13,795 research outputs found
Spatial reasoning about qualitative shape compositions. Composing Qualitative Lengths and Angles
Shape composition is a challenge in spatial
reasoning. Qualitative Shape Descriptors (QSD) have proven to be rotation and location invariant, which make
them useful in spatial reasoning tests. QSD uses qualitative representations for angles and lengths, but their
composition operations have not been defined before. In
this paper, the Qualitative Model for Angles (QMAngles)
and the Qualitative Model for Lengths (QMLengths) are
presented in detail by describing their arity, reference systems and operators. Their operators are defined taking
the well-known temporal model by Allen (1983) as a reference. Moreover, composition tables are built, and the
composition relations of qualitative angles and lengths are
proved using their geometric counterparts. The correctness of these composition tables is also proved computationally using a logic program implemented using SwiProlog
Causation does not explain contextuality
Realist interpretations of quantum mechanics presuppose the existence of
elements of reality that are independent of the actions used to reveal them.
Such a view is challenged by several no-go theorems that show quantum
correlations cannot be explained by non-contextual ontological models, where
physical properties are assumed to exist prior to and independently of the act
of measurement. However, all such contextuality proofs assume a traditional
notion of causal structure, where causal influence flows from past to future
according to ordinary dynamical laws. This leaves open the question of whether
the apparent contextuality of quantum mechanics is simply the signature of some
exotic causal structure, where the future might affect the past or distant
systems might get correlated due to non-local constraints. Here we show that
quantum predictions require a deeper form of contextuality: even allowing for
arbitrary causal structure, no model can explain quantum correlations from
non-contextual ontological properties of the world, be they initial states,
dynamical laws, or global constraints.Comment: 18+8 pages, 3 figure
Structured Knowledge Representation for Image Retrieval
We propose a structured approach to the problem of retrieval of images by
content and present a description logic that has been devised for the semantic
indexing and retrieval of images containing complex objects. As other
approaches do, we start from low-level features extracted with image analysis
to detect and characterize regions in an image. However, in contrast with
feature-based approaches, we provide a syntax to describe segmented regions as
basic objects and complex objects as compositions of basic ones. Then we
introduce a companion extensional semantics for defining reasoning services,
such as retrieval, classification, and subsumption. These services can be used
for both exact and approximate matching, using similarity measures. Using our
logical approach as a formal specification, we implemented a complete
client-server image retrieval system, which allows a user to pose both queries
by sketch and queries by example. A set of experiments has been carried out on
a testbed of images to assess the retrieval capabilities of the system in
comparison with expert users ranking. Results are presented adopting a
well-established measure of quality borrowed from textual information
retrieval
Metallization of solid molecular hydrogen in two dimensions: Mott-Hubbard-type transition
We analyze the pressure-induced metal-insulator transition in a
two-dimensional vertical stack of molecules in x-y plane, and show that
it represents a striking example of the Mott-Hubbard-type transition. Our
combined exact diagonalization approach, formulated and solved in the second
quantization formalism, includes also simultaneous ab initio readjustment of
the single-particle wave functions, contained in the model microscopic
parameters. The system is studied as a function of applied side force
(generalized pressure), both in the -molecular and -quasiatomic states.
Extended Hubbard model is taken at the start, together with longer-range
electron-electron interactions incorporated into the scheme. The stacked
molecular plane transforms discontinuously into a (quasi)atomic state under the
applied force via a two-step transition: the first between molecular insulating
phases and the second from the molecular to the quasiatomic metallic phase. No
quasiatomic insulating phase occurs. All the transitions are accompanied by an
abrupt changes of the bond length and the intermolecular distance (lattice
parameter), as well as by discontinuous changes of the principal electronic
properties, which are characteristic of the Mott-Hubbard transition here
associated with the jumps of the predetermined equilibrium lattice parameter
and the effective bond length. The phase transition can be interpreted in terms
of the solid hydrogen metallization under pressure exerted by e.g., the
substrate covered with a monomolecular film of the vertically stacked
molecules. Both the Mott and Hubbard criteria at the insulator to metal
transition are discussed
A survey of qualitative spatial representations
Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, spatial databases and so on. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work
A discrete, unitary, causal theory of quantum gravity
A discrete model of Lorentzian quantum gravity is proposed. The theory is
completely background free, containing no reference to absolute space, time, or
simultaneity. The states at one slice of time are networks in which each vertex
is labelled with two arrows, which point along an adjacent edge, or to the
vertex itself. The dynamics is specified by a set of unitary replacement rules,
which causally propagate the local degrees of freedom. The inner product
between any two states is given by a sum over histories. Assuming it converges
(or can be Abel resummed), this inner product is proven to be hermitian and
fully gauge-degenerate under spacetime diffeomorphisms. At least for states
with a finite past, the inner product is also positive. This allows a Hilbert
space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4
expanded prospects sectio
Optimal map of the modular structure of complex networks
Modular structure is pervasive in many complex networks of interactions
observed in natural, social and technological sciences. Its study sheds light
on the relation between the structure and function of complex systems.
Generally speaking, modules are islands of highly connected nodes separated by
a relatively small number of links. Every module can have contributions of
links from any node in the network. The challenge is to disentangle these
contributions to understand how the modular structure is built. The main
problem is that the analysis of a certain partition into modules involves, in
principle, as many data as number of modules times number of nodes. To confront
this challenge, here we first define the contribution matrix, the mathematical
object containing all the information about the partition of interest, and
after, we use a Truncated Singular Value Decomposition to extract the best
representation of this matrix in a plane. The analysis of this projection allow
us to scrutinize the skeleton of the modular structure, revealing the structure
of individual modules and their interrelations.Comment: 21 pages, 10 figure
Voronoi-Like grid systems for tall buildings
In the context of innovative patterns for tall buildings, Voronoi tessellation is certainly worthy of interest. It is an irregular biomimetic pattern based on the Voronoi diagram, which derives from the direct observation of natural structures. The paper is mainly focused on the application of this nature-inspired typology to load-resisting systems for tall buildings, investigating the potential of non-regular grids on the global mechanical response of the structure. In particular, the study concentrates on the periodic and non-periodic Voronoi tessellation, describing the procedure for generating irregular patterns through parametric modeling and illustrates the homogenization-based approach proposed in the literature for dealing with unconventional patterns. To appreciate the consistency of preliminary design equations, numerical and analytical results are compared. Moreover, since the mechanical response of the building strongly depends on the parameters of the microstructure, the paper focuses on the influence of the grid arrangement on the global lateral stiffness, therefore on the displacement constraint, which is an essential requirement in the design of tall buildings. To this end, five case studies, accounting for different levels of irregularity and relative density, are generated and analyzed through static and modal analysis in the elastic field. In addition, the paper focuses on the mechanical response of a pattern with gradual rarefying density to evaluate its applicability to tall buildings. Displacement based optimizations are carried out to assess the adequate member cross sections that provide the maximum contribution in restraining deflection with the minimum material weight. The results obtained for all the models generated are compared and discussed to outline a final evaluation of the Voronoi structures. In addition to the wind loading scenario, the efficiency of the building model with varying density Voronoi pattern, is tested for seismic ground motion through a response spectrum analysis. The potential applications of Voronoi tessellation for tall buildings is demonstrated for both regions with high wind load conditions and areas of high seismicity
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