208 research outputs found
some economic applications of scott domains
The present paper is structured around two main constructions, fixed points of functors and fibrations and sections of functors. Fixed points of functors are utilized to resolve problems of infinite regress that have recently appeared in economics. Fibrations and sections are utilized to model solution concepts abstractly, so that we can solve equations whose arguments are solution concepts. Most of the objects (games, solution concepts) that we consider can be obtained as some kind of limit of their finite subobjects. Some of the constructions preserve computability. The paper relies heavily on recent work on the semantics of program- ming languages.scott domains,infinite regress,game theory
Formal Concept Analysis and Resolution in Algebraic Domains
We relate two formerly independent areas: Formal concept analysis and logic
of domains. We will establish a correspondene between contextual attribute
logic on formal contexts resp. concept lattices and a clausal logic on coherent
algebraic cpos. We show how to identify the notion of formal concept in the
domain theoretic setting. In particular, we show that a special instance of the
resolution rule from the domain logic coincides with the concept closure
operator from formal concept analysis. The results shed light on the use of
contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the
suggestions of some referees. The results are the same. The presentation is
completely differen
Logical Relations for Monadic Types
Logical relations and their generalizations are a fundamental tool in proving
properties of lambda-calculi, e.g., yielding sound principles for observational
equivalence. We propose a natural notion of logical relations able to deal with
the monadic types of Moggi's computational lambda-calculus. The treatment is
categorical, and is based on notions of subsconing, mono factorization systems,
and monad morphisms. Our approach has a number of interesting applications,
including cases for lambda-calculi with non-determinism (where being in logical
relation means being bisimilar), dynamic name creation, and probabilistic
systems.Comment: 83 page
Growing Neural Gas with Different Topologies for 3D Space Perception
Three-dimensional space perception is one of the most important capabilities for an autonomous mobile robot in order to operate a task in an unknown environment adaptively since the autonomous robot needs to detect the target object and estimate the 3D pose of the target object for performing given tasks efficiently. After the 3D point cloud is measured by an RGB-D camera, the autonomous robot needs to reconstruct a structure from the 3D point cloud with color information according to the given tasks since the point cloud is unstructured data. For reconstructing the unstructured point cloud, growing neural gas (GNG) based methods have been utilized in many research studies since GNG can learn the data distribution of the point cloud appropriately. However, the conventional GNG based methods have unsolved problems about the scalability and multi-viewpoint clustering. In this paper, therefore, we propose growing neural gas with different topologies (GNG-DT) as a new topological structure learning method for solving the problems. GNG-DT has multiple topologies of each property, while the conventional GNG method has a single topology of the input vector. In addition, the distance measurement in the winner node selection uses only the position information for preserving the environmental space of the point cloud. Next, we show several experimental results of the proposed method using simulation and RGB-D datasets measured by Kinect. In these experiments, we verified that our proposed method almost outperforms the other methods from the viewpoint of the quantization and clustering errors. Finally, we summarize our proposed method and discuss the future direction on this research
Towards Zero-Waste Furniture Design
In traditional design, shapes are first conceived, and then fabricated. While
this decoupling simplifies the design process, it can result in inefficient
material usage, especially where off-cut pieces are hard to reuse. The
designer, in absence of explicit feedback on material usage remains helpless to
effectively adapt the design -- even though design variabilities exist. In this
paper, we investigate {\em waste minimizing furniture design} wherein based on
the current design, the user is presented with design variations that result in
more effective usage of materials. Technically, we dynamically analyze material
space layout to determine {\em which} parts to change and {\em how}, while
maintaining original design intent specified in the form of design constraints.
We evaluate the approach on simple and complex furniture design scenarios, and
demonstrate effective material usage that is difficult, if not impossible, to
achieve without computational support
On the Representation of Stream Functions in Denotational Domains
We investigate the representation of functions on streams in some denota- tional domains. As expected, a total continuous stream function can always be represented by a Scott-continuous function, and moreover by a strongly stable map in the corresponding Hypercoherence. It seems however difficult to represent an arbitrary stream function by a monotone map on Scott domains such that the stream function is continuous if and only if its representant is Scott-continuous. The difficulty is that the set of Scott-approximants of an open subset of a not (topologically) compact set of streams may not be Scott-open. We show that this problem does not occur in the compact case
Quantum Suplattices
Building on the theory of quantum posets, we introduce a non-commutative
version of suplattices, i.e., complete lattices whose morphisms are
supremum-preserving maps, which form a step towards a new notion of quantum
topological spaces. We show that the theory of these quantum suplattices
resembles the classical theory: the opposite quantum poset of a quantum
suplattice is again a quantum suplattice, and quantum suplattices arise as
algebras of a non-commutative version of the monad of downward-closed subsets
of a poset. The existence of this monad is proved by introducing a
non-commutative generalization of monotone relations between quantum posets,
which form a compact closed category. Moreover, we introduce a non-commutative
generalization of Galois connections and we prove that an upper Galois adjoint
of a monotone map between quantum suplattices exists if and only if the map is
a morphism of quantum suplattices. Finally, we prove a quantum version of the
Knaster-Tarski fixpoint theorem: the quantum set of fixpoints of a monotone
endomap on a quantum suplattice form a quantum suplattice.Comment: In Proceedings QPL 2023, arXiv:2308.1548
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