate Change, Pollinators, and Food Security

In this paper, we propose a new approach—understood as a whole-of-community approach—to address a dualistic and dysfunctional human/nature relationship. Of particular concern is the decline in health and numbers of the insects that pollinate an estimated 90 percent of the Earth’s flora and an estimated 35 percent of global crop volume. Specifically, bees provide the majority of biotic pollination and play a critical role in food crop pollination. Multiple factors are contributing to this growing problem including a changing climate. In 2016, the International Commission on Stratigraphy agreed that the concept of the Anthropocene—the human epoch—is of sufficient scale to be considered part of the geological time scale. This indicates that these crises are not random or passive—they are largely the direct result of human activities. Despite decades of awareness of these socio-ecological issues, they continue to worsen. In addition, the growing awareness of the critical role of pollinators is creating a new understanding of our interconnectedness with the “natural” world. We introduce the Bee City movement as a way to operationalize a whole-of-community approach. Individual action is critical, but addressing pollinator health in these forums legitimizes and provides an institutional space for otherwise fringe, or even marginalized, activities and more coherent spaces for habitat creation.

Full Abstraction for Probabilistic PCF

We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-by-name, we allow a call-by-value evaluation for ground-type arguments to provide the language with a suitable algorithmic expressiveness. We describe a denotational semantics based on probabilistic coherence spaces, a model of classical Linear Logic developed in previous works. We prove an adequacy and an equational full abstraction theorem showing that equality in the model coincides with a natural notion of observational equivalence.

Potenziale städtischer Gewerbebrachflächen für eine integrierte Stadtentwicklung

Urban brownfields have been an internationally recognised topic for many years and exist in industrialised countries worldwide. After decades of severe shrinkage, Leipzig, Germany, is now a fast-growing city. It serves as an excellent example to discuss the redevelopment of urban brownfields for an integrated urban development. We investigate the potentials of brownfields through land-use monitoring. In our field work, we mapped 783 brownfields in all of the city's commercial zones, including size, geographic position and spatial assignment, land surface characteristics and surrounding infrastructure. Spatial distribution of brownfields in the planning districts as well as land-use pat- terns was of great concern regarding vegetation succession stages and sealed surfaces. Infrared aerial colour photos supported our field information, gathered in a GIS-based information tool of urban districts for the planning division. More than 80% of all derelict land is less than one hectare in size and thus a major challenge in terms of individual recycling. Private ownership hampers redevelopment. Due to advanced succession stages there is a high potential for renaturalisation into coherent green spaces. Pressures on land use demand the readjustment of green infrastructure development in an urban planning masterplan. The project is based on scientific collaboration with the City of Leipzig's Authority of Urban Planning, Germany.English title: Potential Performance of Commercial Urban Brownfield Sites in Integrated Urban Development – Monitoring for Sustain- able Land-Use Management Based on the Ex- ample of the City of Leipzig

On Banach spaces of sequences and free linear logic exponential modality

We introduce a category of vector spaces modelling full propositional linear logic, similar to probabilistic coherence spaces and to Koethe sequences spaces. Its objects are rigged sequence spaces, Banach spaces of sequences, with norms defined from pairing with finite sequences, and morphisms are bounded linear maps, continuous in a suitable topology. The main interest of the work is that our model gives a realization of the free linear logic exponentials construction.

An explicit formula for the free exponential modality of linear logic

The exponential modality of linear logic associates to every formula A a commutative comonoid !A which can be duplicated in the course of reasoning. Here, we explain how to compute the free commutative comonoid !A as a sequential limit of equalizers in any symmetric monoidal category where this sequential limit exists and commutes with the tensor product. We apply this general recipe to a series of models of linear logic, typically based on coherence spaces, Conway games and finiteness spaces. This algebraic description unifies for the first time a number of apparently different constructions of the exponential modality in spaces and games. It also sheds light on the duplication policy of linear logic, and its interaction with classical duality and double negation completion.

Coherent spaces, Boolean rings and quantum gates

Coherent spaces spanned by a finite number of coherent states, are introduced. Their coherence properties are studied, using the Dirac contour representation. It is shown that the corresponding projectors resolve the identity, and that they transform into projectors of the same type, under displacement transformations, and also under time evolution. The set of these spaces, with the logical OR and AND operations is a distributive lattice, and with the logical XOR and AND operations is a Boolean ring (Stone’s formalism). Applications of this Boolean ring into classical CNOT gates with n-ary variables, and also quantum CNOT gates with coherent states, are discussed.

Function spaces from coherent continuous domains to RB-domains

In this paper, continuing the work of the first and third authors, we study the function spaces from coherent continuous domains to RB-domains. Firstly, we prove that the function spaces from coherent core compact spaces with compact open sets as a basis to bifinite domains (algebraic RB-domains) are algebraic. As an application, we give an example which shows that a function space from a coherent quasi-algebraic domain to a finite domain might not be coherent. Finally, we show that the function space from a coherent continuous domain to an RB-domain is an RB-domain. Particularly, a function space from an FS-domain (introduced by Achim Jung) to an RB-domain is an RB-domain. This addresses an old open problem of whether FS-domains are RB-domains.

Parameter-space metric for all-sky semicoherent searches for gravitational-wave pulsars

The sensitivity of all-sky searches for gravitational-wave pulsars is primarily limited by the finite availability of computing resources. Semicoherent searches are a widely-used method of maximizing sensitivity to gravitational-wave pulsars at fixed computing cost: the data from a gravitational-wave detector are partitioned into a number of segments, each segment is coherently analyzed, and the analysis results from each segment are summed together. The generation of template banks for the coherent analysis of each segment, and for the summation, requires knowledge of the metrics associated with the coherent and semicoherent parameter spaces respectively. We present a useful approximation to the semicoherent parameter-space metric, analogous to that presented in Wette and Prix [Phys. Rev. D 88, 123005 (2013)] for the coherent metric. The new semicoherent metric is compared to previous work in Pletsch [Phys. Rev. D 82, 042002 (2010)], and Brady and Creighton [Phys. Rev. D 61, 082001 (2000)]. We find that semicoherent all-sky searches require orders of magnitude more templates than previously predicted.

Kinship verification in multi-linear coherent spaces

Discovering kinship relations from face images in the wild has become an interesting and important problem in multimedia and computer vision. Despite the rapid advances in face analysis in unconstr...

Suburban Processes of Islandisation in Austria: The Cases of Vienna and Tyrol

Suburban areas are often described as monotonous and generic. In Europe, however, suburban areas show distinct morphological and functional configurations in different regions due to cultural, spatial, economic, and institutional conditions. This paper compares recent suburban developments in Austria in the region south of Vienna and in the region of Tyrol, highlighting significant developments after 1985 in the fields of housing, shopping, leisure, and commercial sites. Using quantitative (aerial images, statistical data, plans) and qualitative (case studies) methods, the paper analyses the distinct morphological similarities of selected case studies and tries to answer two questions. First, how can these developments be assessed from the viewpoint of urban and spatial planning? Second, what spatial strategies could be useful for further interventions? It is concluded that these developments can be understood as island-like developments. This means that hybrid suburban structures have appeared where sharp-edged boundaries separate single elements from adjacent ones. These island-like developments have increased dramatically over the past decades and are today to a large extent characteristic of Austrian suburbs. Capitalism, market liberalisation, and prevailing planning regulations and culture are driving these processes of islandisation. The paper furthermore shows that new spatial strategies are required for creating more coherent spaces. Interstitial landscape as a planning tool seems to be one option for creating more livable and sustainable suburban areas in the future.

Generalized Laplacian eigenmaps for modeling and tracking human motions.

This paper presents generalized Laplacian eigenmaps, a novel dimensionality reduction approach designed to address stylistic variations in time series. It generates compact and coherent continuous spaces whose geometry is data-driven. This paper also introduces graph-based particle filter, a novel methodology conceived for efficient tracking in low dimensional space derived from a spectral dimensionality reduction method. Its strengths are a propagation scheme, which facilitates the prediction in time and style, and a noise model coherent with the manifold, which prevents divergence, and increases robustness. Experiments show that a combination of both techniques achieves state-of-the-art performance for human pose tracking in underconstrained scenarios.

Individual stakes and collective ideology in tension: Looking at physical and spatial obstacles from an experiential perspective

This paper presents a critical hermeneutic interpretation of the meanings, practices and values associated with physical and spatial obstacles present in the shopping experiences of individuals with mobility or visual impairments. The social model of disability, which positions disablement in societal attitudes, understandings, practices, and institutions, has reinforced a view that built environments tend to limit, restrict, segregate, and even oppress differently-abled individuals. Despite the pervasiveness of this view, little research has empirically explored the experiences of, responses to, or evaluations of environmental barriers. In the current study, we interviewed and observed four individuals with visual impairments and four individuals with mobility impairments in hopes of better understanding these topics within a shopping context. Reconstructing participants’ discourses into their implicit narrative structures, we found that participants generally re-established equilibrium in their emplotted encounters with obstacles in the mall, transfiguring challenging and dysfunctional environments into coherent and functional spaces. Our findings challenge the notion that the constructions, meanings, and values of physical and spatial obstacles are universal or intrinsic, and point to the agency of participants in shaping their own plots. We suggest that future research ought to examine physical and spatial obstacles within even broader frameworks of meaning.

Probabilistic coherence spaces are fully abstract for probabilistic PCF

Probabilistic coherence spaces (PCoh) yield a semantics of higher-order probabilistic computation, interpreting types as convex sets and programs as power series. We prove that the equality of interpretations in Pcoh characterizes the operational indistinguishability of programs in PCF with a random primitive. This is the first result of full abstraction for a semantics of probabilistic PCF. The key ingredient relies on the regularity of power series. Along the way to the theorem, we design a weighted intersection type assignment system giving a logical presentation of PCoh.

Modeling linear logic with implicit functions

Just as intuitionistic proofs can be modeled by functions, linear logic proofs, being symmetric in the inputs and outputs, can be modeled by relations (for example, cliques in coherence spaces). However generic relations do not establish any functional dependence between the arguments, and therefore it is questionable whether they can be thought as reasonable generalizations of functions. On the other hand, in some situations (typically in differential calculus) one can speak in some precise sense about an implicit functional dependence defined by a relation. It turns out that it is possible to model linear logic with implicit functions rather than general relations, an adequate language for such a semantics being (elementary) differential calculus. This results in a non-degenerate model enjoying quite strong completeness properties.

Formal Ontologies and Coherent Spaces

The paper contains a short summary – oriented by a logical point of view – of a joint work on Formal Ontologies. We shall show how Formal Ontologies correspond to Coherent Spaces, and operations on Formal Ontologies correspond to operations on corresponding Coherent Spaces. So, we are offering a new way to establish the semantics of Formal Ontologies. Surely, we are giving a contribution towards a geometrical treatment of Formal Ontologies (as decidable organizations of digital data).

Robust Interactive Collision Handling between Tools and Thin Volumetric Objects

Treating the interactions of soft tissue with rigid user-guided tools is a difficult problem. This is particularly true if the soft tissue has a slender shape, i.e., resembling a thin shell, and if the underlying numerical time-integration scheme employs large time steps. In this case, large mutual displacements of both the tool and the soft tissue occur frequently, resulting in deep interpenetrations or breakthroughs. As a consequence, the computation of spatially and temporally coherent contact spaces turns out to be very challenging. In this paper, an approach is proposed that is tailored to these kinds of interactions. To solve this problem, a novel spatially reduced representation of the soft tissue geometry is employed where the dominant dimensions of the object are approximated by a 2D triangle surface, while the third dimension is given in terms of nodal radii. To construct a feasible, nonpenetrating configuration, a novel manifold projection scheme is presented where the colliding triangles are rasterized into a distance field in order to robustly estimate the contact spaces, even for large intersections. The method produces physically plausible results, albeit it is purely geometric, and the material parameters are neglected at the collision response stage. Various examples, including an interactive prototype arthroscopy simulator, underline the wide applicability of the approach.

What is a model for a semantically linear -calculus?

This paper is about a categorical approach to model a simple term calculus, named S�λ - calculus. This is the core calculus underlying the programming language SPCF that have been conceived in order to program only linear functions between Coherence Spaces. In this work, we introduce the notion of S�λ -category, which is able to describe a large class of sound models of S�λ -calculus. S�λ -category extends in the natural way Benton, Bierman, Hyland and de Paiva's Linear Category. We will define two interpretations of S�λ -calculus types and terms into objects and morphisms of S�λ -categories: the first one is a generalization of the translation given in (18) but lacks in completeness; the second one uses the comonadic properties of ! to recover completeness. Finally, we show that this notion is general enough to catch interesting models in Scott Domains and Coherence Spaces.

Coherent and finiteness spaces

This short note presents a new relation between coherent spaces and finiteness spaces. This takes the form of a functor from COH to FIN commuting with the additive and multiplicative structure of linear logic. What makes this correspondence possible and conceptually interesting is the use of the infinite Ramsey theorem. Along the way, the question of the cardinality of the collection of finiteness spaces on N is answered. Basic knowledge about coherent spaces and finiteness spaces is assumed.

Linearity and PCF

Linearity is a multi-faceted and ubiquitous notion in the analysis and the development of programming language concepts. We study linearity in a denotational perspective by picking out programs that correspond to linear functions between coherence spaces. We introduce a language, named Sl PCF * , that increases the higher-order expressivity of a linear core of PCF by means of new operators related to exception handling and parallel evaluation. Sl PCF * allows us to program all the finite elements of the model and, consequently, it entails a full abstraction result that makes the reasoning on the equivalence between programs simpler. Denotational linearity provides also crucial information for the operational evaluation of programs. We formalize two evaluation machineries for the language. The first one is an abstract and concise operational semantics designed with the aim of explaining the new operators, and is based on an infinite-branching search of the evaluation space. The second one is more concrete and it prunes such a space, by exploiting the linear assumptions. This can also be regarded as a base for an implementation.

Probabilistic coherence spaces as a model of higher-order probabilistic computation

We study a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambda-calculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type. Last we suggest a generalization of this approach, using Banach spaces.